Universidad Politécnica de Madrid

Escuela Técnica Superior de Ingenieros deTelecomunicación

Automatic physical activity patternrecognition and meal intake

modelling in type 1 diabetes for theirinclusion in artificial pancreas

systems

Tesis doctoral

Fernando García GarcíaIngeniero de Telecomunicación

Madrid, Julio de 2015

Departamento de Tecnología Fotónica y Bioingeniería

Grupo de Bioingeniería y Telemedicina

E.T.S.I de Telecomunicación

Universidad Politécnica de Madrid

Automatic physical activity patternrecognition and meal intake

modelling in type 1 diabetes for theirinclusion in artificial pancreas

systems

Tesis doctoral

Autor:

Fernando García García

Directora:

Mª Elena Hernando Pérez

Madrid, Julio de 2015

Tribunal nombrado por el Magnífico y Excelentísimo Sr. Rector de la Universidad Politéc-nica de Madrid, el día XX de YYYY de 2015.

Presidente/a: Dr./Dra. Nombre Presidente Doctorado PresidenteCargo PresidenteInstitución Presidente

Vocales: Dr./Dra. Nombre Vocal A Doctorado Vocal ACargo Vocal AInstitución Vocal A

Dr./Dra. Nombre Vocal B Doctorado Vocal BCargo Vocal BInstitución Vocal B

Dr./Dra. Nombre Vocal C Doctorado Vocal CCargo Vocal CInstitución Vocal C

Secretario/a: Dr./Dra. Nombre Secretario Doctorado SecretarioCargo SecretarioInstitución Secretario

Suplentes: Dr./Dra. Nombre Suplente A Doctorado Suplente ACargo Suplente AInstitución Suplente A

Dr./Dra. Nombre Suplente B Doctorado Suplente BCargo Suplente BInstitución Suplente B

Realizado el acto de defensa y lectura de la tesis doctoral el día XX de YYYY de 2015 enMadrid, se acuerda otorgarle la calificación de:

Presidente/a: Vocales:

Secretario/a:

iv

A mi familia, por todo vuestro amor y vuestro cariño,

por el apoyo incondicional que siempre me habéis regalado.

Para correspondéroslo, aunque nunca alcance.

Os quiero mucho.

vi

Agradecimientos

Escribir agradecimientos.

viii

Esta obra está bajo una licencia Creative CommonsReconocimiento-NoComercial-CompartirIgual 4.0 Internacional

This work is licensed under a Creative Commons

Attribution-NonCommercial-ShareAlike 4.0 International license

x

Contents

Contents xi

List of Figures xvii

List of Tables xix

Acronyms xxi

Summary xxvSummary in English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvResumen en castellano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii

I Introduction 1

1 Introduction 31.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Research hypotheses and objectives 72.1 Research hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

II Diabetes and physical activity 9

3 Diabetes 113.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Type 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Type 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.3 Gestational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.4 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Prevalence and incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2.1 Prevalence and incidence for T1D . . . . . . . . . . . . . . . . . . . 14

3.3 Risk factors for T1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 Complications in T1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.5 Treatment of T1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.5.1 Current clinical practise . . . . . . . . . . . . . . . . . . . . . . . . 183.5.1.1 Insulin therapy . . . . . . . . . . . . . . . . . . . . . . . . 183.5.1.2 Dietary considerations . . . . . . . . . . . . . . . . . . . . 193.5.1.3 Physical activity considerations . . . . . . . . . . . . . . . 19

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3.5.2 Experimental treatments . . . . . . . . . . . . . . . . . . . . . . . . 203.5.2.1 Immunological therapies . . . . . . . . . . . . . . . . . . . 213.5.2.2 Gene therapies . . . . . . . . . . . . . . . . . . . . . . . . 213.5.2.3 Compensation of β-cell destruction . . . . . . . . . . . . . 213.5.2.4 Artificial pancreas . . . . . . . . . . . . . . . . . . . . . . 22

4 Physical activity in T1D 254.1 Foundations of exercise physiology . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 Glucose homoeostasis at rest . . . . . . . . . . . . . . . . . . . . . . 254.1.2 Energy sources during exercise . . . . . . . . . . . . . . . . . . . . . 26

4.1.2.1 ATP-CP system . . . . . . . . . . . . . . . . . . . . . . . 264.1.2.2 Lactic acid system . . . . . . . . . . . . . . . . . . . . . . 264.1.2.3 Aerobic system . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Exercise physiology in T1D . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Systematic review: Quantification of the acute effect of exercise on glycaemia

in T1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3.2.1 Eligibility criteria . . . . . . . . . . . . . . . . . . . . . . . 324.3.2.2 Study identification and selection . . . . . . . . . . . . . . 324.3.2.3 Data extraction . . . . . . . . . . . . . . . . . . . . . . . . 334.3.2.4 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . 344.3.2.5 Risk of bias . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.3.1 Study characteristics . . . . . . . . . . . . . . . . . . . . . 354.3.3.2 Risk of bias . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3.3.3 Synthesis of results and statistical analyses . . . . . . . . . 39

4.3.3.3.1 Meta-analyses . . . . . . . . . . . . . . . . . . . . 394.3.3.3.2 Meta-regression . . . . . . . . . . . . . . . . . . . 43

4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.4.1 Main findings . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.4.2 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.4.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3.4.4 Implications for clinical practice and research . . . . . . . 504.3.4.5 Comparison with previous reviews . . . . . . . . . . . . . 50

III Monitoring and recognition of physical activity 53

5 State of the art 555.1 Monitoring and measurement of PA . . . . . . . . . . . . . . . . . . . . . . 56

5.1.1 Direct calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.1.2 Indirect calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.1.3 Doubly labelled water . . . . . . . . . . . . . . . . . . . . . . . . . 595.1.4 Heart rate monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.1.5 Motion sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.1.5.1 Pedometers . . . . . . . . . . . . . . . . . . . . . . . . . . 625.1.5.2 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . 625.1.5.3 Combining accelerometers and heart rate monitors . . . . 64

5.1.6 Techniques with human intervention . . . . . . . . . . . . . . . . . 645.1.6.1 Direct observation . . . . . . . . . . . . . . . . . . . . . . 64

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5.1.6.2 Reports and activity logs . . . . . . . . . . . . . . . . . . 655.1.7 Overview of techniques for PA monitoring . . . . . . . . . . . . . . 66

5.2 Automated PA monitoring and recognition . . . . . . . . . . . . . . . . . . 675.2.1 Activity-specific recognition . . . . . . . . . . . . . . . . . . . . . . 675.2.2 Estimation of energy expenditures . . . . . . . . . . . . . . . . . . . 695.2.3 Activity-independent PA intensity classification . . . . . . . . . . . 70

6 PA intensity and modality classification using accelerometry and HR 716.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.2 Data collection experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2.1 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.2.2 Data collection experiments . . . . . . . . . . . . . . . . . . . . . . 72

6.2.2.1 Experiment A . . . . . . . . . . . . . . . . . . . . . . . . . 736.2.2.2 Experiment B . . . . . . . . . . . . . . . . . . . . . . . . . 736.2.2.3 Dataset overview . . . . . . . . . . . . . . . . . . . . . . . 73

6.3 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.3.1 Preprocessing and feature definition . . . . . . . . . . . . . . . . . . 806.3.2 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . . . . . 81

6.3.2.1 Feature extraction . . . . . . . . . . . . . . . . . . . . . . 826.3.2.1.1 Principal Component Analysis . . . . . . . . . . . 826.3.2.1.2 Linear Discriminant Analysis . . . . . . . . . . . 82

6.3.2.2 Feature selection . . . . . . . . . . . . . . . . . . . . . . . 826.3.2.2.1 Filters . . . . . . . . . . . . . . . . . . . . . . . . 836.3.2.2.2 Wrappers . . . . . . . . . . . . . . . . . . . . . . 84

6.3.3 Pattern identification . . . . . . . . . . . . . . . . . . . . . . . . . . 856.3.3.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.3.3.1.1 K-means clustering . . . . . . . . . . . . . . . . . 856.3.3.1.2 Gaussian Mixture Models . . . . . . . . . . . . . 856.3.3.1.3 Hierarchical clustering . . . . . . . . . . . . . . . 856.3.3.1.4 Self Organizing Maps . . . . . . . . . . . . . . . . 85

6.3.3.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . 866.3.3.2.1 Logistic regression . . . . . . . . . . . . . . . . . 866.3.3.2.2 Multi-Layer Perceptron . . . . . . . . . . . . . . 866.3.3.2.3 Support Vector Machines . . . . . . . . . . . . . 866.3.3.2.4 Bagging . . . . . . . . . . . . . . . . . . . . . . . 876.3.3.2.5 Boosting . . . . . . . . . . . . . . . . . . . . . . . 87

6.3.4 Temporal filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876.3.5 Practical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.3.5.1 Evaluating classification performance and model selection 886.3.5.2 Parameter tuning . . . . . . . . . . . . . . . . . . . . . . . 89

6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.4.1 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . . . . . 906.4.2 Parameter tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916.4.3 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.4.4 Performance in classification . . . . . . . . . . . . . . . . . . . . . . 96

6.4.4.1 Impact of temporal filtering . . . . . . . . . . . . . . . . . 1046.4.4.2 Comparison with other methodologies . . . . . . . . . . . 104

6.4.4.2.1 Standard approaches in the application domain . 1046.4.4.2.2 ML baseline comparison . . . . . . . . . . . . . . 107

6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

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IV Metabolic modelling in T1D 111

7 State of the art 1137.1 Metabolic models for T1D . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.1.1 Padova model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.1.1.1 Glucose subsystem . . . . . . . . . . . . . . . . . . . . . . 115

7.1.1.1.1 Renal excretion . . . . . . . . . . . . . . . . . . . 1157.1.1.1.2 Endogenous glucose production . . . . . . . . . . 1157.1.1.1.3 Glucose utilization . . . . . . . . . . . . . . . . . 115

7.1.1.2 Insulin subsystem . . . . . . . . . . . . . . . . . . . . . . . 1167.1.1.2.1 Subcutaneous insulin absorption . . . . . . . . . 1167.1.1.2.2 Remote effect . . . . . . . . . . . . . . . . . . . . 1177.1.1.2.3 Delayed insulin signal . . . . . . . . . . . . . . . 117

7.1.1.3 Absorption of meal glucose . . . . . . . . . . . . . . . . . 1177.1.1.4 Subcutaneous measurements . . . . . . . . . . . . . . . . . 118

7.1.2 Cambridge model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187.1.2.1 Glucose subsystem . . . . . . . . . . . . . . . . . . . . . . 118

7.1.2.1.1 Glucose renal excretion . . . . . . . . . . . . . . . 1207.1.2.1.2 Endogenous Glucose Production . . . . . . . . . 1207.1.2.1.3 Glucose utilization . . . . . . . . . . . . . . . . . 120

7.1.2.2 Insulin subsystem . . . . . . . . . . . . . . . . . . . . . . . 1217.1.2.2.1 Subcutaneous insulin absorption and kinetics . . 1217.1.2.2.2 Remote effect . . . . . . . . . . . . . . . . . . . . 121

7.1.2.3 Absorption of meal glucose . . . . . . . . . . . . . . . . . 1227.1.2.4 Subcutaneous measurements . . . . . . . . . . . . . . . . . 122

7.2 Overview and extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

8 Metabolic model for the effect of insulin on the disposal of meal glucosein T1D 1258.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.2 Clinical experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1268.3 Modelling methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.3.1 Model specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 1278.3.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 1318.3.3 Model identification and validation . . . . . . . . . . . . . . . . . . 1318.3.4 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.4.1 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.4.2 Model identification, validation and selection . . . . . . . . . . . . . 132

8.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

V Conclusions 139

9 Conclusions 1419.1 Verification of hypotheses and summary of results . . . . . . . . . . . . . . 1419.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

9.2.1 Physical activity monitoring . . . . . . . . . . . . . . . . . . . . . . 1449.2.2 Physical activity modelling in T1D . . . . . . . . . . . . . . . . . . 1459.2.3 Physical activity into artificial pancreas systems . . . . . . . . . . . 145

9.3 Contributions and achievements . . . . . . . . . . . . . . . . . . . . . . . . 146

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9.3.1 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1469.3.2 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

VI Appendix 149

A Mathematical foundations 151A.1 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

A.1.1 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . 151A.1.2 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . 154

A.2 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156A.2.1 K-means clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 156A.2.2 Gaussian Mixture Models . . . . . . . . . . . . . . . . . . . . . . . 157A.2.3 Hierarchical clustering . . . . . . . . . . . . . . . . . . . . . . . . . 158A.2.4 Self Organizing Maps . . . . . . . . . . . . . . . . . . . . . . . . . . 160

A.3 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162A.3.1 Naïve Bayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162A.3.2 Multinomial logistic regression . . . . . . . . . . . . . . . . . . . . . 162A.3.3 Multi-Layer Perceptrons . . . . . . . . . . . . . . . . . . . . . . . . 163A.3.4 Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . 165A.3.5 Decision trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169A.3.6 Meta-classification: Bagging . . . . . . . . . . . . . . . . . . . . . . 171A.3.7 Meta-classification: Boosting . . . . . . . . . . . . . . . . . . . . . . 172

A.4 Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175A.4.1 Evaluation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 177A.4.2 Decoding problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

A.4.2.1 Viterbi’s algorithm . . . . . . . . . . . . . . . . . . . . . . 179A.4.3 Learning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

A.4.3.1 Baum-Welch’s algorithm . . . . . . . . . . . . . . . . . . . 180

Bibliography 183

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List of Figures

3.1 Estimated diabetes cases by world’s region . . . . . . . . . . . . . . . . . . 143.2 Diabetes prevalence by country . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Predicted variations in diabetes cases and prevalence from 2013 to 2035 . . 153.4 Incidence rates of T1D in childhood . . . . . . . . . . . . . . . . . . . . . . 16

4.1 ATP breakdown to release energy . . . . . . . . . . . . . . . . . . . . . . . 284.2 ATP-CP system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Lactic acid system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4 Aerobic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.5 Energy contributions by the different metabolic pathways during exercise . 284.6 Definition of RoC magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . 354.7 Study selection for the systematic review . . . . . . . . . . . . . . . . . . . 374.8 Funnel plots to assess publication bias . . . . . . . . . . . . . . . . . . . . 404.9 Meta-analysis CONT vs. REST . . . . . . . . . . . . . . . . . . . . . . . . 424.10 Meta-analysis IHE vs. REST . . . . . . . . . . . . . . . . . . . . . . . . . 424.11 Meta-analysis RESIST vs. REST . . . . . . . . . . . . . . . . . . . . . . . 424.12 Meta-analysis IHE vs. CONT . . . . . . . . . . . . . . . . . . . . . . . . . 444.13 Meta-analysis RESIST vs. CONT . . . . . . . . . . . . . . . . . . . . . . . 444.14 Meta-regression CONT vs. REST . . . . . . . . . . . . . . . . . . . . . . . 45

5.1 Example MET equivalences from Ainsworth et al.’s Compendium . . . . . 575.2 Metabolic chamber for direct calorimetry . . . . . . . . . . . . . . . . . . . 605.3 Indirect calorimetry equipments, bedside and portable . . . . . . . . . . . . 605.4 Doubly labelled water curves . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.1 Accelerometry and HR equipment and signals . . . . . . . . . . . . . . . . 726.2 PRONAF circuit #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.3 PRONAF circuit #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4 PRONAF circuit #3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.5 Detailed schedule in Experiment B . . . . . . . . . . . . . . . . . . . . . . 776.6 Volunteers participating in Experiment B . . . . . . . . . . . . . . . . . . . 786.7 Individual contributions to the PA intensity dataset . . . . . . . . . . . . . 796.8 Scatter plot matrix – Original feature space . . . . . . . . . . . . . . . . . 916.9 Scatter plot matrix – PCA . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.10 Scatter plot matrix – LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.11 Scatter plot matrix – mRMR filter (Continuous) . . . . . . . . . . . . . . . 936.12 Scatter plot matrix – mRMR filter (Discrete) . . . . . . . . . . . . . . . . . 936.13 Scatter plot matrix – Overall wrapper in greedy search . . . . . . . . . . . 946.14 Scatter plot matrix – Overall wrapper in genetic search . . . . . . . . . . . 946.15 Model selection, clusterers – SBSCV performance PA intensity . . . . . . . 986.16 Model selection, clusterers – SBSCV performance PA intensity . . . . . . . 98

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List of Figures

6.17 Model selection, classifiers – SBSCV performance PA intensity . . . . . . . 1016.18 Model selection, classifiers – SBSCV performance PA intensity . . . . . . . 1026.19 Example outcomes for PA intensity classification by the LDA+K-means

algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.20 Example outcomes for PA intensity classification by the Wrapper (genetic,

specific)+Bagging algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.21 Example outcomes for PA intensity classification by the Wrapper (genetic,

specific)+Bagging algorithm, without HMM temporal filtering . . . . . . . 106

8.1 Schematic schedule of the experimental protocol . . . . . . . . . . . . . . . 1278.2 Common schematic of the six compartmental models proposed . . . . . . . 1288.3 Plasma tracer concentrations over time . . . . . . . . . . . . . . . . . . . . 1328.4 Mean and root-mean-square weighted residuals . . . . . . . . . . . . . . . . 1348.5 Example fit by the CM model . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.1 Example PCA analysis in two dimensions . . . . . . . . . . . . . . . . . . . 153A.2 Example of the K-means iterative training procedure . . . . . . . . . . . . 157A.3 Dendrogram in hierarchical clustering . . . . . . . . . . . . . . . . . . . . . 159A.4 SOM neighbourhood function Λ . . . . . . . . . . . . . . . . . . . . . . . . 161A.5 Schematic example of SOM training . . . . . . . . . . . . . . . . . . . . . . 161A.6 MLP architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164A.7 SVM definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167A.8 SVM for a dataset not satisfying class separability . . . . . . . . . . . . . . 167A.9 Non-linear SVM decision boundary applying the ‘kernel trick’ . . . . . . . 167A.10 First-order Markov chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176A.11 Hidden Markov Model (HMM) . . . . . . . . . . . . . . . . . . . . . . . . . 176A.12 HMM forward induction for α variables . . . . . . . . . . . . . . . . . . . . 178A.13 HMM backward induction for β variables . . . . . . . . . . . . . . . . . . . 178A.14 HMM forward-backward induction for ξ variables . . . . . . . . . . . . . . 178

xviii

List of Tables

4.1 Glucose-rising counter-regulatory hormones . . . . . . . . . . . . . . . . . . 304.2 Expectable exercise-induced trends in glycaemia for T1D . . . . . . . . . . 304.3 Characteristics of the studies in the meta-analysis . . . . . . . . . . . . . . 38

6.1 Summary of the dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.2 Parameter tuning results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.3 Model selection, clusterers – SBSCV performance PA intensity . . . . . . . 976.4 Model selection, classifiers – SBSCV performance PA intensity . . . . . . . 996.5 Model selection, classifiers – SBSCV performance PA intensity . . . . . . . 1006.6 SBSCV performance of the LDA+K-means algorithm . . . . . . . . . . . . 1036.7 SBSCV performance of the Wrapper (genetic, specific)+Bagging algorithm 1036.8 LOSOCV confusion matrix for LDA+K-means in PA intensity . . . . . . . 1036.9 LOSOCV confusion matrix for Wrapper (genetic, specific)+Bagging in PA

intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.1 Input variables for the Padova model . . . . . . . . . . . . . . . . . . . . . 1147.2 Output variables for the Padova model . . . . . . . . . . . . . . . . . . . . 1147.3 State variables for the Padova model . . . . . . . . . . . . . . . . . . . . . 1147.4 Parameters for the Padova model . . . . . . . . . . . . . . . . . . . . . . . 1147.5 Input variables for the Cambridge model . . . . . . . . . . . . . . . . . . . 1197.6 Output variables for the Cambridge model . . . . . . . . . . . . . . . . . . 1197.7 State variables for the Cambridge model . . . . . . . . . . . . . . . . . . . 1197.8 Parameters for the Cambridge model . . . . . . . . . . . . . . . . . . . . . 119

8.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.2 Model identification and validation . . . . . . . . . . . . . . . . . . . . . . 1338.3 Parameter estimates for the six models . . . . . . . . . . . . . . . . . . . . 1358.4 Coefficient of variation of the parameter estimates . . . . . . . . . . . . . . 136

xix

List of Tables

xx

Acronyms

ACSM American College of Sports MedicineADA American Diabetes AssociationADP adenosine diphosphateAIC Akaike information criterionATP adenosine triphosphateATP-CP adenosine triphosphate-creatine phosphate

BIC Bayesian information criterionBMI body mass indexBMR basal metabolic ratebpm beats per minute

CART classification and regression treesCGM continuous glucose monitorCHO carbohydratesCI confidence intervalCM compartmental model with ‘cut-off’ remote effect and mixed initial conditionsCNS central nervous systemCONT continuous physical activityCP creatine phosphateCP compartmental model with ‘cut-off’ remote effect and initial conditions as model pa-

rametersCS compartmental model with ‘cut-off’ remote effect and steady-state initial conditionsCSII continuous subcutaneous insulin infusionCV cross-validation

DKA diabetic ketoacidosisDLW doubly labelled water

ECG electrocardiogramEE energy expenditureEGP endogenous glucose productionEM EGP-mimickingEM expectation-maximization

FCQ F-test correlation quotientFDA Foods and Drugs AdministrationFFA free fatty acids

GD gestational diabetesGMM Gaussian mixture model

HbA1c glycated haemoglobin A1c

xxi

Acronyms

HG high glycaemic-loadHLA human leukocyte antigenHMM hidden Markov modelHR heart rateHRmax maximal heart rateHRbasal basal heart rateHRres heart rate reserve

ICT information and communication technologiesIDF International Diabetes FederationIHE intermittent high-intensity exerciseINGAP islet neogenesis associated proteinIPAQ international physical activity questionnaireITS iterative two-stageIVGTT intravenous glucose tolerance test

JDRF Juvenile Diabetes Research Foundation

LDA linear discriminant analysisLG low glycaemic-loadLM compartmental model with linear remote effect and mixed initial conditionsLOSOCV leave-one-subject-out cross-validationLP compartmental model with linear remote effect and initial conditions as model param-

etersLS compartmental model with linear remote effect and steady-state initial conditions

MDI multiple daily injectionsMeSH medical subject headingsMET metabolic equivalent of taskMIQ mutual information quotientML machine learningMLP multi-layer perceptronMM meal-mimickingMODY maturity-onset diabetes of the youngMPC model-predictive controlmRMR minimum redundancy-maximum relevance

NB naïve BayesNRE non-randomized experiment

OVA one-versus-all

PA physical activityPAEE physical activity-induced energy expenditurePCA principal component analysisPID proportional-integral-derivativePRISMA preferred reporting items for systematic reviews and meta-analysesPRONAF ‘Programas de nutrición y actividad física’ project

RBF radial-basis functionRCT randomized controlled trialRESIST resistance activityREST resting control period

xxii

Acronyms

RM repetitions maximumrms root-mean-squareRoC rate-of-changeRPAQ recent physical activity questionnaire

SBSCV sequence-based stratified cross-validationSEM standard error of the meanSOM self-organizing mapSVM support vector machineSVR support vector regression

T1D type 1 diabetesT2D type 2 diabetesTEE total energy expenditureTTR tracer-to-tracee ratio

VO2max maximum oxygen uptakeVO2basal basal oxygen uptakeVO2res oxygen uptake reserve

WHO World Health Organization

xxiii

Acronyms

xxiv

Summary

Summary in English

Diabetes encompasses a series of metabolic diseases characterized by abnormally high bloodglucose concentrations. In the case of type 1 diabetes (T1D), this situation is causedby a total absence of endogenous insulin secretion, which impedes the use of glucose bymost tissues. In these circumstances, exogenous insulin supplies are necessary to maintainpatient’s life; although caution is always needed to avoid acute decays in glycaemia belowsafe levels.

In addition to insulin administrations, meal intakes and physical activity are fundamentalfactors influencing glucose homoeostasis. Consequently, a successful management of T1Dshould incorporate these two physiological phenomena, based on an appropriate identifi-cation and modelling of these events and their corresponding effect on the glucose-insulinbalance. In particular, artificial pancreas systems –designed to perform an automatedcontrol of patient’s glycaemia levels– may benefit from the integration of this type of in-formation.

The first part of this PhD thesis covers the characterization of the acute effect of physicalactivity on glucose profiles. With this aim, a systematic review of literature and meta-analyses are conduced to determine responses to various exercise modalities in patientswith T1D, assessed via rates-of-change magnitudes to quantify temporal variations in gly-caemia.

On the other hand, a reliable identification of physical activity periods is an essentialprerequisite to feed artificial pancreas systems with information concerning exercise in am-bulatory, free-living conditions. For this reason, the second part of this thesis focuses onthe proposal and evaluation of an automatic system devised to recognize physical activity,classifying its intensity level (light, moderate or vigorous) and for vigorous periods, iden-tifying also its exercise modality (aerobic, mixed or resistance); since both aspects have adistinctive influence on the predominant metabolic pathway involved in fuelling exercise,and therefore, in the glycaemic responses in T1D.

Various combinations of machine learning and pattern recognition techniques are appliedon the fusion of multi-modal signal sources, namely: accelerometry and heart rate mea-surements, which describe both mechanical aspects of movement and the physiologicalresponse of the cardiovascular system to exercise. An additional temporal filtering moduleis incorporated after recognition in order to exploit the considerable temporal coherence(i.e. redundancy) present in data, which stems from the fact that in practice, physicalactivity trends are often maintained stable along time, instead of fluctuating rapid and

xxv

repeatedly.

The third block of this PhD thesis addresses meal intakes in the context of T1D. In par-ticular, a number of compartmental models are proposed and compared in terms of theirability to describe mathematically the remote effect of exogenous plasma insulin concentra-tions on the disposal rates of meal-attributable glucose, an aspect which had not yet beenincorporated to the prevailing T1D patient models in literature. Data were acquired in anexperiment conduced at the Institute of Metabolic Science (University of Cambridge, UK)on 16 young patients. A variable-target glucose clamp replicated their individual glucoseprofiles, observed during a preliminary visit after ingesting either a high glycaemic-load ora low glycaemic-load evening meal.

The six mechanistic models under evaluation here comprised: a) two-compartmentalsubmodels for glucose tracer masses, b) a single-compartmental submodel for insulin’sremote effect, c) two types of activations for this remote effect (either linear or with a‘cut-off’ point), and d) diverse forms of initial conditions.

xxvi

Resumen en castellano

La diabetes comprende un conjunto de enfermedades metabólicas que se caracterizan porconcentraciones de glucosa en sangre anormalmente altas. En el caso de la diabetes tipo 1(T1D, por sus siglas en inglés), esta situación es debida a una ausencia total de secreciónendógena de insulina, lo que impide a la mayoría de tejidos usar la glucosa. En talescircunstancias, se hace necesario el suministro exógeno de insulina para preservar la vidadel paciente; no obstante, siempre con la precaución de evitar caídas agudas de la glucemiapor debajo de los niveles recomendados de seguridad.

Además de la administración de insulina, las ingestas y la actividad física son factoresfundamentales que influyen en la homeostasis de la glucosa. En consecuencia, una gestiónapropiada de la T1D debería incorporar estos dos fenómenos fisiológicos, en base a unaidentificación y un modelado apropiado de los mismos y de sus sorrespondientes efectosen el balance glucosa-insulina. En particular, los sistemas de páncreas artificial –ideadospara llevar a cabo un control automático de los niveles de glucemia del paciente– podríanbeneficiarse de la integración de esta clase de información.

La primera parte de esta tesis doctoral cubre la caracterización del efecto agudo de laactividad física en los perfiles de glucosa. Con este objetivo se ha llevado a cabo una revi-sión sistemática de la literatura y meta-análisis que determinen las respuestas ante variasmodalidades de ejercicio para pacientes con T1D, abordando esta caracterización median-te unas magnitudes que cuantifican las tasas de cambio en la glucemia a lo largo del tiempo.

Por otro lado, una identificación fiable de los periodos con actividad física es un requisitoimprescindible para poder proveer de esa información a los sistemas de páncreas artificialen condiciones libres y ambulatorias. Por esta razón, la segunda parte de esta tesis estáenfocada a la propuesta y evaluación de un sistema automático diseñado para reconocerperiodos de actividad física, clasificando su nivel de intensidad (ligera, moderada o vigo-rosa); así como, en el caso de periodos vigorosos, identificando también la modalidad deejercicio (aeróbica, mixta o de fuerza). En este sentido, ambos aspectos tienen una influen-cia específica en el mecanismo metabólico que suministra la energía para llevar a cabo elejercicio y, por tanto, en las respuestas glucémicas en T1D.

En este trabajo se aplican varias combinaciones de técnicas de aprendizaje máquina y re-conocimiento de patrones sobre la fusión multimodal de señales de acelerometría y ritmocardíaco, las cuales describen tanto aspectos mecánicos del movimiento como la respues-ta fisiológica del sistema cardiovascular ante el ejercicio. Después del reconocimiento depatrones se incorpora también un módulo de filtrado temporal para sacar partido a la con-siderable coherencia temporal presente en los datos, una redundancia que se origina en elhecho de que en la práctica, las tendencias en cuanto a actividad física suelen mantenerseestables a lo largo de cierto tiempo, sin fluctuaciones rápidas y repetitivas.

El tercer bloque de esta tesis doctoral aborda el tema de las ingestas en el ámbito dela T1D. En concreto, se propone una serie de modelos compartimentales y se evalúanéstos en función de su capacidad para describir matemáticamente el efecto remoto de lasconcetraciones plasmáticas de insulina exógena sobre las tasas de eleiminación de la glucosaatribuible a la ingesta; un aspecto hasta ahora no incorporado en los principales modelosde paciente para T1D existentes en la literatura. Los datos aquí utilizados se obtuvierongracias a un experimento realizado por el Institute of Metabolic Science (Universidad de

xxvii

Cambridge, Reino Unido) con 16 pacientes jóvenes. En el experimento, de tipo ‘clamp’con objetivo variable, se replicaron los perfiles individuales de glucosa, según lo observadodurante una visita preliminar tras la ingesta de una cena con o bien alta carga glucémica,o bien baja.

Los seis modelos mecanísticos evaluados constaban de: a) submodelos de doble comparti-mento para las masas de trazadores de glucosa, b) un submodelo de único compartimentopara reflejar el efecto remoto de la insulina, c) dos tipos de activación de este mismo efectoremoto (bien lineal, bien con un punto de corte), y d) diversas condiciones iniciales.

xxviii

Part I

Introduction

1

Chapter 1

Introduction

1.1 Motivation

The present PhD thesis work was carried out under the research area on ‘Applied tech-nologies for the management of diabetes’ at the Biomedical Engineering and TelemedicineGroup, Universidad Politécnica de Madrid. The main purpose of this research area is touse information and communication technologies (ICT) to empower the management ofdiabetes –in its different conditions– by patients and caregivers. Research topics include,but are not restricted to: glucose predictors, decision support systems for the personalizedadjustment of insulin therapy, closed-loop glucose control algorithms (artificial pancreas),and telemedical platforms to track diabetological care data, as well as to monitor and pro-mote healthy diets and physically active lifestyles.

The general term diabetes encompasses various metabolic diseases characterized by abnor-mally high blood glucose concentration levels (hyperglycaemia) at fasting conditions, inturn caused either by an defective secretion and/or by an impaired action of the insulinhormone. Sustained hyperglycaemia inflicts serious damages in different tissues, whichin the long term may lead to cardiovascular problems, renal failure or blindness, amongother severe complications. On the other hand, acute episodes of severe hypoglycaemia –orconversely, hyperglycaemia with ketoacidosis– may be life-threatening.

Currently, diabetes is one of the diseases with highest prevalence: approximately 9% ofworld’s population in 2014 according to estimations by the WHO [World Health Organi-zation, 2015]. Despite being non-communicable, its large growth rates led the WHO toconsider diabetes as a worldwide epidemic, closely related to the incidence of overweightand obesity. Furthermore, WHO projections place diabetes as the seventh most frequentcause of death worldwide by 2030 [Mathers and Loncar, 2006]. In this context, intenseresearch efforts are being conduced from diverse perspectives: ranging from immunologicaland gene therapies to cure diabetes, to technological solutions designed to ease the dailymanagement of the condition (e.g. smart insulin bolus advisors) and to monitor and pro-mote healthy lifestyles –diet, physical activity– which can improve overall diabetologic care.

In this regard, meal intakes and physical activity, along with exogenous insulin admin-istrations (if prescribed), are the main external factors influencing glucose homoeostasis.For this reason, reliable quantitative information about subjects’ degree of involvement inphysical activity –its frequency, duration, intensity or type of exercise– may constitute avaluable contextual input, e.g. to assess patients’ adherence and compliance with exercise

3

1.2. Outline

plans or for artificial pancreas systems incorporating the acute effects of exercise on glucoseconcentrations [Chassin et al., 2007; Breton, 2008; van Bon et al., 2011].

However, current ‘gold standard’ techniques to quantify physical activity are not practicalin ambulatory, free-living environments. As a result, authors from the field of sport sciences[Ainslie et al., 2003; Plasqui and Westerterp, 2006; Westerterp, 2009] advocate for solutionsincorporating simultaneously both accelerometry –which provides objective measurementsof motion mechanics–, as well as heart rate –as a physiological response to exercise–, inorder to overcome the limitation of each technique when applied by separate. This PhDthesis document presents, compares and evaluates an automated system to classify phys-ical activity working on data obtained by the fusion of these two sources of information.Machine learning methods are employed to enhance the robustness of the classifiers by theautomatic recognition of informative signal patterns and temporal trends in data.

Another essential perspective for the consolidation of artificial pancreas systems as glucosecontrollers in type 1 diabetes is the enhancement of the patient models on which vari-ous control strategies are supported, to extend the physiological aspects covered by thesemodels. Resulting from a research visit and collaboration with the Institute of MetabolicScience (University of Cambridge, UK), data were made available from a clinical exper-iment which addressed the absorption patterns of meal glucose in patients with type 1diabetes. Those experimental data are used in this PhD thesis work to develop and tovalidate a mechanistic model reflecting the effect of plasma insulin concentrations on thedisposal rates of meal-attributable glucose, an aspect which had not yet been incorporatedto patient models.

1.2 Outline

The present PhD thesis document is structured in six parts:

• Part I, formed by chapters 1–2, introduces the motivation and context of this workand presents the hypotheses and objectives which drove research.

• Part II, containing chapters 3 and 4, overviews several clinical and physiologicalaspects in relation to diabetes and exercise. In particular, chapter 4 contains asystematic review and meta-analysis addressing the quantitative characterization ofthe acute response to physical activity in type 1 diabetes, in terms of glycaemiaprofiles and their rates of change.

• Part III, covering chapters 5–6, focuses on techniques for the ambulatory, free-livingmonitoring of physical activity. After an overview of the state of the art in themeasurement and recognition of exercise patterns in chapter 5; chapter 6 presents,compares and evaluates various machine learning-based approaches to classify au-tomatically periods of time in accordance to their intensity and exercise modality.Simultaneous processing and analysis of accelerometry and heart rate signals areemployed.

• Part IV, formed by chapters 7 and 8, addresses the mathematical modelling of themetabolic system and glucose-insulin dynamics in type 1 diabetes. Chapter 8 proposesa compartmental model for the remote effect of plasma insulin on the disposal of meal-attributable glucose, validating it on the basis of data from an experimental study.

• Part V –chapter 9– summarizes the main results, conclusions and contributions ex-tracted from this PhD research. Hypotheses postulated in chapter 2 and possiblefuture work lines are discussed.

4

1. Introduction

• Part VI, in the form of Appendix A, overviews the fundamental mathematical prin-ciples behind the machine learning algorithms employed in the automated physicalactivity classifiers developed in chapter 6.

5

1.2. Outline

6

Chapter 2

Research hypotheses and objectives

2.1 Research hypotheses

H1: In the context of type 1 diabetes, it is possible to determine distinctivephysiological responses to exercise of varying intensity and modality, andin particular to quantify their effects in terms of the associated acutevariations in glycaemia.

Information regarding physical activity, as a phenomenon which can greatly influence glu-cose homoeostasis, should be incorporated into systems supporting the therapeutic man-agement of type 1 diabetes (e.g. the artificial pancreas). Contextual aspects about phys-ical activity –such as its intensity or its modality, in close relation with the predominantmetabolic pathway involved in the fuelling of exercise– should also be accounted for. Asystematic literature review will be conduced to quantify these interactions.

H2: It is possible to achieve an accurate, reliable and robust monitoring ofphysical activity intensity and modality in free-living conditions by thesimultaneous processing of multi-modal data which combine accelerometryand heart rate measurements, as well as by the application of machinelearning algorithms to identify patterns in data.

‘Gold standard’ techniques to monitor physical activity are feasible in laboratory conditionsbut not in free-living scenarios; whereas practical solutions, such as accelerometers andheart rate monitors, suffer from a number of drawbacks (e.g. accuracy dependent on thelocation of the sensor, in the case of accelerometers; or non-exercise-induced alterations inheart rate) which limit their applicability and reliability. The simultaneous fusion of thesetwo sources of information –as complementary descriptors of motion and physiologicalaspects of exercise– may provide notable benefits.

In addition, machine learning techniques constitute a mathematically sound framework forthe extraction of informative signal patterns, which are not trivial to identify in multi-dimensional datasets by mere inspection and/or a priori knowledge. Information underly-ing in data’s temporal trends can also be exploited with machine learning-based approaches,adding robustness to classification outcomes.

H3: It is possible to generate a mechanistic mathematical model which de-scribes the effect of insulin on prandial glucose-insulin kinetics in type 1diabetes.

Currently available patient models for type 1 diabetes use compartmental formalisms to de-scribe mathematically (in particular, via sets of mass-balance differential equations) a num-

7

2.2. Objectives

ber of physiological aspects of glucose homoeostasis. These include e.g. glucose appearanceand clearance, insulin absorption and action, endogenous glucose production or renal ex-cretion, among others phenomena. However, various relevant aspects of the glucose-insulinbalance have not yet been incorporated into these patient models. Using experimentaldata from a clinical study conduced by the Institute of Metabolic Science (University ofCambridge, UK), this PhD thesis will propose a novel model concerning the remote effectof plasma insulin concentrations on the clearance rates of meal-attributable glucose.

2.2 Objectives

In relation to hypothesis H1:

O1.1: To develop a methodology to quantify the acute effect of physical activity on gly-caemia profiles for type 1 diabetes, during and immediately after exercise.

O1.2: To apply this method to available literature in order to analyse, aggregate and com-pare quantitatively the relevant scientific evidence.

Regarding hypothesis H2:

O2.1: To develop a machine learning system capable of recognizing automatically temporaltrends for both physical activity intensity and exercise modality, by means of thesimultaneous processing of multi-axial accelerometry measurements and heart ratesignals.

O2.2: To evaluate the classification performance attained by this scheme when trained andtested on experimental data.

With respect to hypothesis H3:

O3.1: To formulate a mechanistic model to describe the role of plasma insulin on the disposalof meal-attributable prandial glucose.

O3.2: To validate the resulting model with experimental data from patients with type 1diabetes.

8

Part II

Diabetes and physical activity

9

Chapter 3

Diabetes

The general term diabetes encompasses a set of metabolic diseases which, despite theirdifferent aetiology and pathogenic processes, are characterized by abnormally high bloodglucose concentrations (hyperglycaemia) which are sustained during long periods of time.These medical conditions result from defects in the secretion and/or in the action of in-sulin, the pancreatic hormone that facilitates the transportation of glucose through the cellmembrane towards its interior, where glucose serves as energy source. In broad terms, de-ficiencies in insulin secretion or in its action –which often coexist– stem respectively from:a) a low or absent production of insulin by the pancreas, and b) from a diminished responseto insulin by tissues, preventing its efficient use [American Diabetes Association, 2010].

In the long term, sustained hyperglycaemia causes severe micro- and macrovascular dam-ages in different tissues and organs (e.g. eyes, kidneys, nerves, heart or blood vessels).On the other hand, acute hypoglycaemia events –which are typically induced by an un-matched exogenous insulin administration– or conversely, episodes of hyperglycaemia withketoacidosis, might become life-threatening for the patient.

3.1 Types

3.1.1 Type 1

Type 1 diabetes (T1D) accounts for approximately 5–10% of the total number of diabetescases worldwide [American Diabetes Association, 2010]. It originates from the destructionof β-cells at the islets of Langerhans, in the pancreas. These β-cells are responsible for theproduction and secretion of the insulin hormone. Hence, their destruction leads towardsan absolute deficiency in terms of endogenous insulin secretion, which in turn imposes theneed for exogenous insulin administrations in order to prevent ketoacidosis and to maintainpatient’s life.

The most common subform of T1D –sometimes referred to as type 1a– is immune-mediated[Maahs et al., 2010], with an abnormal autoimmune reaction attacking and destroyingβ-cells. Although the exact etiopathogenesis of such autoimmune reaction remains stillunknown, various genetic predispositions as well as the exposure to environmental fac-tors (e.g. viral infections) are thought to play a major role in the onset of the disease[American Diabetes Association, 2010]. The rate of β-cell destruction varies notably acrossindividuals, being rapid for some patients –especially children– and slower in other sub-jects –mainly adults– [American Diabetes Association, 2010]. In this regard and although

11

3.1. Types

immune-mediated T1D may be diagnosed at any age, it tends to appear most frequentlyduring childhood and adolescence.

On the other hand, the idiopathic subform of T1D (or type 1b) constitute a minority amongthe total of T1D cases. Its exact aetiology is not yet well known, although a strong inher-ited component is present without evidence for autoimmune reactions [American DiabetesAssociation, 2010].

3.1.2 Type 2

Type 2 diabetes (T2D) represents the ample majority of cases of diabetes, with around90–95% [American Diabetes Association, 2010]. It is either linked to either an excessiveinsulin resistance, a decreased insulin production or to a combination of both phenomena.However and in contrast to T1D, the lowering in insulin production is in relative terms–not absolute– and not mediated by an autoimmune destruction of β-cells.

Research concerning the aetiology of T2D is still ongoing, but most patients with T2Dare obese; whereas obesity is known to cause insulin resistance to some extent [AmericanDiabetes Association, 2010]. Besides, other T2D patients which would not be classified asobese according to traditional diagnosis criteria (based on total body weight) may haveincreased amounts of fat in the abdominal region.

Nevertheless, genetic predisposition has an important role in the development of T2D, evenstronger than for the auto-immune form of T1D [American Diabetes Association, 2010].Additional major risk factors must also be considered [International Diabetes Federation,2013]: advanced age, family history of diabetes, ethnicity, sedentary lifestyles and physicalinactivity, or unhealthy diet, among others. In this regard, many T2D patients are ableto manage their disease with healthy eating habits, regular physical activity and/or oralanti-diabetic medication. However, as the disease progresses and if their diabetic controlworsens, some patients may need exogenous insulin supplies.

T2D tends to be diagnosed during adulthood, although there is an increasing trend forits appearance in children and adolescents with sedentary life and obesity. In addition,T2D is currently experiencing a very pronounced growth worldwide, in association withphenomena such as market-economy globalization, socio-economic and demographic trans-formations (e.g. ageing population, urbanization), rapid dietary changes and sedentarylifestyles [International Diabetes Federation, 2013]. Furthermore, given that symptomsmay take years to be apparent –a period during which hyperglycaemia already damagestissues–, T2D often remains unnoticed and undiagnosed until severe complications arise.

3.1.3 Gestational

During pregnancy, women who develop gestational diabetes (GD) experience increased in-sulin resistance. When this additional resistance is not matched by a comparable rise interms of insulin production, hyperglycaemia occurs. This event, which tends to appeararound the 24th week of gestation, is thought to be induced by hormonal alterations block-ing insulin action [Hunt and Schuller, 2007]. Despite such insulin resistance most oftendisappears after delivery, it poses a notable risk on the mother of suffering GD in subse-quent pregnancies and/or T2D later in life [Hunt and Schuller, 2007]. On the other hand,given that the foetus is at an advanced stage of formation when GD develops, the immediate

12

3. Diabetes

risk for the offspring is not as severe as it would be if the mother had T1D or T2D be-fore pregnancy. Nonetheless, GD can bring serious consequences, including among others:augmented risk of future T2D for both mother and child, foetal macrosomia (i.e. signifi-cantly larger foetuses, with more complicated deliveries and possible need for a caesarean),preeclampsia –a life-threatening sudden rise in blood pressure–, or neonatal hypoglycaemiaepisodes.

Current estimates calculate that approximately 7% of pregnancies are complicated by GD,with these numbers ranging from 1% to 14%, depending on: a) the population understudy, and b) the diagnostic tests employed [American Diabetes Association, 2010].

3.1.4 Others

Other specific forms of diabetes exist, which aggregated may account for only 1–2% oftotal cases [American Diabetes Association, 2010]. These can be grouped into varioustypes [American Diabetes Association, 2010]:

• Genetic defects of the β-cell function. Various forms of diabetes are linked to mono-genetic alterations in β-cell function, with abnormalities in six genetic loci on differentchromosomes currently identified. Insulin secretion is often impaired, but not insulinaction. Besides, sustained hyperglycaemia tends generally to commence in the earlyadulthood –above 25 years old–, reason for which these forms of diabetes are alsoreferred to as maturity-onset diabetes of the young (MODY).

• Genetic defects in insulin action.• Diseases of the exocrine pancreas, e.g. pancreatitis or pancreatic carcinoma which

may lead to severe pancreatic damage and diabetes.• Endocrine disorders. Excesses of certain hormones whose action is antagonist to

insulin (e.g. glucagon, epinephrine, cortisol or growth hormone) can cause diabetes.• Diabetes induced by chemicals or drugs which impair insulin secretion.• Infections by viruses (e.g. congenital rubella) associated with β-cell destruction.• Other uncommon forms of immune-mediated diabetes.• Other genetic syndromes related to an increased incidence of diabetes.

3.2 Prevalence and incidence

The large growth rates in diabetes cases, along with its high prevalence –estimated to beapproximately 9% in 2014 among adults [World Health Organization, 2015]–, have leadthe WHO to consider diabetes as a worldwide epidemic [World Health Organization, 2015],in spite of being a non-communicable disease. The ample majority of cases correspond toT2D, associated with major and rapid changes in socio-economic and demographic factors,such as: ageing, obesity, unhealthy nutrition and physical inactivity –particularly amongthe youth–. However, there are also reports which point out unexplained increases in theincidence of T1D [Patterson et al., 2009], as well as the progression of GD and hypergly-caemia during pregnancy [International Diabetes Federation, 2013].

The most recent estimations by the International Diabetes Federation (IDF) indicate thatapproximately 382 million adults aged 20–79 years old suffered diabetes in 2013 [Interna-tional Diabetes Federation, 2013]. This number represented 8.3% of the total adult popu-lation in the age range 20–79, causing around 5.1 million deaths in 2013. Among those 382million subjects, 175 millions –i.e. 46%– were estimated to remain undiagnosed (Figure

13

3.2. Prevalence and incidence

Figure 3.1: Estimated numbers of people with diabetes [millions] in 2013, divided by regionsof the world. Black circle sectors represent the fraction of undiagnosed cases. (Source: IDFAtlas 2013 [International Diabetes Federation, 2013]).

3.1), mainly suffering from T2D. In particular, Spain had 3.70 million cases, of which 1.26millions were undiagnosed [International Diabetes Federation, 2014]. In addition, the num-ber of yearly births to women with GD or high blood glucose during pregnancy reached21.4 millions worldwide (17%) in 2013 [International Diabetes Federation, 2013].

On the other hand, there were not marked differences in terms of sex distribution; whereasconcerning age, almost one half of the adults (184 millions) belonged to the range 40–59 years old. More than 80% of them lived in countries with low or middle incomes(Figure 3.2), hindering their access to appropriate healthcare and treatment. Remarkableincreases for T2D were reported in childhood and youth, although T1D continues to be themost common form of diabetes among children and youth: with ≥85%, according to theSEARCH for Diabetes in Youth Study Group [2006]). Furthermore, forecasts predict morethan 592 million people affected by year 2035 (Figure 3.3), which would mean a growth by55% in less than 25 years’ time [International Diabetes Federation, 2013; Guariguata et al.,2014].

3.2.1 Prevalence and incidence for T1D

The DiaMond study [Karvonen et al., 2000; DiaMond Project Group, 2006] –published in2000 and promoted by the WHO– estimated a worldwide prevalence of 4.5% children in theage range 0–14, with large differences (more than 350-fold) in incidence across countries andregions: from 0.1 new cases per 100,000 children per year in China or Venezuela, to as manyas 36.5 or 36.8 in Finland or Sardinia, respectively. To explain these variations, authorshypothesized differences in genetic factors, as well as in environmental and behaviouralaspects [Karvonen et al., 2000; DiaMond Project Group, 2006]. Overall, Europe is theregion with highest prevalence of T1D among children 0–14, with approximately 129,000

14

3. Diabetes

Figure 3.2: Comparative prevalence percentages of diabetes by country. (Source: Adaptedfrom IDF Atlas 2013 [International Diabetes Federation, 2013]).

Figure 3.3: Predicted variations from year 2013 to 2035 in: a) diabetes cases –left panel–,and in b) percent prevalence –right panel– across different regions of the world. (Source:Adapted from IDF Atlas 2013 [International Diabetes Federation, 2013]). AFR, Africa;EUR, Europe; MENA, Middle East and North Africa; NAC, North America and Caribbean;SACA, South and Central America; SEA, South-East Asia; WP, Western Pacific.

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3.3. Risk factors for T1D

Figure 3.4: Incidence rates of T1D in childhood (age range 0–14 years old) in 2013; ex-pressed as new cases per 100,000 children per year. (Source: Adapted from IDF Atlas 2013[International Diabetes Federation, 2013]).

patients and an incidence of 20,000 new cases per year [Patterson et al., 2014]. Predictionsbased on 1989–2003 data from the EURODIAB ACE Study Group [2000]; Lévy-Marchalet al. [2001] estimate 160,000 new diagnoses per year in 2020 [Patterson et al., 2009],doubling numbers with respect to 2005.

3.3 Risk factors for T1D

The most widely accepted hypothesis for the aetiology of T1D is an environmentally trig-gered, auto-immune reaction against β-cells in which there is a certain role of geneticallyinherited predisposition [Eisenbarth, 1986; Maahs et al., 2010]. Regarding risk factors, thefollowing have been identified [Maahs et al., 2010]:

• Age: According to the SEARCH for Diabetes in Youth Study Group [2006], incidencerates increase from birth, reach their maximum in the age groups 5–9 and 10–14and subsequently decay after puberty. Nevertheless, approximately 1/4 of new T1Ddiagnoses are adults.

• Sex: Although females are most frequently affected in the majority of auto-immunediseases, in the case of T1D incidences for both sexes are comparable. In addition,regions with high incidence –such as Europe, or populations of European descent–show a male excess; whereas regions with lower incidence report a female excess[Green et al., 1992; Karvonen et al., 1997].

• Ethnicity: Reports do not often address ethnicity as a risk factor in an explicitmanner, presenting their data separated by countries and/or regions (Figure 3.4).The reasons for this choice may be based, at least partially, on the relative ethnichomogeneity within a particular country/region; as well as on the limited size andstatistical power of the sample as to address group differences. However, the highestT1D prevalences in USA were documented among non-Hispanic whites SEARCH forDiabetes in Youth Study Group [2006].

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3. Diabetes

• Genotype: There are several genes related to T1D susceptibility, the most importantof which is the human leukocyte antigen (HLA) complex located in the 6th chromo-some. Two haplotypes are currently considered as principal markers of susceptibility,with 90–95% of children with T1D carrying either or both haplotypes [Mehers andGillespie, 2008]. However, at most 5% of the people with HLA-based susceptibilityeventually develop T1D [Maahs et al., 2010]; whereas HLA allelic variations may onlyexplain up to 40–50% of the total genetic risk component [Concannon et al., 2005].The remaining genetic risk is associated with a considerable number of other genes,each of which contributes with modest individual impact. In addition, studies byVehik et al. [2008]; Hermann et al. [2003] suggest a temporal trend towards lowerproportions of new T1D cases carrying high-risk HLA genotypes, which may indicatean increasing role of environmental factors. Nevertheless, T1D is strongly influencedby genetic aspects [Maahs et al., 2010].

• Other factors: Environmental triggers initiating β-cell destruction are largely un-known, although various nutritional habits have been investigated, such as: breastfeeding, cow’s milk, wheat gluten, or vitamins D and E [Maahs et al., 2010]. Varia-tions in incidence in terms of geographical location and seasonality, both for the onsetof T1D and for birth, have also been described [Maahs et al., 2010].

3.4 Complications in T1D

Among the short-term complications associated with T1D, the two most important andrisky events are: i) hypoglycaemia, and (to a lesser extent) ii) hyperglycaemia with di-abetic ketoacidosis (DKA). DKA occurs mainly in T1D, but it may also appear in T2Dfor some cases [Albright et al., 2000]. DKA stems from insulin insufficiency, which pre-vents the use of glucose as energy source. In this situation, energy is extracted from themetabolization of free fatty acids (FFA), a process in which ketone bodies are produced.In high concentrations, ketones are toxic and can lead to ketoacidosis, which may in turnbring severe acute consequences, including cerebral oedema, renal failure or heart attacksin the most extreme cases. Conversely, hypoglycaemia consists in an acute pronounceddecay of blood glucose levels, which in T1D is typically originated by an unmatched ex-ogenous insulin supply; for example, due to an incorrect amount and/or timing of insulinadministration in relation to meals or physical activity. The effects of hypoglycaemia rangefrom dizziness, headache, shaking or sweating in milder cases to seizures, unconsciousness,coma, brain damage or death [DCCT Research Group, 1997].

On the other hand, long-term complications can be divided in two main groups, namely:micro- and macrovascular damages. In turn, microvascular aggravations encompass mainly:

• Retinopathy: Thin vessels supplying blood to the eyes –and in particular, to retina–become damaged after prolonged exposures to hyperglycaemia, high blood pressureand cholesterol. This damage may lead to severe vision loss and permanent blindness[DCCT Research Group, 1995c], which makes diabetes the most frequent cause ofblindness among adults in the range 20–74 years old.

• Nephropathy: Similarly to retinopathy, vessels to the kidneys get damaged. Kidneys,which are responsible for disposing glucose excesses through renal excretion (i.e. gly-cosuria), lose efficiency in their function or ultimately fail [DCCT Research Group,1995b].

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3.5. Treatment of T1D

• Neuropathy: Prolonged hyperglycaemia may produce severe deteriorations in boththe peripheral and autonomic nervous systems, causing touch insensitivity, loss of co-ordination, pain or other dysfunctions, such as problems with digestion or urination[DCCT Research Group, 1988]. The most frequent damages tend to occur in extrem-ities, particularly in feet, with a loss of sensitivity which may prevent injuries frombeing noticed. In turn, this issue often leads to infections, ulceration, the so-called‘diabetic foot disease’ or even amputations.

Macrovascular complications include a series of cardiovascular and cerebrovascular dis-eases, e.g.: angina, stroke, myocardial infarction, congestive heart failure, ischemic heartor peripheral artery damage. Together they constitute the most common cause of deathand disability among patients with diabetes, where the risk of suffering these diseases issubstantially higher than for the general population [DCCT Research Group, 1995a].

3.5 Treatment of T1D

3.5.1 Current clinical practise

Tight glycaemic control to maintain glucose in safely low levels –aiming at euglycaemia, butalways trying to avoid hypoglycaemia episodes– can reduce significantly the amount andextent of complications associated with T1D [DCCT Research Group, 1993]. Current careguidelines by the ADA [American Diabetes Association, 2014] establish: a) a general goalfor glycated haemoglobin HbA1c<7.0%, which broadly corresponds to an average glycaemiaof approximately 150–160 mg/dL (i.e. 8.3–8.9 mmol/L), b) preprandial glucose levelsbelow 130 mg/dl (7.2 mmol/L), and c) postprandial excursions <180 mg/dl (10.0 mmol/L).However, individualized adaptations of treatment and goals are strongly recommended[American Diabetes Association, 2014]. In this regard, younger and healthier patients mayaim to more stringent targets (e.g. HbA1c<6.5%); whereas subjects in an advanced stageof progression of the disease, older or with complications and/or co-morbidities could havelooser targets (e.g. HbA1c<8.0%). In all cases, avoiding acute hypoglycaemia events mustbe an essential priority.

On the other hand, a decisive component for a successful treatment –specially in T1D–lies in diabetologic education to empower patients for a safe and effective self-managementof their disease. Primarily, patients should learn how to self-administer insulin and tomonitor their glycaemia. Additionally, a highly desirable skill would be the capability toadapt therapy in accordance to different circumstances, e.g. variations in diet with respectto their habits (amounts, nutrients) or changes in insulin dosages to accommodate exerciseand/or other unforeseen situations.

3.5.1.1 Insulin therapy

Two main strategies for the administration of insulin coexist in current clinical practice,namely:

• Multiple daily injections (MDI). This approach consists in supplying: a) sustainedbasal amounts of insulin, via the injection of preparations with slow absorption andprolonged action; plus b) one-time boluses with high doses of rapid-acting insulin,administered immediately prior to meal intakes. This basal-bolus combination was

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3. Diabetes

conceived to mimic the physiological secretion patterns of endogenous insulin in sub-jects without diabetes, which are approximately constant during fasting periods andshow marked peaks with meals.

• Continuous subcutaneous insulin infusion (CSII). Every few minutes (e.g. 5 to 15 min)an electromechanic pump delivers micro-infusions of rapid-acting insulin through asubcutaneous catheter, avoids repeated injections. This strategy also provides cer-tain degree of flexibility in the therapy to accommodate unpredicted circumstances,allowing for immediate adaptations in the infusion rate which are infeasible withMDI.

Important problems with the subcutaneous administration of exogenous insulin –both bymeans of MDI and CSII– are: i) delays in its absorption and action, along with the varioussources of variability for those delays [Heinemann and Anderson, 2004], which include:insulin type, injection site, temperature and blood flux, exercise, alcohol or medications,among others; and ii) insulin resistance, also with multiple inter- and intra-individualfactors influencing it; e.g. insulin sensitivity may fluctuate significantly within a single dayfor the same patient, normally following circadian rhythms [Jungheim and Koschinsky,2002]. These sources of variability pose a major challenge on every therapeutic decisionregarding insulin dosages. Such decisions –which patients need to make by themselves ona daily basis, several times per day– unavoidably embrace a non-negligible component ofuncertainty which hinders self-management.

3.5.1.2 Dietary considerations

In general, healthy eating habits to include a variety of nutrients in appropriate portions arean important component of a successful management of diabetes [Evert et al., 2013], eitherT1D, T2D or GD. Given the wide range of personal circumstances –e.g. individual andcultural preferences, health literacy, access to healthy food choices, or willingness and abilityfor behavioural changes–, individualized medical nutrition therapies based on scientificevidence would be highly desirable [American Diabetes Association, 2014]. If possible,patients with T1D should be capable of carrying out carbohydrate counting procedures inorder to estimate suitable prandial bolus doses in accordance [Laurenzi et al., 2011]; taskfor which education is essential [DAFNE Study Group, 2002]. Further aspects –such asglycaemic index and glycaemic load of food– may also be taken into account, althoughliterature in this regard is complex [Evert et al., 2013].

3.5.1.3 Physical activity considerations

The standard hormonal response to physical activity in healthy subjects without diabetescombines a reduction in circulating insulin concentrations, along with increased secretionsof counter-regulatory hormones, including glucagon and epinephrine, among others (seechapter 4 for further detail). In the contrary, in T1D this response is impeded, primarilyby the fact that the organism cannot re-adapt insulin levels by physiological mechanisms;hence complicating the management of exercise in T1D [Hayes and Kriska, 2008]. However,any level of physical activity –i.e. from recreational to high-performance– can be practisedby patients with T1D, provided that they are in good glycaemic control and do not sufferfrom severe complications.

In this regard, physical activity is beneficial for T1D patients in a number of aspects,including: overall physical fitness and well-being, reduced risk and complications of car-diovascular diseases –whose impact is otherwise exacerbated in T1D–, and lower insulin

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3.5. Treatment of T1D

resistance [Chimen et al., 2012]. However, various studies [Kennedy et al., 2013; Chimenet al., 2012; Wallymahmed et al., 2007; Herbst et al., 2006] showed that overall glycaemiccontrol (measured through glycated haemoglobin A1c) did not experience significant im-provements with exercise plans in T1D; oppositely to the case of T2D, where scientificevidence is solid [Chimen et al., 2012]. Various reasons have been hypothesized to explainthis lack of HbA1c improvement in T1D, including reductions in insulin doses and aug-mented caloric intakes by patients –either as an additional energy source, or to protectagainst eventual exercise-induced hypoglycaemia episodes [Kennedy et al., 2013]–. How-ever, a recent meta-analysis by Kennedy et al. [2013] found beneficial effects in terms ofglycaemic control for a subgroup of studies focused on young subject exercising duringlonger periods. Authors also suggested that longer interventions could potentially havemore positive impacts on HbA1c.

In summary, there is not sufficiently conclusive scientific evidence to consider exercise as aprimary mechanism to improve glycaemic control in T1D. Instead, it constitutes a positivebehaviour with valuable health benefits for patients in other aspects, such as improvedinsulin sensitivity and protection against cardiovascular damage.

According to current standards of medical care by the American Diabetes Association[2014], general exercise recommendations (i.e. non-T1D-specific) are exactly the same thanfor the rest of the adult population: at least 150 min per week of moderate intensity exercise–corresponding to 50–70% of each subject’s maximal heart rate), performed over at leastthree different days; or conversely, 75 min of vigorous activity per week. Specific ADArecommendations for exercising with T1D include [American Diabetes Association, 2004]:

• To arrange a medical evaluation before adhering to an activity routine. In case ofpre-existing complications (e.g. cardiovascular problems or neuropathies), exercisemay be counter-indicated.

• As for the general population, to involve in stretching, warm-up and cool-down ex-ercises for 5–10 min each; both before and after the physical activity session. Inthis manner, muscles and the cardiorespiratory system are subject to a progressiveincrease/decrease of exercise intensity.

• To maintain tight metabolic control before physical activity. In particular, not to ex-ercise if glycaemia at start is above 250 mg/dL (13.9 mmol/L) with ketosis; or to ex-ercise with caution if above 300 mg/dL (16.7 mmol/L) but without ketosis. To ingestsupplementary carbohydrates (CHO) if glycaemia is below 100 mg/dL (5.6 mmol/L).

• To self-monitor blood glucose regularly in order to check that safety margins are notsurpassed, or to take corrective therapeutic actions in accordance. In addition, theself-monitoring of glucose should be continued before, during and also after the exer-cise session in order to learn one’s response to different activity types and conditions.

• To consume rapid-absorption rescue CHO if needed to avoid hypoglycaemia. Theserescue CHO must be available at all time during and after the practise of exercise.

• Abundant hydration.

3.5.2 Experimental treatments

As outlined above, T1D therapies in current clinical practise rely mainly on the admin-istration of exogenous insulin, along with diabetologic education to empower patient’sself-monitoring (e.g. regular glucose measurement), action and decision-making. In theshort-term future, it is expected that insulin will continue to be the main treatment for

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3. Diabetes

the majority of cases; whereas in the long-term, it will probably complement other thera-pies [van Belle et al., 2011]. In this regard, different families of innovative approaches arecurrently under development, including [O’Brien, 2013]:

• Immunological therapies, either antigen-specific or not.• Gene therapies.• Compensations of the destruction of β-cell mass: islet transplantation and/or regen-

eration, β-cell neogenesis or stem cell transplantation.• Artificial pancreas systems.

3.5.2.1 Immunological therapies

Research concerning immunological therapies is focused on two principal aspects: a) pro-moting tolerance to β-cell antigens, and b) blocking the misguided autoimmune destructionof β-cell mass without weakening the overall immune response due to long-term immuno-suppression. However, various issues remain unresolved; e.g. negative effects on regulatoryT-cells (T-lymphocytes) [van Belle et al., 2011].

Combinations of antigen-specific treatments with non-specific approaches (e.g. anti-inflammatoryagents) are currently under development. It is also presumed that immune therapy willplay an important role in combination with transplantations and regenerative therapies, inorder to prevent the new β-cells from being destroyed again [van Belle et al., 2011].

3.5.2.2 Gene therapies

The core idea of gene therapy when applied in T1D consists in promoting the productionof insulin by other cells instead of β-cells; a task for which hepatocytes in the liver arefrequently selected due to their sensitivity to glucose. For example, Callejas et al. [2013]used an adeno-associated viral vector to over-express the genes for insulin and glucokinasein the skeletal muscles of a canine model, resulting in a significant increase of glucoseuptake and a correction of hyperglycaemia which was sustained in the long-term: beyondfour years.

3.5.2.3 Compensation of β-cell destruction

This family of experimental therapies seek to compensate for the drastic reduction of β-cellmass, in turn restoring the ability to produce endogenous insulin. Different approachesexist [van Belle et al., 2011]:

• Stimulation of the remaining β-cells to promote insulin secretion, utilizing analoguesof the incretin hormone GLP-1.

• Neogenesis of β-cells, promoted by gastrin.• Islet regeneration from progenitor cells in the pancreas. This regeneration is induced

by islet neogenesis associated protein (INGAP) peptide, in a similar manner as duringembryonic stage. An extra advantage of this technique resides in that it does notrequire surgery.

• Transplantation of islets of Langerhans from multiple donors, as in the Edmontonprotocol [Shapiro et al., 2000]. This type of experiences show satisfactory resultsduring the first year after transplantation, although outcomes worsen in the long-term: despite immune suppression, after five years less than 10% of patients remained

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3.5. Treatment of T1D

insulin independent [Ryan et al., 2005]. Auto-reactions against the implanted cellsnotably reduced β-cell functionality.As a consequence, these islets transplantations are nowadays an option for specificgroups of patients with the most aggravated cases: severe glycaemic liability, recurrenthypoglycaemia and hypoglycaemia unawareness [de Kort et al., 2010]. The limitednumber of donors is also an important barrier, since two or three islet infusions fromdifferent donors are usually required; although research efforts have been conducedwith a single donor [Hering, 2005].

• Transplantation of stem cells to regenerate β-cell mass, achieved either by: a) thedifferentiation of embryonic or pluripotent stem cells; or b) by reprogramming ofadult stem cells from their initial phenotype into β-like cells.

Either transplanted or newly generated β-cells continue to provide antigens which are sus-ceptible to autoimmune attacks [von Herrath et al., 2007]; whereas islet transplantationsand allogeneic stem cells must also face alloimmune responses. In this sense, research isbeing conduced in the encapsulation of β-cells to create a physical barrier against immuno-logical responses, while allowing the β-cell to sense glucose and to release insulin as needed[McGarrigle and Oberholzer, 2013]. This micro-encapsulation would reduce the need forimmune suppression, although problems arise due to the limited amount of oxygen capableof crossing the barrier, an issue which compromises the energy supply to the cell.

3.5.2.4 Artificial pancreas

Additionally to the biology-focused experimental therapies for T1D listed above, ‘artificialpancreas’ solutions constitute a technological approach to aid in the daily managementof this chronic disease. Artificial pancreas systems –also frequently known as closed-loopglucose controllers– rely on the combination of three elements: a) a continuous glucosemonitor (CGM) to regularly sense glucose levels, b) an insulin pump to deliver micro-dosesof insulin in real time, and c) a control algorithm which, taking into account CGM glucosemeasurements and previous insulin administrations (plus ideally other circumstances, suchas meals or physical activity), suggests suitable insulin infusion regimes to maintain glucoseconcentration stable in safe levels. Thus, the automatic adaptations of therapy as proposedby the controller would assist –or eventually replace– constant human decision making whilepreserving patients’ health and safety.

In-hospital glucose control has been available since the 1970s using the intravenous routefor both glucose measurement and insulin infusion [Clemens et al., 1977]; whereas on thecontrary, ambulatory systems are still under development and demanding intense researchefforts. A major reason for this lies in the fact that practical aspects in ambulatory scenariosvoid the use of the intravenous route, forcing subcutaneous accesses instead. However, thissubcutaneous route introduces considerable delays for glucose measurement, as well as forinsulin absorption and action [Cobelli et al., 2011]. In practise, such cumulative delays posea major challenge for the control algorithms which form the core of the artificial pancreas.

As a consequence, the introduction of these systems into clinical practice is expected to oc-cur gradually [Hovorka, 2011]. More restrained scenarios –in particular, overnight control–are being addressed first, for a subsequent advance towards more complex and variable sit-uations, such as: a) the control of prandial and postprandial periods –probably requiringmanual meal announcement by the patient–, or b) exercise [Chassin et al., 2007; Breton,2008; Hovorka, 2011; van Bon et al., 2011].

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3. Diabetes

In this regard, the main barriers for the consolidation of artificial pancreas solutions arecurrently [Hovorka, 2011]:

• To improve CGM technology, increasing its accuracy –which is yet lower than for glu-cose meters [Hirsch, 2009]– as well as reducing its time lags and long-term deviations(e.g. drifts).

• The relatively slow absorption of insulin through the subcutaneous route, aggravatedby inter- and intra-subject variabilities in pharmacokinetics.

• The need for more advanced control algorithms capable of accommodating the men-tioned limitations: sensor inaccuracies, delays in glucose measurement and insulinaction, as well as inter- and intra-subject variations and other physiological aspectsof glucose homoeostasis.

The two most widespread families control architectures applied to artificial pancreas situa-tions are proportional-integral-derivative (PID) [Marchetti et al., 2008] and model-predictivecontrol (MPC) [Hovorka et al., 2004]; although others exist in literature, e.g. based on fuzzylogic [Atlas et al., 2010], on robust control theory H∞ [Kovács and Paláncz, 2007], or rule-based approaches [Wang et al., 2010; Capel et al., 2014]. PID is a generic feedback controlmechanism governed by three weighted components (namely: error with respect to tar-get, its derivative and its integral); whereas MPC relies on a model –normally groundedon physiological descriptions, although not necessarily– to assess the glycaemic responseto different candidate insulin actions. In this sense, further research work is needed inthe context of MPC controllers to enhance the supporting models so that they better re-flect major events influencing glucose-insulin dynamics, mainly meals and exercise [Chassinet al., 2007; Breton, 2008; Breton et al., 2014; Danne et al., 2014].

In addition, artificial pancreas solutions have been proposed to compensate for the glucose-lowering effects of excessive insulin administrations by means of the delivery of glucose-rising glucagon hormone [El-Khatib et al., 2007, 2009, 2010], with the aim to take correctiveactions to prevent hypoglycaemia events. Furthermore, telemedicine can be an advanta-geous complement to the basic behaviour of artificial pancreas systems, enhancing theirsafety and facilitating clinical supervision if necessary [Gómez et al., 2008; de Leiva andHernando, 2009; Hovorka, 2011].

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3.5. Treatment of T1D

24

Chapter 4

Physical activity in T1D

4.1 Foundations of exercise physiology

This chapter overviews the main physiological mechanisms involved in the metabolic regu-lation of glucose during exercise, in the first place for healthy subjects with diabetes. Lateron, specificities for T1D patients are addressed.

An important note should be made when discussing physiological effects of physical activity:exercise intensity should not be referred by external criteria (e.g. by means of running speedin km/h). Instead, for the sake of comparability, intensity should ideally be expressed as apercentage of each subject’s maximum oxygen uptake (VO2max); where this VO2max upperbound is dependent on several individual factors, including age and sex, height and weight,training status or genetic factors [Nagi, 2006].

4.1.1 Glucose homoeostasis at rest

The brain and central nervous system (CNS) demand a constant glucose supply whichrepresents around one half of the body’s total daily needs in terms of glucose [Shrayyef andGerich, 2009]. Besides, brain and CNS have the distinctive feature of utilizing circulatingblood glucose without the need for insulin; whereas on the contrary, other tissues (e.g.skeletal and cardiac muscles) require insulin in order to make glucose reach the interiorof the cell. With this aim, glucose transporters are mobilized towards the cell membrane,facilitating in this manner the transit through the membrane. In the interior of the cellglucose serves as energy source via a degradation process named glycolysis.

Meals are the primary external source of glucose and any amounts of meal glucose exceedingthe basic, instantaneous requirements must be stored for future use. To do so, glucoseundergoes a process of combination denominated glycogenesis to form larger molecules –glycogen–, which are in turn stored in the liver and in skeletal muscle [Shrayyef and Gerich,2009]. Conversely, in situations where extra energy is demanded, glycogen is mobilizedfrom these storages and broken down again into glucose –glycogenolysis process–. On theother hand, once glycogen depots are already full, glucose is transformed first into freefatty acids (FFA) and then into triglycerides, for storage in adipose tissue. Similarly, thisprocess can be reversed –lipolysis– to carry out a combustion of FFA, from which energyis obtained; as well as ketone bodies as a by-product [Shrayyef and Gerich, 2009]. Inaddition, gluconeogenesis –mainly hepatic, and to a lesser extent renal– also plays a rolefor the maintenance of blood glucose concentrations in normal levels: it is the metabolic

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4.1. Foundations of exercise physiology

pathway responsible for generating glucose from non-CHO substrates such as glycerol,pyruvate, lactate and glucogenic amino-acids [Shrayyef and Gerich, 2009].

4.1.2 Energy sources during exercise

Physiological responses to exercise depend largely on the metabolic mechanisms employedto satisfy the additional energy demands for muscle contraction. In turn, the contributionsof different metabolic pathways depend strongly on the type, intensity and duration ofphysical activity; as well as on the subject’s training and nutritional status. In T1D,additional aspects have an important role (see section 4.2).

The unique process through which muscles can obtain energy for contraction is via thebreakdown of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and phos-phate, with the subsequent release of energy (Figure 4.1). However, muscle cells are capableof storing only small amounts of ATP ready for its use, stores which may last for approxi-mately one second, at most [Colberg, 2009]. Consequently, external mechanisms are neededto externally provide muscles with ATP. Three metabolic pathways exist: i) phosphagen,ii) lactic acid, and iii) aerobic systems. These three mechanisms work as a continuum,which implies that all of them are used to some extent for almost any exercise lasting formore than one minute (Figure 4.5) [Colberg, 2009].

4.1.2.1 ATP-CP system

The ATP-CP pathway –also known as phosphagen system– is almost exclusively involvedin very short and explosive activities which demand high power, e.g. short sprinting ora power lift. Posphagen –i.e. creatine phosphate (CP)– cannot fuel muscular activityin a direct manner, but the rapid energy release obtained from its breakdown serves toresynthesize ATP via the phosphorilation of ADP (Figure 4.2). Given that this processcan operate during around 5 to 9 extra seconds after the initial depletion of ATP whichoccurred in the first second, the ATP-CP energy source cannot be sustained beyond 10 s[Colberg, 2009].

Since oxygen is not required for the ATP-CP metabolic pathway, it is said to be anaerobic.Besides, blood glucose is not involved, meaning that glucose decays should not occur forT1D. On the contrary, the exacerbated release of glucose-rising counter-regulatory hor-mones may lead to a rise in glycaemia [Colberg, 2009] (see section 4.2).

4.1.2.2 Lactic acid system

The so-called ‘lactic acid’ system contributes mainly to activities whose duration rangesfrom approximately 10 s to 2 min, e.g. an 800 m athletics race. Essentially, this pathway ispredominant (Figure 4.5) when the ATP-CP system is already depleted and the intensityof exercise demands high energy supplies which the aerobic system alone cannot match.

Muscle glycogen stored in the involved skeletal muscles is broken down by glycogenolysis.Once released, glycogen produces energy through the metabolic process of glycolysis; inparticular via fast anaerobic glycolysis, which generates ATP plus lactate as by-product(Figure 4.3). In this regard and despite the (misleading) traditional name of the system,at biological pH levels it is –not lactic acid– as well as H+ hydrogen ions which are released[Nagi, 2006]. At rest, the aerobic processing of CHO produces modest amounts of lactate;

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4. Physical activity in T1D

whereas on the contrary, fast anaerobic glycolysis generates much larger quantities whichlead to lowered pH in muscle and blood, linked to the appearance of muscular fatigue.

Similarly to ATP-CP, the lactic acid system is an anaerobic mechanism not demanding O2.Its main advantage resides in its rapid energy contribution, although the use of glucoseis notably inefficient: one molecule of glucose can only produce 3 ATP through anaerobicglycolysis, in contrast to as many as 37–39 ATP via the aerobic procedure [Colberg, 2009].

4.1.2.3 Aerobic system

The aerobic contribution is prevailing in prolonged physical activities –e.g. endurancerunning– because it can provide a steady supply of energy for sustained activities lasting formore than 2 min. This metabolic pathway relies on the aerobic (i.e. O2-based) metabolismof glucose and FFA, along with the breakdown of liver and muscle glycogen (Figure 4.4).

At rest the main source of energy is fat, contributing with around 60% of energy; whereasCHO provides almost the remaining 40%. Nonetheless, there is also a minor contributionfrom protein –below 5%–, except in very prolonged and demanding exercises where thisfuel may reach up to 15% [Nagi, 2006; Colberg, 2009]. Anyhow, the exact mix of fuelsdepends on several factors such as: physical activity’s intensity and duration, diet pre- andduring exercise, subject’s training status and –in the case of patients with T1D– circulatingplasma insulin concentrations.

When exercising, the proportion of energy extracted from CHOs increases with intensity,reaching up to almost 100% in near-maximal exertions. This phenomenon occurs becausethe extraction of ATP and energy from CHOs is more efficient than from fat. As a conse-quence, CHOs –rather than blood glucose– are the major source of glucose for the muscles,accounting for approximately 80% of energy [Colberg, 2009]. On the other hand, duringless intense activity adrenaline hormone mobilizes fat from adipocytes –i.e. fat cells–, thatcirculate in blood as FFA for exercising muscles to take up. Hence, during milder activitymuscles use mainly fat as well as some CHOs. With training, body’s capacity to mobi-lize and to metabolize fats is enhanced, which means that the energy supply becomes lessreliant on glucose and that the rates of depletion of muscle glycogen are lower [Colberg,2009].

4.2 Exercise physiology in T1D

In subjects without diabetes, the normal physiological response to exercise induces a de-crease in plasma insulin levels plus an extra secretion of glucagon to stimulate the liver toproduce additional glucose via hepatic glycogenolysis [Colberg, 2009]. Additional glucose-rising counter-regulatory hormones are also released, namely: catecholamines (epinephrine,norepinephrine), cortisol and growth hormone (Table 4.1). On the other hand and in spiteof the lowered insulin levels, muscles continue to take up glucose because contractions stim-ulate the translocation of glucose transporters to the cell membrane [Thorell et al., 1999].Finally, glycogen stores in muscles and liver are replenished after exercise.

The main differences in T1D stem from the fact that such a normal endocrine response islost [Lumb and Gallen, 2009], as the physiological decrease in insulin cannot be mimickeddue to the subject’s hindered capability to regulate the amounts of circulating insulin inreal time. With MDI, the adjustment of exogenous dosages requires previous planning;whereas in comparison, some extra flexibility is gained with CSII, e.g. by stopping the

27

4.2. Exercise physiology in T1D

Figure 4.1: ATP breakdown to release energy (Source: Adapted from Colberg [2009]).

Figure 4.2: ATP-CP system (Source: Adapted from Colberg [2009]).

Figure 4.3: Lactic acid system (Source: Adapted from Colberg [2009]).

Figure 4.4: Aerobic system (Source: Adapted from Colberg [2009]).

Figure 4.5: Temporal evolutions of the fractions of total energy as contributed by eachmetabolic pathway involved during exercise (Source: Adapted from Colberg [2009]).

28

4. Physical activity in T1D

pump at the onset of physical activity.

As described below, insulin levels during exercise (Table 4.2) play an essential role indetermining the T1D response to exercise [Wasserman and Zinman, 1994]:

OverinsulinizationHigh insulin concentrations may occur for various reasons. For example, bolus doses es-timated in account for sedentary situations may in turn result excessive in the event ofunscheduled physical activity sessions. Alternatively, overinsulinization may also be due toexercise-induced rises in insulin absorption and/or action.

In turn, excessive levels of circulating insulin may reduce severely –or even inhibit– [Wasser-man and Zinman, 1994] the secretion of glucagon and the other counter-regulatory hor-mones, a phenomenon leading to attenuated releases of hepatic glucose. In addition, thescarcity of adrenaline hormone can impair the release of FFA from adipose tissue via lipol-ysis, which would translate to lesser amounts of fat as alternative fuel for contractingmuscles. Furthermore, high insulin levels promote an accelerated uptake of glucose fromthe blood stream [Wasserman and Zinman, 1994]. Therefore, all these events –in combi-nation with the extra glucose consumptions caused by muscular work– pose a high risk ofhypoglycaemia.

To tackle this problem, compensatory reductions of insulin dosage would be desirable. How-ever, and particularly if MDI therapy is used, this requires the patient to schedule his/herexercise session in advance, as well as taking into account the foreseen timing and inten-sity of exercise in order to calculate suitable bolus dosages. Since this pre-compensatorystrategy is not always feasible (e.g. for spontaneous activities), subjects may need to ingestextra CHOs to prevent hypoglycaemias [Gallen, 2014].

UnderinsulinizationUnderinsulinization is often linked to poor diabetologic control and sustained hypergly-caemia [Wasserman and Zinman, 1994]. If physical activity is performed under these cir-cumstances, it may worsen metabolic control: exacerbating hyperglycaemia and ketosis.With low plasma insulin levels, the expected exercise-induced increase in glucose utiliza-tion may be impaired [Wasserman and Zinman, 1994]. This issue, along with: a) thephysiologically normal rise in endogenous hepatic glucose production, and b) an exacer-bated glucagon response, often lead to increased glycaemia levels. In addition, lipolysismay generate excessive ketone bodies.

On the other hand, patients with poor metabolic control usually show an elevated responsein terms of the release of counter-regulatory glucose-rising hormones [Wasserman and Zin-man, 1994].

In summary (Table 4.2): excessive insulin concentrations during physical activity impair–or block– substrate mobilization, leading to hypoglycaemia; whereas insufficient insulin,in association with an exacerbated release of glucose-rising counter-regulatory hormones,may cause hyperglycaemia and ketosis. Besides, apart from insulin concentration, variousother variables influence the glycaemic response to exercise in T1D, which can be dividedin broad terms into two groups:

29

4.2. Exercise physiology in T1D

Hormone Released by Effects

Glucagon PancreasIt stimulates hepatic glycogenolysis andgluconeogenesis from precursors. It also has alarge effect in the increase of glucose release.

Epinephrine(adrenaline)

Adrenalmedulla

It stimulates muscle –and to a lesser extent,hepatic– glycogenolysis. It mobilizes FFA fromadipose tissue.

Nor-epinephrine(nor-adrenaline)

Adrenalmedulla

It stimulates hepatic gluconeogenesis fromavailable precursors. Along with epinephrine,it exerts a ‘feed-forward’ control on glucoseduring intense exercise.

CortisolAdrenalcortex

It stimulates the mobilization of amino-acidsand glycerol as precursor for hepaticgluconeogenesis, along with the release of FFAfor muscle use in lieu of glucose.

Growthhormone

Anteriorpituitary

It stimulates fat metabolism –i.e. the releaseof FFA from adipose tissue– and the storage ofamino-acids, along with an indirectsuppression of glucose use.

Table 4.1: Summary of the effects of glucose-rising counter-regulatory hormones (Source:Adapted from Colberg [2009]).

Plasmainsulin

Hepaticglucose

production

Muscleglucoseuptake

Trend ingly-

caemiaRisk

Low ⇑⇑ ↑ ↑ or ⇑ HyperglycaemiaNormal ⇑⇑ ⇑⇑ → or ց Limited

High ↑ ⇑⇑ ↓ or ⇓ Hypoglycaemia

Table 4.2: Expectable exercise-induced trends in glycaemia for T1D patients under differentconditions in terms of insulinaemia (Source: Adapted from Colberg [2009]).

• Factors in common with the general population: intensity, duration and type ofphysical activity, individual fitness level, nutritional status and previous meals (bothin terms of their content and their timing with respect to the exercixe bout).

• Specific for T1D: timing of last insulin injections and type of preparations used, theirabsorption rates, overall metabolic control or diabetes complications, among others.

Given the number and diversity of factors, it is difficult to provide precise instructionson how to manage exercise in T1D; although general therapeutic guidelines are availablein literature [American Diabetes Association, 2004; Riddell and Perkins, 2006; Lumb andGallen, 2009; Gallen, 2014].

Training diminishes the release of glucose-rising hormones. It also augments subject’s ca-pacity to mobilize and metabolize fats, which in turn reduces the reliance on glucose as fueland leads to slower depletions of muscle glycogen. As a consequence, reductions in insulindosage in order to accommodate exercise do not need to be so drastic as for untrainedindividuals. In addition, training enhances insulin efficiency because glucose is more easilytaken up by muscles. All these aspects combined translate generally into lower daily insulinrequirements, as well as into easier metabolic control.

30

4. Physical activity in T1D

Anyway, hypoglycaemia continues to be the most prominent risk for T1D patients whopractise physical activity. In this regard, hypoglycaemia events may not only occur duringexercise but also afterwards (even up to 12–14 h later, specially in nocturnal periods [Nagi,2006]). Possible mechanisms in charge for this delayed phenomenon are:

a) an attenuation of the endogenous glucose production [Gallen, 2014].b) a prolonged increase in insulin sensitivity caused by exercise [Sonnenberg et al., 1990],

andc) the delayed replenishment of hepatic glycogen stores.

An added problem with hypoglycaemia events occurred within the day previous to a certainexertion is that these episodes augment the risk of another hypoglycaemia [Briscoe et al.,2007]. Besides, hypoglycaemia during physical activity may be difficult to detect [Riddelland Burr, 2011], in part because many of its symptoms (e.g. tiredness, sweating) are normalsensations in exercise. Furthermore, the activation of counter-regulatory hormones –whichwould normally contribute to the restoration of glucose levels– may be reduced or absent[Cryer, 2009].

With respect to different physical activity modalities, continuous exercise of moderate in-tensity is generally associated with a greater risk of hypoglycaemia in T1D [Ertl and Davis,2004]. Conversely, very intense physical activity (above 80% VO2max), as well as anaerobicexercise of short duration (where glucose uptake by muscles is low) can lead to hypergly-caemia [Marliss and Vranic, 2002] due to the release of large amounts of catecholamines,cortisol and growth hormone [Purdon et al., 1993; Gallen, 2014]. Furthermore, the im-possibility of a physiological rise in endogenous insulin secretion during recovery –whichin non-T1D subjects leads to a normalization of glucose levels– can result in prolongedhyperglycaemia [Chu et al., 2011], a situation for which specific therapeutic guidelines arerequired [Riddell and Perkins, 2006; Lumb and Gallen, 2009]. On the other hand, inter-mittent high-intensity exercise (IHE) may be associated with lower rates of hypoglycaemia[Guelfi et al., 2007] as compared to moderate intensity exercise. The glycaemic response toIHE (which is prototypical of team sports, for example) depends on the balance between:a) its part with a sustained –predominantly aerobic– exertion, and b) the proportion ofinterspersed, short but intense bursts –with notable anaerobic contributions–. Nonetheless,this balance is difficult to ascertain in free-living conditions (e.g. recreational sports) [Basuet al., 2014]. Finally, resistance exercise –e.g. strength/weight training– was reported not toalter insulin sensitivity after the performance of exercise [Jiménez et al., 2009], which maydiminish the occurrence of post-exercise hypoglycaemia in T1D with respect to sustainedaerobic activity.

4.3 Systematic review: Quantification of the acute ef-

fect of exercise on glycaemia in T1D

4.3.1 Motivation

As outlined qualitatively in the previous section, the physiological response to physicalactivity in T1D subjects depends on multiple factors, including: exercise type, durationand intensity; amounts of prior CHO intakes and insulin administrations, along with their

31

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

scheduling in relation to the onset of exercise; plasma glucose and insulin levels, or cardio-vascular fitness [American Diabetes Association, 2004; Colberg, 2009; Nagi, 2006; Wasser-man and Zinman, 1994]. This considerable number of influential factors hinders the trans-lation of scientific evidences into exercise counselling, and most importantly, it complicatespatients’ daily self-management of physical activity.

In order to translate the qualitative physiological descriptions covered above into measur-able trends in glycaemia, various works in literature studied the impact that a range ofprotocols –encompassing different exercise modalities– caused on T1D patients’ glucoselevels, as well as on their temporal evolution trends. However, given the limited literatureaddressing the comparison of these effects from a quantitative perspective, a systematicreview and meta-analysis were conduced in the context of this PhD thesis work. Availablestudies were pooled to synthesize the quantitative evidence for acute changes in glycaemiatemporal profiles, as induced during structured exercise sessions and in their immediatelysubsequent recovery stage. Various modalities of physical activity were considered in or-der to ascertain differences among them. Analyses were carried out on the basis of novelrate-of-change magnitudes to summarize variations with exercise time.

4.3.2 Methodology

This systematic review and meta-analysis was elaborated following current methodologicalguidelines on the conduct of systematic reviews for randomized controlled trials (RCTs) assuggested by the PRISMA statement [Moher et al., 2009] and Cochrane Handbook [Higginsand Green, 2011].

4.3.2.1 Eligibility criteria

Eligible studies enrolled human subjects with T1D, regardless of their age or duration ofdiabetes. Only acute interventions consisting of a standardized exercise protocol with con-trolled intensity and timing were considered; therefore, exercise in free-living conditionsand/or prolonged training programs were excluded. Given that the main outcome of inter-est here was the acute change in glycaemia profiles, eligible studies were required to providemeasurements reflecting how glucose concentrations evolved over time: from the start of theexercise session until its cessation, and preferably also for a period immediately afterwards(early recovery stage). In a first iteration of this review, the search was restricted by studydesign to incorporate RCTs only. However, since all of the primarily eligible trials had acrossover design, non-randomized experiments (NREs) were also allowed; these NRE beingcontrolled trials in which the allocation procedure (order of treatments/interventions) wasnot random as in RCT. Within-trial comparisons for the main effect of physical activity onglycaemia were established, either against a control resting period or with respect to profilesfrom another type of exercise (this depending on the particular design of each study).

4.3.2.2 Study identification and selection

Candidate studies were searched using PubMed, ISI Web of Knowledge’s MEDLINE, Sco-pus and the Cochrane Library on-line databases. Last update of the search was conduced inNovember 2013. In a first pass, no publication date restriction was set, but due to the diffi-culty in retrieving full texts of older articles, it was decided to limit the range to year 1992 orlater. Search terms included type 1 diabetes mellitus, blood glucose, physical activity and

32

4. Physical activity in T1D

exercise; as well as their corresponding medical subject headings (MeSH) equivalent terms[Coletti and Bleich, 2001]. These MeSH synonyms were available for PubMed, MEDLINEand Cochrane search engines, but not for Scopus.

Publications were first screened on the basis of their titles and abstracts. Subsequently,full contents of candidate papers were examined in depth for a definitive selection.

4.3.2.3 Data extraction

The main characteristics of the selected studies were recorded, namely: study design, pop-ulation data (e.g. number, sex, age or duration of diabetes) and full description of the pro-posed exercise session (type, duration and intensity), plus the planned food intake and/orinsulin interventions.

To enable analyses independent of the specific exercise protocol used in each study –particularly, independent of its session duration–; instead of focusing on the total glucosechange in absolute terms, a rate-of-change (RoC) magnitude RoCE was defined here as theexcursion in glucose levels measured during exercise, divided by the time span of the bout:

RoCE =gE − g0

tE=

∆gOE

tE(4.1)

where: a) glycaemia measurements are doneted by g’s variables, b) ∆gOE = gE− g0 is theglycaemic excursion from gO (glycaemia at the onset of the activity) to gE (glycaemia atthe end of the exertion), and c) tE is the duration of such exercise session (Figure 4.6).

To characterize the trend of variation in glycaemia observed for the early recovery stage–i.e. immediately after exercise termination–, a similar RoCR magnitude was also proposed:

RoCR =gR − gE

tR=

∆gER

tR(4.2)

where: a) ∆gER = gR − gE is the excursion from gE to gR (glycaemia at the end of theearly recovery period), and b) tR is the duration of the recovery interval. For the purposeof this review, tR was set equal to 30 min post-exercise.

Given the definitions of these two RoC magnitudes in (4.1)–(4.2), it is straightforward thattheir means –denoted here by the operator m(·)– can be calculated as follows:

m(RoCE) =1

tE[m(gE)−m(gO)] (4.3)

m(RoCR) =1

tR[m(gR)−m(gE)] (4.4)

or equivalently, for those studies reporting glycaemia profiles as increments from a baselinevalue:

m(RoCE) =1

tEm(∆gOE) (4.5)

m(RoCR) =1

tRm(∆gER) (4.6)

33

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

For their standard deviations –denoted SD(·)– it can be derived by arithmetic operationsthat:

SD(RoCE) =1

tE

√

SD2(gE) + SD2(gO)− COV (gO, gE) (4.7)

=1

tE

√

SD2(gE) + SD2(gO)− ρ(gO, gE)SD(gO)SD(gE) (4.8)

SD(RoCR) =1

tR

√

SD2(gR) + SD2(gE)− COV (gE, gR) (4.9)

=1

tR

√

SD2(gR) + SD2(gE)− ρ(gE, gR)SD(gE)SD(gR) (4.10)

where COV (·, ·) represents covariance and ρ(·, ·) is Pearson’s correlation coefficient:

ρXY =COVXY

SDXSDY

(4.11)

Eligible works from literature did not report any individualized profiles, aggregating theminstead as mean population profiles. Consequently, direct information concerning the inter-subject statistical variability of RoCs could not be obtained. Hence, neither covariancesCOV (·, ·) nor correlations ρ(·, ·) could be calculated here. To circumvent this issue, gly-caemia values in both extremes of the respective intervals were assumed uncorrelated, i.e.:

ρ(gO, gE) = 0 (4.12)

ρ(gE, gR) = 0 (4.13)

Thus, (4.8), (4.10) reduce to:

SD(RoCE) =1

tE

√

SD2(gE) + SD2(gO) (4.14)

SD(RoCR) =1

tR

√

SD2(gR) + SD2(gE) (4.15)

Since there are not previous works in literature following comparable approaches to theconcept of RoCs as introduced in (4.1)–(4.2), estimations about correlation coefficients ρwere not available. The assumption of uncorrelated measurements used here, althoughperhaps simplistic, may provide a reasonable estimate for RoC values to be pooled in themeta-analysis (and possibly conservative if in practice ρ were > 0).

4.3.2.4 Statistical analysis

In this analysis, three exercise modalities/types were distinguished:

• Continuous physical activity (CONT); consisting in sustained exercise performed atmoderate intensities, with a predominant aerobic component.

• Intermittent high-intensity exercise (IHE); with moderate exercise interspersed withvarious short episodes of maximal or near-maximal intensity.

• Resistance activity (RESIST), such as weight lifting, with a remarkable anaerobiccontribution.

In first place, comparisons were established for each of these three modalities versus acorresponding resting control period (REST). To do so, a detrending procedure was carriedout: the temporal variation observed in the glycaemic profile at REST was subtracted at a

34

4. Physical activity in T1D

Figure 4.6: Definition of RoC magnitudes during the performance of physical activity andin the immediately subsequent recovery period. RoCs approximate the average tempo-ral evolution of glycaemia, from one extreme of the interval to the other, by rectilinearsegments.

study level (i.e. prior to the pooling). In this manner, background spurious trends –whichmay be present in the REST profile due to factors other than exercise itself (for example,caused by the particular experimental protocol in each study, e.g. by insulin administrationstrategies or pre-exercise CHO supplementations)– were mitigated.

Secondly, direct comparisons between pairs of exercise modalities were also performed wher-ever appropriate studies were available. CONT was selected here as the reference modality.Thus, differences with respect to the glycaemia profile for CONT exercise were first calcu-lated at a study level for the purpose of detrending, and subsequently pooled.

DerSimonian & Laird random-effects meta-analyses [Higgins and Green, 2011] were usedhere to ascertain statistical differences in means of continuous outcomes (RoCs), as availablein RevMan software [RevMan, 2012]. RoCE, RoCR values were pooled across studies andtheir heterogeneity assessed using the I2 statistic [Higgins and Green, 2011].

4.3.2.5 Risk of bias

To ascertain the validity of candidate publications, the main indicators for risk of bias incrossover studies [Higgins and Green, 2011] were analysed:

a) Suitability of the crossover designb) Randomness in the allocation of treatmentsc) Presence or absence of carry-over effectsd) Performing appropriate paired statistical analysis.

In addition, publication bias across studies was assessed through funnel plots of meandifferences, in order to check for possible asymmetries resulting from the non-publicationof trials.

4.3.3 Results

4.3.3.1 Study characteristics

The electronic search yielded 540 unique references (Figure 4.7), as well as 54 other itemsdiscarded due to the publication date criterion (not shown in figure). After a preliminary

35

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

screening, 148 out of those 540 references were considered potentially relevant based ontheir titles and abstracts. After evaluating full texts, another 131 studies were dismissedfor not satisfying the pre-specified criteria to be included in the systematic review. Thethree most frequent reasons for exclusions (Figure 4.7) were:

a) Observational and other non-RCT/NRE study designs (e.g. case-controls), n=34b) Studies which comprised a glucose clamp experiment to maintain glycaemia artifi-

cially stabilized during exercise, while measuring other metabolic phenomena (e.g. todetermine exercise-induced changes in peripheral insulin sensitivity), n=24

c) Studies which investigated the impact of auxiliary interventions apart from exerciseitself (e.g. modifications in insulin or diet supplements to accommodate exercise,or changes in session scheduling with respect to meals), n=22. Trial arms in theseexperiments were designed to ascertain the effect of applying or not those auxiliaryinterventions: for example, to compare the different impacts in glucose profiles be-tween exercising after hydration with an isotonic drink containing higher versus loweramounts of CHO [Perrone et al., 2005]. Thus, it would not have been possible to es-tablish a reference control profile to cancel temporal background trends attributableto factors other than exercise.

Out of the remaining 17 candidate articles, another 8 works were excluded from this meta-analysis due to three reasons identified post hoc, namely:

i) In five studies [Dubé et al., 2005, 2006, 2013; Yardley et al., 2012, 2013a], patients weresupplied with rescue dextrose or CHO to avoid severe hypoglycaemia, which impliedthat glucose profiles were artificially altered by those emergency interventions

ii) Two studies [Bussau et al., 2006, 2007] consisted of a single 10-s sprint at the beginningor at the end of a session, and could not therefore be strictly considered to belong toeither CONT or IHE modality

iii) One study [Tsalikian et al., 2005] did not provide any data about inter-subject vari-ability, only mean population profiles.

An extra study [Yardley et al., 2013b] was identified during the process of peer review forjournal publication.

Table 4.3 summarizes the main characteristics of the ten publications finally incorporatedto this systematic review and meta-analysis.

4.3.3.2 Risk of bias

Regarding the possible indicators for risk of bias for crossover studies listed in section4.3.2.5:

a) The comparison of results from studies with crossover design against parallel RCTswas not feasible here, since none of the latter were found in this literature review.

b) Randomization of treatment allocations: A total of 8 out of 10 publications had acrossover RCT design, where the chronological order of the experimental and thecontrol trial arms was set randomly (Table 4.3). Yardley et al. [2013b] did not com-ment explicitly on their randomization process for trial arms and as a consequence,random order could not be assumed; whereas Yamanouchi et al. [2002] employed aNRE design with a fixed order of the trial arms, an aspect which may have introduceda period effect to some extent in this specific study.

c) Carry-over effects: Table 4.3 contains a summary of the wash-out periods proposed ineach study protocol, specified by authors in order to avoid –or at least to minimize–

36

4. Physical activity in T1D

Figure 4.7: Schematic of the study selection process for this systematic review and meta-analysis.

37

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

Tab

le4.3:

Sum

mary

ofth

em

ainch

aracteristicsof

the

tenstu

dies

inclu

ded

inth

ism

eta-analy

sis.

Re

fere

nce

Po

pu

latio

nS

tud

yd

esig

nG

luco

sesa

mp

les

Ex

ercise

inte

rv

en

tion

Wa

sho

ut-p

erio

ds

Nu

mb

er,sex

an

dage

(yea

rs)

Dia

betes

du

ratio

n(y

ea

rs)

BM

I(k

g/

m2

)

VO

2m

ax

(ml/

kg

·min

−1

)

Hb

A1

c(%

)D

ura

tion

(min

)D

escriptio

nan

din

tensity

Ex

ercisety

pes

Betw

eentria

larm

sN

oex

ercisep

re-trial

No

hy

po-

gly

caem

iap

re-trial

Gu

elfiet

al.

[2005a]

8,

sexn

/a

18.6

±2.1

7.0

±4.6

22.1

±1.5

42.4

±7.3

7.0

±0.4

RC

TC

ap

illary

(earlo

be)

20

Passiv

ereco

very

with

eleven

4s

max

imal

sprin

tsev

ery2

min

IHE

vs.

RE

ST

n/a

n/a

n/a

Gu

elfiet

al.

[2005b

]4♂

,3♀

21.6

±4.0

8.6

±5.0

24.7

±3.5

39.3

±7.4

7.4

±1.5

RC

TC

ap

illary

(earlo

be)

30

40%

VO

2m

ax

with

or

with

ou

tsix

teen4

sm

ax

imal

sprin

tsev

ery2

min

IHE

vs.

CO

NT

7d

ay

s24

h48

h

Iscoe

an

dR

idd

ell[2

011]

5♂

,6♀

35.1

±11.6

15.6

±18.6

n/a

42.4

±5.3

7.8

±1.3

RC

TIn

terstitial

(CG

M)

45

55%

max

load

(67.8

±5.0

%V

O2

ma

x)

with

ou

tor

50%

max

load

with

nin

e15

sm

ax

imal

sprin

tsev

ery5

min

(68.9

±5.0

%V

O2

ma

x)

IHE

vs.

CO

NT

vs.

RE

ST

≥3

day

s24

hn

/a

Jan

kovec

etal.

[2011]

12♂

,0♀

33.4

±8.5

16.4

±8.6

25.8

±3.7

n/a

8.4

±1.0

RC

TB

loo

d30

(on

ly

1st

bo

ut)

60%

HR

reserve

CO

NT

vs.

RE

ST

2w

eeks

n/a

Prev

iou

sn

igh

t

Mara

net

al.

[2010]

8♂

,0♀

34±

714.3

±8

24±

2.2

33.7

±6.1

7.1

±0.6

RC

TB

loo

d30

40%

VO

2m

ax

with

or

with

ou

tfi

fteen5

s85%

VO

2m

ax

sprin

tsev

ery2

min

IHE

vs.

CO

NT

≥7

day

s48

h48

h

Peter

etal.

[2005]

12♂

,1♀

33.3

±6.5

>1

26.8

±3.3

n/a

7.6

±1.3

RC

TB

loo

d30

65.2

±10.1

%V

O2

ma

xC

ON

Tv

s.R

ES

T7

day

s12

hn

/a

Rab

asa

-Lh

oret

etal.

[2001]

8♂

,0♀

33.0

±8.8

12.6

±8.8

23.4

±1.7

37.8

±9.9

6.1

±n

/a

RC

TB

loo

d30

or

60

25,

50

or

75%

VO

2m

ax

CO

NT

vs.

RE

ST

n/a

n/a

n/a

So

oet

al.

[1996]

8♂

,1♀

25.8

±7.4

7.3

±6.0

n/a

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38

4. Physical activity in T1D

the presence of carry-over effects between intervention arms. The majority studiesrequired that physical exertions were at least one week apart, with some of them usingshorter wash-outs, although never less than two days. Several researchers instructedparticipants to refrain from any physical activity in the 24–48 hours prior to the test[Guelfi et al., 2005b; Iscoe and Riddell, 2011; Maran et al., 2010] or alternatively, tomaintain their usual lifestyle [Soo et al., 1996]. However, three publications did notclearly comment on preceding physical activity [Rabasa-Lhoret et al., 2001; Guelfiet al., 2005a; Yardley et al., 2013b]. On the other hand, three protocols [Guelfi et al.,2005b; Maran et al., 2010; Jankovec et al., 2011] checked for the absence of hypogly-caemia events during the hours or days prior to the exercise sessions, postponing thestudy in the case of recent hypoglycaemia episodes.

d) Individually-paired statistical analyses were not feasible here, because the eligiblepapers reported only mean population profiles and not individual glycaemia profilesfor each subject by separate.

The resulting funnel plots (Figure 4.8) did not show any evidence of asymmetry whichmay indicate publication bias. However, the number of studies under evaluation here wasclearly insufficient as to allow definitive conclusions to be drawn in this regard.

4.3.3.3 Synthesis of results and statistical analyses

4.3.3.3.1 Meta-analyses

With respect to RESTThis first form of meta-analysis consisted in taking REST as the reference activity –in thiscase, the absence of physical activity-. For each study (i.e. at a study level, prior to thepooling), temporal changes reported during the time scheduled for exercise were detrended.This was achieved by subtracting the average temporal evolution (i.e. RoC) observed atthe REST control period. Hence, given that REST was taken as reference:

• Zero RoCE, RoCR values would mean that the exercise-induced trend in glycaemiacould not be distinguished from the inherent profile at REST, being identical.

• Positive RoCE, RoCR values would reflect a stronger net tendency towards increasingglycaemia levels than in REST. This could be due to either slower decays, or fasterincreases (the latter option normally during recovery periods, when glycaemia wouldbe expectable to rise).

• Conversely, negativeRoCE, RoCR numbers would imply net trends to lower glycaemiathan in the background REST case, either by faster decays or slower rises than inREST.

There were seven studies [Iscoe and Riddell, 2011; Jankovec et al., 2011; Peter et al., 2005;Rabasa-Lhoret et al., 2001; Soo et al., 1996; Yamanouchi et al., 2002; Yardley et al., 2013b]comparing CONT and REST periods, with a total of eleven comparisons:

• Soo et al. [1996] conduced separate interventions to investigate exercise after havingingested either simple or complex CHOs. Hence, that work embraced two compar-isons.

• In Rabasa-Lhoret et al. [2001] three different intensities were addressed: 25, 50 and75% VO2max.

• In Yamanouchi et al. [2002] authors inspected two different morning schedules forexercise: pre- and postprandial.

39

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

Figure 4.8: Funnel plots to assess publication bias. Horizontal axes represent the meanreported effect in each study, i.e. mean values for RoCE (panels in the left column) orfor RoCR (right column); whereas vertical axes depict their corresponding standard error(SE). Panels a, b refer to the CONT vs. REST comparison, panels c, d to IHE vs. RESTand e, f to RESIST vs. REST; whereas panels g, h cover the IHE vs. CONT comparisonand i, j RESIST vs. CONT.

40

4. Physical activity in T1D

Pooled results for the CONT versus REST comparison (Figure 4.9) show that this con-tinuous exercise modality is on average associated with significant reductions in glucoseconcentrations during the practise of exercise, when compared to the resting control ref-erence. It is also related to a slight rise after exercise cessation, which tended to mildlyrestore glucose levels during recovery. Quantitatively:

• RoCE{CONT vs. REST} = −4.43 mmol/L·h−1 (p<0.00001, 95% confidence interval(CI) [−6.06,−2.79] mmol/L·h−1; I2=41%)

• RoCR{CONT vs. REST} = +0.70 mmol/L·h−1 (p=0.46, 95% CI [−1.14,+2.54]mmol/L·h−1; I2=0%).

Results for the IHE versus REST comparison (Figure 4.10) also reflect a pronounced fallin glycaemia during physical activity, along with recovery trends which were positive withrespect to the resting profiles, although not statistically significant so:

• RoCE{IHE vs. REST} = −5.25 mmol/L·h−1 (p<0.00001, 95% CI [−7.02,−3.48]mmol/L·h−1; I2=0%) when aggregating the two relevant studies [Guelfi et al., 2005a;Iscoe and Riddell, 2011]

• RoCR{IHE vs. REST} = +0.72 mmol/L·h−1 (p=0.71, 95% CI [−3.10,+4.54] mmol/L·h−1;I2=0%).

For the RESIST versus REST case (Figure 4.11), only one study [Yardley et al., 2013b]covered this comparison. Outcomes were:

• RoCE{RESIST vs. REST} = −2.61 mmol/L·h−1 (p=0.30, 95% CI [−7.55,+2.34]mmol/L·h−1; I2 not applicable)

• RoCR{RESIST vs. REST} = −0.02 mmol/L·h−1 (p=1.00, 95% CI [−7.58,+7.53]mmol/L·h−1; I2 not applicable).

Between exercise modalitiesWhenever possible, the direct comparison between pairs of exercise modalities was alsoaddressed. However, given the relative scarcity of eligible studies, this was feasible inonly two scenarios, namely: with CONT and IHE (based on three studies [Guelfi et al.,2005b; Maran et al., 2010; Iscoe and Riddell, 2011]), as well as with CONT and RESIST[Yardley et al., 2013b]. Hence, CONT was established as the common reference modality forcomparison purposes. Consequently, negative RoC values signify more pronounced decaysin glycaemia –or milder increases– than in the corresponding CONT reference period,whereas positive RoCs reflect either slower decreases or faster rises than during CONT.

For the IHE versus CONT comparison (Figure 4.12), decays in glycaemia during exercisewere observed to occur more slowly in the case of IHE, as revealed by a positive RoCE

value. On the other hand, RoCR values were similar:

• RoCE{IHE vs. CONT} = +1.57 mmol/L·h−1 (p=0.15, 95% CI [−0.59,+3.73] mmol/L·h−1;I2=53%)

• RoCR{IHE vs. CONT} = +0.37 mmol/L·h−1 (p=0.83, 95% CI [−2.90,+3.63] mmol/L·h−1;I2=0%).

Figure 4.13 based on Yardley et al. [2013b] revealed a milder decrease of glycaemia inRESIST exercise with respect to CONT, as well as a slower recovery:

• RoCE{RESIST vs. CONT} = +2.86 mmol/L·h−1 (p=0.20, 95% CI [−1.49,+7.20]mmol/L·h−1; I2 not applicable)

• RoCR{RESIST vs. CONT} = −2.40 mmol/L·h−1 (p=0.39, 95% CI [−7.87,+3.06]mmol/L·h−1; I2 not applicable)

41

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

Figu

re4.9:

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42

4. Physical activity in T1D

Of note Yardley et al. [2013b] documented negligible fluctuations for glycaemia during theRESIST recovery stage (when viewed in absolute terms), along with positive recoveries inCONT.

4.3.3.3.2 Meta-regressionTo ascertain the dose/response relationship with varying exercise intensities in terms ofresulting RoC values, a post hoc random-effect meta-regression analysis was carried out us-ing ‘metareg’ package in Stata 13 software (StataCorp LP; College Station, Texas, USA).Given the reduced number of studies, this was only feasible for the comparison of CONTactivity versus REST. Exercise intensity was measured through %VO2max, i.e. the percent-age of a subject’s maximal oxygen uptake (VO2max). Intensities reported in Jankovec et al.[2011] and Soo et al. [1996] via heart rate reserve (HRres) –60 and 50% HRres, respectively–were transformed to their equivalent %VO2max values (55 and 46% VO2max) based on pre-vious studies [da Cunha et al., 2011; Gaskill et al., 2004]. For Yamanouchi et al. [2002],an intensity of 20% VO2max was imputed as corresponding to the range 90–110 beats perminute (bpm) [Rotstein and Meckel, 2000].

Figure 4.14 (panel a) depicts a moderate dependency of RoCE with respect to physical ac-tivity intensity, with regression slope equal to −0.0200 mmol/L·h−1 per unit of %VO2max;although not statistically significant (p=0.69). This negative slope reveals more pronounced–i.e. faster– decay rates in glycaemia associated with more vigorous CONT exercise, acrossthe range of intensities covered by the included studies (20–75% VO2max); whereas milderexertions produce decays in glycaemia of a lesser absolute magnitude; hence slower. Con-versely, Figure 4.14 (panel b) shows how glycaemia tended to recover more rapidly aftermore vigorous CONT bouts, with a positive regression slope equaling +0.0117 mmol/L·h−1

per unit of %VO2max (p=0.87, not statistically significant) in the range of intensities coveredby this analysis.

4.3.4 Discussion

4.3.4.1 Main findings

This systematic review and meta-analysis, which aggregated results from a total of tenpublications, evaluated and quantified the acute impact of various types of structuredexercise sessions on the glucoregulatory balance in people with T1D. A key part of itsnovel contribution resides in the fact that no previous work in literature had addressed thequantification of the acute effects of exercise on glycaemia, task which was tackled hereby means of RoC measures. Average RoC values during exercise and in the immediatelysubsequent recovery phases, along with their corresponding 95% CIs, were estimated bydetrending within-study variations in glycaemia over time. Sub-analyses between specificexercise categories were also conduced.

In summary, CONT exercise at moderate intensities (range 20−75% VO2max) was found tobe associated with glucose concentrations which: a) declined during physical activity at arapid rate, if compared to resting periods (RoCE{CONT vs. REST} = −4.43 mmol/L·h−1

on average); and b) slowly reverted after the bout concluded (mean RoCR{CONT vs.REST} = +0.70 mmol/L·h−1). In addition, these results are in reasonable qualitativeand quantitative concordance with glucose RoCs reported during exercise by Dubé et al.[2005, 2006] before rescue dextrose had to be infused intravenously to correct hypogly-caemia events in those experiments. In particular, Dubé et al. [2005] documented RoCE

43

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

Figu

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44

4. Physical activity in T1D

Figure 4.14: Dose/response meta-regression analysis for the influence of exercise intensity–as expressed by % VO2max– on the rate-of-change magnitudes RoCE (panel a) and RoCR

(panel b) for CONT physical activity versus REST.

values respectively equal to −4.8±1.2, −6.3±1.2 and −3.6±0.6 mmol/L·h−1 –expressedas mean±standard error of the mean (SEM)– for their trial arms with 0 g, 15 g or 30 gof CHO supplements pre-exercise; whereas Dubé et al. [2006] reported RoCE values of−9.6±2.4 and −6.0±1.2 mmol/L·h−1 (mean±SEM) for their early and late postprandialexercise arms.

On the other hand, decreases in glycaemia for RESIST physical activity were milder than inthe case of CONT exercise, both in: a) the comparison with REST as a common reference:RoCE{RESIST vs. REST} = −2.61 mmol/L·h−1 on average, against mean RoCE{CONTvs. REST} = −4.43 mmol/L·h−1; and b) in the direct comparison: RoCE{RESIST vs.CONT} = +2.86 mmol/L·h−1. Likewise, recovery rates were slower for RESIST.

However, in the case of IHE exercise quantitative discrepancies arose between compar-isons. RoCE values calculated with respect to the REST reference –based on two studies[Guelfi et al., 2005a; Iscoe and Riddell, 2011]– yielded very pronounced decays (RoCE{IHEvs. REST} = −5.25 mmol/L·h−1 on average) versus the comparatively more restrainedabsolute values for CONT (mean RoCE{CONT vs. REST} = −4.43 mmol/L·h−1). Incontrast, analyses of IHE directly versus CONT indicated slower glucose decreases for IHE(RoCE{IHE vs. CONT} = +1.57 mmol/L·h−1), with results based on the aggregation ofthree studies [Guelfi et al., 2005b; Maran et al., 2010; Iscoe and Riddell, 2011].

4.3.4.2 Strengths

a) A comprehensive systematic review of literature was performed, identifying 10 pub-lished studies as relevant to this meta-analysis. Three exercise types were included:continuous physical activity at moderate intensity (CONT), intermittent high-intensity(IHE) and resistance exercise (RESIST).

b) In addition, a novel methodology was presented for the quantitative evaluation ofacute trends in glycaemia via RoC magnitudes, where temporal variations were ap-

45

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

proximated by rectilinear segments and average rates-of-change were computed forboth exercise and immediate recovery stages.

c) By recording temporal fluctuations in the reference profiles and subtracting them outat a study level (i.e. prior to the pooling), spurious background trends due to factorsother than exercise itself were mitigated in each particular trial. Hence, bias wasreduced.

4.3.4.3 Limitations

a) Discrepancies in the outcomes for IHE modality.

Quantitatively discrepant evidence was encountered regarding the magnitude of exerciseeffects on RoCE for IHE as compared with CONT. In the analyses with REST as commonreference (Figure 4.10), the aggregation of two IHE studies yielded RoCE{IHE vs. REST}= −5.25 mmol/L·h−1 (95% CI [−7.02,−3.48] mmol/L·h−1, I2=0%), versus a compara-tively more restricted decay for CONT: RoCE{CONT vs. REST} = −4.43 mmol/L·h−1

(95% CI [−6.06,−2.79] mmol/L·h−1, I2=41%) calculated on the basis of 7 studies and11 comparisons (Figure 4.9). Conversely, the direct confrontation (Figure 4.12) resultedin RoCE{IHE vs. CONT} = +2.86 mmol/L·h−1 (95% CI [−1.49,+7.20] mmol/L·h−1,I2=41%), with three studies involved; pointing to a slower decline in glycaemia for IHEthan for CONT (p=0.15, not significant). The scarcity of available studies involving IHE–four in total [Guelfi et al., 2005a,b; Iscoe and Riddell, 2011; Maran et al., 2010], withIscoe and Riddell [2011] presenting REST, CONT and IHE trial arms– may explain thisshortcoming to some extent.

Statistical heterogeneity was also encountered (I2=53% for RoCE{IHE vs. CONT}), alongwith substantial methodological diversity among study protocols, in particular when defin-ing the IHE session. Guelfi et al. [2005a] utilized intermittent 4-s short bursts by maximalsprints every 2 min, with subjects remaining seated without physical activity betweensprints –i.e. ‘passive’ recovery–. In another study [Guelfi et al., 2005b], the same re-searchers defined a different protocol in which periods between their 4-s maximal sprintscorresponded to sustained physical activity at 40% VO2max. On the other hand, Maranet al. [2010] utilized submaximal sprints –85% VO2max– with duration 5 s also repeatedevery 2 min. In an even more diverse protocol, Iscoe and Riddell [2011] compared CONTat sustained 55% VO2max versus IHE at sustained 50% VO2max plus 15 s maximal sprintsevery 5 min, with a design which aimed at an identical total mechanical work for bothtasks along the entire session. In terms of glucose variations, Guelfi et al. [2005b] docu-mented a greater absolute decline for CONT (−4.4±1.2 mmol/L in 45 min, mean±SD)versus IHE (−2.9±0.8 mmol/L), with statistical significance (p=0.006); whereas Maranet al. [2010] observed glycaemia measurements that tended to be higher after IHE, but notsignificantly so. Conversely, Iscoe and Riddell [2011] reported virtually identical glycaemicprofiles throughout the CONT and IHE bouts, plus in the recovery stage until 2.25 h post-exercise; although noticeable differences in terms of nocturnal levels: an increased risk ofnocturnal hypoglycaemia events < 4 mmol/L was reported for the CONT trial arm (with2 hypoglycaemia events per night after REST, compared to 5 events after CONT and 3after IHE). Interestingly, these findings are in marked contradiction with those by Maranet al. [2010], who reported 2 nocturnal hypoglycaemia events < 3.33 mmol/L after CONT,against 7 events for IHE (p<0.05).

In conclusion, there appears to be conflicting evidence in the availiable literature regardingthe acute effects of IHE on glycaemia in T1D. Further research in this direction may beneeded.

46

4. Physical activity in T1D

b) Discarded publications.

A collection of studies were found (n=22, Figure 4.7) which, had they been incorporatedinto this systematic review and meta-analysis, would have expanded analyses and mayhave increased their statistical power. This group of articles addressed the effectivenessof auxiliary interventions aimed to ameliorate exercise-induced glucose excursions, includ-ing: modifications of the insulin regimes to accommodate exercise (e.g. alternative insulinpreparations [Arutchelvam et al., 2009], pump cessation [Tsalikian et al., 2006; DirecNetStudy Group, 2005] or bolus reductions [West et al., 2010]), as well as various food sup-plementation strategies [Dubé et al., 2012; Perrone et al., 2005; West et al., 2011], amongothers. Given the particualr study design and focus of such experiments, the strategyunder inspection was either applied (intervention arm) or not (control arm), but subjectsexercised in both trial arms. Therefore, subtracting the inherent within-study backgroundspurious trends in glycaemia would have not been feasible. Thus, those publications weredismissed from this systematic review and meta-analysis to avoid introducing bias in thecalculation of aggregated RoCs.

c) Restriction of the intensity range under analysis.

The meta-regression carried out here to ascertain the dose/response relationship to varyingexercise intensities in RoCE for CONT vs. REST (section 4.3.3.3.2) showed more pro-nounced decays for increasing load. Nonetheless, this conclusion should be restricted tothe range of intensities under analysis (20–75% VO2max), which broadly corresponds tomoderate-to-vigorous exertions. Very vigorous exercise –i.e. >80% VO2max– was reportedto induce post-exercise hyperglycaemia in T1D, mainly due to exacerbated catecholaminereleases causing 7- to 8-fold rises in glucose production which are not matched by glucoseutilization, which increases 3- to 4-fold [Marliss and Vranic, 2002; Sigal et al., 1999, 2000].

d) Potential confounders.

Several aspects of potential relevance were not explicitly addressed in the quantitativeanalyses:

d.1) Method for the measurement of glucose.

Blood sampling –used in 7 out of 10 studies [Jankovec et al., 2011; Maran et al., 2010;Peter et al., 2005; Rabasa-Lhoret et al., 2001; Soo et al., 1996; Yamanouchi et al., 2002;Yardley et al., 2013b]– constitutes the most accurate and reliable technique for measure-ment. Capillary samples –which were obtained in two studies [Guelfi et al., 2005a,b]1– arecomparably more prone to error and delays than venous blood determinations. The thirdalternative, continuous glucose monitor (CGM), has in principle lower accuracy than bothvenous and capillary measurements. Nonetheless, it was the technique of choice for Iscoeand Riddell [2011]; whereas Yardley et al. [2013b] used CGM in addition to blood samplesto study the accuracy achieved by CGM sensors under exercise circumstances. However,all of the data from Yardley et al. [2013b] incorporated into this meta-analysis correspondto blood measurements only.

According to Yardley et al. [2013b], CGM underestimated considerably plasma glucoseat REST (−1.29±1.39 mmol/L, mean±SD, p<0.001), to a lower extent during RESIST(−0.71±1.35 mmol/L, p<0.001) and with non-significant errors for CONT exercise (−0.11±1.71mmol/L, p=0.416). On the contrary, CGM was reportedly associated with substantial er-rors when measuring during exercise for pregnant women with T1D [Kumareswaran et al.,

1Authors in [Guelfi et al., 2005a,b] also collected venous blood samples, although these were used onlyto measure free insulin, glucagon or growth hormone concentrations, among others; not to determineglycaemia.

47

4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

2013a]: 18.4% error with respect to plasma glucose during brisk walking, versus 11.8% atrest (p<0.001). Of note, this study by Kumareswaran et al. [2013a] reported results whichare qualitatively consistent with the meta-analysis here, namely: a decay of 24.6% in termsof relative rate-of-change for exercise, versus 12.3% in sedentary situations (p<0.001).

d.2) Glycaemia level at the onset of the physical activity session.

By means of a glucose clamp experiment, Jenni et al. [2008] reported rates of CHO oxi-dation being higher for exercise performed under hyperglycaemia conditions; whereas lipidoxidation was higher in their euglycaemia clamp. Consequently, more pronounced fallscould have been expected if physical activity was commenced with high glucose values. Inrelation to Jenni et al. [2008], the majority of the studies included in this review reportedexercise carried out with similarly high glucose concentrations, around 10 mmol/L or above:

• Soo et al. [1996]: approximate range 12–13 mmol/L• Rabasa-Lhoret et al. [2001]: 10.7±0.7 mmol/L (mean±SEM) for their 50% VO2max

trial arm• Yamanouchi et al. [2002]: ∼10 mmol/L pre-prandial and ∼15 mmol/L post-prandial• Peter et al. [2005]: approximate range 11–12 mmol/L• Guelfi et al. [2005a]: 10.9±1.9 mmol/L for REST trial arm, and 11.0±1.8 mmol/L

for IHE (mean±SD)• Guelfi et al. [2005b]: 11.0±2.3 mmol/L for CONT trial arm, and 11.5±3.9 mmol/L

for IHE (mean±SD)• Yardley et al. [2013b]: ∼10 mmol/L for their CONT trial arm.

Conversely, other studies commenced at more restrained glycaemia levels:

• Jankovec et al. [2011]: approximately range 7–8 mmol/L• Rabasa-Lhoret et al. [2001]: 8.8±0.55 mmol/L for their 25% VO2max trial arm;

8.5±1.3 mmol/L for 75% VO2max (mean±SEM)• Yardley et al. [2013b]: ∼8.5 mmol/L for their RESIST trial arm.

Information in this regard was not provided by Maran et al. [2010]; whereas Iscoe andRiddell [2011] mentioned an absolute fall of approximately −5 mmol/L and ∼50% relativedecay, although explicit data were not reported in either text or graphs.

Among the included publications, the most marked decay rates were reported in this orderby:

• Yamanouchi et al. [2002], post-breakfast exercise arm• Rabasa-Lhoret et al. [2001], 50% VO2max arm• Peter et al. [2005]• Rabasa-Lhoret et al. [2001], 75% VO2max arm• Yardley et al. [2013b], CONT arm.

In view of these data, there does not appear to be an evident direct relationship betweenthe higher blood glucose concentrations at exercise onset on the one side, and the moresubstantial RoCE values on the other hand.

d.3) Plasma insulin concentrations during exercise.

Plasma circulating insulin during the physical activity session may have also had a rolein the glucoregulatory response to exercise, then impacting the analyses as a confounder.In this regard, Chokkalingam et al. [2006] studied whole-body and muscle metabolismin exercise by means of an euglycaemic clamp experiment –glucose fixed at approximately8 mmol/L– under two hyperinsulinaemic regimes at different levels: plasma insulin at ∼150or ∼540 pmol/L (which correspond to typical pre- and postprandial concentrations in T1D

48

4. Physical activity in T1D

patients). Authors observed markedly higher exogenous glucose utilization in the trial armat 540 pmol/L. However, the amount of muscle glycogen utilized in both situations wassimilar, and CHO oxidation rates were only around 15% higher in the trial arm with largerinsulinaemia. Consequently, the influence of distinct plasma insulin levels in otherwiseequivalent exercise conditions remains unclear [Chokkalingam et al., 2006].

Concerning the studies included here, experimental data on insulin concentrations werenot provided in three articles [Yardley et al., 2013b; Iscoe and Riddell, 2011; Maran et al.,2010]. In other three cases, patients exercised at insulin levels lower than both conditionsin Chokkalingam et al. [2006]:

• Jankovec et al. [2011]: average insulinaemia ∼80 pmol/L, along with large inter-subject variability –nonetheless, without statistically significant differences versusREST–.

• Soo et al. [1996]: basal 84±18 pmol/L (mean±SEM). Authors reported no significantcorrelation between basal free insulin and glycaemic response.

• Yamanouchi et al. [2002] preprandial trial arm: 55.3±21.5 pmol/L (mean±SD).

Peter et al. [2005] documented an average plasma insulin of approximately 300 pmol/Lduring both REST and CONT, without statistical differences between trials in terms ofarea under the curve for insulinaemia (p=0.116). On the other hand, physical activity boutsin the remaining studies took place at values comparable with the 150 pmol/L selected byChokkalingam et al. [2006]:

• Rabasa-Lhoret et al. [2001]: insulin bolus 90 min prior to exercise onset, peak insuli-naemia at 188.5±28.0 pmol/L (mean±SD) occurring 30 min pre-exercise

• Yamanouchi et al. [2002] postprandial trial arm: insulin bolus 90 min before exercisestart, with peak at 231.9±162.3 pmol/L (mean±SD)

• Guelfi et al. [2005a]: IHE exercise commenced at 198.1±148.0 pmol/L (mean±SD);no statistically significant difference with respect to REST

• Guelfi et al. [2005b]: IHE and CONT exercise bouts commenced respectively ataround 160 and 140 pmol/L; without statistical differences in insulinaemia profiles atany point of exercise or recovery.

d.4) Time of the day.

The time of the day at which exercise sessions were performed was not incorporated intothe quantitative meta-analyses, although it may have influenced outcomes to some extent.In an euglycaemic clamp experiment in which exercise was performed in the afternoon(16:00 h), McMahon et al. [2007] showed that glucose infusion rates, necessary to maintainglycaemia stable, peaked in a biphasic manner: i) during exercise and early recovery, plusii) in the night afterwards (00:00 h to 04:00 h). Conversely, in an otherwise equivalentexperimental design but with exercise performed at 12:00 h, Davey et al. [2013] did notobserve the same biphasic behaviour in glucose infusion rates, which were in turn elevatedfor 11 hours post-exercise.

It is difficult to draw solid conclusions in this regard from the studies included here, sinceall except three experiments were carried out in the morning; the exceptions being: Maranet al. [2010] –exercise at approximately 14:00 h–, along with Iscoe and Riddell [2011] andYardley et al. [2013b] –both at 17:00 h–.

d.5) Fitness status and age.

The eligible studies did not always provide explicit information on participants’ degree offitness or prior physical training status: only five did (Table 4.3). This aspect may havehad an effect on subjects’ glucoregulatory response, such as glucose uptake into skeletal

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muscle, which may vary even at a fixed relative intensity, i.e. at the same %VO2max

[Fujimoto et al., 2003]. Moreover, the population studied by Guelfi et al. [2005a] consistedof adolescents, whose hormonal response to physical activity may differ from that of matureadults [Riddell, 2008].

4.3.4.4 Implications for clinical practice and research

Better understanding of the acute effects on glycaemia due to physical activity is of con-siderable importance to clinicians and T1D patients aiming at a tighter management ofacute, exercise-related glucose excursions. Currently, guidelines for exercising with T1Dare based on small studies or observational evidence.

The glycaemia RoC magnitudes presented here, and expressed in measurable units [mmol/L·h−1]of temporal variation, may provide an accessible means of translating the effect of exerciseon acute glucose dynamics into applicable information that may benefit patients’ self-management and the estimation of expectable temporal trends in glucose levels.

This systematic review confirmed and quantified the known glucose lowering effects of mod-erate physical activity, with rapid decays under various circumstances followed by mild in-creases post-exercise. Resistance activity was associated with the most modest decreases.As major novelty, trends in blood glucose during and after exercise were quantified via tworate-of-change magnitudes RoCE, RoCR. This quantitative information –mean RoCs andtheir 95% CIs– may be useful when advising patients on strategies to maintain optimal glu-cose control and to avoid post-exercise hyper- and (especially) hypoglycaemias, improvingsafety and quality of life for physically active people with T1D.

This review also identified the lack of parallel controlled studies comparing physiologicalresponses to different exercise categories. In addition, conflicting evidence was encounteredregarding the effects of IHE physical activity in subjects with T1D. More homogeneousIHE exercise protocols –particularly in terms of sprint duration, frequency of repetitionand intensity– may be needed, along with further research.

4.3.4.5 Comparison with previous reviews

Tonoli et al. [2012] reviewd and analysed the overall effect on glycaemic control of a singlebout of physical activity, based on the pooling of 15 acute exercise studies: 9 aerobic and6 IHE. Authors also surveyed the impact on HbA1c of regular/chronic exercise trainingmaintained for up to several months, although such aspect is out of the scope of currentdiscussion. In the mentioned publication [Tonoli et al., 2012], Cohen’s d statistic [Cohen,1988] was used as the main outcome to characterize the glucoregulatory impact of physicalactivity. Overall, substantial decreases in venous glucose levels due to acute aerobic exercisein adults were reported (−6.0 mean Cohen’s d value; 95% CI [−6.87,−5.14]), these reduc-tions being considerably larger than for acute IHE activity (−4.35; 95% CI [−6.41,−2.65]for Cohen’s d).

Whereas those results are in qualitative agreement with findings here, quantitative com-parisons are not feasible because Cohen’s d is a dimensionless magnitude which reflects theaverage difference in a relative manner, i.e. normalized by the standard deviation in eachstudy [Cohen, 1988]. In contrast and as a major contribution of this work, glucose varia-tions were ascertained in measurable terms via the novel RoCE, RoCR outcomes. TheseRoC magnitudes –expressed in tangible units: [mmol/L·h−1]– should provide a more ac-cessible and straightforward manner of estimating exercise-related glucose dynamics; hence

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4. Physical activity in T1D

more easily translated into clinical practice and patients’ self-management. Furthermore,the analysis of glucose dynamics by Tonoli et al. [2012] was extended here by incorporatingthe early recovery stage.

On the other hand, authors agreed with the current discussion regarding the limitationsof available literature: i) pointing out the difficulty for pooling studies given the markeddiscrepancies in terms of exercise protocols, and ii) advocating for more standardizationand broader populations of subjects in the studies.

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4.3. Systematic review: Quantification of the acute effect of exercise on glycaemia in T1D

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Part III

Monitoring and recognition ofphysical activity

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Chapter 5

State of the art

Physical activity (PA) is a complex behaviour whose characterization involves various im-portant aspects, including [Valanou et al., 2006] but not limited to: PA intensity, durationand frequency of its practise; exercise modality and the predominant metabolic pathwayinvolved in energy fuelling; or whether PA is performed for leisure, for transportation or aspart of the subject’s occupation. Consequently, these and other contextual factors wouldideally be required for a detailed understanding of the nature of PA patterns and the degreeof involvement of individuals and/or populations in regular PA. This information is impor-tant, for instance, to study the interaction between PA and different health conditions, orto address the effectiveness of PA-based medical interventions [Westerterp, 2009].

Specifically, two aspects have attracted most attention and research effort, namely: i) de-termining PA intensity levels, and ii) calculating energy expenditure (EE) induced byexercise, which are in turn closely related to PA intensity. In this regard, three processescontribute to the total energy expenditure (TEE) in humans [Kumahara et al., 2006]:

a) Basal metabolic rate (BMR), which is the component responsible for covering energyneeds for the basic physiological functioning. It constitutes the major contribution toTEE –estimated around 60% TEE for sedentary individuals [Kumahara et al., 2006]–,although its absolute magnitude depends largely on each subject’s body size [Ainslieet al., 2003].

b) Diet-induced thermogenesis, often estimated to represent 10% of TEE for an averagemixed diet that meets energy requirements [Westerterp, 2004].

c) Physical activity-induced energy expenditure (PAEE).

Obviously, the contribution of PAEE –which may account for approximately 30% of TEEin sedentary individuals– is strongly dependent on each subject’s lifestyle. However, theabsolute values of PAEE –generally expressed in [kcal/h] or [kJ/h] units– are primarilyinfluenced by body weight via the energy cost of moving one’s own body mass. Otherfactors, such as the mechanical efficiency of performing a certain task, also play a roleon PAEE, although variations in efficiency are small across most subjects. Consequently,absolute PAEE numbers are not the preferred way to reflect the intensity at which anactivity was performed, because they would not be suitable for establishing comparisonsacross individuals with different sizes. In this sense, PAEE measured in [kcal/h·kg−1] –i.e. normalized by body weight– would serve better for fair comparisons. Nevertheless,alternative magnitudes such as metabolic equivalents of task (METs) are often employed.

MET conceptualization is conceived to express the energy cost of a certain activity as amultiple of the BMR at rest. Hence, METs are commonly viewed as a simple descriptorof workload levels across activity modalities and populations [Byrne, 2005]. For example,

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5.1. Monitoring and measurement of PA

according to the most recent version of Ainsworth et al. [2011]’s Compendium of physicalactivities and MET values (Figure 5.1); a subject who practised mountain bike would onaverage spend during this activity 8.5 times his/her BMR. By convention, 1.0 MET isassumed equivalent to 1.0 kcal/min·kg−1, based on the original study presenting the METconcept with one 70-kg, 40-year-old male [Wasserman et al., 1994]. However, O2 consump-tions during rest were reported to be significantly lower than this figure (up to 20–35%lower) for a considerably large and heterogeneous population [Byrne, 2005], an issue whichimplies that quantifying PAEE based on METs could result in significant overestimations[Byrne, 2005].

Nonetheless and despite these known limitations, METs are very widely used in clinicalpractise to assess the degree of physical activeness and to prescribe exercise plans. Inparticular, the ACSM [American College of Sports Medicine, 2011; Garber et al., 2011]provides its guidelines for exercise prescription expressed in METs –more precisely, in[MET·min/week]–, distinguishing five levels of interest regarding PA intensity, namely:i) very light (i.e. below 2 MET), ii) light (2–3 MET), iii) moderate (3–6 MET), iv) vig-orous (6–8.8 MET), and v) very vigorous (above 8.8 MET). However, these five levels arefrequently summarized into three [Pate, 1995]: i) low (i.e. under 3 MET), ii) moderate(3–6 MET), and iii) vigorous (above 6 MET).

Other relatively common ways of establishing comparisons of exercise intensity [Ameri-can College of Sports Medicine, 2011; Garber et al., 2011] are expressing it as a frac-tion/percentage of each individual’s:

• maximum oxygen uptake (VO2max),• maximal heart rate (HRmax);

or alternatively, with respect to the corresponding reserves, these calculated in terms ofthe difference between maximal and basal (i.e. resting) values:

• oxygen uptake reserve (VO2res)=VO2max−VO2basal

• heart rate reserve (HRres)=HRmax−HRbasal.

In broad terms and according to the American College of Sports Medicine [2011]; Garberet al. [2011], 3 MET are approximately equivalent to 40% VO2res or HRres, to 46% VO2max

and 64% HRmax; whereas 6 MET would correspond to 60% VO2res or HRres, to 64% VO2max

and 77% HRmax.

Anyway, the accurate quantification of EE is a notably challenging task, particularly due tothe fact that many inter- and intra-individual factors (in addition to those mentioned above)affect the final energy and oxygen consumptions: age, sex, body size, cardiorespiratoryfitness, adiposity and body fat percentage, altitude, humidity, ambient temperature, fatigueor anaerobic contributions, among others.

5.1 Monitoring and measurement of PA

The ideal technique to measure PA should be: objective, accurate and precise, robust andsimple to use, with high temporal resolution, scalable to large populations, cost-effective,minimally invasive and comfortably acceptable for the subjects being monitored. However,there is not any technique gathering all those features. Therefore, this section will addressthe comparison of those approaches which are currently available in common practise,briefly reviewing their respective main strengths and limitations.

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Figure 5.1: Example MET equivalences for a series of bicycling activities under vari-ous circumstances and degrees of exertion. Ainsworth et al.’s Compendium of PAs andMETs was first released in 1993 [Ainsworth et al., 1993], with subsequent updates in 2000[Ainsworth et al., 2000] and 2011 [Ainsworth et al., 2011]. (Source: Ainsworth et al. [2011]https://sites.google.com/site/compendiumofphysicalactivities.

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5.1.1 Direct calorimetry

The direct calorimetry technique consists in a subject who stays in a thermally-isolatedchamber during the tracked period, in rest and/or performing exercise. The chamber isequipped with sensors to determine the total amount of heat dissipated by his/her body,via the measurement of the temperatures of ingoing and outgoing water from a closed-circuit refrigeration system which is in charge of maintaining the chamber at a constanttemperature (Figure 5.2).

Advantages

• Theoretically grounded, carrying out direct measurements of heat fluxes• High precision and accuracy –with an estimated error below 1% TEE [Valanou et al.,

2006]– in quasi-stationary thermal conditions.

Disadvantages

• High technological demand• Expensive costs• Impractical or infeasible for the majority of situations, as it cannot be applied to

extra-laboratory conditions• Not scalable to large populations• Low temporal resolutions given that heat flows through the air are a slow process, an

issue which translates to time lags and insensitivity to rapid variations.

5.1.2 Indirect calorimetry

With this type of solutions, body’s energy demands are measured via the determination ofrespiratory gas fluxes, specifically O2 consumption and CO2 production rates. Assumingthat: a) all inhaled oxygen is employed to oxidise fuels, b) all of the CO2 producedin oxidation is exhaled, and that c) those airflows can be measured accurately by theequipment, the total amount of energy involved in the process can be calculated usingappropriate formulae [Ainslie et al., 2003].

Different technological implementations exist. Closed-circuit systems, which are particu-larly suitable for measuring resting BMR (Figure 5.3, left panel), operate in isolation withrespect to outside ambient air. The respirometer initially contains pure O2 only, and thesystem proceeds by determining the amounts of CO2 which are continuously eliminatedfrom the circuit. On the contrary, open-circuit solutions use normal ambient air, analysingthe contents of O2 and CO2 in the airflow. Finally, commercial portable systems (Figure5.3, right panel) facilitate a relatively unobstructive monitoring, with the subject carryingthe equipment during exercise. Of note, these portable devices can measure pulmonary gasexchanges breath by breath.

Advantages

• Physiologically grounded solution• High accuracy and precision, up to the point of serving often as a ‘gold standard’ for

comparison with respect to other techniques estimating EEs• Portable devices allow the monitoring of exercise in more diverse and realistic condi-

tions.

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5. State of the art

Disadvantages

• High technological demand• Expensive costs• Not scalable to large populations, mainly due to its costs, which limit its practical

applicability to studies with a reduced number of participants• Possible uncomfort caused by the airflow system; in particular, by the mask.

5.1.3 Doubly labelled water

The doubly labelled water (DLW) technique requires participants to consume an oral doseof water with a known amount of stable –i.e. non-radioactive– tracers diluted in it. Dilutedhydrogen (2H, deuterium) and oxygen isotopes (18O) serve as biological markers to tracethe rates at which they are excreted from the body. After a few hours from ingestion, DLW(2H2

18O) is mixed with the normal –i.e. non-labelled– hydrogen and oxygen in body fluids.

When energy is expended, the body produces CO2 and water, which are subsequently elim-inated. In particular, CO2 is lost through breathing; whereas water is evacuated via breath,urination, sweat and other evaporations. Thus, the 18O tracer is part of both eliminatedwater and CO2; whereas 2H tracer is only contained in water but not in CO2. As a con-sequence, 18O becomes disposed at quicker rates than 2H (Figure 5.4), and their differencereflects the rate of CO2 production, in turn strongly related to total EE. Different formulaeallow the EE estimation from the rate of CO2 production, based on certain assumptions[Ainslie et al., 2003].

Isotope concentrations are measured from body fluid samples –blood, saliva and urine–taken at the beginning and at the end of the period being tracked, which typically lies ina range between 4 days to 3 weeks.

Advantages

• Physiologically grounded methodology• High accuracy, precision and validity; often used as ‘gold standard’ for comparison

purposes [Ainslie et al., 2003]• Non-invasive and non-intrusive to normal activity patterns• The most reliable alternative to measure PAEE in free-living conditions.

Disadvantages

• Demands considerable expertise and technology• Expensive costs• Not scalable to large groups of users• Lack of temporal resolution. It is only possible to determine the total EE accumulated

over the whole period of observation, when fluid samples are taken. Consequently,there is not information about the number of PA sessions, their frequency, durationor intensity.

• Slight errors –below 5% [Ainslie et al., 2003]– may arise in field applications due touncertainties in the respiratory quotient with respect to the assumed values. Errorsstem from the fact that DLW can actually measure CO2 production rates instead ofO2 consumptions.

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5.1. Monitoring and measurement of PA

Figure 5.2: Diagram of a metabolic chamber for direct calorimetry, including its refrigera-tion system. (Source: Satake, Japan – Manufacturer’s website).

Figure 5.3: Two different technologies for indirect calorimetry systems: at bedside (left) forthe determination of resting BMR, and portable equipment (right) to be employed duringthe practise of exercise. (Source: Cosmed, Italy – Manufacturer’s website).

Figure 5.4: DLW curves for 18O and 2H tracer concentrations (Source: Adapted fromAinslie et al. [2003]).

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5. State of the art

5.1.4 Heart rate monitors

This technique’s operating principle resides in tracking heart rate (HR) as a relevant phys-iological response to exercise by the organism. During PA, increases in terms of exerciseintensity, energy consumptions and O2 requirements are closely related to rises in HR. Thisrelationship holds true over a considerable range of intensities, specially around intermedi-ate exertion levels (at approximately 110–150 beats/min), where the EE-HR relationshipis fairly linear [Freedson and Miller, 2000].

The most widely accepted method to estimate EE from HR measurements is the so-called‘flex’ approach [Spurr et al., 1988], although others exist, e.g. Montgomery et al. [2009].‘Flex’ is based in the fact that at rest or during very light activities, variations in HR donot reflect changes in energy demands in a proportional manner, as they however do formore vigorous intensities. Consequently, for low HR readings, ‘flex’ imputes the restingBMR as its estimation for energy consumptions; whereas for higher HR values –above anempirically found ‘flex’ point, hence its name– EE calculations follow an estimation curvewhich must be calibrated individually.

Advantages

• HR is a physiological response in good relation with exercise intensity and O2 con-sumption rates

• Easy to measure, an aspect which makes this technique particularly suitable for theambulatory assessment of overall physical activeness in free-living conditions

• Affordable equipment, with manageable costs for medium-sized populations• Good temporal resolution, providing information about PA intensity in different time

intervals, as well as duration and frequency of exertions.

Disadvantages

• Wearing the chest strap for long periods may become uncomfortable• Several factors besides PA have a noticeable effect on HR responses, e.g. body pos-

ture, stress or fatigue, illness, medication, caffeine and other stimulators, temperatureor humidity, among others

• Subject characteristics –such as age, sex, or his/her cardiovascular fitness level– alsoplay a role on measured HR values. Thus, if accurate EE estimations are desired,individual calibrations of the ‘flex’ HR-EE curves are needed in order to preventexcessive inter-subject errors. However, these individualized calibration proceduresmay be considerably time- and resource-consuming [Valanou et al., 2006]

• The cardiovascular response to high-volume circuit resistance exercise –a modalitywith notable anaerobic contributions– was reported to be considerably different tomoderate-intensity aerobic PA [Gotshalk et al., 2004].

In addition, other comparable physiological magnitudes –such as pulmonary ventilationrates, or even body temperature– might also be monitored. As in the case of HR, ventilationrates are a good indicator of the stress induced by PA on the cardiorespiratory system, inturn related to O2 consumptions. However, similar disadvantages apply: for example,dependencies with respect to fitness, stress, temperature or humidity, among other factors.

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5.1.5 Motion sensors

This section covers various devices which, being based on different sensing principles andtechnologies, collect data streams that reflect motion patterns. In brief: pedometers recog-nize and count steps, whereas accelerometers detect accelerations induced by displacements.A third family of sensors are gyroscopes, which track angular orientation and momentum.However, its use in literature is considerably scarcer than the other two technologies.

5.1.5.1 Pedometers

This type of sensors is conceived to detect steps and strides, in general with simple designsand modest technological requirements. Detection is typically achieved by means of athreshold on vertical acceleration, and depending on the particular equipment, devicesmay be worn on hip, waist, ankle or shoe.

Advantages

• Low cost and scalability• Devices can be worn in a comfortable and unobstructive manner in free-living condi-

tions• Easy to use, with low technological demand• Good choice for interventions focused on the monitoring of walking or running activi-

ties. In this regard, walking is a very frequent recommendation in those interventionswhose aim is to promote active lifestyles among sedentary populations.

Disadvantages

• Lack of sensitivity to any activity other than walking or running• Lack of detailed descriptive information about walking patterns, e.g. stride length or

speed, if climbing up-/downhill or up-/downstairs• Scarce utility in the overall prediction of EE• Limited or absent temporal resolution –specially in low- and mid-end commercial

devices–, since normally just total cumulative results are available. Thus, it is notpossible to analyse step counts by separate time periods.

5.1.5.2 Accelerometers

This technology is founded on recording accelerations caused by motion in one or multipleaxes, perpendicular to each other. Devices normally incorporate a piezoelectric sensor that,as a response to movement, suffers certain deformation which translates into voltage changeswhose amplitude is in proportion to the magnitude of acceleration [Chen and Bassett, 2005].In general, their raw accelerometry signal may contain a large gravitational component,although this contribution is often removed by internal pre-processing algorithms (e.g. high-pass filtering) within the devices. This is for example the case of commercial accelerometersspecifically designed for PA monitoring.

There is a wide range of technological deployments: from a single uni-axial sensor withrelatively low sampling frequency –such as 1 Hz–, up to a network of several triaxial ac-celerometers placed on different body locations (typically hip, waist, chest, arm, wristand/or ankle, among others) working at higher frequencies –up to 64 Hz– [Chen and Bas-sett, 2005]. In this regard, the maximal frequency of the center of mass in human motion

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was estimated to lie below 8 Hz [Winter et al., 1976], although band-pass filters around therange 0.25–7 Hz [Chen and Bassett, 2005] are often used in order to discard both gravityand high-frequency noisy components.

However, the most widespread commercial accelerometers –in particular, those conceivedfor its dedicated use as PA monitors in the fields of sports science and epidemiologicalresearch– do not provide the raw (i.e. unprocessed) acceleration signal as their defaultoutput. Instead, these commercial equipments carry out preconditioning tasks on the rawaccelerometry signal via proprietary algorithms. Output is then produced in the formof the so-called ‘accelerometry counts’ –also known as ‘activity counts’– which despiteextremely common, suffer from the important problem of lacking a straightforward physicalor physiological interpretation [Chen and Bassett, 2005].

Activity counts are accumulated over ‘epochs’, which are the basic analysis periods, oftenconfigurable by the researchers. The accumulation is performed following one of the variousexisting strategies, namely:

a) when the raw acceleration signal crosses a pre-set threshold value, assumed represen-tative of meaningful motion

b) in proportion to the maximum amplitude reached by the signal along current epoch,with higher amplitudes corresponding to more counts

c) integrating the rectified accelerometry signal over the epoch.

The latter alternative, which is the most robust against noise among the three, is also themost frequently applied one [Chen and Bassett, 2005]. Nonetheless, details in the propri-etary algorithms implemented by each company, as well as internal hardware configurations(e.g. amplification gains), result in final output counts that are totally manufacturer-specific. This issue hinders critically –or prevents altogether– the direct comparison ofaccelerometry outcomes between different brands.

As a matter of practice, the translation from accelerometry counts into PA intensity levelshas been mainly performed by means of validated thresholds on counts –most commonlyknown in the field as ‘cutpoints’ [Freedson et al., 1998; Hendelman et al., 2000; Swartzet al., 2000]–; whereas EEs have been traditionally estimated via linear regression formu-lae, also based on counts [Crouter et al., 2006]. Those formulae were derived and validatedin experiments with specific exercise protocols and population groups, with their accuracyin terms of EE estimations addressed by several publications [Crouter et al., 2006; Plasquiand Westerterp, 2007; Lyden et al., 2010; Altini et al., 2015]. In general, notable variationswith respect to achieved accuracy were reported, with less accurate results being obtainedif applying the estimators to activities which were not closely related (in terms of simi-lar movement mechanics, intensity and/or population characteristics) compared to thoseemployed in the experiment from which the formula was derived [Crouter et al., 2006].Consequently, systematic over- or underestimations may arise, depending on the specificactivity being monitored. In conclusion, there is not any single equation which can performacceptably well across a wide range of situations. On the contrary, different formulae maybe reasonably suitable for particular activities.

Advantages

• Objective quantification of body movement• Capability to track motion along different axes simultaneously• High temporal resolution and good levels of information detail, in terms of degree of

PA intensity, frequency and duration of the session• Sensitivity to subtle movements and low levels of activity

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5.1. Monitoring and measurement of PA

• Devices can generally be worn in a comfortable manner, not becoming obstructive infree-living conditions.

Disadvantages

• Moderate to high costs• Movements can show very complicated signal patterns, which may be difficult to

characterize and/or to interpret• Activity counts, due to the methodology used for their computation, cannot capture

relevant parts of the information contained in the signal, e.g. spectral components• Reduced or eventually null sensitivity to exercises which do not involve movement

of the body part to which the sensor is attached (e.g. static muscular work). Thisissue may in turn lead to a marked variability in the overall accuracy in terms ofPA recognition, depending on the location of the sensor in relation to the movementpattern

• Lack of standardization across manufacturers in terms of units for ‘counts’• Variability in the accuracy achieved by the different existing EE estimation formulae.

Some of these drawbacks –particularly those concerning ‘counts’– may be solved if re-searchers by-pass counts and instead take full control of the raw acceleration signal. In thisregard, a promising strategy might be to use accelerometer-enabled general purpose sensors(e.g. those embedded in smartphones), with the advantages of their high penetration alongwith their decreasing costs. The interested reader is referred to ‘Future works’ (section 9.2)for a further discussion regarding this topic.

5.1.5.3 Combining accelerometers and heart rate monitors

Accelerometry –which involves primarily mechanical aspects of PA– along with the HRsignal –as a physiological response to exercise– constitute two complementary sources ofinformation whose combination may provide richer PA descriptions than addressing thesesame magnitudes by separate. This approach may in turn help to overcome the limitationsof each methods alone; up to the point that numerous works from the field of sports scienceadvocate for this type of promising combinations [Freedson and Miller, 2000; Ainslie et al.,2003; Corder et al., 2005; Plasqui and Westerterp, 2005, 2006, 2007; Valanou et al., 2006;Westerterp, 2009].

5.1.6 Techniques with human intervention

5.1.6.1 Direct observation

With this approach, a subject’s PA behaviour is tracked by an external observer agent,who keeps a detailed record on information concerning PA along a period of time. In somecases, such as paediatric studies, this direct observation is a convenient option Valanouet al. [2006]. On the other hand and based on those PA records, simple EE estimationscan be derived applying tabulated MET values in Ainsworth et al. [2011]’s Compendium.

Advantages

• Rich contextual information about PA is provided: e.g. type of activity, location, etc.• Very limited technological demand

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5. State of the art

Disadvantages

• The external observer may interfere ostensibly with the observed subject’s normalPA behaviour

• Subjective component for the observer –specially in the grading of PA intensity–, anissue which imposes the need for qualified observers in order to ensure quality in thedata collection

• Inter- and intra-observer variability• Time- and resource-consuming technique, which translates into restrained coverage

periods.

5.1.6.2 Reports and activity logs

Several approaches are based on requesting participants to conduce self-reports or relatedvariants. These solutions, which are mainly used in large-scale epidemiological studies toassess the degree of physical activeness of a population, differ in a number of aspects,including: reporting periodicity, total time span covered by the report, factors of PA beingaddressed (e.g. intensity, duration, frequency or type), or method to summarize data andto score PA. In this regard, four major categories can be distinguished [Valanou et al.,2006]:

a) Activity diaries and logs: Subjects are required to produce detailed annotationsof the activities they perform with their durations, including as well either a de-scription of the activity (diary) or a correspondence with a PA category within aprefixed set of PA options (log). The main advantage of these approaches resides inthe rich contextual information which is obtained; whereas limitations include: theintensive effort, motivation and cooperation demanded from participants given thatthe registration may become tedious, subjective factors –especially regarding exer-cise intensity descriptions–, sensitivity to oversights and possible alterations of thesubject’s patterns with respect to his/her common PA habits.

b) Quantitative history questionnaires: These surveys examine PA retrospectively,following a detailed collection of items conceived with the aim of retrieving profounddescriptions about PA, at the expense of a considerable burden for the participantin filling out the questionnaire. Similar disadvantages apply as those mentionedabove for the case of diaries and logs, with additional risks in terms of retrospectiveoversights.

c) Recall questionnaires: Shorter and simpler than the previous option, they encom-pass fewer questions, thus demanding less effort to the participant. As a consequence,these recall questionnaires are usually applied to stratify populations in broad cate-gories regarding general activeness.

d) Global self-report questionnaires: Brief survey which provide a general overviewdescription of each subject’s PA habits, usually spanning over long periods. They aremost often intended to distinguish sedentary people from active.

In general, all self-reporting. logs and questionnaire-based methods have the majority ofstrengths and limitations in common.

Advantages

• Very low technological demand• Suitable for large-scale epidemiological studies• Useful for ranking/stratifying degrees of physical activeness

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5.1. Monitoring and measurement of PA

• Affordable costs• Considerable amount of detail and contextual information can be potentially achieved,

although this aspect depends ultimately on the particular report methodology em-ployed and on the cooperation and willingness of participants.

Disadvantages

• Reliance on subjects’ memory• Answers can be biased by aspects such as participant’s expectations or social accept-

ability• Sensitivity to misinterpretations and incompleteness• Low accuracy, validity and reliability.

Nonetheless, various validated methodologies exist: for instance, Bouchard et al. [1983]proposed a dairy/log with entries expected as often as every 15 min, applied to cover a3-day period and grouping exercise in 12 categories. Other examples of validated question-naires with widespread use are the International physical activity questionnaire (IPAQ)[Craig et al., 2003] or the Recent physical activity questionnaire (RPAQ) [Baecke et al.,1982; Golubic et al., 2014]. As a remark, practical advices by specialists [Valanou et al.,2006] stress the importance of selecting an appropriate reporting mechanism which is inaccordance with the particular aims of the study and with the specificities of the targetedcohort.

5.1.7 Overview of techniques for PA monitoring

As outlined above, there does not exist an universally superior method to monitor PA withall of the ideally desirable characteristics: high accuracy, precision and reliability, robust-ness, affordability in terms of both cost and resource requirements, minimal intrusiveness,scalability and suitability for free-living conditions. Consequently, a trade-off among theseaspects must be taken into account for the choice of a particular methodology. In thisregard, considerations must be made attending to: the size of the targeted population,the duration of the monitored period, the required level of detail (in terms of accuracy,temporal resolution and need for extra contextual information), the environment in whichthe experiment will be conduced (i.e. if in a laboratory setup or free-living conditions); aswell as concerning budget constraints, technological barriers or social aspects.

DLW and indirect calorimetry are currently considered the ‘gold standards’ in terms ofaccuracy, precision and reliability. However, they suffer from considerable limitations, suchas scalability problems, cost-inefficiency, DLW’s lack of temporal resolution and indirectcalorimetry’s inapplicability to extra-laboratory conditions. On the other hand, a promisingsolution to objectively track PA in free-living, ambulatory scenarios without the need forhuman intervention may be the fusion of accelerometry and HR sensors [Freedson andMiller, 2000; Ainslie et al., 2003; Corder et al., 2005; Plasqui and Westerterp, 2006, 2007;Valanou et al., 2006; Westerterp, 2009]. Following this approach, this PhD thesis workwill propose an automated system based on the simultaneous computational analysis ofaccelerometry and HR signals to identify PA patterns, employing pattern recognition andmachine learning methodologies.

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5. State of the art

5.2 Automated PA monitoring and recognition

This section overviews and summarizes the state of the art concerning published method-ologies to address the automated extraction of high-level information about PA from ac-celerometry signals, with particular focus on those based in the use of machine learning(ML) solutions. In broad terms, there are two predominant perspectives: a) estimatingPA-induced energy expenditures (PAEE), and b) classifying activity patterns to recognizespecific activities from a predefined, fixed set of PA options under consideration. A thirdtype of approaches would consist in the activity-independent stratification of PA accordingto its intensity level, although this research topic has received notably less attention fromthe automated signal processing and pattern recognition communities.

5.2.1 Activity-specific recognition

This family of approaches commence by specifying a closed set of target activities, amongwhich authors aim to discern. In literature, those activities often encompass body postures–most typically lying, sitting and standing– and/or transition events between pairs of pos-tures. Other frequent choices include a range of common free-living, spontaneous PAs andsports such as walking, jogging or cycling; but also sometimes rowing or Nordic walking,for example.

A notable variety of ML-based schemes have been proposed in literature for the recognitionof PAs, the vast majority of which match the general framework outlined by Preece et al.[2009b]’s review, where authors presented the following pipeline of stages:

a) Division of the signals into small time segments known as windows (generally withconstant duration)

b) Feature generation to describe the characteristics and morphology of the capturedsignals. Different types of features can be proposed, such as: time-domain statistics,spectral descriptors based on frequency analyses or wavelet transformations, plus ad

hoc features devised to incorporate prior knowledgec) Dimensionality reduction methods aiming to extract the most relevant fraction of

information contained in the departure high-dimensional feature spacesd) Classification algorithms to generate appropriate correspondences between data pat-

terns and ground truth PA class assignments.

Nevertheless, solutions available in literature employed remarkably diverse strategies foreach of the stages mentioned above, as well as in terms of how many and which sensorswere used for data collection, or in the set of targeted activities for recognition. Theseassorted differences discourage notably (or prevent altogether) the establishment of directcomparison of performance among methods. Of note, the mathematical complexity of theML algorithms for the final classification stage is remarkably dissimilar, ranging from rela-tively simple ‘nearest neighbours’ strategies (e.g. [Bao and Intille, 2004]) to notably moreelaborated ensembles of classifiers (e.g. [Lester et al., 2006]).

Some authors proposed ad hoc decision schemes which they built on the basis of priorknowledge. For example, Bonomi et al. [2009] used an intuitive decision structure to dis-tinguish among seven body postures and activities. In that work, decisions were madeby means of time-domain statistical descriptors calculated from the accelerometry signal,which was in turn captured with a triaxial sensor device placed in the subject’s lower back.

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5.2. Automated PA monitoring and recognition

Similarly, He et al. [2007] utilized an array of three accelerometers worn on chest and boththighs to discern among three stable postures –lie, sit or stand– plus five posture transitions.States were classified by means of an ad hoc decision scheme which operated by thresh-olding at each decision node; whereas a hidden Markov model (HMM) was subsequentlyapplied to account for temporal information. Besides, Ermes et al. [2008] recognized ninePAs, including vigorous exercises like cycling, rowing, Nordic walking or football. Subjectswore two triaxial accelerometers on wrist and hip, plus a GPS device to measure the ve-locity of outdoor displacements. Their proposal combined ad hoc intuitive modelling andML capabilities: first, authors employed a priori knowledge to build a decision structure;whereas for each node, they trained an artificial neural network in the form of a multi-layerperceptron (MLP) to perform binary decisions on the branching at that specific node.

On the contrary, the ample majority of works in literature refrained from assuming any a

priori decision flow, making use instead of general-purpose ML classification algorithms.For example, Preece et al. [2009a] applied nearest neighbours classification on a featurespace computed by wavelet analysis; whereas Siirtola et al. [2009] employed C4.5 decisiontrees trained for the recognition of nine heterogeneous sport activities (including e.g. skat-ing or racket sports), which operate on accelerometry data recorded by a wrist-worn biaxialsensor. Besides, de Vries et al. [2011] proposed a MLP classifier with a standard architec-ture, formed by a single layer of hidden neurons. This MLP distinguished sitting, standing,stair climbing, walking and cycling on the basis of measurements coming from two uniaxialaccelerometers which were worn on hip and ankle. In addition, Lau et al. [2008] exploredsupport vector machines (SVMs) with data from two biaxial accelerometers and two gyro-scopes –placed on shank and foot– to detect five different walking patterns. Compound MLschemes, also known as meta-classifiers, have also been explored in the form of ensemblesof ‘weak’ (i.e. basic) learners [Lester et al., 2005, 2006; Casale et al., 2011]. In particular,Lester et al. [2005, 2006] used Boosting on a dataset which merged information collectedby an uniaxial accelerometer, plus a microphone, digital compass, barometer thermometerand photodetector. In this manner, authors discerned between sitting, standing, walkingon a flat surface or up-/downstairs, using an elevator and teeth-brushing. Additionally,Casale et al. [2011] used an ensemble of decision trees named ‘random forest’ restrictingdata collection to accelerometry measurements only.

Unsupervised clustering techniques have also been explored by a number of researchers,including Gaussian mixture models (GMMs) [Allen et al., 2006; Nguyen et al., 2007], andself-organizing maps (SOMs) [Krause et al., 2003].

Interestingly, Bao and Intille [2004]; Gyllensten and Bonomi [2011] compared classificationperformances achieved by various ML algorithms: nearest neighbours, versus naïve Bayes(NB) classifiers and C4.5 decision trees for Bao and Intille [2004]; C4.5 trees versus MLPsand SVMs in Gyllensten and Bonomi [2011]. However, given the disparity of results, gen-eral conclusions about an hypothetically superior performance by any specific ML methodcannot be drawn. Furthermore, Bao and Intille [2004] also studied the suitability of fivedifferent body locations where to place their biaxial accelerometry sensors, namely: hip,wrist, arm, ankle and thigh). The effect of location on recognition performance was ad-dressed, concluding that accuracy did not suffer severe deteriorations when the classifiersused only data from wrist and thigh.

On the other side, the simultaneous combination of accelerometry and HR continues to bean under-explored option. Munguia Tapia et al. [2007] evaluated this possibility, althoughcounter-intuitively, authors discarded to include the HR signal since it did not provide suffi-

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5. State of the art

ciently satisfactory increases in recognition performances as achieved by their C4.5 decisiontrees and naïve Bayes classifiers. On the contrary, notorious success was reported by Reissand Stricker [2013]; Li et al. [2010]. Li et al. [2010] accurately recognized three conglom-erates of postures and activities using signals from an electrocardiogram (ECG) device tocapture cardiac information, plus three triaxial accelerometers –worn on wrist, waist andankle–; whereas patterns were classified by means of a SVM. Similarly, Liu et al. [2012]successfully integrated accelerometry with ventilation rate information, as an indicator ofthe physiological response by the cardiorespiratory system to exercise; recognizing up to13 activities with notable accuracy.

5.2.2 Estimation of energy expenditures

A minority of the published methods to estimate PAEE use ML-based solutions [Bassettet al., 2012]. Instead, linear –or less frequently, non-linear [Crouter et al., 2006]– regressionequations were derived from experimental data. Those regression formulae tend to operateon accelerometry measurements –in particular, activity counts– plus on anthropometricmagnitudes, such as sex, age and/or body weight. The overall accuracy of the resultingPAEE estimation is reported to be strongly dependent on the particular activities beingmonitored [Crouter et al., 2006; Plasqui and Westerterp, 2007; Lyden et al., 2010; Altiniet al., 2015], since the mechanics of movement for each specific PA can greatly influencethe output in terms of counts up to a large extent. In addition, other ad hoc regressionschemes incorporated HR information [Brage et al., 2004; Strath et al., 2001, 2002, 2005]with reasonable success.

Among the methods employing ML-based approaches for PAEE estimation, the algorithmwhich has gained most attention and spread is the MLP neural net working as a non-linearregression system; although other less frequent options also exist, such as cross-sectionaltime series models adding HR information [Zakeri et al., 2008]. Rothney et al. [2007]applied a MLP on data captured by a biaxial accelerometer which was worn on hip. Authorsproduced minute-by-minute PAEE estimations, comparing their results versus ground truthmeasurements obtained in a direct calorimetry chamber. In addition, Staudenmayer et al.[2009] used their MLP to predict MET values on the basis of data from an ActiGraph(ActiGraph, USA) uniaxial accelerometry device. Authors trained another MLP networkto function as an activity-specific classifier, in which four PA groups (sedentary, householdor locomotion activities, plus vigorous PA) were distinguished. Both Freedson et al. [2011];Trost et al. [2012] followed very similar strategies to Staudenmayer et al. [2009]: MLP-basedMET regression from ActiGraph uniaxial accelerometry data, along with activity-specificrecognition. As a novelty, these two works addressed the stratification of PA into intensitylevels in accordance to their resulting MET predictions [Freedson et al., 2011; Trost et al.,2012].

On the other hand, an increasingly extended approach consists in a two-stage procedure: inthe first place, an activity-specific recognition is carried out, subsequently followed by PAEEestimators tuned ad hoc for each particular PA class. For example, Albinali et al. [2010]conduced an activity-specific recognition of 25 PAs via C4.5 decision trees, which worked onthe combination of data from three accelerometers. For PAEE estimation, authors evalu-ated both MET look-up tables and activity-dependent regression models. Similarly, Atallahet al. [2011] considered eleven lifestyle and sport activities for PAEE prediction, evaluatedboth in a task-known and a task-blind scenarios. The latter case made use of Boostingclassification schemes for a preliminary PA recognition. Besides, Altini et al. [2015] usedfive accelerometers –worn on chest, ankle, thigh, wrist and waist– for their capture of data.

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5.2. Automated PA monitoring and recognition

Authors compared the accuracy of PAEE estimations as obtained by standard count-basedregression formulae versus schemes combining: a) activity recognition algorithms, in thiscase via a SVM, which achieved high accuracies in the discernment of five aggregated PAgroups); and on the other hand, b) activity-specific MET estimators, either by MET look-up correspondences or by linear regressions. Similarly, Liu et al. [2011, 2012] consideredfour activity groups –loosely related to PA intensity–, SVM classification and subsequentMET predictions by support vector regression (SVR). Authors combined signals from twotriaxial accelerometers plus a ventilation rate monitor. Lin et al. [2012] grouped PAs intothree intensity range-based groups and employed data from three triaxial accelerometers,plus an ECG sensor to obtain HR-related information. Authors performed activity recog-nition via decision trees; whereas the subsequent activity group-dependent MET regressionwas carried out by means of artificial neural networks.

5.2.3 Activity-independent PA intensity classification

Non-ML-based approaches, which are the largely predominant solution for this task of PAintensity classification, rely on the application of thresholds on activity counts, also knownas in the field as ‘cutpoints’ [Freedson et al., 1998; Hendelman et al., 2000; Swartz et al.,2000; Ham et al., 2007; Sasaki et al., 2011]. Therefore, the separation of intensity levelsbased on activity counts is performed in a simple and static manner, although most cer-tainly oversimplified and not robust. Anyway, such cutpoint-based approach is the optionimplemented by the companion analysis software for two of the most commonly used com-mercial devices: ActiGraph’s waist-worn sensors [ActiGraph LLC, 2010] and BodyMedia’sSenseWear armband [Liden et al., 2002; Jakicic et al., 2004; Malavolti et al., 2007; Benitoet al., 2011].

On the other hand, this problem of activity-independent PA intensity classification hasattracted limited attention from the ML research community. Literature available in thisregard is scarce. Freedson et al. [2011]; Trost et al. [2012] developed MLP-based MET re-gression schemes which subsequently assigned activities into a certain intensity level in ac-cordance to MET estimation outputs. In a complementary manner, chapter 6 now presentsa novel approach explicitly conceived to identify PA time periods on the basis of their re-lated intensity level (as well as the predominant exercise typology), as a core contributionof this PhD thesis work.

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Chapter 6

Automatic physical activity intensityand modality classification usingaccelerometry and heart rate data

6.1 Motivation

The promotion of physically active lifestyles is essential for the prevention and/or thetreatment and management of a wide variety of chronic diseases with large prevalence andimpact on public health, e.g. obesity [Shaw et al., 1996; Fogelholm, 2010], T2D [Albrightet al., 2000; Thompson et al., 2003; Colberg et al., 2010], cardiovascular [Thompson et al.,2003] and respiratory diseases [Chavannes et al., 2002], hypertension, cancer [Lee, 2003;Holmes, 2005] or depression, among others. In this regard, a reliable automated detectionand quantification of PA, along with its evolution over time, can empower lifestyle inter-ventions on populations by facilitating, among other aspects: the recording and analysisof data about exercise sessions, the monitoring of patients’ compliance with prescribedPA plans, or the provision of enhanced and individually tailored feedback to patients andcaregivers. Thus, PA-based lifestyle interventions demand robust, accurate and scalableautomatic mechanisms to monitor patients’ degree of adherence to PA, as well as to as-sess how intensely PA was performed. Furthermore, in the particular application scenarioof T1D, distinguishing not only PA intensity but also exercise modality may be of majorinterest, since different modalities induce remarkably distinct acute responses in glycaemia(sections 4.2–4.3). As a consequence, the adjustment and personalization of therapeuticstrategies for the daily self-management of non-sedentary patients with T1D may stronglybenefit from objective information about PA intensity and modality. This should also bethe case for automated closed-loop glycaemia control scenarios incorporating PA [Chassinet al., 2007; Breton, 2008; van Bon et al., 2011].

As discussed in section 5.1, ‘gold standard’ techniques to quantify PA –i.e. DLW andindirect calorimetry– are costly, not scalable to large populations and suitable only for lab-oratory environments [Ainslie et al., 2003]. Conversely, this PhD thesis work explores thesimultaneous combination of accelerometry and HR information sources, addressing thesuitability of a number of ML schemes for the robust identification of PA. In particular,the schemes under study here were designed to discern between three standard PA inten-sity levels [Pate, 1995]: i) rest, sedentary and low intensity situations (below 3 MET),ii) moderate PA (3–6 MET), and iii) vigorous exercise (above 6 MET). Additionally, for vig-

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6.2. Data collection experiments

Figure 6.1: Equipment for data collection (left panel), comprising the ActiTrainer biaxialaccelerometer and the Polar Wearlink chest strap for HR monitoring. Example signals(right) –red for acceleration counts registered in the main axis, blue for the secondaryaxis–. (Source: Adapted from ActiGraph LLC [2010]’s user manual).

orous periods a further distinction in terms of exercise modality is considered here among:a) sustained, predominantly aerobic exercise, b) resistance –mainly anaerobic– effort, andc) a mixed exercise type, in which both aerobic and anaerobic bouts were alternated.

6.2 Data collection experiments

6.2.1 Equipment

Commercial ActiTrainer (ActiGraph, USA) accelerometry devices were selected to be em-ployed here for data collection, due to their thoroughly documented validity and fieldreliability [Bassett et al., 2000; Hendelman et al., 2000; Welk et al., 2004, 2007; Sasakiet al., 2011], as well as for their capability to establish wireless communication with a Po-lar Wearlink (Polar Electro, Finland) HR monitor transparently. In addition, ActiGraph’spedometer functionality [Le Masurier and Tudor-Locke, 2003] was also utilized.

As other comparable commercial accelerometers specifically dedicated for PA monitoring,the ActiTrainer device produces its output measurements in the form of ‘activity counts’over a epoch with configurable duration [ActiGraph LLC, 2010].

During the experiments, participants wore the ActiTrainer biaxial accelerometer (86×33×15 mmsize, 51 g weight, ±3G dynamic range, 30 Hz sampling frequency) tightly attached to theirwaist, with main and secondary axes oriented in respectively vertical and antero-posteriordirections, as suggested by manufacturer’s guidelines [ActiGraph LLC, 2010]. For the HRsignals to be handled appropriately, ActiTrainer’s firmware imposed a minimum epoch withduration 10 s, which was the choice here in order to have as much temporal resolution aspossible.

6.2.2 Data collection experiments

The ML-based identification of PA patterns relies on the automated extraction of knowledgefrom the provided ground truth dataset. Therefore, reference data should be representa-tive of those expected to be encountered in the final intended application. Consequently,two distinct data collection experiments were conduced here, aiming at the construction

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6. PA intensity and modality classification using accelerometry and HR

of a thorough, descriptive reference dataset which reflects the heterogeneity of PAs whichmay take place in practise. One of these two experiments (A) covered free-living condi-tions in ambulatory scenarios, whereas he other was carried out in a controlled laboratoryenvironment (B).

6.2.2.1 Experiment A

Experiment A enrolled seven healthy subjects: 3 males and 4 females, with age range25–43 years old and diverse lifestyles varying from sedentary to regular sports practice.Volunteers received instructions on how to wear the sensors and were requested to producewritten activity logs with as much detail as possible, including both timing informationand intensity descriptions. Subjects were encouraged to record: i) daily life situations,ii) the use of means of transportation, as well as iii) their preferred PAs at self-selectedintensities.

6.2.2.2 Experiment B

Experiment B took place in a fitness center, under strict timing control and direct super-vision by the research team. Three alternative types of circuit were considered (Figures6.2 to 6.4). Circuits #1 (Figure 6.2) and #2 (Figure 6.3) comprised upper- and lower-limbresistance exercise –i.e. strength training–, respectively with free weights and fitness ma-chines (Johnson Health Tech Iberica, Spain). oppositely, circuit #3 (Figure 6.4) combinedfree weights and aerobic exercise –i.e. treadmill running– performed in short alternatingbouts. Each 64-min session (Figure 6.5) started with a 5-min warm-up phase –treadmill orelliptical walk– plus a preliminary circuit lap with duration 7 min 45 s and light load: at30% of each subject’s 15 repetitions maximum (RM). Thereafter, three more circuit lapswere performed with high load: at i.e. 70% of 15 RM. Laps were separated by 5 min ‘activerecovery’ periods –i.e. walking–. A complete description of exercises, circuits and protocolscan be found elsewhere [Benito Peinado et al., 2010; Zapico et al., 2012]: PRONAF study(trial registration NCT01116856 at ClinicalTrials.gov).

Nine subjects took part: 6 males and 3 females, with an age range 20–49 years old. Threewere healthy, moderately active males, whereas the remaining six individuals suffered mod-erate overweight (BMI = 28.1±1.3 kg·m−2, mean±SD). Informed consent was obtained inall cases.

Along with the ActiTrainer accelerometer and a Polar HR monitor, participants wore aSenseWear armband (BodyMedia, USA) [Liden et al., 2002; Malavolti et al., 2007] on theirdominant arm; as well as a Jaeger Oxycon Mobile (CareFusion, USA) portable indirectcalorimeter (Figure 6.6) to measure PAEE via O2 consumption and C02 production rates.However, PAEE data were not employed in this work; but instead served to evaluate theaccuracy of ActiTrainer’s and SenseWear’s EE estimation formulae in strength trainingscenarios1.

6.2.2.3 Dataset overview

A heterogeneous set of free-living activities in ambulatory scenarios was acquired duringExp. A. This included daily life situations –e.g. sleeping, household or office work– and

1Article submitted by the PRONAF research team, approval pending.

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6.2. Data collection experiments

Figure 6.2: Schematic depiction of PRONAF circuit #1. Each of the three 7 min 45 scircuit laps (actually four, considering the preliminary warm-up lap at a lighter intensity)comprised eight stages of 45 s duration each, with 15 s in between for transitions. At eachstage, subjects performed 15 repetitions at a fixed cadence: 1 s concentric phase, 2 s eccen-tric phase [Zapico et al., 2012]. Loads were calculated to represent 70% of each subject’s15 RM, except for the warm-up lap, where they were 30% of 15 RM [Benito Peinado et al.,2010]. Stages for circuit #1 were in this order: shoulder press, squat, barber row, lateralsplit, bench press, front split, biceps curl and French press for triceps. (Source: Adaptedfrom PRONAF).

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6. PA intensity and modality classification using accelerometry and HR

Figure 6.3: Schematic depiction of PRONAF circuit #2. Differences with respect to #1resided in the selected exercise routines, where each exercise had similar characteristics tothe corresponding stage in circuit #1, but performed with fitness machines in this case:shoulder press with machine, ‘hack’ squat, Gironda chest row, leg press, bench press withmachine, lying leg extension, Scott bench biceps curl and triceps pull down. (Source:Adapted from PRONAF).

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6.2. Data collection experiments

Figure 6.4: Schematic depiction of PRONAF circuit #3. Differences with circuits #1 and#2 again consisted in the routines at each stage: on the one side, exercises two, four,six and eight comprised 45 s treadmill running; whereas stages one, three, five and sevencorresponded to free-weight strength exercises: squat, Gironda chest row, bench press andfront split. (Source: Adapted from PRONAF).

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6. PA intensity and modality classification using accelerometry and HR

Fig

ure

6.5:

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hed

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77

6.2. Data collection experiments

Figure 6.6: Three volunteers participating in data collection for Exp. B. Red squares(left, top right) and arrow (bottom right) emphasize the location of the ActiTrainer sensor.Additionally, figures show Oxycon’s face mask and other equipment –worn on chest– asneeded for the portable indirect calorimeter.

the use of means of transportation –specifically bus, car, subway and elevator–, along witha notable variety of exercises at assorted intensities, including: walking at different paces,dancing, jogging, vigorous endurance running, karate, football (soccer) and mountain bike.The elimination of ambiguously annotated periods yielded a total of 148.50 h of usabledata, split in 72 sessions (Table 6.1, upper part). Session duration was 119 [93–149] min(median [inter-quartile range]), with minimum at 18 min and maximum at 216 min. Thedetailed distribution regarding the volumes of data per individual is depicted in Figure6.7 (panel A), with median time per participant at 10.40 h. Of note, the subject withidentification code #A7 contributed with only 18 min; whereas on the contrary, subject#A5 –a moderately active, 26-year-old male– was very enthusiastic and participative inthe data collection procedure and contributed with a total of 81.87 h.

In contrast, Exp. B in a controlled laboratory environment was markedly more homoge-neous than Exp. A in terms of exercise activities covered. Differences in the volumes ofdata for each subject (Figure 6.7, panel B) had two sources:

• The number of sessions in which each volunteer participated, which depended onhis/her availability for the experiment. Five overweight individuals (subjects withidentification codes #B4 to #B7, plus subject #B9) completed all three circuit ver-sions in different days and random order; whereas one healthy subject (#B1) exercisedfor two sessions, and the remaining three participants (two healthy males #B2, #B3and one overweight female #B8) completed only one circuit; randomly assigned inall cases. Hence, a total of 20 sessions were registered.

• The pre- and post-exercise resting time which was recorded in addition to the 64-mincircuit protocol.

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6. PA intensity and modality classification using accelerometry and HR

Table 6.1: Summary of the dataset

Experiment A Experiment B Total

7 participants 9 participants 16 participants72 sessions 20 sessions 92 sessions

PA intensity 148.50 h (83.13%) 30.13 h (16.87%) 178.63 h (100.00%)

Low (<3 MET) 104.73 h (70.53%) 12.37 h (41.04%) 117.10 h (65.55%)Moderate (3–6 MET) 26.30 h (17.71%) 7.57 h (25.11%) 33.87 h (18.96%)Vigorous (>6 MET) 17.47 h (11.76%) 10.20 h (33.85%) 27.67 h (15.49%)

1 participant 9 participants 10 participants5 sessions 20 sessions 25 sessions

PA modality 6.80 h (40.00%) 10.20 h (60.00%) 17.00 h (100.00%)

Sustained aerobic 6.80 h (100.00%) 0.00 h (0.00%) 6.80 h (40.00%)Mixed 0.00 h (0.00%) 3.45 h (33.82%) 3.45 h (20.29%)

Resistance 0.00 h (0.00%) 6.75 h (66.18%) 6.75 h (39.71%)

Figure 6.7: Individual contributions to the dataset concerning PA intensity; divided byexperiments (panels A, B), by participants and intensity levels.

Data were manually divided into separate PA intensity classes by MET levels accordingto Ainsworth et al. [2000]’s Compendium. Three standard intensity ranges [Pate, 1995]were employed, namely: i) low-intensity activities below 3 MET –which therefore includesedentary situations–, ii) moderate PA (3–6 MET), and iii) vigorous exercise (>6 MET).Additionally, 17.00 h of vigorous PA data included further information regarding the exer-cise modality involved (Table 6.1, lower part): either sustained aerobic, mixed or resistanceactivity –i.e. strength/weight training– .

6.3 Algorithms

This PhD thesis work proposes a pipeline of ML algorithms which broadly correspondsto the steps outlined by Preece et al. [2009b]’s review on activity-specific PA recognitionmethods. In addition, major novelties with respect to the procedures described in [Preeceet al., 2009b] include: i) the use of unsupervised clustering techniques for pattern ex-traction and vector quantization [Duda et al., 2000]; and ii) a final Hidden Markov Model(HMM) as an extra temporal filtering module, which exploits time redundancy in the dataseries in order to enhance robustness in classification.

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6.3. Algorithms

6.3.1 Preprocessing and feature definition

The multi-modal signals captured by the ActiTrainer biaxial accelerometer were: a) activ-ity counts for its main and secondary axes a1, a2, b) step count st –pedometer functionality–,and c) heart rate data hr, as measured and transmitted by the Polar Wearlink chest strap.Signals were first divided in non-overlapping analysis windows with duration equal to 2 min(N=12 epochs per window, at 10 s per epoch). Several alternative window lengths weretested in a preliminary stage, where these 2 min were found to be a satisfactory trade-offbetween: on the one side a) capturing information-rich patterns in the signals –task forwhich longer analysis segments would be desirable–; and on the other hand b) sufficienttemporal resolution –i.e. low time granularity–, which would imply short windows.

Additionally, activity counts in both the main and secondary axes a1, a2 were combinedinto an extra magnitude called here ‘pseudo-norm’ activity counts apn defined as:

apn =√

a21 + a2

2 (6.1)

For each window and each of the five signals under consideration (a1, a2, apn, st and hr),the following time-domain statistical descriptors were computed:

• Mean x and standard deviation sdx:

x =1

N

N∑

i=1

x(ti) (6.2)

sdx =

√

√

√

√

1

N − 1

N∑

i=1

[x(ti)− x]2 (6.3)

where x(t) represents a generic signal sampled at instants ti.• Difference between mean x versus median xmed values:

mmdx = x− xmed (6.4)

a feature which was devised in order to contribute in the protection against outliers,because medians are less sensitive to outliers than means.

• Maximum, minimum value and total range:

xmax = maxi=1,...,N

x(ti) (6.5)

xmin = mini=1,...,N

x(ti) (6.6)

xrange = xmax − xmin (6.7)

where xmin is exclusively used in the subsequent computation of xrange but not in thefinal feature space, since preliminary tests revealed its low discriminative power.

• Signal variability svx within a certain window, defned here as the accumulation ofabsolute differences between a certain sample x(ti) of signal x at time ti and itsprevious value:

svx =N∑

i=2

|x(ti)− x(ti−1)| (6.8)

• A coefficient of dispersion cdx with respect to the median value xmed of the signalwithin the window:

cdx =

{

1N

∑Ni=1

|x(ti)−xmed|xmed

if xmed 6= 0

0 otherwise(6.9)

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6. PA intensity and modality classification using accelerometry and HR

Nonetheless, after visual inspection and preliminary tests, a modified version of cdx

was used instead: more specifically, exponentiated by a constant γ, where γ washeuristically assigned to 1/4 in order to increase the spread of values obtained for thismodified dispersion feature cdγ

x with respect to cdx.

In addition, it was observed that features computed from acceleration counts –i.e. thosestatistics derived from signals a1, a2 and apn; but neither from st, nor from hr– yieldedvalues which spanned through various orders of magnitude, an issue which could pose amajor challenge to the subsequent learning algorithms, specially to those based on dis-tances between data instances. Consequently, the following truncated signed logarithmictransformation was applied to those features, as suggested by Zumel and Mount [2014]:

sign log(x) =

{

sign(x) log |x| if |x| ≥ 10 otherwise

(6.10)

where: a) sign considerations were necessary to accommodate negative feature values,which –given the aforementioned definitions of features and taking into account that a1,a2 are per se non-negative natural numbers (integers)– could only arise in those featuresconcerning mean-median differences; and b) this signed log-transformation was not appliedto the exponentiated coefficients of dispersion cdγ

x, since those feature did not suffer thescale problems described above.

Finally, other extra ad hoc features were defined:

• Three paired products between mean ‘pseudo-norm’ counts apn (log-transformed),mean HR and mean number of steps, along with the combined product of the threeformer magnitudes, i.e.:

hr · sign log(apn) (6.11)

st · sign log(apn) (6.12)

hr · st (6.13)

hr · st · sign log(apn) (6.14)

In this manner, multi-modal information captured by the device was merged explic-itly.

• Histogram of counts for the main axis a1, where ActiGraph default cutpoints –i.e.1952 and 5725 counts [Freedson et al., 1998; ActiGraph LLC, 2010]– were used as areference for setting binning intervals in the histogram. More precisely, those Acti-Graph default cutpoints were first rescaled by a proportionality factor equal to 1/6

in order to adapt them to the use of 10 s epochs, instead of the original 60 s epochsemployed in the original work by Freedson et al. [1998]. Therefore, these ad hoc

histogram features are inspired in the replication of the standard, threshold-basedintensity classification procedure implemented in ActiGraph’s commercial analysissoftware [ActiGraph LLC, 2010].

In total, 42 time-domain features were computed: 7 statistical descriptors for each of the 5signals under consideration, plus 4 combined products (6.11)–(6.11) and 3 cutpoint-basedfeatures2.

6.3.2 Dimensionality reduction

This works explores different techniques whose aim is to retain as much information from theoriginal high-dimensional feature space as possible, while reducing the number of variables

2Two cutpoints define three histogram intervals.

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6.3. Algorithms

and hence the complexity of the subsequent automated learning task. In this manner,unnecessary redundancy (as well as to some extent, also noise) becomes cancelled out fromthe dataset, which is in turn transformed to have fewer features, although more descriptiveand information-rich.

Nevertheless, prior to the dimensionality reduction stage itself and given that the featuresused here are clearly not commensurate (in first place, because their units are different), thefeature space was standardized: first subtracting the sample mean in each dimension, andlater normalizing by its standard deviation. Besides, this step prevented relevant informa-tion contained in the low-scaled features from being shaded by variables with high variance,an aspect which is specially critical when applying distance-based learning schemes, e.g.K-means, hierarchical clustering or SVMs.

6.3.2.1 Feature extraction

These dimensionality reduction procedures consist in obtaining a series of new featurescomputed as linear combinations of the original ones, in such a manner that those newfeatures cover most of the relevant information in data. In turn, there exist differentcriteria about what to consider relevant information.

6.3.2.1.1 Principal Component AnalysisPrincipal component analysis (PCA) projects data onto a vector subspace defined to pre-serve as much randomness as possible from the original high-dimensional feature space.Such a subspace is specified by the eigenvectors with largest eigenvalues from data’s covari-ance matrix (appendix A.1.1). Anyway, given the pre-standardization step, this covariancematrix coincides with the correlation matrix of the original –i.e. untransformed– datafeatures [Rencher and Christensen, 2012].

6.3.2.1.2 Linear Discriminant AnalysisLinear discriminant analysis (LDA) is a procedure conceived to preserve as much of theclass discriminatory information as possible once data have been projected. Consequently,LDA requires information about ground truth class assignments; in contrast to PCA, whichis an unsupervised algorithm. Mathematically speaking, the core of the LDA algorithm(appendix A.1.2) resides in solving a generalized eigenvalue problem where the within- andbetween-class scatter matrices are indicators of class separability [Rencher and Christensen,2012]. In general, the dimensionality of LDA’s output subspace equals the number of classesunder consideration minus one.

6.3.2.2 Feature selection

As seen above, feature extraction approaches (e.g. PCA or LDA) reduce data dimension-ality via the generation of new characteristics as an appropriately weighted linear combi-nation of the original. Instead, feature selection methodologies search for a suitable subsetof features which retains relevant information in accordance to certain optimality crite-rion [Kohavi and John, 1997; Guyon and Elisseeff, 2003]. These techniques have thereforean advantage over feature extraction in terms of the interpretability of resulting features,which in practice becomes very limited after PCA or LDA linear combinations. In addition,unselected features would not need to be calculated for an eventual final deployment of theclassifier.

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6. PA intensity and modality classification using accelerometry and HR

6.3.2.2.1 FiltersThese procedures consist in selecting features according to their respective ability to maxi-mize a certain target or merit function, in turn defined to quantify the appropriateness of thecandidate feature subset following criteria stemming from information theory. This workemployed merit functions corresponding to the so-called minimum redundancy-maximumrelevance (mRMR) criterion, as formulated by Peng et al. [2005]; Ding and Peng [2005]. Ateach iteration, one feature is selected –i.e. ‘filtered’– in a greedy near-optimal [Peng et al.,2005] manner to optimize the trade-off between:

a) Additional information supplied by the inclusion of the new candidate feature, i.e.maximizing the relevance of the feature set; and

b) Redundancy existing between the new candidate feature and those already selected,with the objective of minimizing the overall redundancy.

As specified by [Ding and Peng, 2005], the mRMR filter, in its variant for discrete –i.e.categorical– data, uses mutual information I(x, y) between features x, y as part of both itsrelevance and redundancy criteria, where:

I(x, y) =∑

i

∑

j

p(xi, yj) logp(xi, yj)

p(xi)p(yj)(6.15)

being p(xi), p(yj) the marginal frequentist probabilities for each possible discrete value xi,yj, and p(xi, yj) their joint probability.

On the other hand, for the version of mRMR operating on continuous data:

• Relevance of feature x is determined by the F-test statistic:

F (x, c) =1

σ2

1

C − 1

C∑

c=1

nc (xc − x)2 (6.16)

where the problem consists of C classes under consideration and where σ2 is theoverall variance across the dataset:

σ2 =1

n− C

C∑

c=1

(nc − 1)σ2c (6.17)

being x the overall mean across data instances; nc, xc, σ2c respectively the number of

samples in the c-th class, its within-class mean and variance; and n the total numberof samples available in the dataset.

• Redundancy is calculated as the average of the absolute values of Pearson’s correlationcoefficients |ρx,y| between pairs of features x, y [Ding and Peng, 2005].

To evaluate the balance between relevance and redundancy, and in order to rank featuresin relation to such trade-off, this work employs the mutual information quotient (MIQ) andF-test correlation quotient (FCQ) metrics, as suggested by Ding and Peng [2005].

In addition, given that all of the features used here are continuous variables instead ofdiscrete/categorical data, it was compulsory to perform a quantization of values before ap-plying the discrete version of the mRMR filter procedure. This quantization was carried outby binning each feature into eight intervals symmetrically placed around its sample mean,with interval widths equal to half of the sample standard deviation. In the standardizedfeature space, such a definition of binning intervals is equivalent to use the following ranges:(−∞, − 3/2); [ − 3/2,−1); [−1, − 1/2); [ − 1/2, 0); [0, 1/2); [1/2, 1); [1, 3/2) and [3/2,+∞).

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6.3.2.2.2 WrappersThe essential difference between ‘filter’- and ‘wrapper’-based feature extraction procedureslies in their optimality metrics: filters target at a goal function grounded on informa-tion theory measures, whereas wrappers focus on maximizing the recognition performanceachieved by a certain classification algorithm embedded in the process –i.e. ‘wrapped’,hence their name– [Kohavi and John, 1997; Guyon and Elisseeff, 2003]. In general, animportant advantage of this ‘wrapper’-based feature selection consists in the fact that itsoptimization metric is more closely related to the final use of the system for classificationpurposes than information theory measures.

On the other hand, estimations about the classification accuracy achieved by the wrappedclassifiers should be assessed by cross-validation (CV) schemes in order to prevent –or atleast to ameliorate– overfitting. Coming sections 6.3.3.2 and 6.3.5 respectively describe inmore detail the classification algorithms being wrapped here and the custom performancemetric employed.

Concerning the strategy to explore the search space of candidate feature subsets, it isstraightforward to conclude that, in practise, exhaustive search becomes infeasible veryrapidly because the cardinality of possible sets grows exponentially with the number offeatures: for d features, there exist 2d candidate sets. Thus, heuristic search algorithms areneeded. This work explored two different approaches with considerably unequal computa-tional demand, namely:

• Greedy best-first forward sequential search. Starting from an empty set, one featuregets added to this candidate set at each iteration; specifically the one which mostimproves the performance of the wrapped classifier. This procedure is repeated iter-atively until noticeable increases in performance do not longer occur in spite of theeventual addition of extra –most likely, redundant– features.

• Genetic search. This approach consists in a stochastic search strategy inspired bybiological evolutionary procedures. A random initial collection –named ‘population’–of tentative candidate solutions –i.e. ‘individuals’– are evaluated according to a cer-tain fitness function, which in this case corresponds to the classification performanceas attained by the ‘wrapped’ classifier when trained on the dataset with reducedfeatures.In turn, this fitness score establishes the probability of survival [Goldberg, 1989]for each individual solution within the population towards the following iteration –i.e. ‘generation’–. Surviving solutions either experience ‘replication’ –i.e. remainingunchanged–, undergo ‘mutation’ –i.e. small random changes– or suffer a ‘cross-over’operation –i.e. being merged with another candidate solution in order to produce an‘offspring’, generally with large changes–. Due to these stochastic alterations, thereare occasional major modifications in the candidates, a characteristic behaviour ofgenetic search schemes which is highly beneficial when exploring complex optimizationspaces (as it is often the case in feature selection problems [Duda et al., 2000]).

In this work, two different ‘wrapper’-based feature selection procedures are conduced foreach supervised classification algorithm under study here (i.e. those listed in section6.3.3.2): one with a greedy best-first selection strategy, plus another with genetic search.On the other hand, wrappers tend to produce solutions which may excessively fit the par-ticular ‘wrapped’ scheme employed [Kohavi and John, 1997; Guyon and Elisseeff, 2003].As a consequence, the subset of selected features may potentially suffer from a lack of suffi-cient generalization power as to apply it practise. For this reason and in order to augmentoverall generalizability, two extra procedures were conduced: one greedy, one genetic. Inthem, the performance scores attained by each classifier are averaged to obtain an overall

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6. PA intensity and modality classification using accelerometry and HR

fitness metric, which ultimately guides the features selection. In this manner, the eventualbias in favour of any particular classifier should be unlikely.

6.3.3 Pattern identification

This stage forms the core of the ML process, where the underlying informative patterns indata are automatically discovered and extracted for recognition purposes.

6.3.3.1 Clustering

In the first place, four unsupervised algorithms were explored here. These techniques didnot make use of information about ground truth class correspondences. Instead, input datawere arranged into homogeneous clusters, which in principle did not correspond directlyto the desired classification outcomes. Hence, cluster would have lacked of an intuitiveinterpretation if addressed solely. However, they achieved a ‘smart quantization’ of thedata space [Duda et al., 2000], and in turn served as the ‘observed’ states for the subsequentHMM-based temporal filtering.

6.3.3.1.1 K-means clusteringK-means is arguably the most renowned algorithm for clustering purposes. In broad terms,its training procedure consists in an iterative update of cluster centroids in two stages.Centroids partition the data space in multi-dimensional Voronoi areas which determine thecorrespondence between a given data point and its cluster assignation. See appendix A.2.1for a formal mathematical description of the K-means methodology.

6.3.3.1.2 Gaussian Mixture ModelsGaussian Mixture Models (GMM) approximate the probability density function of data as amixture –i.e. as a weighted linear combination– of multidimensional Gaussian distributions,whose parameters –means, covariance matrices and weights– must be estimated during thetraining stage (appendix A.2.2). Expectation-maximization (EM) algorithms are commonlyemployed in such parameter estimation procedures.

6.3.3.1.3 Hierarchical clusteringThis work adopted an agglomerative –i.e. bottom-up’ (appendix A.2.3)– approach forhierarchical clustering. A Preliminary tests to select suitable configuration parametersresulted in the choice of Euclidean distance and Ward’s linkage criterion between sub-clusters (appendix A.2.3) as the options providing highest performances.

6.3.3.1.4 Self Organizing MapsSOMs are a form of artificial neural networks whose training is based on competitive learn-ing (appendix A.2.4). They were used here to map the input feature space onto a 2D grid ofneurons. Subsequently, SOM neurons were clustered using a hierarchical approach, whichsupposed a remarkable decrease in terms of computational load with respect to the formercase operating on the whole cloud of data instances.

SOM’s network topology (a hexagonal grid) and its number of neurons (20×20) were refinedpreliminarily. Distance metrics between pairs of neurons were computed via Dijkstra’s al-gorithm, with costs corresponding to the Euclidean differences between grid-adjacent SOM

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6.3. Algorithms

neuron weights. In addition, the ‘average’ linkage criterion was employed for hierarchicalclustering. All these parameter choices were made attending to preliminary tests.

6.3.3.2 Classification

In addition to the four aforementioned clustering approaches, this work studied the suit-ability of five supervised classification algorithms. Training procedures were conduced foreach of the data feature spaces under consideration (i.e. those reduced via PCA, LDA,filters and wrappers), given the ground truth class correspondence assignments. Those fivealgorithms allowed to cover a wide spectrum of methodologies with diverse working prin-ciples and varying degrees of computational complexities. Besides, Naïve Bayes classifiers(appendix A.3.1) were also explored in a preliminary stage, although they were discardeddue to their poor overall classification performance.

6.3.3.2.1 Logistic regressionWith this method, the natural logarithms of class-likelihood ratios are modelled as a mul-tivariate linear function of features values, with a different set of regression coefficientsfor each class (appendix A.3.2). For a definitive classification, the maximum estimatedprobability value determines the predicted class correspondence.

6.3.3.2.2 Multi-Layer PerceptronMLPs count with high popularity among the supervised learning schemes, being widelyused in assorted fields of application. Their working principle resides in building a com-pound, non-linear mapping function by means of the cascade connection of various layersof neurons, whose input weighing factors are appropriately tuned and with a non-linear ac-tivation (appendix A.3.3). The classical feed-forward MLP architecture –i.e. with a singlelayer of hidden neurons– was used here; since it has been proved [Duda et al., 2000] thatthis general, although relatively simple network structure can achieve arbitrary complexityprovided that sufficient neurons are placed on its hidden layer.

6.3.3.2.3 Support Vector MachinesSupport Vector Machines (SVM) are maximal-margin classifiers based on finding the opti-mal separation hyperplane –in either the original feature space, or in a transformed versionof it via kernel functions (appendix A.3.4)– which divides the space of data in two regions;fulfilling the condition that the distance (i.e. ‘margin’) between this boundary hyperplaneand the closest, most limiting samples (known as ‘supporting vectors’) must be as wide aspossible. This in turn translates into quadratic optimization problems often solved usingLagrangian formulations (appendix A.3.4).

Gaussian radial-basis function (RBF) kernels k (·, ·) are a common choice for SVMs, wherethese kernels incorporate distances between data pairs ~x, ~xj according to the followingformula:

k (~x, ~xj) = exp[

−1

2σ2‖~x− ~xj‖

2]

(6.18)

In the case of the dataset under consideration in this work, preliminary explorations showedbetter classification performances for RBF-based SVMs than for the basic linear formula-tion.

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6. PA intensity and modality classification using accelerometry and HR

On the other hand and given that: a) the original SVM methodology was conceived forbinary classification only, and considering that b) the problems addressed here are multi-class; a one-versus-all (OVA) approach was adopted. OVA consisted in generating a seriesof binary SVMs, each of which specifically trained to discern between a certain class ofinterest and all the remaining other. However, OVA brings an extra issue in the form of‘ties’, i.e. whenever more than one SVM happens to classify positively a certain input datapoint ~x; or conversely, whenever none does. This work employed posterior SVM probabilityscores in order to break ties, resolving the prediction outcome for ~x in correspondence tothe class whose SVM yielded highest posterior score for ~x:

postscoreSVM(~x) =nSV∑

j=1

αjyjk (~x, ~xj) + b (6.19)

where: a) ~xj are each of the nSV ‘supporting vectors’, b) yi ∈ ±1 are their ground truthclass assignments, c) b is the offset term for the SVM, and finally d) αj are the Lagrangemultipliers resulting from the training of the SVM [Vapnik, 1998].

6.3.3.2.4 BaggingThe Bagging technique is a type of meta-classification scheme in which the outcomes pro-duced for a given input by a series of so-called ‘weak’ classifiers are averaged in order toobtain an ‘ensembled’ or ‘robust’ classification result. The distinctive aspect of Baggingwith respect to other meta-classifiers lies in the fact that each of those ‘weak’ learners hadbeen trained on a resampled collection of input data, stemming from the original datasetand generated via bootstrap resampling methods (i.e. random with replacement, appendixA.3.6).

In this work’s implementation, classification and regression trees (CART) were used as‘weak’ learners. In particular, CART trees had MATLAB’s default configuration parame-ters [MathWorks Documentation, 2015], including Gini’s diversity index as splitting crite-rion and branch pruning based on classification errors (appendix A.3.5).

6.3.3.2.5 BoostingAs in the case of Bagging, Boosting works as a meta-classification system aggregating (i.e.ensembling) ‘weak’ learners, which in this case received a voting weight in accordance totheir estimated classification accuracy. Therefore, a new weak classifier is trained at eachiteration, with augmented focus on those input samples which were misclassified duringthe previous step (appendix A.3.7).

Again, CART decision trees were chosen here as the template algorithm for weak learners,using also MATLAB’s default configuration [MathWorks Documentation, 2015]. Besides,this work opted for the AdaBoost.M2 version of the algorithm (appendix A.3.7) in orderto address multi-class problems.

6.3.4 Temporal filtering

Various works in literature proposed activity-specific PA recognition schemes based on theuse of Hidden Markov Models (HMM) [Lester et al., 2006; Pober et al., 2006; Chang et al.,2007; He et al., 2007; Mannini and Sabatini, 2011], mainly to detect and characterize tran-sition events between body postures. Conversely, this work uses HMMs from a differentperspective: as a non-linear informed filtering module, capable of exploiting temporal re-dundancies for the sake of robustness in classification. Indeed, this particular scenario of

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6.3. Algorithms

PA monitoring presents a strong temporal coherence; in other words, a clear time inter-dependency between neighbour windows segments. At the view of data collected duringthe experiments, it is straightforward to observe that in free-living conditions, the intensityat which PA was performed –as well as its modality– did not tend to vary in a quick,fluctuating manner. Instead, long-term trends were most often maintained stable withoutchanges for periods that in general broadly exceeded the duration of the 2-min analysiswindow. To gain benefit from this behaviour, changes in PA intensity and modality weremodelled here as a Markovian process (appendix A.4), assumption which allowed the useof a HMM filtering approach for classification purposes.

The information provided by the clustering algorithms was incorporated in the followingmanner: a) cluster assignments were treated as the ‘observable’ Markovian process, eachcluster being considered an ‘observable symbol’ in HMM terminology; whereas b) the ‘hid-den’ process of interest would correspond to those PA classes (either for PA intensity ormodality, this depending on the problem being addressed) which most likely generated theobserved sequence of cluster assignments. Therefore, once the HMM had been trained –i.e.its emission and transition matrices estimated–, the application of Viterbi’s algorithm (ap-pendix A.4) retrieved the most likely succession of hidden states, which in turn representthe HMM outcomes in terms of the recognition of PA classes.

On the other hand, such a HMM filtering procedure would not be strictly necessary inthe case of using supervised classifiers, since the outcome predictions by those algorithmsdirectly correspond to the target PA classes. Consequently, a translation from clustersto classes as in the former situation is no longer required. Nevertheless, the HMM isstill potentially beneficial to help exploit temporal redundancy. Paralleling the approachdescribed above for clusterers, the observable Markov process would now be formed byPA predictions by the classifiers, whereas the hidden Markov process would correspondto the final –i.e. HMM-filtered– PA recognition. In this manner, this procedure allowsto integrate information about temporal trends and correlations from adjacent windows,aspects which cannot be taken into account solely by the classifiers from section 6.3.3.2,since they are general-purpose algorithms designed to treat each input data sample ascompletely independent and separate from the rest (i.e. without temporal relationships).

6.3.5 Practical aspects

6.3.5.1 Evaluating classification performance and model selection

The most frequent way to measure the performance attained by a certain classificationalgorithm is by means of its overall accuracy. However, here it was decided to use adifferent performance metric when selecting the most suitable model, i.e. the combinationof dimensionality reduction method plus pattern identification scheme which behaved beston these data. The rationale is that accuracy –calculated as the fraction of correctlyclassified samples– cannot reflect fairly achievements for under-represented classes [Formanand Scholz, 2010]; an issue which might in turn become critical in this case, due to themarked imbalance of examples representing each PA intensity class in the dataset (Table6.1, upper part). Instead, this works defines a custom performance metric as a compositescore aggregating: a) classification accuracy, and b) f -measures for each class underconsideration:

Score =1

C + 1

[

Accuracy +C∑

i=1

f -Measure(Classi)

]

(6.20)

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6. PA intensity and modality classification using accelerometry and HR

where C represents the total number of classes under consideration (being C = 3 for boththe PA intensity and modality problems), and where f -measure represents a performancemetric commonly used in the field of information retrieval [Forman and Scholz, 2010]. Moreprecisely, f -measure is defined as the harmonic mean between: a) precision –i.e. positivepredictive value–, and b) recall –i.e. sensitivity–:

f -Measure = 2Precision · Recall

Precision + Recall(6.21)

Precision =TruePos

TruePos + FalsePos(6.22)

Recall =TruePos

TruePos + FalseNeg(6.23)

Therefore, by definition (6.21) f -measure can only reach high values when both precisionand recall are simultaneously high.

For the sake of reliability in the assessments of performance, a stratified 10-fold cross-validation (CV) was carried out for PA intensity classification, repeating the whole pro-cess n=30 times in order to ascertain its variability. When allocating data across CVfolds, stratification was not done on a sample basis, because such procedure would havedismissed any information about temporal redundancy trends underlying in consecutivewindows. Instead, a block-based, or sequence-based stratified cross-validation (SBSCV)was implemented: each sequence –i.e. each block of PA data recorded during the same PAsession– was randomly assigned to a certain CV fold. Subsequently, folds were checked toverify if: a) the relative occurrence of the C classes in each fold did not deviate notablyfrom the overall priors (Table 6.1); and b) if the total number of data samples were similarfor all folds. In the event that any of these two conditions was violated, the randomizationwas repeated until both conditions were satisfied.

On the other hand, for the study of performance results in the task of classifying PAmodality, 5-fold SBSCV procedures –instead of 10-fold– were carried out due to the morerestrained number of sequences available about modality, which totalled 25 (Table 6.1).

6.3.5.2 Parameter tuning

All of the automated learning schemes under study here –except for logistic regression– re-quired the choice of certain key configuration parameters, often known as hyperparametersin the context of ML. Hyperparameters define important aspects of the learning procedure,for instance: the topology of the MLP network. Hence, an essential part of this work con-sisted in determining the most suitable values for those hyperparameters given the datasetunder study, with the aim at optimizing the performance of the classifiers as measuredvia the custom score metric presented in (6.20). For this tuning procedure, the space ofpossible parameter values was explored using grid search, with nested 10×10-fold SBSCVcarried out on data regarding PA intensity in order to assess performance.

For all of the clustering algorithms, a suitable number of clusters needed to be established.Other relevant hyperparameters –e.g. the linkage criterion in hierarchical clustering, orthe size and topology of the SOM network– were tested and chosen in a preliminary stage.This was done for simplicity reasons, i.e. to keep the parameter tuning procedure tractablein practise.

For the multinomial logistic regression, parameters were not required; whereas for theMLP, a suitable number of neurons in the hidden layer had to be selected. For the two

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6.4. Results

meta-classifiers (Bagging and Boosting), assuming that the hyperparameters for the ‘weaklearners’ (CART trees) were fully specified by MATLAB’s defaults, the parameter tuningprocedure consisted here in selecting an optimal number of ensembles, i.e. how manytraining iterations were performed. The most demanding case was for SVMs, where twohyperparameters needed to be set, namely: i) kernel bandwidth –σ in equation (6.18)–,and ii) the box constraint Cbox, which constitutes a penalty for misclassified samples duringtraining, thus regulating an eventual overfitting [Vapnik, 1998] (appendix A.3.4).

6.4 Results

6.4.1 Dimensionality reduction

Data items in the original 42-dimensional feature space are depicted in the scatter plotmatrix of Figure 6.8. The PCA projection was capable of covering >90% of total variance(exactly 91.43%) in a subspace built with only the 8 eigenvectors with highest associatedeigenvalues (Figure 6.9); whereas the LDA projection (Figure 6.10) generated two discrim-inants (i.e. C − 1, with C=3 PA classes under consideration here).

In the two cases of mRMR filter-based feature selection and for comparability reasons withrespect to PCA, the number of selected features was set fixed at 8. Among those eight, atotal of 5 features were selected by both the continuous (Figure 6.11) and discrete (Figure6.12) mRMR versions, namely:

• mean HR: hr• maximum HR: maxhr

• maximum step count: maxst

• mean HR multiplied by mean ‘pseudo-norm’ acceleration counts (log-transformed):hr · sign log(apn)

• percentage of activity counts in the main axis (a1) falling between ActiGraph’s defaultlower and upper cutpoints, as published by Freedson et al. [1998] (but rescaled by 1/6

to match 10 s epochs).

Iterative procedures for wrapper-based feature selections, either with greedy best-first orgenetic search strategies, were terminated whenever increases in the custom performancescore from (6.20) –assessed via SBSCV procedures– did no longer occur or were negligible.Specific feature selections were carried with each classification algorithm from section 6.3.3.2being wrapped. However, for brevity reasons Figures 6.13 and 6.14 depict only the outcomesfor those feature selection procedures in which the overall ‘wrapped’ performance score wascomputed as the average of scores attained by each classifier. In this case, the greedysequential search yielded an optimal subset composed of 9 features; whereas the solutionfound by genetic search contained notably more features, up to 27. The intersection betweenboth sets consisted of six common features. These were:

• mean activity counts in the main axis: a1

• mean step counts: st• mean HR: hr (in common with both mRMR filter-based solutions)• mean HR multiplied by mean ‘pseudo-norm’ acceleration counts, log-transformed:hr · sign log(apn) (also in common with both mRMR filters)

• maximum-to-minimum range for counts in the main axis (log-transformed): sign log(maxa1)• signal variability (log-transformed) for the ‘pseudo-norm’ activity counts: sign log(svapn

).

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6. PA intensity and modality classification using accelerometry and HR

Figure 6.8: Scatter plot matrix of the original 42-dimensional feature space. Each row andeach column in the matrix represent a feature, in such a manner that subpanels depictthe 2D projection of the dataset onto the two corresponding dimensions, hence allowing toshow mutual correlations. Subgraphs in the main diagonal depict 1D histograms for eachfeature. Blue, green and red points correspond respectively to low, moderate and vigorousPA intensities. A total of 5359 data instances (178.63 h) are plotted.

Of note, the cardinalities of subsets obtained by greedy procedures were consistently andmarkedly lower than for their genetic equivalents: ranging from 5 features in the Boosting-specific greedy solution to 10 in the Bagging-specific greedy wrapper; compared with 18features for the Boosting-specific genetic wrapper and with 29 in the SVM-specific geneticsolution. This behaviour may indicate that –at least for these classifiers and on the currentdataset– problems in performance associated with the so-called ‘curse of dimensionality’did not appear to be relevant until a relatively high number of dimensions.

6.4.2 Parameter tuning

Table 6.2 contains the final choices of hyperparameter values for each combination of di-mensionality reduction method and ML algorithm under consideration. Wrapper-basedfeature selection cases were not covered for any of the clustering approaches, since thesewrapper procedures rely by definition on a classifications which clusterers cannot provideon their own.

Of note, considerable variability can be observed in terms of choices for values, an aspectwhich points out the importance of this parameter tuning stage.

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6.4. Results

Figure 6.9: Scatter plot matrix of the reduced feature space resulting from PCA analysis:8 projected dimensions (i.e. newly extracted PCA features).

Figure 6.10: Scatter plot matrix of the reduced feature space resulting from LDA projection:2 extracted features.

92

6. PA intensity and modality classification using accelerometry and HR

Figure 6.11: Scatter plot matrix of the reduced feature space as obtained by mRMR filtering(continuous version): 8 selected features.

Figure 6.12: Scatter plot matrix of the reduced feature space as obtained by the mRMRfiltering (discrete version): 8 selected features.

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6.4. Results

Figure 6.13: Scatter plot matrix of the reduced feature space obtained by ‘wrapper’-basedselection algorithms, searching with a greedy best-first strategy and an overall performancescore averaging all five classifiers under consideration: 9 selected features.

Figure 6.14: Scatter plot matrix of the reduced feature space obtained by ‘wrapper’-basedselection algorithms, searching with a genetic strategy and an overall performance scoreaveraging all five classifiers under consideration: 27 selected features.

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6. PA intensity and modality classification using accelerometry and HR

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95

6.4. Results

6.4.3 Model selection

Tables 6.3–6.5 and Figures 6.15–6.18 summarize outcomes in terms of performance metrics(accuracy, f -measures and custom scores) for the task of PA intensity classification, asobtained during 10-fold SBSCV procedures for model selection.

Among the schemes based on clustering techniques for pattern identification, the highestperformance was achieved by the LDA+SOM combination, with a score of 84.67±0.57% andaccuracy 89.09±0.42% (mean±SD); followed by LDA+K-means and LDA+Hierarchicalclustering, both with slightly lower –although virtually identical– average scores (Table6.3). For a definitive selection, these three models were trained and evaluated in the recog-nition of PA modality during vigorous exercise, yielding respective scores of 77.94±5.93%,82.61±7.16% and 80.08±4.90%. Therefore, the LDA+K-means scheme was ultimatelyselected. Table 6.6 details its SBSCV performance in both PA intensity and modalityclassification.

On the other hand, among the schemes built on supervised classifiers, the best resultswere attained by the Bagging algorithm when applied on the feature space selected by theBagging-specific wrapper with genetic search methods. In particular, this model achieved atotal SBSCV performance score of 85.17±0.49%, with accuracy 89.66±0.35% (mean±SD)in the task of PA intensity recognition, as well as score 97.90±1.12% in the identificationof PA modality during vigorous exercise periods (Table 6.7).

6.4.4 Performance in classification

For a definitive assessment of the classification performance attained by the selected schemes,a leave-one-subject-out cross-validation (LOSOCV) was carried out. In this procedure, se-quences of data belonging to all individuals except one were used in successive turns totrain the algorithms, whereas data from the unseen subject served for testing purposes.

For the task of classifying PA intensity levels, LDA+K-means obtained a total performancescore of 84.65%, with accuracy 88.86% and respective f -measures of 95.59%, 72.28% and81.86% for low, moderate an vigorous intensity ranges (Table 6.8). Of note, when subject#A5 –who contributed with 45.83% of the total volume of data– was left aside from thetraining and used instead for testing, an outstanding recognition was reached, with a scoreas high as 96.69%. However, a similar LOSOCV procedure was not feasible for PA modal-ity identification, since only this individual #A5 collected data for the sustained aerobicmodality. On the other hand, the ML model formed by the combination of wrapper-basedfeature selection (genetic search, Bagging-specific wrapper) plus a Bagging classifier gener-alized with slightly lower performances than LDA+K-means, in particular: 83.06% scoreand 88.62% accuracy (Table 6.9); whereas its behaviour for subject #A5 was again abovethe average, with a score of 90.40%.

Figures 6.19–6.20 depict various example sequences concerning the classification of PA in-tensity, respectively generated by the LDA+K-means and Wrapper (genetic, specific)+Baggingalgorithms when trained by means of LOSOCV procedures. In general, mismatches withrespect to the ground truth tended to appear in either two situations:

i) around transitions in temporal trends in PA intensity ground truth, e.g. at approxi-mately 11/2, 21/2, 3, 6, 14 or 17 hours (panels A from both Figures 6.19 and 6.20), orat around 31/2, 12 or 17 h (panels B).

ii) where ground truth fluctuates rapidly in the short-term (panels C, D).

96

6. PA intensity and modality classification using accelerometry and HR

Tab

le6.

3:M

odel

sele

ctio

n,

clust

erin

gal

gori

thm

s–

SB

SC

Vp

erfo

rman

ces

inP

Ain

tensi

tycl

assi

fica

tion

Dim

ensi

onal

ity

redu

ctio

n:P

CA

Dim

ensi

onal

ity

redu

ctio

n:L

DA

mea

n±SD

K-m

ean

sG

MM

Hie

rarch

SO

MK

-mean

sG

MM

Hie

rarch

SO

M

(n=

30)

8fe

atur

es2

feat

ures

Accu

racy

84.6

7±0.

64%

86.8

5±0.

56%

84.5

9±0.

63%

84.8

4±0.

64%

88.8

3±0.

45%

88.2

3±0.

60%

88.8

1±0.

45%

89.0

9±0.

42%

f-Meas.

Low

93.5

4±0.

51%

94.5

0±0.

31%

93.3

8±0.

44%

93.7

1±0.

42%

95.5

6±0.

31%

95.3

7±0.

36%

95.5

8±0.

31%

95.8

5±0.

25%

Mod

erat

e64

.61±

1.15

%68

.35±

1.15

%66

.19±

1.46

%65

.90±

1.52

%71

.90±

1.11

%70

.50±

1.46

%71

.95±

1.05

%72

.22±

1.16

%V

igor

ous

74.3

4±1.

49%

78.7

6±1.

55%

72.5

3±1.

92%

72.5

0±1.

47%

82.0

1±0.

65%

80.7

6±1.

11%

81.7

7±0.

84%

81.3

8±0.

77%

Sco

re

79.2

9±0.

72%

82.1

1±0.

76%

79.1

7±0.

76%

79.2

4±0.

82%

84.5

7±0.

54%

83.7

2±0.

78%

84.5

3±0.

57%

84.6

7±0.

57%

Dim

ensi

onal

ity

redu

ctio

n:F

ilte

r–

mR

MR

Co

nti

nu

ou

sD

imen

sion

alit

yre

duct

ion:

Fil

ter–

mR

MR

Dis

crete

mea

n±SD

K-m

ean

sG

MM

Hie

rarch

SO

MK

-mean

sG

MM

Hie

rarch

SO

M

(n=

30)

8fe

atur

es8

feat

ures

Accu

racy

87.0

9±0.

61%

87.2

4±0.

61%

87.3

6±0.

59%

87.4

7±0.

43%

86.7

5±0.

35%

86.4

8±0.

47%

86.6

6±0.

54%

87.5

7±0.

57%

f-Meas.

Low

95.1

7±0.

37%

95.1

5±0.

30%

95.4

1±0.

39%

95.4

3±0.

33%

95.4

3±0.

27%

94.4

3±0.

28%

95.0

6±0.

31%

95.5

6±0.

40%

Mod

erat

e67

.86±

1.26

%67

.76±

1.42

%68

.10±

1.36

%68

.49±

1.03

%66

.64±

0.91

%68

.19±

1.29

%66

.84±

1.20

%68

.71±

1.21

%V

igor

ous

77.8

2±1.

20%

78.6

4±1.

31%

77.8

5±1.

01%

77.8

0±1.

00%

75.9

7±0.

88%

76.5

6±1.

29%

76.9

6±1.

06%

76.9

1±1.

10%

Sco

re

81.9

9±0.

76%

82.2

0±0.

85%

82.1

8±0.

72%

82.3

0±0.

55%

81.2

0±0.

44%

81.4

1±0.

67%

81.3

8±0.

68%

82.1

9±0.

68%

97

6.4. Results

Figure 6.15: SBSCV performance scores (%) in the task of PA intensity classification forthe different combinations of dimensionality reduction scheme and clustering algorithm,grouped first by dimensionality reduction method.

Figure 6.16: SBSCV performance scores (%) in the task of PA intensity classification forthe different combinations of dimensionality reduction scheme and clustering algorithm,grouped first by pattern identification procedure.

98

6. PA intensity and modality classification using accelerometry and HR

Tab

le6.

4:M

odel

sele

ctio

n,

clas

sifica

tion

algo

rith

ms

–SB

SC

Vp

erfo

rman

ces

inP

Ain

tensi

tycl

assi

fica

tion

(Con

tinues

.)

Dim

ensi

on

ali

tyre

du

ctio

n:

PC

AD

imen

sion

ali

tyre

du

ctio

n:

LD

A

mea

n±

SD

Lo

gis

tRe

gr

ML

PS

VM

Ba

gg

ing

Bo

ost

ing

Lo

gis

tRe

gr

ML

PS

VM

Ba

gg

ing

Ba

gg

ing

(n=

30)

8fe

atu

res

2fe

atu

res

Accu

ra

cy

86.4

0±

0.2

9%

86.0

9±

0.5

3%

87.1

9±

0.3

7%

88.7

7±

0.2

2%

84.9

3±

0.3

1%

88.1

0±

0.2

3%

87.6

7±

0.3

7%

88.2

5±

0.2

6%

88.6

6±

0.2

7%

87.3

6±

0.3

2%

f-Meas.

Low

94.5

5±

0.1

7%

93.8

6±

0.3

8%

94.6

4±

0.2

1%

95.9

2±

0.1

4%

93.9

6±

0.2

4%

94.9

7±

0.1

9%

94.6

5±

0.2

9%

95.0

8±

0.2

0%

95.8

7±

0.2

2%

94.5

3±

0.2

8%

Mo

der

ate

66.3

3±

0.6

9%

66.7

5±

1.0

4%

69.0

3±

0.8

9%

69.4

1±

0.6

8%

66.0

9±

0.6

1%

70.3

3±

0.5

4%

69.4

3±

0.8

6%

70.5

7±

0.6

4%

70.1

3±

0.7

1%

69.0

0±

0.6

2%

Vig

oro

us

77.5

1±

0.7

4%

78.9

1±

1.1

2%

78.8

5±

0.7

5%

79.9

8±

0.4

7%

73.6

0±

0.7

2%

81.6

5±

0.3

8%

81.5

5±

0.5

6%

81.5

9±

0.5

8%

79.5

6±

0.6

3%

80.9

6±

0.7

2%

Sco

re

81.2

0±

0.4

1%

81.4

0±

0.6

4%

82.4

3±

0.4

8%

83.5

2±

0.2

9%

79.6

4±

0.3

6%

83.7

6±

0.2

6%

83.3

2±

0.4

2%

83.8

7±

0.3

2%

83.5

5±

0.3

5%

82.9

6±

0.3

7%

Dim

ensi

on

ali

tyre

du

ctio

n:

Fil

ter–

mR

MR

Co

nti

nu

ou

sD

imen

sion

ali

tyre

du

ctio

n:

Fil

ter–

mR

MR

Dis

cre

te

mea

n±

SD

Lo

gis

tRe

gr

ML

PS

VM

Ba

gg

ing

Bo

ost

ing

Lo

gis

tRe

gr

ML

PS

VM

Ba

gg

ing

Bo

ost

ing

(n=

30)

8fe

atu

res

8fe

atu

res

Accu

ra

cy

86.6

2±

0.2

7%

86.7

2±

0.3

8%

86.9

2±

0.3

3%

88.7

1±

0.3

1%

86.3

2±

0.2

3%

85.9

3±

0.2

7%

86.2

6±

0.4

1%

87.6

6±

0.3

4%

88.4

9±

0.3

0%

86.2

8±

0.2

1%

f-Meas.

Low

94.3

5±

0.1

8%

94.0

2±

0.2

6%

94.3

4±

0.2

5%

95.7

6±

0.1

6%

94.2

7±

0.1

7%

94.4

9±

0.2

0%

94.1

0±

0.2

8%

94.8

2±

0.2

2%

95.7

5±

0.1

6%

94.2

8±

0.1

6%

Mo

der

ate

67.7

0±

0.7

7%

68.4

7±

0.8

7%

68.3

5±

0.6

8%

70.3

1±

0.7

8%

66.7

6±

0.4

4%

65.3

2±

0.5

7%

66.9

5±

0.9

0%

70.6

5±

0.7

6%

69.6

6±

0.7

6%

66.6

6±

0.4

4%

Vig

oro

us

78.7

6±

0.5

6%

80.0

0±

0.9

9%

79.6

8±

0.5

7%

80.2

1±

0.8

6%

78.5

1±

0.4

9%

76.1

5±

0.6

6%

78.6

0±

1.0

9%

79.4

7±

0.9

7%

79.4

2±

0.7

3%

78.3

3±

0.5

0%

Sco

re

81.8

6±

0.3

5%

82.3

0±

0.5

0%

82.3

2±

0.3

8%

83.7

5±

0.4

5%

81.4

7±

0.2

7%

80.4

7±

0.3

4%

81.4

8±

0.5

6%

83.1

5±

0.4

8%

83.3

3±

0.4

2%

81.3

9±

0.2

6%

99

6.4. Results

Tab

le6.5:

Model

selection,

classification

algorithm

s–

SB

SC

Vp

erforman

cesin

PA

inten

sityclassifi

cation

Dim

ensio

nality

redu

ction

:W

ra

pp

er–

Se

qu

en

tial

(Gre

ed

y)

Sp

ecifi

cD

imen

sion

ality

redu

ction

:W

ra

pp

er–

Se

qu

en

tial

(Gre

ed

y)

Ov

era

ll

mea

n±

SD

Lo

gistR

eg

rM

LP

SV

MB

ag

gin

gB

oo

sting

Lo

gistR

eg

rM

LP

SV

MB

ag

gin

gB

ag

gin

g

(n=

30)

9fea

tures

6fea

tures

9fea

tures

10

featu

res5

featu

res9

featu

res

Accu

ra

cy

87.1

9±

0.2

8%

86.6

2±

0.8

2%

87.6

4±

0.4

3%

89.2

9±

0.2

4%

86.1

9±

0.2

2%

87.1

0±

0.2

6%

86.6

5±

0.4

3%

88.1

9±

0.5

8%

89.1

7±

0.3

3%

86.1

1±

0.3

1%

f -Meas.

Low

94.4

4±

0.2

0%

94.0

5±

0.3

3%

94.2

6±

0.2

2%

95.8

1±

0.1

3%

94.6

1±

0.1

6%

94.3

5±

0.1

8%

94.2

2±

0.2

9%

94.4

7±

0.2

6%

95.9

5±

0.1

7%

94.4

9±

0.2

2%

Mo

dera

te68.5

8±

0.5

7%

67.7

9±

1.9

1%

70.9

5±

0.8

6%

71.8

8±

0.5

9%

66.9

1±

0.5

1%

68.5

6±

0.5

6%

67.4

2±

0.9

4%

72.3

8±

1.0

2%

71.7

8±

0.7

7%

66.8

2±

0.6

4%

Vig

oro

us

80.4

5±

0.6

1%

79.9

1±

1.5

6%

81.7

7±

1.2

6%

81.6

5±

0.6

2%

75.9

9±

0.2

9%

80.5

3±

0.5

1%

79.7

2±

1.0

9%

82.3

2±

1.6

0%

80.4

4±

1.1

9%

76.2

4±

0.3

6%

Sco

re

82.6

7±

0.3

3%

82.0

9±

1.1

0%

83.6

5±

0.6

0%

84.6

6±

0.3

4%

80.9

2±

0.2

6%

82.6

3±

0.3

1%

82.0

0±

0.5

5%

84.3

4±

0.8

0%

84.3

4±

0.5

3%

80.9

2±

0.3

4%

Dim

ensio

nality

redu

ction

:W

ra

pp

er–

Ge

ne

ticS

pe

cifi

cD

imen

sion

ality

redu

ction

:W

ra

pp

er–

Ge

ne

ticO

ve

ra

ll

mea

n±

SD

Lo

gistR

eg

rM

LP

SV

MB

ag

gin

gB

oo

sting

Lo

gistR

eg

rM

LP

SV

MB

ag

gin

gB

oo

sting

(n=

30)

21

featu

res17

featu

res29

featu

res19

featu

res18

featu

res27

featu

res

Accu

ra

cy

87.3

8±

0.3

7%

87.5

1±

0.4

4%

87.2

7±

0.2

9%

89.6

6±

0.3

5%

86.5

1±

0.2

6%

86.8

6±

0.3

8%

86.8

3±

0.4

7%

86.9

7±

0.4

7%

89.2

4±

0.2

8%

86.3

1±

0.2

4%

f -Meas.

Low

94.4

4±

0.2

6%

94.5

7±

0.2

9%

94.1

0±

0.2

4%

96.0

0±

0.1

6%

94.4

1±

0.1

9%

94.0

3±

0.3

0%

93.9

9±

0.3

3%

94.1

2±

0.2

8%

96.0

4±

0.1

4%

94.3

0±

0.1

6%

Mo

dera

te69.2

1±

0.7

8%

69.5

0±

0.9

7%

70.3

1±

0.6

2%

72.3

8±

0.7

7%

66.9

2±

0.5

5%

67.9

8±

0.8

1%

68.8

6±

1.0

8%

69.7

1±

0.8

5%

71.4

8±

0.5

9%

66.6

2±

0.4

6%

Vig

oro

us

81.1

1±

0.9

0%

80.9

9±

1.1

5%

81.0

4±

0.7

2%

82.6

4±

0.9

2%

78.6

2±

0.5

5%

81.1

3±

0.5

7%

80.4

1±

0.9

3%

79.8

2±

1.3

0%

81.0

7±

0.9

9%

78.4

4±

0.5

0%

Sco

re

83.0

4±

0.4

8%

83.1

5±

0.5

9%

83.1

8±

0.3

5%

85.1

7±

0.4

9%

81.6

1±

0.3

1%

82.5

0±

0.4

2%

82.5

2±

0.5

8%

82.6

5±

0.6

2%

84.4

6±

0.4

3%

81.4

2±

0.2

9%

100

6. PA intensity and modality classification using accelerometry and HR

Fig

ure

6.17

:SB

SC

Vp

erfo

rman

cesc

ores

(%)

inth

eta

skof

PA

inte

nsi

tycl

assi

fica

tion

for

the

diff

eren

tco

mbin

atio

ns

ofdim

ensi

onal

ity

reduct

ion

schem

ean

dsu

per

vis

edcl

assi

fica

tion

algo

rith

m,

grou

ped

firs

tby

dim

ensi

onal

ity

reduct

ion

met

hod.

101

6.4. Results

Figu

re6.18:

SB

SC

Vp

erforman

cescores

(%)

inth

etask

ofP

Ain

tensity

classification

forth

ediff

erent

combin

ations

ofdim

ension

alityred

uction

schem

ean

dsu

perv

isedclassifi

cationalgorith

m,

group

edfirst

by

pattern

iden

tification

pro

cedure.

102

6. PA intensity and modality classification using accelerometry and HR

Table 6.6: SBSCV performance of the LDA+K-means algorithm

mean±SD PA intensity (10-fold SBSCV) PA modality (5-fold SBSCV)(n=30) Low Moderate Vigorous Sustained aerobic Mixed Resistance

Accuracy 88.83±0.45% 83.37±6.93%

Precision 97.23±0.18% 72.32±1.47% 76.44±0.77% 81.33±6.03% 77.22±17.02% 92.35±3.45%Recall 93.94±0.51% 71.49±1.17% 88.46±0.90% 84.89±16.51% 77.94±7.33% 84.70±5.69%

f -Measure 95.56±0.31% 71.90±1.11% 82.01±0.65% 82.36±10.95% 76.46±10.60% 88.26±3.83%

Score 84.57±0.54% 82.61±7.16%

Table 6.7: SBSCV performance of the Wrapper (genetic, specific)+Bagging algorithm

mean±SD PA intensity (10-fold SBSCV) PA modality (5-fold SBSCV)(n=30) Low Moderate Vigorous Sustained aerobic Mixed Resistance

Accuracy 89.66±0.35% 98.08±0.97%

Precision 95.23±0.14% 78.50±1.82% 78.63±0.60% 98.27±1.93% 98.14±2.02% 97.92±0.90%Recall 96.77±0.31% 67.18±0.66% 87.09±1.62% 98.92±0.47% 95.14±3.85% 98.79±1.14%

f -Measure 96.00±0.16% 72.38±0.77% 82.64±0.92% 98.58±1.06% 96.57±2.29% 98.35±0.73%

Score 85.17±0.49% 97.90±1.12%

Table 6.8: LOSOCV confusion matrix for PA intensity classification, as attained by theLDA+K-means combination of algorithms. Each data item corresponds to a 2-min window.

Classification outcome

Low Moderate Vigorous

Gro

un

d

tru

th

Low 3297 194 22

Moderate 83 743 190

Vigorous 5 103 722

Table 6.9: LOSOCV confusion matrix for PA intensity classification, as attained by theBagging classifier when operating on the feature space reduced by the Bagging-specificwrapper with genetic search.

Classification outcome

Low Moderate Vigorous

Gro

un

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Low 3419 83 11

Moderate 140 694 182

Vigorous 18 176 636

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6.4. Results

These latter fluctuations had their origin in the specific exercise scheduling for Exp. B(PRONAF study protocol), where three vigorous bouts with duration 73/4 min were alter-nated with 5 min ‘active recovery’ periods. Long-term discrepancies rarely occurred sinceerrors tended to be brief in duration.

6.4.4.1 Impact of temporal filtering

In those scenarios embracing clustering techniques (section 6.3.3.1) for the identification ofrelevant signal patterns, the subsequent HMM stage served not only to transform clusterassignments –as a ‘smart quantization’ of data vectors [Duda et al., 2000]– into PA classes;but also to incorporate temporal trends beyond the scale of a single 2-min analysis window.Conversely, such a HMM filtering procedure would no longer be strictly necessary in thecase of supervised classifiers, since their outcome predictions correspond directly to thetargeted PA classes. Nevertheless, the application of HMMs can still be beneficial toexploit temporal redundancy across consecutive samples. In order to verify this aspect,the Bagging algorithm was evaluated under the same procedures as in precedent sections,although without the use of HMM.

In the SBSCV situation and with respect to Table 6.7, performances for the task of iden-tifying PA intensity decreased by ∼1% if HMMs were not employed; yielding a score of84.14±0.38% (mean±SD), accuracy 88.50±0.23% and respective f -measures for low, mod-erate and vigorous PA: 94.44±0.08%, 71.83±0.55% and 81.77±0.82% (n=30). A similarbehaviour was also observed for PA modality classification, with even more pronounceddecays (∼6%), to a score of 91.99±0.55%, accuracy 92.28±0.48% and f -measures for sus-tained aerobic, mixed and anaerobic exercises, respectively: 92.08±0.58%, 89.87±1.19%and 93.73±0.37%. In addition, the LOSOCV evaluation for PA intensity showed perfor-mance metrics which were also lower without HMMs, descending by ∼2–3% from a score83.06% and accuracy 88.62% (Table 6.9) to respectively 80.74% and 86.62%.

Besides, the positive effect in terms of classification performance and robustness, attributableto the incorporation of the HMM-based temporal filtering module, can be observed in avery illustrative, graphical manner. Figure 6.21 depicts recognition results obtained forthe same ground truth sequences as in Figures 6.19–6.20, in this occasion when not usingHMMs. Without HMM-based temporal filtering, automatic PA class assignments fluc-tuated remarkably more than in the ground truth data. This included cases in whichrecognition outcomes varied repeatedly from low to vigorous PA intensity and vice versawithin a few windows, a behaviour which is expectable to be extremely rare for groundtruth in practice, and which HMMs were successful in cancelling.

6.4.4.2 Comparison with other methodologies

6.4.4.2.1 Standard approaches in the application domainThe de facto standard technique to identify PA intensity levels with accelerometers con-ceived for PA monitoring is by means of ‘cutpoints’, i.e. by thresholds applied on the activ-ity counts recorded in the main accelerometry axis a1 [Freedson et al., 1998; Sasaki et al.,2011]. Indeed, this simple approach is the procedure implemented by ActiGraph’s com-mercial analysis software [ActiGraph LLC, 2010], which is extensively used and validatedby sports scientists and epidemiologist who study the degree of physical activeness acrosspopulations. For the sake of establishing fair comparisons, such cutpoint-based methodwas applied on the dataset under study here, where activity counts recorded for a1 wereaccumulated over 1 min epochs to match the methodology used in the original proposal

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6. PA intensity and modality classification using accelerometry and HR

in literature [Freedson et al., 1998]. This procedure yielded a modest performance scoreof 63.60%, with accuracy 77.45% and f -measures 87.19%, 61.01% and 28.56% respectivelyfor low, moderate and vigorous PA intensity categories.

In addition, this work also examined a MET estimation formula for ActiGraph accelerom-eters [Crouter et al., 2006], which is based on non-linear regressions for counts and widelyaccepted. MET estimation outcomes were subsequently grouped into their correspondingPA intensity level (<3, 3–6 or >6 METs). Results in this case were slightly inferior thanfor the former approach: score 63.15%, accuracy 77.56% and f -measures 87.46%, 62.20%and 25.39%.

Notably, both methods presented an important fraction of their errors corresponding tovigorous resistance exercise from Exp. B, which being static with respect to waist move-ments –i.e. the location where the accelerometry sensor was placed–, became classified asof low intensity as a consequence of accounting solely for activity counts.

6.4.4.2.2 ML baseline comparisonIn is important to remark that none of the two standard techniques inspected above (section6.4.4.2.1) were designed to incorporate HR-related information, an issue which may –atleast partially– explain their poor overall classification performance; in particular, theirfailure to recognize resistance activity appropriately. In order to compare results fromthe core proposal of this PhD thesis work with respect to methods capable of addressingthe merge of accelerometry and HR sources, two basic ML algorithms were implementedhere as baseline comparison, specifically CART decision trees and naïve Bayes classifiers.These two schemes were applied on a two-dimensional feature space combining: on the oneside a) the total activity counts in the main axis a1, accumulated over the 2 min windowperiods, and on the other hand b) the average HR. These two magnitudes should be –atleast intuitively [Brage et al., 2005]– the most informative signal descriptors, covering bothmechanical and physiological phenomena in relation to PA. CART decision trees performedslightly better with activity counts a1 expressed in natural units (score 72.27%, accuracy80.31% and f -measures 92.01%, 52.94% and 63.82% in LOSOCV); whereas the naïve Bayesclassifier worked best when operating on log-transformed a1 counts (score 76.79%, accuracy82.941% and f -measures 93.08%, 60.63% and 70.49% in LOSOCV).

Therefore, these two ML-based methods incorporating HR managed to improve notablythe performance outcome metrics with respect to the standard approaches in the domain(section 6.4.4.2.1), in overall and also concerning vigorous resistance patterns from Exp.B. Nonetheless, their scores are yet markedly inferior than those by the main proposalpresented here.

6.5 Discussion

This work proposed, compared and evaluated a series of ML algorithms for the activity-independent PA classification based on biaxial accelerometry and HR measurements, mergedtogether in order to combine motion and physiological aspects of PA, and to overcome thelimitations of each individual technique by separate. PA intensity levels, as well as exercisemodality for vigorous periods, were recognized.

In literature, the majority of ML-based PA classification strategies follow an activity-specific recognition approach, having proved themselves capable of discerning –with notable

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accuracies– among a closed set of activity options performed in controlled laboratory envi-ronments. However, the range of activities embraced by these activity-specific approaches(generally: lie, sit, stand, walk, run and/or bicycle) may in practise be excessively limitedas to apply these methods in the monitoring of free-living ambulatory scenarios, where aconsiderably more varied collection of both PA and non-PA patterns occur. In this regard,the dataset under consideration in this work encompassed an appreciable variety of situ-ations, including daily life activities and the use of means of transportation (allowing thealgorithms to learn eventual artefact patterns caused by them), as well as assorted PAs,e.g.: dancing, karate, soccer or resistance/weight training, which correspond to real-lifescenarios rarely covered by other works conduced in laboratory environments.

To address such heterogeneity, an activity-independent PA classification approach wasadopted to discern between standard intensity levels (<3, 3–6, >6 METs). Furthermore,this work constituted the first known attempt to identify PA modality, an aspect which canbe of interest in practical applications, e.g. in artificial pancreas systems for the manage-ment of T1D, where distinct acute glycaemic responses occur depending on the predominantmetabolic pathway involved in the fuelling of exercise.

The aggregation of accelerometry –reflecting displacements– and HR –as a physiologicallysound marker in close relation to PA-induced loads on the cardiovascular system– consti-tutes a promising strategy for which sports scientists advocate [Freedson and Miller, 2000;Ainslie et al., 2003; Valanou et al., 2006; Westerterp, 2009]. However, this approach has notyet gained extensive benefit from the application of ML algorithms, since research effortshave been mainly focused on mining exclusively accelerometry data, specially for activity-specific recognition. In this regard, it is surprising and counter-intuitive that Munguia Tapiaet al. [2007] discarded HR-based features for not improving sufficiently their activity-specificPA recognition; whereas, on the contrary, notorious success in PA intensity classificationwas reported by Lin et al. [2012] when merging accelerometry and ECG data. Authorsemployed a sensor network formed by three triaxial accelerometers (placed on wrist, waistand ankle) plus an ECG recorder to obtain outstanding classification rates. However,their approach suffers from certain limitations, mainly: a) the constraint heterogeneity oftheir data –which were collected in a controlled laboratory environment with few differentactivities–, b) the complexity of the sensor network, and c) eventual validity issues of thedevices during field use. In this regard, this work opted for widely validated commercialdevices as ActiGraph, which are among the de facto standard equipment in the ambulatorymonitoring of PA by sports scientists and epidemiologists. Nevertheless, their output inthe form of counts, along with the 10-s epoch limitation imposed by ActiGraph’s firmwarewhen registering HR data, prevented from carrying out any spectral or wavelet analysis onthe accelerometry signals, which could have provided information-rich features [Bao andIntille, 2004].

A total of 178.63 h (5359 windows, each with duration 2 min) of multi-modal data werecollected here in 92 sequences/sessions from a diverse population formed by 16 subjects (9males and 7 females, age range 20–49), healthy and overweight individuals with differentlifestyles. Despite the limited number of participants, results concerning performance inthe PA intensity classification task as obtained in the LOSOCV procedures were compa-rable (scores: 83.06% for Wrapper+Bagging, 84.65% for LDA+K-means) to those fromthe SBSCV used during model selection (mean scores: 85.17% and 84.57%, respectively),although slightly inferior for the case of Bagging. In addition, the LOSOCV partial re-sults obtained when leaving subject #A5 (81.87 h of data) out of the training set were

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highly satisfactory, with a performance score of 90.40% for Wrapper+Bagging and 96.69%for LDA+K-means. These two aspects indicate good generalization capabilities by bothalgorithms, with a perceptible advantage for the LDA+K-means scheme in terms of gen-eralizability. Hence, overfitting to the available data is unlikely to have occurred. On theother hand, there was a marked superiority of Wrapper+Bagging in the task of PA modal-ity classification: mean score 97.90% versus 82.61% in LDA+K-means.

Classifiers employed HR measurements without the need for subject-specific resting basalHR compensations, an aspect which may constitute a major advantage for the monitoringof large populations, removing the burden of individualized calibration procedures [Valanouet al., 2006].

In order to establish fair evaluations of the performance obtained on this work’s particulardataset by different types of solutions –and inspired by the approach followed by [Freedsonet al., 2011] to validate their proposal–, results were compared against two methods whichcan be considered current standards in this application domain: Freedson et al. [1998];Crouter et al. [2006]. Both schemes suffered serious performance problems, particularly toidentify vigorous resistance exercise periods from Exp. B. This behaviour should not behowever surprising, since this type of PA did not involve pronounced waist movements andoperated only with ActiGraph’s accelerometry data, not incorporating HR as a relevantsource of physiological information. In this regard, two additional ML-based classifiers –specifically CART trees and naïve Bayes (NB)– were implemented as baseline comparisons.These CART and NB schemes learnt from data comprising: a) the total activity countsin the main axis a1, and b) the mean HR along the window; considered as the two mostinformative features, at least intuitively [Brage et al., 2005]. With scores 72.27% and 76.79%in LOSOCV, these two methods outperformed the aforementioned approaches withoutML [Freedson et al., 1998; Crouter et al., 2006], although they were yet considerably lessaccurate than this PhD works’ proposals.

Freedson et al. [2011]; Trost et al. [2012], in the context of developing MLP-based METestimators for respectively adult and paediatric populations, also addressed the problem ofPA intensity classification. Results reported by Freedson et al. [2011] (score 75.78%, accu-racy 76.99% and f -measures 84.36%, 75.08% and 66.67%) show a perceptible, yet moderateimprovement with respect to the non-ML standard methodologies [Freedson et al., 1998;Crouter et al., 2006], which yielded scores 70.03%, 71.52%. Nevertheless, this improve-ment due to their MLP neural networks is more modest than in this work’s case. On theother hand, the different criterion adopted by [Trost et al., 2012] when defining their fourintensity intervals, along with their methodology to report results (which was focused onrecall/sensitivity criteria only), prevented establishing direct comparisons in terms of per-formance.

Finally, given that most of classification errors tended to appear around transients in groundtruth, instead of as long-term mismatches (Figures 6.19-6.20), the overall impact and po-tential loss of quality in the recognition –as caused by those transient errors– should bein practice limited for realistic ambulatory applications. In this regard, the HMM was ca-pable of exploiting successfully temporal redundancy in data, when long-term trends weremaintained stable. However, it had moderate difficulties to match quick fluctuations inthe ground truth from the short-interval training protocol from Exp. B. Anyhow, it isexpected that such quick oscillations would be infrequent in practical free-living scenariosand lifestyle monitoring.

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Part IV

Metabolic modelling in T1D

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Chapter 7

State of the art

Mechanistic metabolic models for T1D –i.e. mathematical descriptions of the physiologicalfluxes which lead to glucose-insulin homoeostasis– are essential for the development andevaluation of new therapies, in particular for the progress and consolidation of artificialpancreas systems. As one of their key applications, metabolic models allow for simulatingand validating in silico decision support strategies and closed-loop controllers in a safer,quicker and more affordable manner than animal or human experiments. This includesthe virtual simulation of certain situations which would otherwise pose major health risksto patients. Nonetheless, clinical trials on humans will remain to be the unique means ofevaluating the suitability of therapeutic proposals under real circumstances [Cobelli et al.,2009].

7.1 Metabolic models for T1D

Since the first models for glucose-insulin homoeostasis were proposed in the late 1970s –mainly by Guyton et al. [1978]; Bergman et al. [1979]–, a considerable number of othermodels have been added. Whereas a profound review of those can be found elsewhere [Co-belli et al., 2009]; this section overviews two models which are arguably the most renownedin literature.

7.1.1 Padova model

Approved in 2008 by USA’s Foods and Drugs Administration (FDA) as a substitute toanimal tests [Kovatchev et al., 2009], the Padova model [Dalla Man et al., 2006, 2007]was developed using a dataset with glucose profiles from 204 healthy individuals withoutdiabetes, who underwent a meal experiment [Dalla Man et al., 2006] with a triple-tracerprotocol in order to obtain temporal curves about relevant glucose and insulin fluxes in avirtually model-independent manner [Basu et al., 2003]. The version of the model presentedhere includes certain particularizations to adapt it for T1D [Magni et al., 2008], e.g. witha lack of endogenous insulin production.

Superindices b are onwards used to denote steady-state basal regimes applied to the initialconditions for the mass-balance differential equations which are constitutive of the model.

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Table 7.1: Input variables for the Padova model

IIR(t) Insulin infusion rate (exogenous) [pmol/kg·min−1]D(t) Rate of glucose ingestion [mg·min−1]

Table 7.2: Output variables for the Padova model

GIV (t) Intravenous (i.e. plasma) glucose concentration [mg/dL]GSC(t) Subcutaneous (i.e. interstitial) glucose concentration [mg/dL]

I(t) Insulin concentration in plasma [pmol/L]

Table 7.3: State variables for the Padova model

GP (t) Glucose mass in the plasma compartment [mg/kg]GT (t) Glucose mass in tissues equilibrating slowly with plasma [mg/kg]

EGP (t) Endogenous glucose production [mg/kg·min−1]E(t) Renal excretion [mg/kg·min−1]

RA(t) Rate of appearance of meal-attributable glucose in plasma [mg/kg·min−1]UII(t), UID(t) Insulin-independent and insulin-dependent glucose utilizations, respectively [mg/kg·min−1]

VM (t) Michaelis-Menten V variable modulating UID(t) [mg/kg·min−1]X(t) Insulin concentration in interstitial fluid [pmol/L]

IL(t), IP (t) Insulin mass in liver and plasma, respectively [pmol/kg]S1(t), S2(t) Subcutaneous masses of non-monomeric (S1) and monomeric (S2) insulin [pmol/kg]

ID1(t), ID2(t) Concentration of delayed insulin in compartments #1 and #2 [pmol/L]QSto(t) Total glucose mass in the stomach [mg]

QSto1(t), QSto2(t) Glucose mass in the stomach, respectively in solid and liquid phases [mg]QGut(t) Glucose mass in the intestine [mg]

Table 7.4: Parameters for the Padova model

VG Distribution volume for glucose [dL/kg]k1, k2 Rate of glucose transfer from plasma to interstitium (k1) and vice versa (k2) [min−1]

kE1 Rate of renal excretion [min−1]kE2 Glucose threshold for renal excretion [mg/kg]kP 1 Endogenous glucose production extrapolated at zero glucose and zero insulin [mg/kg·min−1]kP 2 Liver glucose effectiveness [min−1]kP 3 Amplitude of insulin action on the liver [mg/kg·min−1 per pmol/L]

FCNS Glucose uptake from the central neural system, brain and erythrocytes [mg/kg·min−1]KM0 Michaelis-Menten K parameter of glucose utilization at zero insulin action [mg/kg]VM0 Michaelis-Menten V parameter of glucose utilization at zero insulin action [mg/kg·min−1]

VMXSensitivity of the Michaelis-Menten V parameter to changes in insulin concentration X

[mg/kg·min−1 per pmol/L]VI Distribution volume for insulin [dL/kg]

m1, m2 Rate of insulin transfer from liver to plasma (m1) and vice versa (m2) [min−1]m3, m4 Rate of insulin disposal from liver (m3) and from plasma (m4) [min−1]

kA1, kA2 Rate of absorption for non-monomeric (kA1) and monomeric (kA2) insulin [min−1]kD Rate of insulin dissociation [min−1]

p2U Rate constant for insulin action on peripheral glucose utilization [min−1]kI Rate constant for the delay between insulin signal and action [min−1]

kGri, kGut, kAbs Rate of grinding, gastric emptying and intestinal absorption, respectively [min−1]f Fraction of intestinal absorption appearing in plasma [dimensionless]

BW Body weight [kg]kMax, kMin Maximal and minimal values for kGut [min−1]

b, d Rate parameters regulating the speed of change for kGut over time [dimensionless]tI , tF Initial and final times for meal intake, respectively [min]

kSC Rate of transfer for subcutaneous glucose concentrations [min−1]

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7.1.1.1 Glucose subsystem

This part of the model comprises two glucose mass compartments, where: i) the accessibleone represents plasma and tissues which equilibrate rapidly with respect to plasma glucoseconcentrations, and where ii) the non-accessible compartment encompasses other tissueswhich equilibrate in a slower manner.

Mass-balance differential equations regulating fluxes are stated by the authors as follows:

d

dtGP (t) = −k1GP (t) + k2GT (t) + EGP (t)− UII(t)− E(t) +RA(t) (7.1)

d

dtGT (t) = k1GP (t)− k2GT (t)− UID(t) (7.2)

GP (t = 0) = GbP (7.3)

GT (t = 0) = GbT (7.4)

where (7.3)–(7.4) cover the basal steady-state conditions.

Besides, plasma glucose concentration –as it would be measured if intravenous blood sam-ples were to be taken– is associated to GP mass in plasma by the following relationship:

GIV (t) =GP (t)

VG

(7.5)

7.1.1.1.1 Renal excretionAuthors model renal excretion with a thresholded activation behaviour, in which a) excre-tion only occurs when glucose mass surpasses a certain level kE2, and b) its rate of excretionis in proportion with the excess of mass over such kE2 threshold:

E(t) =

{

kE1 [GP (t)− kE2] if GP (t) > kE2

0 if GP (t) ≤ kE2(7.6)

7.1.1.1.2 Endogenous glucose productionBody’s endogenous glucose production (EGP) is assumed to be modulated by: a) currentplasma glucose GP , and b) a delayed insulin signal ID2 detailed later on in section 7.1.1.2.3:

EGP (t) = max {0, kP 1 − kP 2GP (t)− kP 3ID2(t)} (7.7)

EGP (t = 0) = EGP b (7.8)

where (7.7) includes a particularization for T1D situations [Magni et al., 2008] with respectto the general model first published by Dalla Man et al. [2007], which consists in dismissingendogenous insulin in the portal vein (i.e. IP o = 0), since in T1D there does not exist anyendogenous insulin production altogether.

7.1.1.1.3 Glucose utilization

Insulin-independentThe Padova model characterizes the insulin-independent glucose utilization UII as a con-stant uptake in response to sustained glucose demands from the brain and central nervoussystem. Therefore:

UII(t) = FCNS (7.9)

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Insulin-dependentThe portion of absorbed glucose UID which is dependent on insulin concentrations is as-sumed by authors to follow a non-linear Michaelis-Menten relationship:

UID(t) =GT (t)

KM0 +GT (t)VM(t) (7.10)

where its K parameter is constant and equal to KM0, and where its V term introduces inturn the effect of insulin X in the process:

VM(t) = VM0 + VMXX(t) (7.11)

7.1.1.2 Insulin subsystem

Two insulin compartments with masses IL, IP are defined, the first of which correspondsto the liver and the second one to plasma:

d

dtIL(t) = − (m1 +m3) IL(t) +m2IP (t) (7.12)

d

dtIP (t) = m1IL(t) + (m2 +m4) IP (t) + kA1S1(t) + kA2S2(t) (7.13)

IL(t = 0) = IbL (7.14)

IP (t = 0) = IbP (7.15)

In practise, blood samples would be taken from plasma in order to measure insulin con-centrations I, which would be proportional to the total insulin mass IP and distributed inthe corresponding volume for insulin VI :

I(t) =IP (t)

VI

(7.16)

In formulae (7.12)–(7.13), several T1D-specific modifications apply with respect to theoriginal model for healthy subjects [Dalla Man et al., 2007]. These particularizations are[Magni et al., 2008]: i) m3 is assumed to be constant, ii) there does not exist any S termaddressing pancreatic insulin secretion in equation (7.12) for IL; but instead iii) masses S1,S2 are introduced in equation (7.13) to represent exogenous insulin absorptions towardsthe plasma insulin compartment IP .

7.1.1.2.1 Subcutaneous insulin absorptionExogenous insulin infused through the subcutaneous route at a known rate IIR passestwo diffusion compartments, modelled by masses S1, S2. S1 accounts for the amount ofnon-monomeric insulin, which is either transformed into the monomeric form at a rate kD,or enters circulation at a different rate kA1; whereas in turn the mass of monomeric insulinS2 becomes absorbed at a rate kA2:

d

dtS1(t) = − (kA1 + kD)S1(t) + IIR(t) (7.17)

d

dtS2(t) = kDS1(t)− kA2S2(t) (7.18)

S1(t = 0) = Sb1 (7.19)

S2(t = 0) = Sb2 (7.20)

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7.1.1.2.2 Remote effectMagnitude X covers the influence of the insulin signal on glucose absorption (section7.1.1.1.3). Authors model this remote action X via a single compartment, governed bythe following first-order linear differential equation:

d

dtX(t) = −p2UX(t) + p2U

[

I(t)− Ib]

(7.21)

X(t = 0) = 0 (7.22)

where Ib in (7.21) represents the basal insulin concentration in steady-state conditions. Atthe view of (7.15) and (7.16), Ib must equal:

Ib =Ib

P

VI

(7.23)

7.1.1.2.3 Delayed insulin signalFor the delayed insulin signal affecting EGP, authors consider two compartments withidentical transfer rate kI and the same initial conditions as in (7.23):

d

dtID1(t) = −kIID1(t) + kII(t) (7.24)

d

dtID2(t) = kIID1(t)− kIID2(t) (7.25)

ID1(t = 0) = Ib (7.26)

ID2(t = 0) = Ib (7.27)

7.1.1.3 Absorption of meal glucose

According to authors’ proposal, three compartments are involved in the absorption of mealglucose by the intestine: two of which correspond to glucose masses temporarily stored inthe stomach (either in solid QSto1 or liquid phase QSto2), plus a third compartment QGut

for the gut:

d

dtQSto1(t) = −kGriQSto1(t) +D(t) (7.28)

d

dtQSto2(t) = kGriQSto1(t)− kGut (t, QSto)QSto2(t) (7.29)

d

dtQGut(t) = kGut (t, QSto)QSto2(t)− kAbsQGut(t) (7.30)

QSto1(t = 0) = 0 (7.31)

QSto2(t = 0) = 0 (7.32)

QGut(t = 0) = 0 (7.33)

where the total amount of glucose in the stomach must therefore sum:

QSto(t) = QSto1(t) +QSto2(t) (7.34)

Magnitude D in (7.28) is the rate at which the subject ingests glucose [mg/min], and RA

in (7.1) is the rate of appearance of meal-attributable glucose in the blood stream, derivedfrom QGut according to the following expression:

RA(t) = fkAbs

QGut(t)

BW(7.35)

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7.1. Metabolic models for T1D

Of note, the rate of gastric emptying kGut in (7.29)–(7.30) comprises an intricate time-varying non-linear dependency on the total mass of glucose in the stomach QSto (7.34),namely:

kGut (t, QSto) = kMin +kMax − kMin

2

{

tanh[

α(

QSto − bD)]

− tanh[

β(

QSto − dD)]

+ 2}

(7.36)where parameters α, β in turn depend on b, d (Table 7.3):

α =5

2D(1− b)(7.37)

β =5

2Dd(7.38)

D = QSto(tI) +∫ tF

tI

D(τ)dτ (7.39)

7.1.1.4 Subcutaneous measurements

A simple diffusion equation is proposed to describe the relationship between plasma glucoseconcentrations and their subcutaneous counterparts, i.e. levels in interstitum, where CGMmeasurements are taken:

d

dtGSC(t) = −kSCGSC(t) + kSCGIV (t) (7.40)

GSC(t = 0) = GIV (t = 0) =Gb

P

VG

(7.41)

with initial steady-state conditions (7.41) in accordance to (7.3), (7.5).

7.1.2 Cambridge model

First introduced in 2002 [Hovorka et al., 2002], the Cambridge glucoregulatory model forT1D constitutes the core of an in silico simulation environment with 18 virtual patientswhose parameters were directly obtained by fitting clinical data from real patients withT1D [Wilinska et al., 2010]. Moreover, it is also the supporting patient model for a MPCartificial pancreas control algorithm which has consistently shown very meritorious andpromising results in a series of clinical trials in diverse scenarios: from the critical careunit [Leelarathna et al., 2013] to free-living outpatient environments [Elleri et al., 2014;Leelarathna et al., 2014; Thabit et al., 2014; Hovorka et al., 2014], as well as applied onadolescent subjects [Elleri et al., 2013b], T2D patients [Kumareswaran et al., 2013b] andpregnant women with T1D [Murphy et al., 2011].

Superindices 0 onwards denote steady-state initial conditions at t = 0.

7.1.2.1 Glucose subsystem

The Cambridge model characterizes glucose kinetics with a two-compartmental model cov-ering the distribution, production and utilization of glucose; along with the remote influenceof insulin on all those three processes. Notably, the validity of this glucose model –as well

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7. State of the art

Table 7.5: Input variables for the Cambridge model

UI(t) Rate of insulin administration (exogenous) [pmol/kg·min−1]D(t) Rate of carbohydrate ingestion [µmol/kg·min−1]

Table 7.6: Output variables for the Cambridge model

GIV (t) Intravenous (i.e. plasma) glucose concentration [mmol/L]GSC(t) Subcutaneous (i.e. interstitial) glucose concentration [mmol/L]

I(t) Insulin concentration in plasma [pmol/L]

Table 7.7: State variables for the Cambridge model

Q1(t), Q2(t) Glucose masses in the accessible and non-accessible compartments, respectively [µmol/kg]EGP (t) Endogenous glucose production [µmol/kg·min−1]

F01(t) Total non-insulin-dependent glucose flux [µmol/kg·min−1]FR(t) Renal glucose clearance [µmol/kg·min−1]UG(t) Glucose absorption flux from the gut [µmol/kg·min−1]k21(t) Rate of glucose transfer from the accessible to the non-accessible compartment [min−1]k02(t) Rate of glucose disposal from the non-accessible compartment [min−1]X1(t) Remote effect of insulin on glucose distribution and transport [min−1]X2(t) Remote effect of insulin on glucose disposal [min−1]X3(t) Remote effect of insulin on endogenous glucose production [dimensionless]

SSC1(t), SSC2(t) Insulin masses in subcutaneous compartments #1 and #2 [pmol/kg]SP (t) Insulin mass in plasma [pmol/kg]

G1(t), G2(t) Glucose masses in gut compartments #1 and #2 [µmol/kg]

Table 7.8: Parameters for the Cambridge model

VG Glucose distribution volume [L/kg]k12 Rate of glucose transfer from the non-accessible to the accessible compartment [min−1]

RCl Renal clearance rate [min−1]RT hr Renal clearance threshold [mmol/L]

EGP0 Endogenous glucose production extrapolated to zero insulin concentration [µmol/kg·min−1]F01 Non-insulin-dependent glucose disposal flux [µmol/kg·min−1]VI Insulin distribution volume [L/kg]

kA, kE Insulin absorption and elimination rates, respectively [min−1]kA1, kA2, kA3 Deactivation rates for remote effects X1, X2 and X3, respectively [min−1]

SIT Insulin sensitivity of glucose transport and distribution [min−1 per mU/L]SID Insulin sensitivity of glucose disposal [min−1 per mU/L]SIE Insulin sensitivity of suppression of endogenous glucose production [per mU/L]Bio CHO bioavailability [dimensionless]

tMax Time-to-maximum for CHO absorption [min]

kA,IntTransfer-rate constant between plasma glucose and subcutaneous/interstitial compartments[min−1]

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7.1. Metabolic models for T1D

as of its counterpart for insulin action (section 7.1.2.2)– was demonstrated for healthy sub-jects during an intravenous glucose tolerance test (IVGTT) [Hovorka et al., 2002; Wilinskaet al., 2010]. Fluxes are described by the following mass-balance differential equations:

d

dtQ1(t) = −k21(t)Q1(t) + k12Q2(t) + EGP (t)− F01(t)− FR(t) + UG(t) (7.42)

d

dtQ2(t) = k21(t)Q1(t)− [k12 + k02(t)]Q2(t) (7.43)

Q1(t = 0) = Q01 (7.44)

Q2(t = 0) = Q02 (7.45)

Glucose mass Q1 in the accessible compartment is distributed in the corresponding volumefor glucose VG. Therefore, the relationship between Q1 and the intravenous –i.e. plasma–glucose concentration GIV is as follows:

GIV (t) =Q1(t)

VG

(7.46)

7.1.2.1.1 Glucose renal excretionThe elimination of glucose excesses by the kidneys is assumed to commence above a certainthreshold valueRT hr, with a clearance rate which grows linearly with glycaemia levels higherthan RT hr:

FR(t) =

{

RCl [GIV (t)−RT hr]VG if GIV (t) ≥ RT hr

0 otherwise(7.47)

Of note, this particular aspect of the glucose-insulin dynamics is equivalent in both theCambridge and Padova model proposals.

7.1.2.1.2 Endogenous Glucose ProductionAuthors capture the remote effect of insulin on EGP by means of an auxiliary magnitudeX3 which acts by lowering glucose production as a consequence of higher insulin levels:

EGP (t) =

{

EGP0 [1−X3(t)] if X3(t) < 10 otherwise

(7.48)

where EGP0 represents a reference endogenous production rate extrapolated to a limit casein which insulin is not available at all, i.e. when X3 = 0.

7.1.2.1.3 Glucose utilization

Insulin-independentThe most recent version of the Cambridge model [Wilinska et al., 2010] characterizes therate at which a portion of glucose gets disposed from plasma (in a regime totally inde-pendent from insulin concentrations) by means of a saturable process whose disposal fluxfollows a Michaelis-Menten relationship:

F01(t) =1

F S01

GIV (t)

KM +GIV (t)F01 (7.49)

being F S01=0.85 (dimensionless) a known correction factor [Wilinska et al., 2010], and where

KM=1.0 mmol/L is a fixed constant across individuals.

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7. State of the art

Insulin-dependentIn this case, the insulin-dependent glucose utilization is formed by two components. Onthe one side, it comprises a remote effect of insulin X1 which equals by definition the rateof glucose distribution/transport from the accessible to the non-accessible compartment.Thus:

k21(t) = X1(t) (7.50)

On the other hand, it also incorporates a remote effect of insulin X2 on the rates of disposalfrom the non-accessible glucose compartment:

k02(t) = X2(t) (7.51)

7.1.2.2 Insulin subsystem

7.1.2.2.1 Subcutaneous insulin absorption and kineticsThe block which describes the absorption of insulin is formed by three compartments[Wilinska et al., 2005]: two subcutaneous insulin depots –one accessible SSC1 and one non-accessible SSC2, both characterized by identical transfer rates kA– plus a subsequent plasmacompartment whose mass is represented by the variable SP as follows:

d

dtSSC1(t) = −kASSC1(t) + UI(t) (7.52)

d

dtSSC2(t) = kASSC1(t)− kASSC2(t) (7.53)

d

dtSP (t) = kASSC2(t)− kESP (t) (7.54)

SSC1(t = 0) = S0SC1 (7.55)

SSC2(t = 0) = S0SC2 (7.56)

SP (t = 0) = S0P (7.57)

where UI denotes the rate of exogenous insulin infusion.

Accordingly, plasma insulin concentration –as it would be measured through blood samples–corresponds to the total insulin mass in plasma SP divided by the corresponding distributionvolume for insulin VI . Hence:

I(t) =SP (t)

VI

(7.58)

7.1.2.2.2 Remote effectOriginating from a study which involved multiple-tracer experiments in healthy subjects[Hovorka et al., 2002], this module of the Cambridge model characterizes insulin action byencompassing three different remote effects of insulin on various aspects of glucose kinetics:i) the influence of insulin on the transport and distribution of glucose, ii) its effect ondisposal, and finally iii) on EGP. This part of the Cambridge model originated from an studyinvolving multiple-tracer experiments in healthy subjects . Relevant model parametersinclude, among others, three insulin sensitivities SIT , SID, SIE which are respectively

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7.1. Metabolic models for T1D

associated to X1 (transport/distribution), X2 (disposal) and X3 (EGP suppression):

d

dtX1(t) = −kA1X1(t) + kA1SIT I(t) (7.59)

d

dtX2(t) = −kA2X2(t) + kA2SIDI(t) (7.60)

d

dtX3(t) = −kA3X3(t) + kA3SIEI(t) (7.61)

X1(t = 0) = 0 (7.62)

X2(t = 0) = 0 (7.63)

X3(t = 0) = 0 (7.64)

7.1.2.3 Absorption of meal glucose

Authors represent the physiological processes for the absorption of meal-attributable glu-cose which occurs in the gut by means of a two-compartmental model, in which bothcompartments in the chain share identical fractional transfer rates. Of note, this part ofCambridge model was shown to be adequate in the capture and representation of glucose’srate of appearance in plasma from the gastrointestinal tract [Hovorka et al., 2007; Wilinskaet al., 2010]. In particular, it comprises two key parameters: i) CHO bioavailability Bio,and ii) time tMax for the appearance of a peak (i.e. maximum) in terms of glucose levels:

d

dtG1(t) = −

1

tMax

G1(t) +Bio ·D(t) (7.65)

d

dtG2(t) =

1

tMax

G1(t)−1

tMax

G2(t) (7.66)

G1(t = 0) = 0 (7.67)

G2(t = 0) = 0 (7.68)

being UD the rate of ingestion of CHO by the subject, expressed in [µmol/kg·min−1]. Inaccordance, the resulting absorption rate by the gut UG to be used in (7.42) can be derivedfrom glucose masses as follows:

UG(t) =G2(t)

tMax

(7.69)

7.1.2.4 Subcutaneous measurements

Interstitial glucose kinetics is represented by a diffusion process between plasma and inter-stitium compartments, characterized by a constant transfer rate kA,Int which defines thedelay of subcutaneous glucose GSC with respect to the intravenous plasma kinetics GIV :

d

dtGSC(t) = −kA,IntGSC(t) + kA,IntGIV (t) (7.70)

GSC(t = 0) = GIV (t = 0) =Q0

1

VG

(7.71)

where initial conditions (7.71) are in accordance with (7.44), (7.46).

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7. State of the art

7.2 Overview and extensions

The Padova model gained important renown after being approved by the FDA in 2008 forin silico simulations in replacement for animal tests. Nevertheless, the same authors havepublished a number of extensions ever since. Notably, Dalla Man et al. [2009]– proposedand compared three candidate modifications to incorporate the known physiological effectsof PA in the form of decays in glycaemia. The first of those models assumed: a) anexercise-induced rise in non-insulin-dependent glucose clearance, with quick activation anddeactivation; plus b) a rapid increase in insulin sensitivity, followed by a slow return tonormal levels [Breton, 2008]. On the other hand, their second model did not account forrapid changes in glucose clearance, but instead augmented glucose utilization. Finally,their third model (and authors’ ultimate choice attending to the results of simulated clampexperiments) was similar to their first proposal, although with an extra increase in insulinaction in proportion to the accumulated exercise intensity and duration.

Dalla Man et al. [2009] used the over-resting HR (i.e. excesses with respect to resting basalHR) as their indicator of exercise intensity, assuming a linear relationship between bothmagnitudes. Although non-linearities are known to occur –specially in light and heavyexercise intensities [Freedson and Miller, 2000]–, this relatively simple assumption may bea reasonable starting point. However, one of the main limitation of this proposal resides inthe lack of data –either from healthy or T1D subjects– as to justify and support model as-sumptions, or in order to fit model parameters to experimental profiles. In addition, otherknown physiological events related to PA (e.g. hyperglycaemia episodes induced by markedcatecholamine secretions, these in turn caused by high-intensity exercise sessions) cannotbe covered by Dalla Man et al. [2009]’s model, devised to reflect exclusively PA-induceddecays in glycaemia.

The Cambridge model has repeatedly proven its outstanding value as the core component ofthe Cambridge’s automated glucose controller. This MPC-based artificial pancreas systemhas been successfully applied in a number of clinical trials under various circumstancesincluding outpatient, free-living environments. On the other hand and in comparison toother existing patient models –e.g. Padova’s (which was derived on the basis of dataobtained from healthy subjects, subsequently particularized to specific situations in T1D)–, the Cambridge model stands out for its sound physiological ground, being tuned andconfirmed for real T1D patient data: with 15 patients [Hovorka et al., 2004].

For the context and purpose of this PhD thesis work, the Cambridge model served hereas the starting point from which an extension is proposed, aiming to address the effect ofinsulin on the disposal of meal-attributable glucose (see coming chapter 8).

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7.2. Overview and extensions

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Chapter 8

Metabolic model for the remoteeffect of insulin on the disposal ofmeal-attributable glucose in T1D

8.1 Motivation

Meal intakes are the most prominent source of major excursions in glycaemia for T1D,ahead of unmatched insulin administrations or physical activity. On a daily basis and forevery meal, patients need to decide by themselves suitable prandial insulin boluses, aim-ing: a) to restrain glucose rises after meals, and at the same time b) to minimize therisk of postprandial hyper- and/or hypoglycaemia episodes, respectively caused by insuffi-cient or excessive amounts of insulin. However, even experienced patients often estimatethe amount and/or timing of boluses inappropriately [Ahola et al., 2010]. In turn, thisissue carries important health implications from a clinical perspective, since those hyper-or hypoglycaemia events due to inappropriate boluses have a notable impact on overallglycaemic control as reflected by glycated haemoglobin HbA1c [Borg et al., 2010].

Common strategies to manage postprandial glucose include CHO counting [Laurenzi et al.,2011] and bolus calculators [Zisser et al., 2008]. However, more detailed mechanistic de-scriptions of the prandial dynamics of glucose-insulin balance in T1D would be desirable.In this regard, the patient models outlined in previous chapter 7 do not address explicitlythe role of exogenous insulin on the clearance of meal-attributable glucose; a gap whichmay possibly stem from the lack of experimental data as to support the modelling and ver-ification of this aspect. Despite various publications in literature have studied postprandialabsorption patterns for healthy, non-T1D individuals after ingesting glucose [Dalla Manet al., 2006, 2007; Toffolo et al., 2008] and standard meals [Wachters-Hagedoorn et al., 2006,2007; Priebe et al., 2008], it has not been however until recently [Elleri et al., 2013a] thatabsorption patterns were reported for T1D patients after having consumed mixed mealswith complex CHO. Elleri et al. [2013a] compared two type of evening meals: one withhigh glycaemic-load (HG), and another with low glycaemic-load (LG). Authors reportedabsorption rates for meal-related glucose (RA,meal) reaching their maximum at higher valuesand later times for HG than for LG meals. Over the first 30 min after ingestion, plasmaglucose profiles for both HG and LG meals were similar, with comparable increases in gly-caemia being measured. Nonetheless, differences arose along the rest of the experiment: inthe case of the HG meal, glucose peaked higher than for LG, and then decayed to reachbasal levels within a period of 5–6 h; whereas on the contrary, after the LG meal glucose

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8.2. Clinical experiment

continued to rise progressively and did not return to basal levels within 8 h post-ingestion[Elleri et al., 2013a].

In a complementary manner to Elleri et al. [2013a] and based on data from the same clinicalexperiment –supplied by the Institute of Metabolic Science (University of Cambridge, UK)–, six mathematical models are proposed and evaluated here in terms of their ability tocharacterize the influence of plasma circulating insulin on observed postprandial glucosekinetics. More specifically, this chapter explores whether compartmental models comprisinga remote effect of plasma insulin on meal glucose disposal are supported by the experimentaldata.

8.2 Clinical experiment

Sixteen young volunteers (7 females and 9 males, age range 16–24), diagnosed with T1Dfor at least 6 months, were recruited for an experiment to reproduce glycaemia profilesobserved after HG and LG evening meals by means of a variable-target glucose clamp. Thestudy was approved by the local ethics committee and all participants provided writteninformed consent.

Subjects were admitted to the Wellcome Trust Clinical Research Facility (Addenbrooke’sHospital, Cambridge, UK) on two different occasions separated by one to five weeks. Ona preliminary visit, from 6:00 p.m. and over 20 min (Figure 8.1) participants consumed amixed meal with complex CHO, either LG (macaroni cheese: glycaemic load 54, n=8) orHG (vegetable shepherd’s pie: glycaemic load 105, n=8) . Meals were matched for totalCHO (121 g), but not for fat or protein contents. Venous blood samples were taken every10–30 min to determine plasma glucose and insulin concentrations.

On a subsequent visit, patients underwent a variable-target glucose clamp which titratedintravenous dextrose infusion rates in order to reproduce each individual’s postprandial glu-cose profile as measured during his/her preliminary visit. An adaptive MPC system (gMPCversion 1.0.2, University of Cambridge, UK) was employed for this purpose. Participantswere admitted after breakfast and fasted from 10:00 h. to 17:30 h. In this time period,intravenous insulin was delivered to obtain stable plasma glucose levels at 6.0 mmol/L(Figure 8.1). Starting from 17:30 h (used here as the origin/reference time point here,i.e. t=0) and until the cessation of the experiment at 02:00 h (t=510 min), intravenousinsulin supply consisted of a constant basal delivery plus a variable infusion to mimic thesystemic appearance of a subcutaneous bolus of rapid-acting insulin analogue with peakabsorption at 50 min [Wilinska et al., 2005]. The total amount of insulin was adjusted foreach subject’s requirements to match 121 g CHO.

[6,6-2H2] glucose (Cambridge Isotope Laboratories, USA) was infused intravenously to EGPfluxes, including the expected post-meal EGP suppression from 18:00 h (i.e. t=30 min).Therefore, [6,6-2H2] glucose served here as an EGP-mimicking tracer species (abbreviatedEM onwards). In addition, [U-13C;1,2,3,4,5,6,6-2H7] glucose was infused to mimic the ex-pected appearance of glucose due to a standard meal; thus functioning as a meal-mimicking(MM) tracer. For the sake of accuracy in measurement, both EM and MM infusion pat-terns were predefined aiming to minimize changes over time in terms of tracer-to-traceeratios (TTRs) [Basu et al., 2003; Haidar et al., 2012].

Blood samples were immediately centrifuged and separated for later analysis. Plasmaglucose was measured with an YSI2300 STAT Plus Analyzer (YSI, UK); whereas TTRs

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8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

Figure 8.1: Schematic schedule of the protocol followed during experiments. Shaded areasindicate those procedures which differed between the preliminary visit and the experimentalintervention. IV=intravenous, EGP=endogenous glucose production. (Source: Adaptedfrom Elleri et al. [2013a]).

were calculated following the procedure described by Hovorka et al. [2002, 2007] in orderto correct for recycled glucose and spectra overlap [Rosenblatt et al., 1992]. Furthermore,a full description of the experimental protocol can be found in [Elleri et al., 2013a].

8.3 Modelling methodology

8.3.1 Model specification

Mass-balance dynamics for the infused EM and MM glucose tracers are respectively char-acterized here by a two-compartmental model, sharing a common structure between bothmodules (see Figure 8.2 and Table 8.1 for nomenclature). In particular, the set of differ-ential equations which govern the mass transfer fluxes for the EM species –i.e. [6,6-2H2]glucose tracer–, are proposed as follows:

d

dtQ1,EM(t) = − [k01(t) + k21]Q1,EM(t) + k12Q2,EM(t) + UEM(t) (8.1)

d

dtQ2,EM(t) = k21Q1,EM(t)− [k02(t) + k12]Q2,EM(t) (8.2)

Q1,EM(t = 0) = Q01,EM (8.3)

Q2,EM(t = 0) = Q02,EM (8.4)

with initial conditions as expressed in (8.3)–(8.4).

A similar formulation applies for the MM tracer, i.e. [U-13C;1,2,3,4,5,6,6-2H7] glucose:

d

dtQ1,MM(t) = − [k01(t) + k21]Q1,MM(t) + k12Q2,MM(t) + TDP · UMM(t) (8.5)

d

dtQ2,MM(t) = k21Q1,MM(t)− [k02(t) + k12]Q2,MM(t) (8.6)

Q1,MM(t = 0) = 0 (8.7)

Q2,MM(t = 0) = 0 (8.8)

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8.3. Modelling methodology

Table 8.1: Nomenclature

G(t) Total plasma glucose concentration [mmol/L]G0 Initial condition (t=0) for G(t) [mmol/L]

Species EM EGP-mimicking tracer: [6,6-2H2] glucose

Species MM Meal absorption-mimicking tracer: [U-13C;1,2,3,4,5,6,6-2H7] glucose

GS(t) Plasma concentration of each glucose tracer species S [mmol/L]

Q1,S(t), Q2,S(t)Amount of glucose tracer species S in the accessible (Q1,S) and nonaccessible (Q2,S)compartments per unit of body weight [µmol/kg]

Q0

1,S , Q0

2,S Initial conditions (t=0) for Q1,S(t), Q2,S(t) [µmol/kg]US(t) Appearance rate of tracer species S (infused) [µmol/kg ·min−1]

U0

S Initial condition (t=0) for US(t) [µmol/kg ·min−1]TDP Tracer dilution purity factor [unitless]

VG Distribution volume for glucose[L/kg]F01,S(t) Non-insulin-dependent disposal flux of glucose species S [µmol/kg ·min−1]

F01 Total non-insulin-dependent glucose disposal flux [µmol/kg ·min−1]

k01(t), k02(t)Fractional clearance rates from the accessible and non-accessible compartments,respectively [min−1]

k12, k21

Transfer rates from the non-accessible to the accessible glucose compartment (k12)and vice versa (k21) [min−1]

kA Insulin deactivation rate constant [min−1]SI Insulin sensitivity [min−1 per pmol/L]

I(t) Plasma insulin concentration [pmol/L]I0 Initial condition (t=0) for I(t) [pmol/L]

X(t) Remote insulin effect [min−1]X0 Initial condition (t=0) for X(t) [min−1]XC Cut-off value for the activation of X(t) [min−1]

Figure 8.2: Common schematic of the models under study, including two compartments–one accessible (i.e. where measurements are made; left) and one non-accessible (right)–for each of the glucose tracer species, along with a single compartment (down) for theremote insulin effect X(t). Broken lines represent the influential role of X(t) in fractionalclearance rates k02(t).

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8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

In both cases, accessible compartments represent plasma; whereas non-accessible compart-ments correspond to other tissues and fluids which equilibrate slowly with respect to plasma,e.g. interstitium. For each species S, tracer masses in the accessible compartments (i.e.Q1,S) depend on: a) the measured plasma tracer concentrations in plasma GS and b) thedistribution volume for glucose VG:

GS(t) =Q1,S(t)

VG

(8.9)

Nevertheless, two aspects distinguish equations for the MM species from the otherwiseidentical EM model, namely:

• A multiplicative, dimensionless factor TDP applied to the infusion rate UMM in (8.5),which accounts for differences in purity of the tracers dilution

• Initial conditions in (8.7)–(8.8), which are both fixed to a zero value because theexogenous MM tracer started to be infused at t=30 min in order to replicate theonset of the reproduced meal intake [Elleri et al., 2013a].

Hence, except for TDP and initial conditions Q01,S, Q0

2,S in (8.3)–(8.4), all other parametersare shared between both EM and MM blocks.

In addition, it is assumed that non-insulin-dependent disposal fluxes F01,S(t) from theaccessible compartments are proportional to: a) the total glucose disposal flux F01, andb) the tracer-to-tracee ratio of the corresponding species S, i.e. TTRS:

F01,S(t) ∝ F01 (8.10)

F01,S(t) ∝ TTRS(t) =GS(t)

G(t)(8.11)

Consequently:

F01,S(t) = F01 · TTRS(t) = F01GS(t)

G(t)(8.12)

where a) total plasma glucose concentration G(t) is determined experimentally and as-sumed free of measurement error for modelling purposes, and b) F01 represents the totalglucose outflow, which is considered here as constant over time, constituting a model pa-rameter for each individual [Hovorka et al., 2002]. Making use of (8.9) and (8.12), thefractional clearances or disposal rates k01,S(t) from the accessible compartments yield:

k01,S(t) =F01,S(t)

Q1,S(t)=F01

✘✘✘GS(t)G(t)

✟✟

✟✟GS(t)VG

=F01

G(t)VG

(8.13)

regardless of the particular species S. For this reason, distinctions are not made betweentracer disposal rates for EM or MM in (8.1) and (8.5).

For the purpose of modelling the role of insulin on the clearance of glucose tracers, a remoteeffect variable X(t) is defined through a single-compartmental model with initial conditionX0 at t = 0:

d

dtX(t) = −kAX(t) + kASII(t) (8.14)

X(t = 0) = X0 (8.15)

Magnitude X(t) modulates the disposal rates k02(t) from the non-accessible compartmentsof glucose tracer masses Q2,S. Two types of remote effects are considered here for theirevaluation:

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8.3. Modelling methodology

• First an approach in which the disposal rate directly equals X(t), onwards referredto as ‘linear’ formulation:

k02(t) = X(t) (8.16)

• Alternatively, a second option is evaluated in which the fractional clearance k02(t)varies in proportion to changes in X(t), but only above a certain threshold XC ;whereas on the contrary, disposal is totally suppressed below such value XC :

k02(t) =

{

X(t)−XC if X(t)−XC ≥ 00 otherwise

(8.17)

or using an equivalent formulation for compactness:

k02(t) = R [X(t)−XC ] (8.18)

where R[·] denotes the ramp function. This behaviour is onwards referred to as‘cut-off’ activation.

Besides, the suitability of different forms of initial conditions for (8.3), (8.4) and (8.15) areinvestigated. In the first place, the assumption of steady-state conditions for X(t) at t=0would impose:

d

dtX(t = 0) = 0⇒ X0 = SII

0 (8.19)

where I0 is the insulin concentration measured experimentally at start time (t=0), andwhere SI represents insulin sensitivity to the disposal of glucose tracers (Table 8.1). Forthe ‘linear’ remote effect, (8.19) implies that the disposal rates k02(t) from the non-accessiblecompartments at time t=0 would equal:

k02(t = 0) = X0 (8.20)

Alternatively, for the ‘cut-off’ approach it is obtained:

k02(t = 0) = R[

X0 −XC

]

(8.21)

Steady-state initial conditions for the EM tracer masses can also be solved algebraically,yielding:

ddtQ1,EM(t = 0) = 0

ddtQ2,EM(t = 0) = 0

}

⇒

Q01,EM = k02(t=0)+k12

[k02(t=0)+k12]

[

F01G0VG

+k21

]

−k12k21

U0EM

Q01,EM = k21

[k02(t=0)+k12]

[

F01G0VG

+k21

]

−k12k21

U0EM

(8.22)

where: i) U0EM represents the infusion rate for the EM tracer at t=0 as employed in the

experiments, ii)G0 is the total glucose concentration measured at start time; and iii) k02(t =0) is obtained either from (8.20) or from (8.21), whichever is applicable depending on theassumed behaviour for X(t) (linear or cut-off).

A substitutive to the steady-state assumption consists in taking Q01,EM , Q0

2,EM and X0 asextra model parameters. This option implies to consider that the metabolic system is in anon-steady situation (i.e. d/dt 6= 0) at the onset of the experiment (t=0). Furthermore, amixed case is also proposed here, in which the remote effect of insulin X(t) is considered insteady-state but the EM tracer masses are not. Thus, Q0

1,EM , Q02,EM become model parame-

ters, whereas the condition from either (8.20) or (8.21) does apply although (8.22) does not.

130

8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

In summary, this work explores: a) two different configurations for the remote effect X(t)of insulin on glucose disposal: either ‘linear’ (L) or with ‘cut-off’ (C); along with b) threealternative assumptions for the initial conditions of EM masses and remote effect: ‘steady-state’ (S), as model ‘parameters’ (P), or with a ‘mixed’ situation (M) between steady-stateand parameters. Therefore, a total of six model combinations are evaluated and comparedhere, namely: LS (linear remote effect plus steady-state initial conditions), CS (cut-offactivation of X plus steady-state), LM (linear plus mixed initial conditions), CM (cut-offbehaviour plus mixed), LP (linear plus initial conditions as model parameters) and CP(cut-off plus parameters).

All models verify a priori identifiability conditions [Carson et al., 1983; Cobelli and Carson,2008].

8.3.2 Parameter estimation

For the purpose of estimating model parameters, measurement errors were assumed hereto be normally distributed with zero mean. Errors associated with the measurement ofthe EGP-mimicking [6,6-2H2] glucose tracer were modeled as multiplicative with coeffi-cient of variation (CV) equal to 5% [Haidar et al., 2012]. Correspondingly, errors for themeal-mimicking [U-13C;1,2,3,4,5,6,6-2H7] glucose tracer were assumed multiplicative withCV=5% for concentrations greater than 0.02 mmol/L, and otherwise additive with zeromean and standard deviation 0.001 mmol/L. This additive error was determined empiri-cally and signifies that, at low concentrations, instrumentation has precision independentof the measured value.

Model parameters were estimated by means of an iterative two-stage (ITS) populationkinetics analysis [Steimer et al., 1984; Hovorka and Vicini, 2001] using SAAM II soft-ware (The Epsilon Group, USA). After a preliminary parameter fitting for each individual–initialization stage–, ITS population analysis performed an Expectation-Maximization es-timation, consisting of two steps: i) a parameter estimation procedure –Expectation step–including a Bayesian term which penalizes deviations from the current population-basedmean estimate, weighted by the reciprocal of the population-based variance of parame-ters [Steimer et al., 1984]; and ii) an update of population statistics –Maximization step–in accordance to the outcome of the current parameter fitting. This iterative procedurewas repeated until convergence, which was assumed to occur when consecutive parameterestimates differed by <1%.

8.3.3 Model identification and validation

Parameter estimates were checked for physiological plausibility against reference valuesfrom previously validated studies in T1D subjects [Hovorka et al., 2002]. Posterior identifi-ability of each parameter was assessed by means of the accuracy of its estimate, consideringthe estimation as satisfactory if the CV was below 75%, acceptable in the range 75–100%,and non-identifiable if CV>100%.

Runs tests (one-sample Wald-Wolfowitz) were performed to ascertain the randomness ofeach model’s weighted residuals of fitting [Wald and Wolfowitz, 1940].

131

8.4. Results

Figure 8.3: Plasma tracer concentrations over time in the accessible compartments for theEGP-mimicking tracer (panel a) and the meal-mimicking tracer (panel b), measured duringthe variable-target glucose clamp experiments reproducing either a HG or LG evening meal.Values are depicted as mean±SEM (n=8).

8.3.4 Model selection

The principle of parsimony was employed here to identify which of the six models bestrepresented experimental observations, balancing on the one side the accuracy of the curvesfitted to data –assessed by means of the weighted residual sum of squares–, and on the otherhand the number of model parameters. Akaike (AIC) and Bayesian (BIC) informationcriteria were computed by SAAM II software. Models should ideally minimize those scores.

8.4 Results

8.4.1 Experimental data

Baseline characteristics for the two meal-type groups were statistically comparable: 3/5females/males, age 20.8±3.3 years, BMI 24.0±1.5 kg/m2, HbA1c 8.7±1.5%, diabetes du-ration 7.1 (2.9–20.9) years and total daily insulin 0.8±0.2 U·kg−1·day−1 for the group inwhich the LG meal was reproduced; versus 4/4 females/males, age 18.1±4.0 years, BMI22.8±1.2 kg/m2, HbA1c 8.7±2.0%, diabetes duration 7.4 (3.6–11.2) years and total daily in-sulin 0.9±0.1 U·kg−1·day−1 for the HG meal group. Results are all expressed as mean±SD,except diabetes duration which is as median (inter-quartile range).

The variable-target glucose clamp achieved by the University of Cambridge’s adaptiveMPC controller replicated satisfactorily those individual glucose profiles obtained duringthe preliminary visit [Elleri et al., 2013a]. Average plasma tracer concentrations in theaccessible compartments GEM(t), GMM(t) are depicted in Figure 8.3.

8.4.2 Model identification, validation and selection

Table 8.2 summarizes the results obtained for the procedures of model identification andvalidation. All six models showed physiological plausibility, although two of them –LMand LP– yielded values for the F01 parameter (∼4 µmol/kg·min−1, Table 8.3) which lie

132

8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

Table 8.2: Model identification and validation – Results

Modelname

Physiologicalplausibility

Precision of parameterestimates

Runstest∗

Akaike score(mean±SD)

Bayes score(mean±SD)

LS Yes Satisfactory 31/32 −2.79±2.88 −2.66±2.88CS Yes Satisfactory 31/32 −3.61±0.44 −3.46±0.44LM Yes Satisfactory† 31/32 −2.91±2.95 −2.77±2.95CM Yes Satisfactory 32/32 −3.73±0.36 −3.55±0.36LP Yes Satisfactory‡ 31/32 −2.91±2.96 −2.76±2.96CP Yes Satisfactory‡ 32/32 −3.64±0.67 −3.48±0.67

∗ Fraction of Runs tests passed with p <0.05 (n = 16 subjects, each of which implied two series ofresiduals of fitting: one for EM, another for MM).† Individual values converged to an identical estimate for one parameter.‡ Individual values converged to an identical estimate for two parameters.

around the lower bound of those found by previous validated studies [Hovorka et al., 2002].Posterior identifiability was satisfactory, with CV<75% in all parameter estimates (Table8.4). However, in three occasions the ITS population fitting process resulted in either oneparameter (F01 for the LM model) or two parameters (F01 plus X0 for the LP model;Q0

2,EM and X0 for CP) becoming fixed by converging to an identical estimated value for allsubjects.

Weighted residuals of model fits are depicted in Figure 8.4. In addition to the averageweighted residual at each time point, their root-mean-square (rms) value was also computedin order to quantify the variability of residuals across individual profiles. Furthermore, Runstests were applied to the series of weighted residuals. Table 8.2 presents the fraction ofcases which passed the test, meaning whenever the null hypothesis (which represents therandomness of residuals) could not be rejected with 95% confidence (i.e. p <0.05).

Based on the principle of parsimony and accounting for AIC and BIC scores, the modelwith highest overall a posteriori identifiability was CM, hence best representing these ex-perimental data. CM also showed the tightest weighted residuals, both in terms of meanand rms values (Figure 8.4). An example curve fit to data as generated by the CM modelis depicted in Figure 8.5.

Finally, neither independent t-tests nor Mann-Whitney tests (i.e. their non-parametriccounterparts) found any statistically significant difference between the HG, LG subgroupsin terms of the values for any of the model parameters as fitted by CM.

8.5 Discussion

A number of works in literature studied glucose absorption patterns in healthy individualsafter the intake of glucose [Dalla Man et al., 2006, 2007; Toffolo et al., 2008] or meals[Wachters-Hagedoorn et al., 2006, 2007; Priebe et al., 2008]. Recently, a clamp experimentaddressed mixed meals with complex CHO in patients with T1D [Elleri et al., 2013a].Using data from this experiment by Elleri et al. [2013a], this works covers the modellingof a remote effect of plasma insulin concentrations on the disposal of meal-attributableglucose, a phenomenon which had not been addressed previously.

Six mechanistic models were proposed to characterize mathematically the clearance regimesof EGP- and meal-mimicking glucose tracers from the non-accessible compartments rep-resenting interstitium, among other tissues. These six non-linear models comprised mass-balance differential equations for the EM and MM tracer species with a common two-

133

8.5. Discussion

Figure 8.4: Mean (n=16) and root-mean-square (rms) weighted residuals of fitting for eachof the six models with respect to measured EM (panels a, b) and MM concentrations (c,d).

Figure 8.5: Example fit to experimental data produced by the CM model.

134

8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

Tab

le8.

3:P

aram

eter

esti

mat

esfo

rth

esi

xm

odel

s

Mo

del

TD

PF

01

VG

SI

kA

k1

2k

21

XC

Q0 1

,EM

Q0 2

,EM

X0

10

−2

[un

itle

ss]

[µm

ol/

kg

·min

−1

]1

0−

2[L

/k

g]

10

−6

[min

−1

per

pm

ol/

L]

10

−2

[min

−1

]1

0−

2[m

in−

1]

10

−2

[min

−1

]1

0−

2[m

in−

1]

[µm

ol/

kg

][µ

mo

l/k

g]

10

−2

[min

−1

]

LS

85.1

58.6

916.2

238.0

86.7

66.7

68.0

3–

––

–(7

9.7

7–91.4

7)

(6.5

1–10.1

4)

(12.6

7–19.0

7)

(28.4

1–56.4

3)

(3.0

2–9.1

9)

(2.3

0–22.0

7)

(2.7

9–19.8

1)

CS

82.2

611.7

719.8

674.2

54.9

24.9

93.1

60.6

7–

––

(77.9

9–90.4

6)

(6.9

5–13.2

4)

(14.1

7–20.9

5)

(41.0

0–126.5

5)

(3.5

3–8.2

3)

(3.1

1–6.4

8)

(1.9

4–4.4

0)

(0.0

0–1.8

2)

LM

81.8

64.0

4†

18.8

067.2

14.8

13.5

23.6

5–

26.0

416.5

4–

(76.7

8–91.3

1)

(16.8

3–20.4

3)

(49.1

3–81.5

8)

(2.9

2–6.6

9)

(1.7

9–14.6

2)

(2.6

3–7.0

9)

(23.6

8–29.1

4)

(13.2

4–21.4

9)

CM

79.5

810.1

920.1

4135.8

14.4

93.1

92.2

41.7

428.0

015.9

6–

(76.2

7–87.6

9)

(9.0

2–10.9

8)

(16.6

0–21.7

4)

(75.7

9–211.3

0)

(3.8

9–8.1

9)

(2.4

5–5.1

4)

(1.4

4–3.5

3)

(0.8

1–2.5

0)

(23.7

1–30.7

8)

(12.5

8–19.5

9)

LP

82.1

14.0

8†

18.2

966.5

75.2

13.5

83.6

5–

25.9

317.1

70.5

7†

(76.5

9–89.3

6)

(16.7

0–20.2

5)

(45.4

9–79.8

5)

(3.0

3–6.9

1)

(1.9

6–12.4

5)

(2.7

5–6.7

7)

(23.0

2–28.9

1)

(13.2

1–21.0

5)

CP

78.8

09.2

419.9

0116.7

35.4

82.7

22.2

61.5

727.4

514.0

9†

0.5

0†

(76.0

2–87.7

8)

(7.9

4–10.9

1)

(17.6

1–21.1

1)

(78.6

4–175.2

7)

(3.8

7–9.4

7)

(2.0

8–4.6

2)

(1.5

7–2.9

3)

(0.9

2–2.0

6)

(26.2

2–30.2

8)

Val

ues

are

expr

esse

das

med

ian

(int

er-q

uart

ilera

nge)

wit

hn

=16

indi

vidu

als.

†In

divi

dual

valu

esco

nver

ged

toan

iden

tica

les

tim

ate.

135

8.5. Discussion

Tab

le8.4:

Coeffi

cient

ofvariation

CV

(%)

forparam

eterestim

ates

Mo

del

TD

PF

01

VG

SI

kA

k1

2k

21

XC

Q01

,EM

Q02

,EM

X0

LS

2.1

55.1

714.2

015.9

024.8

934.5

636.2

8–

––

–(2

.11–2.3

5)

(3.2

5–7.6

9)

(6.3

3–16.7

1)

(13.1

8–20.1

0)

(16.9

3–37.1

5)

(27.5

8–40.7

6)

(23.8

1–47.9

2)

CS

2.3

712.5

26.2

820.9

226.2

730.1

326.3

642.9

3–

––

(2.3

1–2.7

0)

(1.7

3–17.9

0)

(5.2

4–10.4

2)

(15.0

7–27.2

9)

(17.3

7–35.4

7)

(22.8

3–38.5

6)

(17.8

4–32.5

7)

(28.2

9–63.8

4)

LM

2.3

1N

A‡

5.2

614.6

320.1

824.2

211.2

0–

6.6

922.1

2–

(2.1

7–2.4

3)

(4.1

1–7.7

7)

(12.8

9–20.7

4)

(14.6

2–26.6

2)

(21.4

3–29.4

7)

(8.3

9–21.0

2)

(5.5

9–8.8

5)

(16.9

9–26.0

4)

CM

2.4

619.6

54.5

022.9

123.6

926.1

414.8

342.3

36.1

621.0

0–

(2.3

4–2.6

8)

(12.1

4–25.7

1)

(4.1

1–7.6

9)

(18.9

1–27.9

4)

(18.8

2–28.0

8)

(21.8

3–32.6

9)

(13.2

6–23.4

1)

(31.3

4–65.3

4)

(5.4

9–8.5

7)

(15.2

4–25.6

8)

LP

2.2

8N

A‡

5.2

914.1

519.9

924.8

512.1

4–

6.7

322.0

9N

A‡

(2.2

0–2.4

2)

(4.1

4–8.5

51)

(12.4

0–19.5

7)

(15.3

6–27.4

7)

(20.6

4–28.8

8)

(8.3

9–23.8

9)

(5.6

1–9.4

1)

(17.8

1–26.1

3)

CP

2.3

418.6

44.0

218.1

720.9

219.0

513.6

134.6

74.8

8N

A‡

NA

‡

(2.2

8–2.4

3)

(11.7

0–27.9

7)

(3.8

9–4.8

6)

(15.5

6–20.9

4)

(13.6

0–28.4

9)

(17.3

6–25.0

1)

(11.0

2–15.9

9)

(24.6

2–48.8

2)

(4.7

7–5.2

4)

Values

areexpressed

asm

edian(inter-quartile

range)w

ithn

=16

individuals.N

A‡

Not

Available,

individualvalues

convergedto

anidentical

estimate.

136

8. Metabolic model for the effect of insulin on the disposal of meal glucose in T1D

compartmental structure for each, as well as a remote effect X(t) of plasma insulin con-centration on the disposal rate k02(t) from the non-accessible compartments with massesQ2,S. In all models, the non-insulin-dependent disposal flux F01,S(t) from the accessiblecompartments Q1,S was assumed to be proportional to both the total flux F01 and thecorresponding tracer-to-tracee ratio TTRS. A dimensionless parameter TDP was incor-porated to UMM(t) in order to account for variations in the purity of tracer dilutions.Differences among the six models resided in two aspects: a) whether the disposal ratek02(t) was assumed to be ‘linear’ with the remote effect X(t) or if, conversely, disposal wasactivated only above a certain ‘cut-off’ value XC ; and b) in the type of initial conditionsfor various differential equations (if steady-state was assumed, or a fully non-steady casewith all initial conditions taken as model parameters, or an intermediate case with X(t) insteady state but not masses Q1,EM , Q2,EM).

Models were evaluated in terms of their ability to fit experimental data from n=16 youngindividuals with T1D who underwent a variable-target clamp to replicate glucose profilesobserved after LG or HG evening meals containing complex CHO. All six models were a

priori identifiable and also proved a posteriori identifiability, with remarkable precision ofparameter estimates, as shown by the low CVs obtaines (Table 8.4). Nevertheless, threemodels converged to either one or two fixed values for certain parameters, an issue whichmay suggest suboptimal or inadequate fits, possibly due to an undesired convergence tolocal optima by the ITS numerical algorithm.

In general terms, the three models with a ‘cut-off’ activation of X(t) behaved better thantheir corresponding ‘linear’ counterpart with the same type of initial conditions. Overall,the best fit to data (i.e. the one with smallest weighted residuals and lowest AIC and BICscores) was obtained by the CM model. Of note, the XC threshold was well supportedby data, with CV=42.33 (31.34–65.34)% (n=16) [median (inter-quartile range)]. Besides,profiles for both EM and MM tracer concentrations were accurately reconstructed by theCM model, with weighted residuals having passed all Runs tests and therefore not showingsystematic deviations from randomness. In addition to the ‘cut-off’ remote effect of insulinon disposal, CM comprised steady-state conditions for the compartment X(t) representingthis remote effect, although not for the masses of the EM tracer species. This behaviourcould be originated in the particular time course of the experimental protocol used here,in which insulin had been infused for seven hours prior to the onset of the clamp (Figure8.1); whereas the EM tracer had been infused for two hours [Elleri et al., 2013a] and a tran-sient might still be present at t=0. Figure 8.3(panel a) supports this idea, depicting EMconcentration profiles which do not remain flat at t=0, but instead peak around t ∼30 min).

Given the complexity of the study, the experiments did not replicate both types of mealson the same population of patients. However, subjects’ characteristics were very similarbetween the two populations, with a therefore limited impact on the outcomes.

A final consideration should be made concerning the applicability of the mechanistic metabolicmodel derived here for the kinetics of meal-attributable glucose. This model could be in-tegrated into the in silico simulation of meals [Wilinska et al., 2009; Magni et al., 2009;Clarke et al., 2009; Grosman et al., 2010; Turksoy et al., 2013], which may in turn be usedto test and optimize postprandial insulin infusion regimes aiming to restrain meal-inducedglucose excursions. The model could be as well applied in the context of MPC controlalgorithms for the artificial pancreas in T1D [Hovorka, 2011].

137

8.5. Discussion

138

Part V

Conclusions

139

Chapter 9

Conclusions

9.1 Verification of hypotheses and summary of results

H1: In the context of type 1 diabetes, it is possible to determine distinctivephysiological responses to exercise of varying intensity and modality, andin particular to quantify their effects in terms of the associated acutevariations in glycaemia.

Hypothesis partially confirmed.

In this PhD thesis work, two novel rate-of-change magnitudes RoCE, RoCR were definedto characterize in a systematic, quantitative manner the acute exercise-induced variationsobserved in T1D patients’ glycaemia as a response to various types of physical activity,during exercise and in the immediately subsequent early recovery stage.

On this basis, a systematic review and meta-analysis was conduced to aggregate the avail-able scientific evidence. To avoid introducing bias, glucose profiles were detrended ata study level (prior to the pooling), hence discounting background spurious trends at-tributable to factors other than exercise itself. Random-effect DerSimonian & Laird statis-tical meta-analyses were carried out, first with a resting control period (REST) as reference,plus direct comparisons between pairs of exercise modalities –when feasible in terms of pub-lications availing–.

Continuous exercise at sustained, moderate intensities (CONT) –with predominantly aer-obic contributions– was found to be associated with the most rapid decays in glycaemiaduring exercise, at an average rate of RoCE{CONT vs. REST} = −4.43 mmol/L·h−1; andmild recoveries afterwards, with mean RoCR{CONT vs. REST} = +0.70 mmol/L·h−1.Resistance exercise (RESIST) –with notable anaerobic contributions– showed more con-strained average decays and recoveries than CONT: RoCE{RESIST vs. CONT} = +2.86mmol/L·h−1, RoCR{RESIST vs. CONT} = −2.40 mmol/L·h−1. However, quantitativediscrepancies in RoCs and conflicting evidence (e.g. in terms of the occurrence of noctur-nal post-exercise hypoglycaemia events) were encountered regarding the magnitude of theeffect of intermittent high-intensity exercise (IHE).

H2: It is possible to achieve an accurate, reliable and robust monitoring ofphysical activity intensity and modality in free-living conditions by thesimultaneous processing of multi-modal data which combine accelerometryand heart rate measurements, as well as by the application of machinelearning algorithms to identify patterns in data.

Hypothesis confirmed.

141

9.1. Verification of hypotheses and summary of results

Data were collected in two different scenarios: i) a laboratory environment comprisingfixed exercise circuit protocols in a fitness center, with tight schedules and intensities, andunder direct supervision by the research team; and additionally, ii) in ambulatory free-living conditions which included a notable variety of self-selected physical activities, as wellas resting periods, daily life activities and the use of means of transportation. These datawere used to train and validate a ML-based system for the classification of time periods interms of their PA intensity (either low, moderate or vigorous) and –for the case of vigorousepisodes– also their exercise modality (sustained aerobic, resistance and mixed). In thisregard, ML techniques provided a sound framework for the extraction of relevant patternsin multi-modal signals: biaxial accelerometry, step count and HR.

A pipeline of ML schemes was proposed, including:

a) Feature definition. A total of 42 time-domain statistical descriptors were defined tocharacterize the evolution of signals along the basic unit of analysis: a 2-min window,whose duration was selected preliminarily in order to balance descriptiveness andtime granularity.

b) Dimensionality reduction to overcome the so-called ‘curse of dimensionality’. In thismanner, the number of features considered was decreased –and hence, the complexityof the automated learning task– while maintaining as much relevant information insignals as possible. To do so, various methodologies were explored, ranging from theextraction of new features by linear combination of the original ones (PCA or LDAprojections) to ‘filter’- and ‘wrapper’-based feature selection.

c) Identification of patterns in data, either by clustering algorithms –employed here as‘smart’ vector quantization procedures– or by means of supervised classifiers. ThisPhD thesis work covered a considerable variety of state-of-the-art algorithms –both inclustering and classification set-ups– with diverse underlying mathematical principlesand computational complexities: from relatively simpleK-means or logistic regressionschemes to compound classification ensembles (Bagging or Boosting).

d) Temporal filtering to exploit information about sustained long-term trends and redun-dancies in the time course of data. A Markovian process modelling was undertaken,making use of HMM capabilities to relate an observable process (i.e. the identifiedpatterns) with a hidden process, in this case the sequence of PA classes which mostlikely generated the given sequence of observations.

This ML framework was used to select a combination of schemes which yielded best valuesfor a custom performance metric, which –given the notable class imbalance present in thedataset– was formulated to reflect overall accuracy in recognition, as well as achievements inunder-represented PA classes (i.e. moderate and vigorous). As a result of this model selec-tion procedure, the combination ‘wrapper’-based feature selection (genetic search, Bagging-specific wrapper) plus Bagging as classification algorithm showed highest performancescores in PA intensity and modality recognition. Besides, good robustness and general-ization capabilities were observed (especially for the LDA+K-means scheme) through theLOSOCV procedure, in which data sequences from all but one participant were used inturns for the training of the classifier and data from the remaining subject were used fortesting purposes. This aspect points out that overfitting is unlikely to have occurred. Fur-thermore, the proposed classifiers outperformed notably the domain-specific standard PAintensity classification approaches (‘cutpoint’-based, i.e. by thresholding [Freedson et al.,1998; Sasaki et al., 2011]), specially in the recognition of static resistance exercise not in-volving waist movements, where the accelerometer was attached. This improvement wasfacilitated by the incorporation of HR to provide information physiological responses toexercise by the cardiovascular system. In addition, the proposed classifiers also outper-

142

9. Conclusions

formed clearly baseline ML schemes established for comparison purposes (naïve Bayes andCART decision trees), which worked on data combining accelerometry and HR measure-ments. On the other hand, scores for the task of PA modality recognition were also notablysatisfactory: ∼98%.

In terms of the temporal behaviour of classification outcomes, thanks to the incorporationof the HMM, most errors were observed to appear consistently as short-duration mis-matches, specially around transients, e.g. with quick fluctuations in the ground truth dueto the short-interval circuit training protocol in the laboratory environment. However,these fluctuations are infrequent in real free-living scenarios, with classification errors ex-pected therefore to have a low impact in terms of eventual decays in the overall accuracy,robustness and reliability in the ambulatory 24 h-based PA monitoring.

H3: It is possible to generate a mechanistic mathematical model which de-scribes the effect of insulin on prandial glucose-insulin kinetics in type 1diabetes.

Hypothesis confirmed.

The role of insulin on the clearance of meal-attributable glucose had not yet been addressedexplicitly by prevailing T1D patient models. To do so, this work made use of data obtainedby the Institute of Metabolic Science (University of Cambridge, UK) during a variable-target glucose clamp conceived to study and replicate the absorption patterns of commonmixed meals with complex CHO for n=16 young patients with T1D. Glucose fluxes weredetermined in a virtually model-independent manner by means of a triple tracer techniquein which the expected post-prandial EGP reduction and appearance of meal glucose weremimicked via the tritration of infusion regimes for the glucose tracers.

Based on those experimental data, various compartmental models were proposed here todescribe mechanistically –via mass-balance differential equations– the clearance of glucosetracers from non-accessible compartments, and in particular, the role of plasma insulinconcentrations on disposal rates. Six non-linear models were studied, differing in: a) theform of the remote effect of insulin –either following a ‘linear’ behaviour of with ‘cut-off’activation above a certain threshold value XC–, and b) in the type of initial conditionsfor the differential equations: i.e. steady-state assumed or not. All models were a priori

identifiable and showed notable precision of the fitted parameter values, in physiologicalranges comparable to previous experiments [Hovorka et al., 2002]. Attending to physi-ological plausibility, fitting residuals and parsimony criteria (AIC, BIC), the model bestexplaining the experimental observations was selected. This model CM encompassed a‘cut-off’ behaviour for the remote effect of insulin on the clearance of meal-attributableglucose, as well as initial conditions characterized by a mixed situation: steady-state forthe insulin compartment; but oppositely, non-steady for the masses of the tracer mimickingEGP.

This interaction between insulin concentrations and the clearance of meal-attributable glu-cose (which had not been described before) can be incorporated to the current physiologicalT1D patient models. This enhancement can in turn improve the in silico simulation of pran-dial periods, which may be useful for the tailoring of meal bolus regimes and in closed-loopcontrol (i.e. the artificial pancreas).

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9.2. Future works

9.2 Future works

9.2.1 Physical activity monitoring

Commercial accelerometers, such as ActiGraph’s devices used here or SenseWear armbands,are widely extended and consolidated in sport sciences and in the professional PA moni-toring. These equipments have a major advantage in the considerable amount of publishedevidence [Bassett et al., 2000; Hendelman et al., 2000; Welk et al., 2004, 2007; Sasaki et al.,2011] concerning their field validation and assessing their accuracy. However, their internalproprietary processing algorithms to generate ‘activity counts’ prevent researchers fromhaving full control of the raw accelerometry signal: during this procedure, signal is sum-marized by the computation of counts, discarding potentially very valuable informationsuch as the detailed waveform or its spectral content. Newer commercial PA monitoringdevices –e.g. Zephyr [Johnstone et al., 2012a,b,c]– are starting to shift away from this‘counts paradigm’ in favour of raw accelerometry signals. Besides, they incorporate therecording of other relevant physiological magnitudes: not only HR, but also ventilation orbody temperature.

On the other hand, the high penetration of accelerometer-enabled smartphones providesaccess to affordable monitoring devices, which patients are accustomed to carry with them.Hence, the use of smartphones as PA tracking systems is very promising, added to thefact that manufacturers of HR monitoring equipments have commenced to adopt stan-dard wireless communication protocols which smartphones can implement (e.g. Bluetooth,Bluetooth Low Energy or ANT+).

Scientific literature is slowly starting to show research efforts in this line [Gyllensten andBonomi, 2011; Bort-Roig et al., 2014], although the use of commercial, validated equipmentis still markedly dominant.

The automatic ML-based PA recognition schemes proposed in this work are flexible as toaccommodate the handling of raw accelerometry signals; although a number of adaptationswould be required:

a) Signal preprocessing should be drastically modified in order to adapt to the particularnature of raw accelerometry, notably different from counts. This would include, forexample, band-pass filtering to discard the gravity component in acceleration andhigh-frequency noise.

b) Feature definition should be enhanced to capture additional information available:spectral analysis and/or wavelets, characteristics describing signal morphology orvariability of times between consecutive heartbeats, among others.

c) Attention should be paid to the adjustment of the computational demands of prepro-cessing and classification schemes to match the capabilities of smartphones, balancingthe complexity of the algorithms to prevent overloading the processor or eventual bat-tery drains, among other issues.

d) New data collection experiments would also be required to train the ML systems.

In this sense, part of the work along this PhD thesis was devoted to the coaching of severalMSc theses –mainly González Martín [2013]– developing preliminary prototypes in this line.Work is still pending in various manners; in the improvement and verification of preprocess-ing schemes, in the selection of ML algorithms and hyperparameter values, or in performingan exhaustive validation of the system. Open issues exist regarding the accuracy, validityand reproducibility of accelerometry measurements inter- and intra-device. In this regard,disparities in terms of the available sampling frequencies have been detected, along with

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9. Conclusions

unequal ranges of measurement even for the same hardware (i.e. identical accelerometermicrochip model), which are due to operating system configuration details.

9.2.2 Physical activity modelling in T1D

PA has not yet been thoroughly addressed from the perspective of producing physiologicallygrounded mathematical models to describe its effects on glucose homoeostasis in T1D. Inthis sense, the three models presented by Dalla Man et al. [2009] were conceived to replicateexercise-induced decays in glucose, as observed for T1D patients during moderate-intensitysustained PA. Therefore, these models cannot reflect other known physiological responses toexercise, such as hyperglycaemia episodes induced by very vigorous bouts which produce anexacerbated release of catecholamines Marliss and Vranic [2002]; Lumb and Gallen [2009].Consequently, further research is needed to generate mechanistic models covering morephysiological aspects of PA in T1D, in particular its interaction with glucose homoeostasis.

Until now, a critical limiting factor has been the lack of experimental data on which toformulate and validate such models. Ideally, tracer experiments should be conduced in asimilar manner to the one described in chapter 8 to investigate meal absorption. How-ever, the design of those experiments may encompass theoretical and practical limitations,including complex issues such as pre-establishing infusion regimes which maintain the ex-pected tracer-to-tracee ratios approximately stable, or the number of tracer isotopes neededto identify univocally the relevant fluxes, among others.

9.2.3 Physical activity into artificial pancreas systems

Artificial pancreas systems in T1D –currently under development stages or undergoing pre-liminary clinical trials– do not yet incorporate the explicit consideration of PA as a source ofchanges in glucose-insulin kinetics for T1D. In this sense, a first possibility to integrate PAinto the closed-loop glucose controllers would be through physiologically detailed, white-box descriptive models embedded in MPC algorithms, with the limitations of modellingPA discussed above. Another option could be through black-box approaches, e.g. a MLPneural network trained to predict exercise-induced trends in glycaemia without the needfor explicit physiological knowledge.

In literature, various pilot studies have been conduced on T1D patients performing exerciseduring the period in which glycaemia was controlled. However, either PA was not tackledspecifically –i.e. not considering that changes in glycaemia may be induced by PA–, orsimple intuitive approached were followed. Among the second family of approaches, Sten-erson et al. [2015] used a Kalman filter to predict glucose values 30 min ahead, suspendingthe infusion of insulin by the pump: a) for predictions below 80 mg/dL (4.44 mmol/L), inthe case of high accelerometry values were measured; or b) for HR above 90 beats/min incombination with glycaemia below 180 mg/dL (10.0 mmol/L) and decreasing. Similarly,Breton et al. [2014] used a Kalman filter to predict hypoglycaemia risk, taking correctiveactions –reductions in insulin infusion– in accordance to such risk. To accommodate exer-cise, the estimation of this hypoglycaemia risk was increased in relation to HR values inexcess of resting, basal HR.

In summary, the strategies explored until now in literature for the integration of the manage-ment of PA into artificial pancreas systems can be characterized by their relative simplicity.Whereas the glucose-lowering effect of sustained moderate PA is taken into consideration,rises originated by vigorous bouts are not. Besides, actions taken by the controller are

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9.3. Contributions and achievements

governed by simple rules: thresholds on accelerometry outcomes and/or HR [Stenersonet al., 2015], or increased hypoglycaemia risks [Breton et al., 2014]. Therefore, there isconsiderable room for research on the integration of PA into the artificial pancreas, whichcan in turn benefit from improvements in the monitoring of PA (reliable determination ofits intensity and modality/predominant metabolic pathway) and in the modelling of itseffect on glucose-insulin dynamics.

9.3 Contributions and achievements

9.3.1 Publications

Journal articles

• F. García-García, K. Kumareswaran, R. Hovorka, M.E. Hernando. Quantifyingthe acute changes in glucose with exercise in type 1 diabetes: A systematic reviewand meta-analysis. Sports Med, 45(4):587–599, 2015. doi:10.1007/s40279-015-0302-2– JCR, Q1.

• I. Capel, M. Rigla, G. García-Sáez, A. Rodríguez-Herrero, B. Pons, D. Subías,F. García-García, M. Gallach, M. Aguilar, C. Pérez-Gandía, E. J. Gómez, A.Caixàs, M. E. Hernando. Artificial pancreas using a personalized rule-based con-troller achieves overnight normoglycemia in patients with type 1 diabetes. Diabetes

Technol Ther 16(3):172–179, 2014. doi:10.1089/dia.2013.0229 – JCR, Q3.

Journal articles (under review)

• F. García-García, R. Hovorka, M. E. Wilinska, D. Elleri, M. E. Hernando. Mod-elling the effect of insulin on the disposal of meal-attributable glucose in type 1diabetes. Submission: Med Eng Phys – JCR, Q2 (Date submitted: January 2015).

• F. García-García, P. J. Benito, M. E. Hernando. Classification of physical ac-tivity intensity and modality merging accelerometer and heart rate measurements.Submission: Expert Syst Appl – JCR, Q1 (Date submitted: March 2015).

• A. Rodríguez-Herrero, G. García-Sáez, F. García-García, C. Pérez-Gandía, B.Pons, I. Capel, D. Subías, M. Rigla, M. E. Hernando. Predictive rule-based arti-ficial pancreas: in silico experiments. Submission: Comput Meth Prog Bio – JCR,Q2.

• L. Florianópolis, A.B. Peinado, A. Zapico, F. García-García, M.E. Hernando, P.J.Benito. Comparative study of energy expenditure measured by different devices incircuit resistance training.

International conferences

• A. Rodrígues-Herrero, G. García-Sáez, F. García-García, C. Pérez-Gandía, M.Rigla, M. E. Hernando. Personalized rule-based closed-loop control algorithm for type1 diabetes. 7th International Conference on Advanced Technologies and Treatments

for Diabetes (Vienna, Austria), February 2014. doi:10.1089/dia.2014.1515 [IndexedJCR].

• M. Rigla, I. Capel, G. García-Sáez, A. Rodríguez-Herrero, D. Subías, B. Pons,F. García-García, M. Gallach, M. Aguilar, C. Pérez Gandía, M.E. Hernando.Overnight normoglycemia using a Personalized Rule-Based Controller in Type 1 Dia-betes. 73th Scientific Sessions of the American Diabetes Association, (Chicago, USA),June 2013.

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9. Conclusions

• B. Pons, M. E. Hernando, I. Capel, G. García-Sáez, D. Subías, A. Rodríguez-Herrero,M. Aguilar, F. García-García, M. Rigla. Inverted U-shaped distribution of theaccuracy of continuous glucose monitoring values: worse results for the extremes.6th International Conference on Advanced Technologies and Treatments for Diabetes,(Paris, France), February 2013.

• I. Martínez-Sarriegui, F. García-García, G. García-Sáez, M. E. Hernando Pérez, M.Luck. TRHIOS: Trust and reputation in hierarchical and quality-oriented societies.7th Iberian Conference on Information Systems and Technologies (Madrid, Spain),June 2012. Proceedings ISBN: 978-1-4673-2843-2 [Indexed JCR].

• A. Rodríguez-Herrero, C. Pérez-Gandía, F. García-García, M. Rigla, M. E. Her-nando, E. J. Gómez. Parametric inicialization method for closed-loop algorithms inType 1 diabetes. 5th International Conference on Advanced Technologies and Treat-

ments for Diabetes (Barcelona, Spain), February 2012.

• C. Pérez-Gandía, F. García-García, G. García-Sáez, A. Rodríguez-Herrero, E. J.Gómez, M. Rigla, M. E. Hernando. Using a causal smoothing to improve the per-formance of an on-line neural network glucose prediction algorithm. 5th Interna-

tional Conference on Advanced Technologies and Treatments for Diabetes (Barcelona,Spain), February 2012.

• F. García-García, A. Marcano-Cedeño, I. Martínez-Sarriegui, P. J. Benito, E. J.Gómez, M. E. Hernando. An Artificial Intelligence Algorithm for Automatic As-sessment of Physical Activity Intensity and Metabolic Type Using Multiaxial Ac-celerometry and Heart Rate. Diabetes Technology Meeting (San Francisco, USA),October 2011. Proceeding published in J Diabetes Sci Technol, 6(2):462–465, 2012.doi:10.1177/193229681200600235 [Indexed PubMed].

• F. García-García, G. García-Sáez, P. Chausa, I. Martínez-Sarriegui, P. J. Ben-ito Peinado, E. J. Gómez, M. E. Hernando. Statistical Machine Learning for Au-tomatic Assessment of Physical Activity Intensity using Multi-axial Accelerometryand Heart Rate. 13th Conference on Articial Intelligence in Medicine (Bled, Slove-nia), July 2011. Proceeding published in Lect Notes Artif Intel 6747:70–79, 2011.doi:10.1007/978-3-642-22218-4_9 [Indexed ISI Web of Knowledge].

• F. García-García, I. Martínez-Sarriegui, E. J. Gómez, M. Rigla, M. E. Hernando.Automatic Assessment of Physical Activity Using Multi-Axial Accelerometry andHeart Rate. 4th International Conference on Advanced Technologies and Treatments

for Diabetes (London, UK), February 2011. Proceeding published in Diabetes Technol

Ther 13(2):182, 2011. doi:10.1089/dia.2010.1219 [Indexed JCR].

National conferences

• I. Capel, M. E. Hernando, G. García-Sáez, D. Subías, B. Pons, A. Rodríguez-Herrero,M. Aguilar, I. Gallach, C. Pérez Gandía, F. García-García, M. Rigla. Páncreasartificial con controlador basado en reglas: Resultados preliminares de la primeraexperiencia clínica. XXIII Annual Congress of the Spanish Diabetes Society (Vigo,Spain), April 2012.

• F. García García, P. J. Benito Peinado, E. J. Gómez Aguilera, M. E. HernandoPérez. Un algoritmo de inteligencia artificial para la detección automática de nivel deintensidad y mecanismo metabólico predominante durante la actividad física medi-ante acelerometría multiaxial y ritmo cardíaco. XXIX Annual Congress of the Span-

ish Society of Biomedical Engineering (Cáceres, Spain), November 2011. ProceedingsISBN: 978-84-614-2693-4, pp. 181–184.

• C. Pérez Gandía, G. García-Sáez, F. García García, A. Rodríguez-Herrero, M.

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9.3. Contributions and achievements

Rigla, D. Subías, B. Pons , E. J. Gómez Aguilera, M. E. Hernando Pérez. Com-paración de modelos de predicción de glucosa: redes neuronales vs. tasa de variaciónde la glucemia. XXIX Annual Congress of the Spanish Society of Biomedical Engi-neering (Cáceres, Spain), November 2011. Proceedings ISBN: 978-84-614-2693-4, pp.515–518.

• F. García García, E. J. Gómez Aguilera, M. E. Hernando Pérez. Detección depatrones de actividad física mediante acelerometría y pulso cardiaco. XXVII Annual

Congress of the Spanish Society of Biomedical Engineering (Cádiz, Spain), November2009. Proceedings ISBN: 978-84-608-0990-6, pp. 73–76.

9.3.2 Awards

Awards in international conferences

• 1st prize to the best student paper, 13th Conference on Artificial Intelligence inMedicine – AIME (Bled, Slovenia), July 2011.

• 3rd prize to the best student contributions, Juvenile Diabetes Research Foundation(JDRF) Student Research Awards in the Diabetes Technology Meeting (San Fran-cisco, USA), October 2011.

148

Part VI

Appendix

149

Appendix A

Mathematical foundations

This appendix overviews the mathematical formalisms which constitute the core of the dif-ferent machine learning algorithms employed to build the PA classifiers under considerationin chapter 6.

A.1 Feature extraction

This type of procedures aim to reduce the dimensionality of the original feature spaceby means of linear combinations of features, projecting data onto a subspace with less at-tributes than the input. Those projection are devised to retain as much relevant informationas possible by discarding redundancy in highly correlated features.

A.1.1 Principal Component Analysis

The linear combination proposed by Principal Component Analysis (PCA) is optimizedto retain as much variance as possible in the projected subspace. Such a formulationis equivalent to finding a set of orthogonal directions along which data observations aremaximally spread [Rencher and Christensen, 2012]. In this manner, when there are featureswhich show strong correlations to each other, most of the total variability present in thedataset can be covered by just a few of the first components found by PCA [Rencher andChristensen, 2012].

Algebraic formulation

Given the dataset D ={

~xi ∈ X ⊂ Rd}n

i=1containing n instances or observations in a d-

dimensional feature space, whose sample mean ~mX and covariance matrix SX are respec-tively:

~mX =1

n

n∑

i=1

~xi (A.1)

SX =1

n− 1

n∑

i=1

(~xi − ~mX) (~xi − ~mX)T (A.2)

Let us consider scalar magnitudes zi computed as the linear combination of feature valuesfrom each sample vector ~xi ∈ D belonging to the dataset D. More precisely, a centredversion of data ~xi − ~mX should be used instead in order to obtain outcomes with zero

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A.1. Feature extraction

mean. For simplicity reasons and compactness in notation, the linear combination can bespecified via a projection vector ~e which governs the relative weight of each feature, i.e.:

zi = ~e · (~xi − ~mX) = ~eT (~xi − ~mX) ∀i = 1, . . . , n (A.3)

With this projection, it can be proved [Rencher and Christensen, 2012] that the resultingset of zi values has sample variance sZ equalling:

sZ = ~eTSX~e (A.4)

However, it is not convenient to try to maximize sZ in (A.4), since it is a not boundedmagnitude unless the norm ‖~e‖2 = ~eT~e is restricted. Therefore, the aim of PCA mustinstead be to maximize a normalized version λ:

λ =~eTSX~e

~eT~e(A.5)

It can also be proved [Rencher and Christensen, 2012] that maxima for (A.5) are found bysolving the following eigenvalue problem:

(SX − λI)~e = 0 (A.6)

Geometric interpretationWithout loss of generality, let us assume that the cloud of points {~xi ∈ D}

n

i=1 resembles anhyperellipsoid in R

d. If features are correlated, then this hyperellipsoid does not have itsnatural orientation axes aligned with the coordinate axes (Figure A.1). With this idea inmind, PCA can be interpreted as the procedure to find those natural axes.

Let us first carry out a translation of the new coordinate system to point ~mX in orderto have the cloud centred around the origin of coordinates. Let us also apply a rotationoperation, defined by a d × d square matrix A; where A is orthogonal, hence fulfillingATA = I. In this new coordinate system, a certain data sample vector ~xi ∈ D wouldtherefore be transformed into vector ~zi where:

~zi = A(~xi − ~mX) (A.7)

For data rotated in this manner, mean and covariance yield [Rencher and Christensen,2012]:

~mZ = 0 (A.8)

SZ = ASXAT (A.9)

The aim of this rotation procedure resides in having features in ~z which are uncorrelated.This in turn implies a covariance matrix SZ will all-zero elements outside the main diagonal:

SZ =

s2Z1

. . . 0s2

Zj

0 . . .

s2Zd

(A.10)

Hence, from (A.9) and (A.10) it follows that matrix A diagonalizes SX ; where λj are theeigenvalues of SX :

λj = s2Zj

∀j = 1, . . . , d (A.11)

152

A. Mathematical foundations

Figure A.1: Schematic depiction of an example PCA procedure in a two-dimensional featurespace. In panel a (left) the two variables x1, x2 are clearly correlated, with the point cloudresembling an ellipse with an oblique orientation of its natural axes. Standard deviationssX1 , sX2 have comparable values. In panel b (center), axes are translated and rotatedfollowing PCA results to get the dataset represented in a new coordinate system, as shownin panel c (right). The first projected feature z1 carries notably more variance –and hence,more information according to PCA principles– than z2 and x1.

and where the rows of A correspond to the transposed version of the eigenvectors �ej for SX

(normalized to be ‖�ej‖ = 1).

As a result of these PCA operations, the scalar value zj is said to be the j-th principalcomponent of �x:

zj = �eT

j �x (A.12)

By convention, eigenvalues are ordered from largest to lowest:

λ1 ≥ . . . ≥ λj ≥ . . . ≥ λd ≥ 0 (A.13)

The fraction fP CA of total variance in data which can be covered by the first dP CA principalcomponents is stated as follows:

fP CA =

∑dP CAi=1 λj

∑di=1 λj

(A.14)

In this regard, when there are highly correlated features, the first eigenvalues are muchlarger than the rest. Thus, most of the total variability can be explained by just a fewprincipal components –i.e. dP CA � d–, a property which justifies the use of PCA fordimensionality reduction. Normally, the number dP CA of selected components is establishedas the minimum to cover a certain fraction of total variance, e.g. fP CA =80%, 90%, 95%or 99%.

PCA from the correlation matrixThe original definition of PCA relies in the calculation of eigenvectors from the samplecovariance matrix SX . However, taking instead the correlation matrix RX can be moreconvenient in certain situations [Rencher and Christensen, 2012]; especially when variancess2

Xidiffer excessively from one feature to another, or if the units of measurement are not

commensurate. In those cases, the eigenvector analysis of SX is strongly dominated by vari-ables with large variance and high scales; whereas the remaining features would contributevery little despite potentially carrying useful information.

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A.1. Feature extraction

A.1.2 Linear Discriminant Analysis

PCA is conceived to retain as much variance from data as possible after projection. There-fore, PCA is unsupervised, in the sense that it does not utilize information about groundtruth class assignments. Oppositely, Linear Discriminant Analysis (LDA) exploits thoseground truth class correspondences in order to find the linear combination of features whichmaximizes the separability of classes in the newly projected space.

LDA for binary problemsFor clarity, let us first address a binary problem with two classes ω0, ω1 under consid-

eration. Given the dataset D ={

(~xi, yi) | ~xi ∈ X ⊂ Rd, yi ∈ Y = {0, 1}

}n

i=1containing n

d-dimensional data instances ~xi and their paired ground truth class assignments yi, withn0 samples belonging to class ω0 and the remaining n1 = n − n0 instances to ω1; samplemeans ~mX0 , ~mX1 and the scatter matrices SX0 , SX1 for each class are calculated as follows:

~mX0 =1

n0

∑

~xi|yi∈ω0

~xi (A.15)

~mX1 =1

n1

∑

~xi|yi∈ω1

~xi (A.16)

SX0 =∑

~xi|yi∈ω0

(~xi − ~mX0) (~xi − ~mX0)T (A.17)

SX1 =∑

~xi|yi∈ω1

(~xi − ~mX1) (~xi − ~mX1)T (A.18)

In addition, the sum of the matrices in (A.17)–(A.18) is often known as the within-classscatter matrix SXW

= SX0 + SX1 .

Let us consider a certain unit projection vector ~e (where ‖~e‖ = 1) which is in charge ofweighing the relative contribution of each feature in the LDA linear combination. Applying~e to data yields:

~zi = ~e · ~xi = ~eT~xi ∀i = 1, . . . , n (A.19)

yields sample means and scatter values:

mZ0 = ~eT ~mX0 (A.20)

mZ1 = ~eT ~mX1 (A.21)

s2Z0

= ~eT SX0~e (A.22)

s2Z1

= ~eT SX1~e (A.23)

s2ZW

= s2Z0

+ s2Z1

= ~eT SXW~e (A.24)

LDA’s objective consists in maximizing class separability, defined as the difference betweenprojected means mZ0 , mZ1 and divided by a measure of spread, in this case the square rootof the aggregated within-class scatter value sZW

[Duda et al., 2000]:

mZ1 −mZ0

sZW

(A.25)

However, the numerator in (A.25) can become negative. For this reason, the problem ofmaximizing class separability should be formulated on the squared version of (A.25):

(mZ1 −mZ0)2

s2ZW

=[~eT (~mX1 − ~mX0)]2

~eT SXW~e

(A.26)

154

A. Mathematical foundations

It can be proved [Rencher and Christensen, 2012] that the quotient in (A.26) is maximizedby taking the projected vector ~e as:

~e = S−1XW

(~mX1 − ~mX0) (A.27)

LDA extension for multi-class problemsLet us now consider having C ∈ N possible classes {ωc}

C

c=1, where C > 2. The binary LDAformulation –summarized in the optimization of target quotient (A.26)– can in this case beextended to the maximization of a generalized quotient λ:

λ =~eT SXB

~e

~eT SXW~e

(A.28)

where [Duda et al., 2000]:

• SXWis the within-class scatter matrix, which aggregates the C scatter matrices cal-

culated for each class by separate:

SXW=

C∑

c=1

∑

~xi|yi∈ωc

(~xi − ~mXc) (~xi − ~mXc

)T (A.29)

• SXBis the between-class scatter matrix, defined as follows:

SXB=

C∑

c=1

nc (~mXc− ~mX) (~mXc

− ~mX)T (A.30)

• ~mXcis the sample mean vector for the c-th class, formed by nc data instances:

~mXc=

1

nc

∑

~xi|yi∈ωc

~xi ∀c = 1, . . . , C (A.31)

• ~mX is the overall sample mean across classes:

~mX =1

n

∑

~xi∈D

~xi =1

n

C∑

c=1

nc ~mXc(A.32)

Maximizing (A.28) is equivalent to solving the following generalized eigenvalue problem[Rencher and Christensen, 2012]:

(

S−1XW

SXB− λI

)

~e = 0 (A.33)

On the other hand, the number dLDA of eigenvectors ~e in (A.33) which correspond to anon-zero eigenvalue λ equals [Rencher and Christensen, 2012]:

dLDA = rank SXB= min {C − 1, d} (A.34)

In practice, for the vast majority of feature extraction problems addressed with LDA theprimary limitation is dLDA = C − 1. As a consequence, the dimensionality of the featuresubspace resulting from LDA projection is equal to the number of classes under consider-ation minus one.

155

A.2. Clustering

A.2 Clustering

This family of problems consist in finding non-predefined homogeneous groupings of data,known as ‘clusters’, in such a way that their internal similarity –i.e. the resemblance amongthose data elements within the same cluster– is maximized, whereas the external similarity–i.e. across different clusters– is minimal. Given that explicit data categories or predefinedcorrespondences are not available during training, clustering constitutes an unsupervisedlearning procedure for the discovery of ‘natural’ similarity structures in the dataset. Inthis PhD thesis, clustering approaches were used as a ‘smart preprocessing’ technique, or‘smart feature extraction’ stage [Duda et al., 2000], to quantize high-dimensional vectordata onto a discrete set of options (clusters).

A.2.1 K-means clustering

K-means is the most extensively used clustering technique, at least in part due to its relative

simplicity, both conceptual and computational. Given the dataset D ={

~xi ∈ X ⊂ Rd}n

i=1,

its aim is to partition D in a total of K ∈ N clusters, where the number K is assumed tobe known beforehand. The proposed partition is fully specified by a set of cluster centroids{

~ck ∈ Rd}K

k=1in such a manner that a certain input data instance ~x is assigned to cluster

Ck (with centroid at ~ck) if and only if it is closer to ~ck than to any other centroid, i.e.:

~x ∈ Ck ⇔ k = arg minj=1,...,K

dist(~x,~cj) (A.35)

where dist(·, ·) is a suitable distance metric in the input space Rd. Typically, the squared

Euclidean distance ‖~x−~cj‖2 is used, although other possible choices exist, e.g. city block,

or Hamming distances.

as a consequence, training the model Θ consists in finding the set of centroids Θ = {~ck}K

k=1

which are best adapted to the spatial distribution of input data distribution, where opti-mality is understood in the sense of minimizing the following cost function J(Θ):

J(Θ) =K∑

k=1

∑

~x∈Ck

‖~x− ~ck‖2 (A.36)

where in this case J(Θ) accounts for the sum of squared Euclidean distances from eachdata point ~x to the centroid ~ck of the particular cluster Ck to which it is associated.

In practise, J(Θ) is minimized iteratively. First, cluster centroids are initialized at randomlocations. Afterwards, each data item is associated to the cluster whose temporary centroidis nearest (Figure A.2). Subsequently, each centroid location ~ck is updated to the averageposition of data corresponding to Ck; hence its name of centroid, as a center of mass. Thisiterative process continues until displacements of centroids with respect to their formerposition at the previous iteration do no longer occur. However, this is an heuristic proce-dure which cannot guarantee an optimal solution, i.e. a global minimum for J(Θ); sinceit may converge to local minima. In particular, the process is specially sensitive to theinitial centroid locations. To address this issue, a common is approach consists in selectingrandom points from D. In addition, and given that the iterative training is generally notvery heavy from a computational perspective –especially if K is low–, the procedure maybe repeated several times with different random initializations, finally choosing the solutionwith lowest cost J(Θ).

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A. Mathematical foundations

Figure A.2: Example depiction of the iterative training procedure for K-means, with K=3clusters. Panel a shows unassigned data instances –yellow diamonds–; whereas panel breflects a random initialization of cluster centroids –red, blue and green circles– for training.Panel c depicts the first cluster associations, according to the initial locations of tentativecentroids. Panels d to f illustrate the iterative update of centroids and cluster assignmentsuntil a final solution is reached in f. In panel e, dotted circles mark those data instanceswhose cluster associations changed with respect to the previous iteration.

Of note, the number of clusters K is an essential model parameter which must alwaysbe specified in order to proceed with the training of the algorithm. The choice for K isoften done manually, at the sight of the cloud of input data points in D or inspecting theoutputs for various tentative values for K. However, it is infrequent to reach to a clear,undisputed answer about what the optimal value for K should be. Therefore, parametertuning procedures for setting K are often required.

On the other hand and as outlined above, K-means has the disadvantage of being sensitiveto the initialization of cluster centroids, an aspect which may cause a convergence to localoptima. Finally, it is also vulnerable to outliers.

A.2.2 Gaussian Mixture Models

Mixture modelsLet us assume that the n available data instances �x ∈ D are drawn from K different clusters{Ck}K

k=1; where both K and prior cluster probabilities P (Ck) are known –at least for themoment–, but the actual cluster correspondences for each data item are ignored. Let usalso consider that the general form of the conditional probability densities is:

p (X = �x | Ck; θk) ∀k = 1, . . . , K (A.37)

where θk represents the unknown collection parameters which fully determine the specificconditional probability density function for the k-th cluster Ck.

In these general mixture models, the process to draw data instances �x ∈ D occurs in twoconsecutive stages:

1. Randomly selecting a certain cluster Ck, with prior probability P (Ck)

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A.2. Clustering

2. Generating ~x in accordance to the specific conditional density function p (X = ~x | Ck; θk)of cluster Ck in (A.37).

Hence, the overall probability density function for data would be:

p (X = ~x |Θ) =K∑

k=1

p (X = ~x | Ck; θk)P (Ck) (A.38)

formed by theK components, each weighted by its corresponding prior; and being Θ = {θk}K

k=1

the yet unknown collection of parameters for the aggregated mixture model.

Therefore, the datasetD ={

~xi ∈ X ⊂ Rd}n

i=1must be used in order to generate a suitable a

posteriori estimate Θ of model parameters, ideally to match the original Θ from which datainstances were drawn. This estimation is normally performed through maximum-likelihoodprocedures, which aime to maximize the likelihood of the observed samples given tentativemodel parameters:

Θ = arg maxΘ

{p(D |Θ)} = arg maxΘ

{

n∏

i=1

p (X = ~xi |Θ)

}

(A.39)

In general, (A.39) encompasses very complex search problems in high-dimensional spaces,which are solved by iterative numerical algorithms including expectation-maximization(EM) approaches [Duda et al., 2000]. If priors P (Ck) are also unknown –as it is often thecase–, maximum-likelihood estimates for P (Ck) can also be employed.

Once a suitable estimate Θ has been calculated, the mixture can be decomposed into itsprimary components, a decomposition which allows to ascertain the cluster associationsC(i) for each data item ~xi. This task is carried out with a maximum a posteriori procedure(Bayes theorem) on the derived densities:

C(i) = arg maxk=1,...,K

{

p(

X = ~xi | Ck; θk

)

P (Ck)}

(A.40)

Gaussian mixturesGaussian Mixture Models (GMM) constitute a particularization of the more general caseformulated above in which each cluster-specific density function in (A.37) is modelled as amultivariate normal distribution –i.e. Gaussian– with mean vector ~µk ∈ R

d and covariancematrix Σk ∈ R

d×d [Reynolds, 1995]:

p (X = ~x | Ck; θk) =1

(2π)d2 |Σk|

12

e− 12

(~x−~µk)T Σ−1k

(~x−~µk) (A.41)

Aiming to simplify and accelerate the EM learning of GMM parameters, extra assumptionsare sometimes made about the form of the covariance matrices Σ, restricting their numberof free parameters: e.g. by assuming Σ to be diagonal. However, such restrictions were notemployed in this work.

A.2.3 Hierarchical clustering

Hierarchical clustering methods propose an ordered sequence of cluster groupings or un-

groupings which partition the dataset D ={

~xi ∈ X ⊂ Rd}n

i=1. This sequence of partitions,

which can be represented in a very practical and intuitive graphical manner by means

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A. Mathematical foundations

Figure A.3: Dendrogram representation of a hierarchical sequence of grouping (for bottom-up approaches) or ungrouping operations (for top-down schemes) among sub-clusters. De-pending on the number of clusters which are specified as the target final outcome, thedendogram’s tree structure should be ‘cut’ at a certain depth or another.

of a dendrogram (Figure A.3), may progress from n clusters –all singletons– towards anunique cluster containing all n samples, or vice versa. In a bottom-up (i.e. agglomerative)approach, the algorithm starts from the n singletons and proceeds by iteratively mergingthose two clusters Ci, Cj which are nearest to each other than any other possible pair. Onthe contrary, top-down (i.e. divisive) strategies commence with one universal cluster con-taining all n instances and progress by finding the two maximally separated sub-clusters,splitting them and proceeding recursively.

As for other methodologies (e.g. K-means), hierarchical clustering requires a desired num-ber of clusters to be established. In addition, two types of distance metrics need to bespecified as well, namely:

1. Distance between two individual data instances or points �x, �x′; being Euclideandistance the most frequent option:

dist (�x, �x′)Eucl = ‖�x − �x′‖ =

√

√

√

√

√

d∑

j=1

(xj − x′j)

2 (A.42)

although various other suitable metrics exist: e.g. Mahalanobis distance, city-block,Minkowski or Hamming metrics.

2. Distance l between two clusters, also known as ‘linkage’ criterion. Common choicesfor this ‘linkage’ function are:

• minimal –or ‘single’– criterion, defined as the distance between the nearest pairof points, one in each cluster:

lmin (Ci, Cj) = min�x∈Ci,�x′∈Cj

dist (�x, �x′) (A.43)

• maximal –or ‘complete’– criterion, i.e. the distance between the two furthestpoints belonging to each cluster:

lmax (Ci, Cj) = max�x∈Ci,�x′∈Cj

dist (�x, �x′) (A.44)

• average criterion, where the mean of all possible pairs is computed:

lavg (Ci, Cj) =1

ninj

∑

�x∈Ci

∑

�x′∈Cj

dist (�x, �x′) (A.45)

being ni, nj the number items (i.e. the cardinality) for clusters Ci and Cj,respectively.

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A.2. Clustering

• centroid criterion, defined as the distance between the geometric centres of massfor each of the two clusters under consideration:

lcentr (Ci, Cj) = dist (~mi, ~mj) (A.46)

~mi =1

ni

∑

~x∈Ci

~x (A.47)

~mj =1

nj

∑

~x′∈Cj

~x′ (A.48)

• Ward’s distance criterion, calculated as the incremental sum of square errors(SSE) [Ward, 1963]:

lW ard (Ci, Cj) = SSECi,Cj−(

SSECi+ SSECj

)

(A.49)

where:

SSECi=

ni∑

i=1

dist2 (~xi, ~mi) (A.50)

SSECj=

nj∑

j=1

dist2(

~x′j, ~mj

)

(A.51)

SSECi,Cj=

ni∑

i=1

dist2 (~xi, ~mij) +nj∑

j=1

dist2(

~x′j, ~mij

)

(A.52)

~mij =ni ~mi + nj ~mj

ni + nj

(A.53)

A.2.4 Self Organizing Maps

Self Organizing Maps (SOM) are a form of artificial neural networks first introduced by[Kohonen, 1990]. They were conceived to produce a low-dimensional representation –typically a 2D grid map– which discretises the high-dimensional input data space.

Their training phases consists in adjusting neurons’ weights vectors, which determine prox-imity with respect to data instances. After weights ~w ∈ R

d have been randomly initialized,an iterative procedure is started. At the t-th iteration, training proceeds by picking a

certain input vector ~x from the dataset D ={

~xi ∈ X ⊂ Rd}n

i=1in order to calculate which

neuron y⋆ has its weight ~wy⋆ most similar to ~x:

y⋆ = arg miny‖~x− ~wy‖ (A.54)

This neuron y⋆ is declared ‘winner’ (in a so-called ‘competitive’ learning), and its weight~wy⋆ updated to be pulled a fraction η closer to input ~x. Along with neuron y⋆, its closestneighbours in the topology of the neural network (Figure A.4) also undergo the followingupdate of their respective neuron weights for next iteration t+ 1:

~wy[t+ 1] = ~wy[t] + η[t]Λ(|y − y⋆|) {~x− ~wy[t]} (A.55)

where the learning rate η[t] ∈ (0, 1) decreases slowly with iterations; as it also does theradius of action of Λ(·), the neighbourhood function. Typical neuron topologies for SOMare hexagonal lattices (Figure A.5) and square grids.

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A. Mathematical foundations

Figure A.4: SOM neighbourhood function Λ(·).

Figure A.5: Example depicting various iterations of the SOM training algorithm. Panel ashows the initial distribution of neurons in an hexagonal 2D lattice. In panel b, an inputdata instance �x (red diamond) is taken, which activates primarily the winning neuron (redcircle) and, to a lesser extent, also its neighbours (orange and yellow circles). Those neuronsundergo an update of their weights towards �x in panel c. Panels d to h illustrate additionaliterations of training.

The biological inspiration of this type of artificial neural networks resides in that neuronswhich are topologically near within the network structure, will have similar functionalityand responses for a certain input. In this regard, once training is complete (which tendsto demand a large number of iterations), the network will have learnt the distributionpatterns in data, in such a way that adjacent neurons will respond similarly; whereasdissimilar inputs will activate distant regions of the SOM map. In other words, input dataitems which are close to each other in the original, high-dimensional feature space are inturn related to neighbouring neurons in the SOM representation. Hence, the SOM producesa low-dimensional –typically 2D– mapping, in which distances and proximity relationshipsare preserved as much as possible. In this manner, SOMs achieve a discrete approximationto the underlying probability density function of data, especially if the number of neuronsis high. If fewer neurons, SOMs cluster the input space [Kohonen, 1990; Kaski, 1997].

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A.3. Classification

A.3 Classification

Classification problems in ML can be formalized as the process to find a suitable functionmatching data inputs with their corresponding ground truth class assignments, which areprovided for reference during the training stage. Thus, classification belong to supervisedlearning, as opposed to clustering schemes in which a desired output is not explicitly knowna priori.

Ideally, a classifier should have high accuracy (i.e. low output error), as well as goodgeneralizability, which means that its performance remains in satisfactory levels for newinputs which were not seen during the training stage. On the other hand, the number ofclasses under consideration must be finite.

A.3.1 Naïve Bayes

Given a dataset D ={

(~xi, yi) | ~xi ∈ X ⊂ Rd, yi ∈ Y = {1, . . . , C} ⊂ N

}n

i=1which contains

n input data samples ~xi, along with their ground truth correspondences yi to one out ofthe C possible classes. If the underlying model Θ was fully known, the output classificationassignment y for a certain input item ~x would be obtained by means of its maximum a

posteriori probability:y = arg max

c=1,...,C

{p(Y = c |X = ~x; Θ)} (A.56)

where in accordance to Bayes rule, the posterior probability in (A.56) can be expressed asfollows:

p(Y = c |X = ~x; Θ) =p(X = ~x | Y = c; Θ)P (Y = c)

∑Cc=1 p(X = ~x | Y = c; Θ)P (Y = c)

(A.57)

∝ p(X = ~x | Y = c; Θ)P (Y = c) (A.58)

Given D, the estimation of priors P (Y = c) in (A.58) is straightforward; whereas likelihoodsp(X = ~x | Y = c; Θ) may in general be considerably difficult to model and to identify.For this reason, the Naïve Bayes (NB) approach assumes these likelihoods to be class-conditionally independent for each feature with respect to all other dimensions, i.e. [Dudaet al., 2000]:

p(X = ~x | Y = c; Θ) ∼d∏

j=1

p(X(j) = xj | Y = c; Θ) (A.59)

This premise entails that the problem of estimating a complicated multivariate probabilitydensity function (pdf) in R

d can instead be reduced in NB schemes to estimate d simplerunivariate pdfs. Besides, for continuous variables it is common to model these univariatepdfs as Gaussians ∼ N (µ, σ).

Accepting this NB assumption in (A.59), and once the general form of pdfs has beenestablished –e.g. as Gaussians–, training the NB classifier consists in estimating suitableparameter values Θ to specify univariate pdfs fully; e.g. in the case of Gasussians: meansµj,c and standard deviations σj,c, along with priors P (c). This task is usually carried outvia maximum likelihood estimations [Duda et al., 2000].

A.3.2 Multinomial logistic regression

Given dataset D, logistic regression is founded on the estimation of posterior probabilitiesfor each of the C classes by means of linear regression formulae. In particular, the natural

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A. Mathematical foundations

logarithms of the ratios between the posteriors of the c-th and the C-th (i.e. last) classesare computed. Mathematically:

log

[

p(Y = c |X = ~x; Θ)

p(Y = C |X = ~x; Θ)

]

= β0,c + ~βc · ~x = β0,c + ~βT

c ~x ∀c = 1, . . . , C − 1 (A.60)

where scalar β0,c is a bias or intercept term and vector ~βc ∈ Rd represents the set of weights

for each of the d features in ~x. From (A.60) it can be easily derived that:

p(Y = c |X = ~x; Θ) = p(Y = C |X = ~x; Θ)eβ0,c+~βTc ~x (A.61)

Given that the posteriors must sum to 1, from (A.61) it follows:

p(Y = c |X = ~x; Θ) =eβ0,c+~βT

c ~x

1 +∑C−1

c=1 eβ0,c+~βTc ~x

∀c = 1, . . . , C − 1 (A.62)

p(Y = C |X = ~x; Θ) = 1−C−1∑

c=1

p(Y = c |X = ~x; Θ) =1

1 +∑C−1

c=1 eβ0,c+~βTc ~x

(A.63)

Parameters β0,c and ~βc ∈ Rd for each class (except the C-th one) are estimated iteratively

via maximum likelihood schemes. Once the logistic regression model is trained, classifica-tion is carried out simply by choosing the maximum a posteriori probability.

A.3.3 Multi-Layer Perceptrons

Feed-forward multi-layer perceptrons (MLPs) are a family of artificial neural networksin which neurons are arranged in layers, almost always with full interconnection betweenadjacent layers (Figure A.6) and non-linear neuron activation responses. MLPs can be usedfor both ML classification and estimation problems, a flexibility which has made them themost frequent neural network architecture across a wide variety of fields of application.

Mathematically, the behaviour of a neuron with m inputs {uj}mj=1 and a single output v

can be described as follows:

v = f

w0 +m∑

j=1

wjuj

= f (w0 + ~wT~u) (A.64)

The linear combination of inputs uj, weighted by factors wj –plus a bias weight w0–, is fedto a non-linear response function f(·) (Figure A.6, panel a), where common choices for fare sigmoid curves, e.g.:

f(u) = tanh u (A.65)

f(u) =1

1 + e−u(A.66)

The classical MLP network architecture is depicted in Figure A.6 (panel b): input andoutput layers plus one additional ‘hidden’ layer interspersed between both. The inputlayer is in charge of transporting data to the neurons in the hidden layer, which in turnactivate according to (A.64). Outcomes from these hidden neurons are then supplied assuccessive input for the neurons in the output layer. Connections between pairs of neuronsare characterized by their weights, which –along with biases– fully specify the response of

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A.3. Classification

Figure A.6: MLP architecture. Panel a (left) illustrates the internal functioning of a singleneuron, connected by its inputs to m other neurons and characterized by a non-linearactivation. Panel b (right) shows the layered arrangement and interconnection of neuronsin the network.

the MLP model. Hence, being Θ the collection of weights and biases across the network,the MLP implements a non-linear mapping function gΘ(·):

�y = gΘ(�x) (A.67)

Despite its relatively simple modular formulation, gΘ(·) encompasses high expressive power.In this regard, Kolmogorov proved [Duda et al., 2000] that, with a sufficiently high numberof hidden neurons, appropriate weights and suitable non-linearity functions f , any contin-uous function g(·) can be implemented through a MLP with an unique hidden layer.

Given the dataset D ={

(�xi, yi) | �xi ∈ X ⊂ Rd, yi ∈ Y = {1, . . . , C} ⊂ N

}n

i=1with input data

�xi and ground truth class assignments yi, a MLP classifier devised to be applied in thisproblem must have the following structure [Duda et al., 2000]: a) as many neurons inthe input layer as dimensions d in data ; and b) as many neurons in the output layer asthe number C of classes under consideration. In this regard, for the purpose of trainingthe MLP, desired outputs �y ∈ R

C in (A.67) must be binary vectors reflecting ground truthclass assignments yi, in such a manner that the c-th vector coordinate of �y equals 1 if andonly if yi = c; and 0 otherwise.

The process of training the MLP consists in finding a suitable set Θ of connection weights wj

and biases w0 for all neurons in the network. The appropriateness of a certain combinationof model parameters Θ is determined by its ability to minimize a certain cost function J :

Θ = arg minΘ

J(Θ) (A.68)

where J(Θ) accumulates penalizations in the form of squared differences between the ideallydesired output vectors �yi and the actual results obtained by the non-linear mapping gΘ(·),i.e.:

J(Θ) =1

2

n∑

i=1

‖�yi − gΘ(�xi)‖2 (A.69)

Once the MLP network is trained, classification outcomes are achieved by determiningwhich of its C output neurons becomes maximally activated when presenting a certain newinput to the network. However, given the high number of parameters (weights, biases) which

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A. Mathematical foundations

must be tuned to minimize (A.69), training constitutes an arduous non-convex optimizationproblem in a high-dimensional search space, for which a globally optimal solution cannot beguaranteed. For this reason, various numerical optimization algorithms based on gradientdescent approximations can be applied to the training of MLPs, the most popular beingknown as ‘back-propagation’, for which a series of practical considerations apply [Dudaet al., 2000]. In particular, regarding the number of neurons in the hidden layer: the usershould either specify it manually, rely on ‘rules of thumb’ or use automatic parametertuning procedures.

A.3.4 Support Vector Machines

support vector machines (SVMs) are maximal-margin classifiers. Although originally con-ceived for binary problems, SVMs can also be applied to multi-class classification taskswith relatively simple extensions.

Binary problem with linear class separability

Let us consider a binary (two-class) datasetD ={

(~xi, yi) | ~xi ∈ X ⊂ Rd, yi ∈ Y = {±1}

}n

i=1which satisfies the property of linear separability between both classes. In this case, thereare infinitely many valid linear boundaries which achieve perfect classification (Figure A.7).Those decision boundaries can be expressed mathematically as a hyperplanes in R

d, charac-terized by their normal vector ~w ∈ R

d and a scalar offset b. According to this formulation,the outcome decision y regarding the classification of a data point ~x would correspond tothe application of the following expression:

y = sign (~w · ~x+ b) (A.70)

Taking into account (A.70), let us define the ‘functional margin’ γi of certain pair {~xi, yi}as a magnitude measuring its separation with respect to the decision boundary hyperplane:

γi = yi(~w · ~x+ b) (A.71)

where this functional margin satisfies γi > 0 for all pairs in D if the hyperplane understudy is a valid boundary solution achieving perfect separation of classes. Consequently,γi may become an useful indicator of the confidence in the classification provided by theseparation hyperplane, because it reflects –up to a scale factor– the geometric distancefrom ~xi to the decision boundary. In addition, it is interesting to have large margins as aprotection against eventual noisy data instances. For this reason and aiming to enhancerobustness in classification, the SVM framework focuses on proposing a methodology tofind the appropriate separation hyperplane which maximizes margins.

Considering the most limiting case –i.e. taking the minimal γi value from the dataset–, alower bound for all functional margins can be set:

γ = mini=1,...,n

γi ⇒ yi(~w · ~xi + b) ≥ γ ∀i = 1, . . . , n (A.72)

It can be proved [Vapnik, 1998] that the ‘geometrical margin’ (which constitutes the ul-timate optimization goal for SVMs) is related to the ‘functional margin’, equalling 2 γ

‖ ~w‖.

Furthermore, in order to address a scale-invariant problem (i.e. not sensitive to the rescal-ing of parameters), it can be assumed without loss of generality that γ = 1 [Vapnik, 1998].

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A.3. Classification

Hence, the former margin-maximization problem can be restated as a minimization in thefollowing terms:

min~w,b

1

2‖~w‖2 | yi(~w · ~xi + b) ≥ 1 ∀i = 1, . . . , n (A.73)

where the right-hand side of (A.73) restricts the search of possible pairs {~w, b} to onlythose hyperplanes which produce valid decision boundaries that separate classes in a correctmanner. On the other hand, and given that the optimization problem contained in (A.73) isconvex [Fradkin and Muchnik, 2000], it can be solved efficiently by quadratic programmingalgorithms.

Problems not satisfying linear class separabilityDatasets D satisfying the property of perfect linear class separability are extremely rare inpractice. Nonetheless, the SVM formalism presented above can still be employed, providedthat the user is willing to accept certain errors ξi (Figure A.8). In such case, in order toaccommodate tolerated errors ξi ∈ [0, 1), constraints in the right-hand side of (A.73) shouldbe substituted by:

yi(~w · ~xi + b) ≥ 1− ξi ∀i = 1, . . . , n (A.74)

and the optimization goal in its left hand side should now become:

min~w,b

1

2‖~w‖2 + Cbox

n∑

i=1

ξi (A.75)

where Cbox –a regularization term, commonly known as ‘box constraint’– is a positive scalarvalue which encompasses a trade-off between the tolerance of errors and the prevention ofoverfitting. This situation is often referred to as ‘soft margin’ SVM classification; whereason the contrary, if Cbox → ∞, then classification errors become heavily penalized (‘hardmargin’) and (A.75) tends to (A.73).

Dual (Lagrangian) SVM formulationLagrange multipliers can be used to accommodate the constraints from the right-handside of (A.73), reformulating the former optimization problem as the minimization of thefollowing target function L(~w, b, α):

L(~w, b, α) =1

2~w · ~w −

n∑

i=1

αi [yi(~w · ~xi + b)− 1] (A.76)

where Lagrange multipliers α satisfy:

{

αi = 0 if yi(~w · ~xi + b) > 1; constraint is irrelevantαi > 0 if yi(~w · ~xi + b) = 1; constraint becomes relevant (i.e. ~xi is a ‘supporting vector’)

(A.77)It can be proved [Vapnik, 1998] that minimizing (A.76) subject to (A.77) is equivalentto solving problem (A.73). Once (A.76)–(A.77) are solved, normal vector ~w plus offsetb, which characterize the optimal SVM decision boundary hyperplane, can be derived asfollows:

{

~w =∑n

i=1 αiyi~xi

b = yk − ~w · ~xk for any k | αk 6= 0(A.78)

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A. Mathematical foundations

Figure A.7: SVM definition as a maximal-margin classifier. For linearly separable problems,there are infinitely many valid boundary planes (black lines) which separate correctly databelonging to each class. SVMs focus on the particular solution plane (green line) whichcomes not closer to either class than strictly necessary, thus optimizing the distance –i.e.margin– to data items. The most limiting cases (emphasized by pink circles) are known as‘supporting vectors’, hence the name of the methodology.

Figure A.8: SVM boundary hyperplane for a dataset without perfect linear separability.By introducing ξi terms, a fraction of erroneously classified samples are allowed.

Figure A.9: Non-linear SVM decision boundaries generated via the application of ‘kerneltricks’, achieving either perfect separation (left panel) or not (right).

Furthermore, incorporating (A.78) into (A.76) and applying Karush-Kuhn-Tucker condi-tions [Vapnik, 1998], then (A.76)–(A.77) can be rewritten as the maximization of:

n∑

i=1

αi −1

2

n∑

i=1

n∑

j=1

αiαjyiyj�xi · �xj |n

∑

i=1

αiyi = 0; αi ≥ 0 ∀i = 1, . . . , n (A.79)

which can be solved efficiently by quadratic programming algorithms.

Finally, in order to address problems without perfect class separability, the ‘box’ constraintCbox needs to be incorporated into the right-hand side of (A.79) in the following manner:

Cbox ≥ αi ≥ 0 ∀i = 1, . . . , n (A.80)

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A.3. Classification

KernelsLinear separation hyperplanes may not always result flexible enough for realistic applicationscenarios in which decision boundaries with more complex shapes are required (Figure A.9).Nevertheless, SVMs can still accommodate these cases by means of the application of theso-called ‘kernel trick’, where the dot product of vectors ~xi, ~xj in (A.79) may be substitutedby a suitable kernel function κ:

κ(~xi, ~xj) = φ(~xi) · φ(~xj) (A.81)

This can be done even without the need for knowing the transformation φ(·) explicitly,since Mercer’s theorem states that positive semi-definiteness is the necessary and sufficientcondition for a symmetric function κ(·, ·) to be a valid kernel [Burges, 1998]. Commonchoices for κ include:

• homogeneous polynomial kernels (where p > 0):

κ(~xi, ~xj) = (~xi · ~xj)p (A.82)

• inhomogeneous polynomial kernels (where p, k0 > 0)

κ(~xi, ~xj) = (~xi · ~xj + k0)p (A.83)

• Gaussian kernels, also known as radial basis functions (RBF) (where σ2 > 0):

κ(~xi, ~xj) = exp

[

−‖~xi − ~xj‖

2

2σ2

]

(A.84)

• hyperbolic tangent kernels (where η > 0, ν < 0):

κ(~xi, ~xj) = tanh(η~xi · ~xj + ν) (A.85)

Despite not having the explicit definition of φ(·) for these kernels, a new input ~x′ can stillbe processed by the SVM, generating an outcome classification y′ ∈ {±1} according to thefollowing formula:

y′ = sign (~w · φ(~x′) + b) (A.86)

where:{

~w · φ(~x′) =∑n

i=1 αiyiκ(~x′, ~xi)b = yk −

∑ni=1 αiyiκ(~xk, ~xi) for any k | Cbox > αk > 0

(A.87)

Multi-class SVM extensionIf instead of a binary classification problem, C possible classes are considered (where C >2 ∈ N); then the procedure requires adaptations with respect to the standard binary SVMalgorithms detailed above. The most common strategy (and adopted in this PhD work)is known as the one-versus-all (OVA) approach. OVA consists in producing C differentSVM classifiers, each of which must be trained to distinguish one class from all of theremaining others aggregated together. Another possibility, named one-versus-one, leads tothe training of a SVM for each one of the

(

C

2

)

= C(C−1)2

possible pairs of classes.

Practical aspectsWhen using SVMs in practical applications, various essential configuration options –i.e.‘hyperparameters’ in ML terminology– need to be selected, constituting a challenging sit-uation which can greatly influence the resulting overall performance of the SVM model.

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A. Mathematical foundations

In first place: the type of kernel to be employed, where linear and RBF are the two mostcommon choices in literature. In addition, an appropriate value for the regularizationparameter Cbox must be established. If Cbox is set too small, then errors may not be suffi-ciently penalized; leading in turn to an oversimplified SVM classifier with the subsequentrisk of underfitting (i.e. high bias problem). Conversely, if Cbox is assigned a too highvalue, errors may gain excessive attention, leading to a SVM model overfitting the dataused during training (high variance problem) and hence losing generalization power. Fur-thermore, in the case of RBF kernels, a similar effect may occur with magnitude σ2, i.e.kernel width: large σ2 values may induce oversimplified models (high bias); whereas toolow σ2 choices could pose a risk of overfitting (high variance). As a consequence, automaticparameter tuning procedures are often the preferred manner of selecting appropriate SVMhyperparameter values.

A.3.5 Decision trees

Decision trees represent, in a very natural and interpretable manner, a structured sequenceof tests (‘queries’) concerning data properties. Depending on the result of the specific queryat a certain point (known as ‘node’), the decision flow progresses through a separate path(‘branch’). This process terminates and produces an outcome –in this case, a classificationassignment– whenever it reaches a node in which further queries are not specified (‘leaf’).Therefore, the process of training a decision tree consists in determining a suitable sequenceof queries in a structured manner. A considerable variety of tree algorithms exist, althoughthis section overviews the system known as classification and regression trees (CART),which is a flexible, general-purpose framework that covers the main principles of almost allof the algorithms devised for the automatic creation of decision trees.

Given a datasetD for training, whereD contains data items and their corresponding groundtruth class assignments, tree building algorithms in general progress recursively to generatequeries which split D into smaller and more homogeneous subsets. Of note, this procedureis said to be non-metric because the splitting is not based on distance criteria betweensamples.

Tree splittingAt each node, its query’s outcome routes the progress of the decision flow through a certainbranch in the tree. Consequently, the branching factor B –determined by the number ofpossible outcomes for the query– depends on the type of data being inspected and onhow the query is defined. In general terms, a node can derive into more than two childbranches (i.e. B > 2), although those situations can be made equivalent to a succession ofbinary decisions (B = 2). For this reason, explanations here are primarily –although notexclusively– oriented to binary trees.

The strategy to search how to split the tree at a node is a design choice, but following theprinciple of parsimony, simple and compact trees with fewer nodes tend to preferred; forwhich a greedy heuristic is commonly used. At a certain node N , this greedy heuristicconsists in seeking for a query/test τ which makes the data samples which reach the im-mediate descendent nodes as ‘pure’ as possible. Let i(N ) be a metric of data ‘impurity’ atthe current node N , the aim is to find a test τ which maximizes the change in impurity∆i, reflecting an increase in purity:

∆i(N ; τ) = i(N )− [PP os,τ i(NP os,τ ) + PNeg,τ i(NNeg,τ )] (A.88)

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A.3. Classification

where PP os,τ , PNeg,τ are the fractions of data patterns at node N which give respectivelypositive and negative answers to the test τ . Besides, NP os,τ , NNeg,τ are the immediatepositive/negative descendent nodes following query τ at N . Therefore, the greedy heuristicperforms a local optimization, because it evaluates the immediate progression of the tree,at a single node and only one depth level further. This aspect entails an advantage in termsof restraining the algorithm’s complexity and computational load; although at the expenseof preventing the guarantee of achieving globally optimal decision structures.

On the other hand, when B > 2 (‘multi-ways splits’) the straightforward extension of(A.88) would be:

∆i(N ; τ) = i(N )−B∑

b=1

Pb,τ i(Nb,τ ) (A.89)

However, this definition in (A.89) is known to favour in excess decisions with large branchingfactors B. For this reason, a ‘gain impurity ratio’ is often preferred as target:

∆iB(N ; τ) =i(N )−

∑Bb=1 Pb,τ i(Nb,τ )

−∑B

b=1 Pb,τ log2 [Pb,τ ](A.90)

For the maximization of ∆i(N ; τ) in (A.88) or ∆iB(N ; τ) in (A.90), the space T of candi-date tests τ needs to be explored as efficiently as possible. Consequently and in order tospeed up the search, tests should ideally be quick to compute, which in practise is oftenachieved by tests consisting in the application of thresholds on a single feature.

Another important aspect is how to quantify the ‘impurity’ i(N ) at a certain node. Letus denote as P (ωj) or P (~x ∈ ωj | N ) the fraction of patterns ~x at node N which belong tothe j-th ground truth class ωj. Frequent choices for the impurity function i(N ) are [Dudaet al., 2000]:

• Entropy H:iH(N ) = −

∑

j

P (ωj) log2

[

P (ωj)]

(A.91)

• Gini’s diversity index G:

iG(N ) =∑

j

∑

k 6=j

P (ωj)P (ωk) =1

2

1−∑

j

P 2(ωj)

(A.92)

• Misclassification rate M :iM(N ) = 1−max

jP (ωj) (A.93)

where iM(N ) estimates the minimum probability for a training sample to be classifiedincorrectly at node N if treated as a leaf node.

Theoretically, trees could be grown until the purity of the patterns which reach a particularleaf node is maximal (e.g. all belong to the same ground truth class). However, this pro-cedure can be counter-productive in terms of the overall classification accuracy attained,since it carries a notable risk of overfitting the tree to the training set; hence losing gener-alization power for new patterns unseen during the training stage. To prevent this issue,two major alternative strategies exist, namely: a) stop splitting, and b) pruning.

Stopped splittingVarious criteria are available to ascertain suitable points to stop the splitting procedure.For example, the performance of the tree can be evaluated via cross-validation methods,

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A. Mathematical foundations

decreeing to stop its growth when the cross-validated performance worsens. The disad-vantage of such a methodology resides however in the notable computational loads whichare involved. Another option would be to define a certain threshold value ∆iT hr (where∆iT hr > 0, although small) in such a way that if maxN ′ ∆i(N ′) ≤ ∆iT hr, then training isterminated. Yet another possible solution could be to test for the statistical significance ofthe reductions in impurity [Duda et al., 2000].

Tree pruningIt is widely acknowledged that the stopped splitting strategy described above tends tofavour trees in which the highest reductions in impurity occur near the root node, a be-haviour which might however lead to premature stops [Duda et al., 2000]. As an alternativeapproach to stopped splitting, pruning commences by growing the tree completely: i.e. un-til its leaf nodes have the minimum possible impurity. Subsequently, all pairs of neighbourleaves –i.e. those leaf nodes linked to a common antecedent exactly one level above– areconsidered for elimination. Then, any pair whose elimination would yield a sufficientlysmall increase in overall impurity is pruned: its pending nodes are merged together to thecommon antecedent, which is hence declared a leaf, and consequently new candidate forfurther pruning. Such a procedure continues recursively until the pruning of any pair ofleaf nodes would lead to an unacceptably high increase in impurity.

Pruning tends to produce better overall outcomes than stopped splitting schemes, and istherefore generally preferred in practise [Duda et al., 2000].

Other tree algorithmsThere are a number of different tree algorithms in addition to CART, being ID3 and C4.5arguably the most renowned schmes. The ID3 algorithm (Interactive Dichotomizer 3) isrestricted to work with nominal (unordered, discrete) input data, so if continuous real-valued attributes are involved, these need to be binned into discrete intervals beforehand.In turn, the C4.5 methods is a refinement of ID3 which has reached notable popularity. InC4.5, real-valued variables are treated as in CART; whereas multi-ways splits (B > 2) areallowed for nominal data, based on the impurity gain ratio in (A.90). In addition, C4.5’sheuristic for pruning relies on analysing the statistical significance of splits.

A.3.6 Meta-classification: Bagging

Bagging is an acronym which stands for ‘Bootstrap Aggregation’. Bootstrap refers to astatistical resampling technique in which a dataset D with n items is randomly resampledn times with repetition to form a related training set D′; where D′ contains on average(1 − e−1) ≃ 63.2% unique samples [Alpaydin, 2014], being the rest duplicates. The termaggregation stems from the fact that in this methodology, final decisions are obtained bymajority voting –i.e. aggregation– of a number of component classifiers known as ‘weaklearners’; where each of these components had been previously trained on a different randomdataset instance D′ generated from D by bootstrapping.

Consequently, these ‘weak learners’ are the fundamental constituent of Bagging, whicheffectively relies on them to achieve classification outcomes. For this reason, Bagging isreferred to as a ‘meta-classification’ scheme. Furthermore, for this aggregation strategyto be practical, the ensembled learners should be to some extent ‘weak’, i.e. sensitive insuch a manner that slight changes in the dataset D′ from an iteration to another may leadto relatively pronounced differences in the structure of the ‘weak learner’ resulting from

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A.3. Classification

the training process. This behaviour occurs for example in decision trees generated with agreedy splitting heuristic [Duda et al., 2000].

A.3.7 Meta-classification: Boosting

Boosting algorithms are meta-classifiers which combine ‘weak learners’ in order to increase–i.e. to ‘boost’– the overall performance attained by those learners when considered byseparate, even if they are only slightly better than pure random guessing [Freund andSchapire, 1997]. To do so, Boosting encompasses an iterative process in which learners areadded to form a robust ensemble in which individual outcomes are weighted to produce afinal classification. More specifically, relative weights depend on the performance shown byeach learner during its training stage.

For brevity reasons, this appendix focuses on the AdaBoost algorithm (acronym whichstands for ‘Adaptive Boosting’), although several other Boosting variants exist, e.g. LP-Boost, TotalBoost, BrownBoost, MadaBoost or LogitBoost.

AdaBoostGiven dataset D =

{

(~xi, yi) | ~xi ∈ X ⊂ Rd, yi ∈ Y = {±1}

}n

i=1for binary classification and

the space H of possible ‘weak’ binary learners h(·) : X 7→ Y ; let us assume that thenumber T of iterations over which to perform training is known. The AdaBoost scheme isnamed adaptive because it embraces a distribution of weights ~w[t] ∈ [0, 1]n ⊂ R

n (where∑n

i=1 wi[t] = 1) which governs the relative importance of each input data instance. Astraining progresses, this set of weights becomes updated: wi[t] at the t-th iteration areadjusted depending on whether the temporary weak learner succeeded or failed in classifyingthe associated data sample ~xi. Hence, adaptation occurs in the sense that previouslymisclassified inputs gain importance (i.e. weight) to allow for more focus during subsequenttraining iterations.

In general terms, AdaBoost tends to achieve good generalization power, being less proneto overfitting than other schemes; although it may be sensitive to noise and outliers.

AdaBoost’s training algorithm can be described is as follows [Freund and Schapire, 1997]:

• Previously yo the first iteration, weights vector ~w[t] for t = 1 must be initialized inorder to start with equally distributed importance weights for all data samples, i.e.:

wi[t = 1] =1

n∀i = 1, . . . , n (A.94)

• Iterate for t = 1, . . . , T , where T is the pre-established number of training cycles:– Across the space H of all possible weak learners, pick h[t] : X 7→ Y to minimize

the overall classification error in which current weights ~w[t] for instances in D aretaken into account. In case that a weight-based training is not feasible for thetypology of weak learners in H, a practical solution would consist in obtaininga modified version D′[t] of the dataset, randomly drawn from D with selectionprobabilities in accordance to the distribution of weights ~w[t].

– Calculate the weighted error rate ǫ[t] obtained by the candidate classifier h[t]:

ǫ[t] =n∑

i=1h[t](~xi)6=yi

wi[t] =n∑

i=1

wi[t]|h[t](~xi)− yi|

2(A.95)

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A. Mathematical foundations

Without loss of generality, it can be assumed that ǫ[t] ≤ 12: otherwise, the binary

complementary of h[t] –i.e. a classifier assigning the opposite outcome to h[t]for all inputs– would have performed better.

– Calculate an auxiliary factor α[t]:

α[t] =1

2log

(

1− ǫ[t]

ǫ[t]

)

(A.96)

where α[t] ≥ 0 since 0 ≤ ǫ[t] ≤ 12. Given that α[t] increases as the error ǫ[t]

decreases, α[t] can be used as a measure of confidence regarding the currentweak learner h[t].

– Update the distribution of weights for next iteration t+ 1: �

wi[t+ 1] =wi[t]

Z[t]·

{

e−α[t] if h[t](~xi) = yi

e+α[t] if h[t](~xi) 6= yi(A.97)

=wi[t]

Z[t]exp[−α[t]yih[t](~xi)] (A.98)

where Z[t] is a mere normalization scalar which guarantees that weights continueto sum to one, i.e.

∑ni=1 wi[t + 1] = 1. The update of weights from (A.97)–

(A.98) is conceived in such a manner that those samples which were erroneouslyclassified by h[t], i.e. whenever h[t](~xi) 6= yi, get their weights increased by a

factor e+α[t]

Z[t]for iteration t+1; whereas on the contrary, successfully classified data

instances (i.e. h[t](~xi) = yi) see their weights decreased in a similar proportione−α[t]

Z[t]. Thus, the new weak learner that will be trained at iteration t + 1 can

adapt and focus on the most difficult data items.• Once the iterative training detailed above is complete, the final ‘robust’ classifierHT : X 7→ Y is built as a weighted ensemble of the T ‘weak’ learners; where therelative importance of each of these h[t] corresponds to its confidence factor α[t]:

HT (~x) = sign

(

T∑

t=1

α[t]h[t](~x)

)

(A.99)

Since weighted error rates satisfy ǫ[t] ≤ 12, magnitude γ[t] = 1

2− ǫ[t] ≥ 0 reflects how much

better h[t] is in comparison to pure random guessing, which in binary problems producesan average random error rate equal to 1

2. It can be proved [Freund and Schapire, 1997] that

the total error rate ǫ, obtained by the final robust classifier HT (·) when applied on trainingdata, has an upper bound as follows:

ǫ ≤T∏

t=1

2√

ǫ[t](1− ǫ[t]) =T∏

t=1

√

1− 4γ2[t] ≤ exp

{

−2T∑

t=1

γ2[t]

}

(A.100)

Hence, if each and all of the T weak learners are at least slightly better than random:

0 ≤ ǫ[t] <1

2∀t = 1, . . . , T ⇒ ∃γ > 0 | γ[t] ≥ γ ∀t = 1, . . . , T (A.101)

In consequence, the upper bound for ǫ as stated in (A.100) can be substituted by anotherupper bound (more relaxed than (A.100), although anyhow still valid):

ǫ ≤ e−2T γ2

(A.102)

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A.3. Classification

Therefore, this upper bound for ǫ decreases exponentially with T at a rate which dependson γ. This behaviour, combined with other bounds on generalization error [Freund andSchapire, 1997], point out why the AdaBoost algorithm works as a boosting scheme: givensufficient data, it can efficiently employ weak learners – which perform always at leastslightly better than random– to build a strong classifier with an arbitrarily low error rateon the training set.

On the other hand, an upper bound can also be established for the generalization error, i.e.for the rate of misclassifications in new data not used during the training stage. That upperbound relates to: a) the error resulting from the training stage P [HT (~x) 6= y], b) samplesize n, c) the dimensionality dH of the space H of weak learners, and d) the number ofboosting iterations T [Freund and Schapire, 1997, 1999]:

P [HT (~x) 6= y] +O

√

TdH

n

(A.103)

Being T in the numerator inside the square root, (A.103) suggests that AdaBoost overfitsif it is run for too many iteration, i.e. as T becomes excessively large. In practise, T isan essential hyperparameter for AdaBoost which needs to be pre-specified by the user, aswell as the internal configuration options governing the behaviour of the weak classifiers.In this regard, those weak learners do not need to be especially accurate; otherwise, thegain supplied by the Boosting ensemble may be scarce.

AdaBoost.M2 extension for multi-class problemsAdaBoost was originally designed to deal with binary classification problems (ground truthclass assignments yi ∈ {±1})). Nonetheless, multi-class classification problems can also beaddressed, although adaptations are required. In this regard, AdaBoost.M1 is a directgeneralization of AdaBoost suitable to work with weak learners which are robust enough asto guarantee ǫ[t] ≤ 1

2even when the algorithms progresses for many iterations. However,

taking into account that such a condition may be too restrictive in practice, other exten-sions have been described, of which the most commonly used is AdaBoost.M2 [Freund andSchapire, 1997].

Given dataset D ={

(~xi, yi) | ~xi ∈ X ⊂ Rd, yi ∈ Y = {1, . . . , C} ⊂ N

}n

i=1, with C > 2 ∈

N classes. Algorithmically, AdaBoost.M2 for multi-class problems is strongly based onAdaBoost’s standard version, with the following modifications:

• Weak learners:

h[t](~x, y) : X × Y 7→ [0, 1] ⊂ R (A.104)

For a certain data input ~x ∈ X and a candidate class correspondence y ∈ Y , theweak classifier h(~x, y) yields a real-valued output in the interval [0, 1] which shows itsdegree of belief that instance ~x actually belongs to the y-th class.

• Weights: in order to accommodate for multiple class options, weights wi[t] need to beexpanded into the more general concept of ‘misclassification penalties’ wi,y[t] for thei-th data item and the y-th candidate class. The former initialization of weights in(A.94) must be reformulated in consequence, again guaranteeing that penalties sumto 1:

wi,y[t] =1

n

1

C − 1

∀i = 1, . . . , n∀y ∈ Y − {yi}

(A.105)

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A. Mathematical foundations

• Error rates: the former binary weighted error rate ǫ[t] in (A.95) is substituted inAdaBoost.M2 by a multi-class ‘pseudo-loss’, defined as follows:

ǫ[t] =1

2

n∑

i=1

∑

y∈Y −{yi}

wi,y[t] {1− h[t](~xi, yi) + h[t](~xi, y)} (A.106)

• The update of penalties in (A.98) now becomes:

wi,y[t+ 1] =wi,y[t]

Z[t]exp (−α[t]{1 + h[t](~xi, yi)− h[t](~xi, y)}) (A.107)

• The final robust classifier HT : X 7→ Y is built as follows:

HT (~x) = arg maxy∈Y

{

T∑

t=1

α[t]h[t](~x, y)

}

(A.108)

A.4 Hidden Markov Models

Discrete-time Markov processes are a flexible mathematical framework, widely used acrossmany fields to model the random evolution of an stochastic process over time. Their mainapplications include the extraction of temporal information from streams of data and theirdynamics. The simplest form of a Markovian model, on which all other constructions arebased, is known as the first-order Markov chain (Figure A.10). It encompasses two basicassumptions, namely:

1. Limited horizon (Markov property): The probability of encountering the processat a certain state Yt at the discrete time instant t depends only on the immediatelyprecedent state, i.e.:

p(Xt |Xt−1, Xt−2, . . . , X1) = p(Xt |Xt−1) (A.109)

2. Stationarity of the process: The probability of transitioning between any pair ofstates does not change over time:

p(Xt |Xt−1) = p(X2 |X1) ∀t (A.110)

Additionally, Hidden Markov Models (HMM) constitute an extension of first-order Markovchains. HMMs cover a common situation in which the observable output process Y isa random variable which in turn depends on another random variable X which is non-measurable (i.e. non-accessible or ‘hidden’). Being X the core precess of interest, it can bemodelled via a first-order Markov chain (Figure A.11) which influences observations Y .

In addition to the two previous premises, HMMs incorporate one extra assumption:

3. Conditional independence of observations Yt: Given X = {Xτ}Tτ=1, the sequence

of all hidden states for X, as well as all other observations Yt = {Yτ}Tτ=1τ 6=t

, then

observable states Yt is only conditionally dependent on the hidden state Xt at thesame instant t, and not on any other future or past, hidden or observable situations:

p(

Yt |X, Yt

)

= p (Yt |Xt) ∀t (A.111)

175

A.4. Hidden Markov Models

Figure A.10: Graphical representation of a first-order Markov chain. Arrows, which repre-sent conditional dependency, connect a certain state only with the immediately successiveone.

Figure A.11: Graphical representation of a Hidden Markov Model (HMM).

Those three assumptions in (A.109)–(A.111) can be summarized in the scheme of FigureA.11 and in the following expressions [Rabiner, 1989]:

p (X) = p(X1)T

∏

t=2

p(Xt | Xt−1) (A.112)

p (X, Y) = p(X1)p(Y1 | X1)T

∏

t=2

p(Xt | Xt−1)p(Yt | Xt) (A.113)

where X = {Xt}Tt=1 and Y = {Yt}

Tt=1. In addition, let {si}

Ni=1 be the set of N possible

hidden states for X, and {ok}Mk=1 the M possible observable symbols for process Y . Notably,

formulae in (A.112)–(A.113) admit a powerful and convenient matrix form [Rabiner, 1989]with:

• Transition matrix A of size N × N , whose elements ai,j reflect the probabilityof moving from a certain hidden state si to another state sj in the immediatelysubsequent instant, i.e.:

A(ai,j) ai,j = p (Xt = sj | Xt−1 = si) ∀i, j = 1, . . . , N (A.114)

• Emission matrix B of size N × M , with elements bj,k representing the probabilityof a certain observable state ok for Y , given that the hidden Markov process X iscurrently at state sj:

B(bj,k) bj,k = p (Yt = ok | Xt = sj)∀j = 1, . . . , N∀k = 1, . . . , M

(A.115)

• Initial conditions vector Π of size 1×N , where its elements πi cover the distributionof priors for all of the possible hidden states at the initial instant t = 1:

Pi(πi) πi = p (X1 = si) ∀i = 1, . . . , N (A.116)

Considering these definitions (A.114)–(A.116), the vector Λ(t) of size 1 × M which reflectsthe distribution of probabilities for each the observable outputs at a time point t can becalculated as follows [Rabiner, 1989]:

Λ(t) = ΠAt−1B ∀t = 1, . . . , T (A.117)

As a consequence, the HMM is fully specified with the set of parameters Θ = {Π, A, B}.

In the field of automated pattern recognition, there are three main situations of interest inwhich HMMs may be useful [Rabiner, 1989]:

176

A. Mathematical foundations

1. To calculate the probability of occurrence for a certain sequence of observations Y –‘evaluation problem’.

2. To find the optimal sequence of hidden states X which most likely originated a givensequence of observable outputs – ‘decoding problem’.

3. To estimate the most suitable set of HMM model parameters Θ from observations Yand hidden states X – ‘learning problem’.

A.4.1 Evaluation problem

Let Y = {Yt = ok[t]}Tt=1 be a known sequence of observable states ok[t] at time instants

t. Given that in the context of this problem, model parameters Θ = {Π, A,B} are alsocompletely specified, it would be possible to attempt to calculate the probability p(Y|Θ)by ‘brute force’ strategies, i.e. enumerating all possible hidden sequences X and workingon this basis. However, there are as many as NT different combinations X with length T .Thus, brute force might only be tractable for small values of T . Instead, there exists amuch more efficient approach, known as the ‘forward-backward’ procedure [Rabiner, 1989].

Let us consider ‘forward’ variables αt(i), defined as the following probability term:

αt(i) = p(

{Yτ = ok[τ ]}tτ=1;Xt = si |Θ

)

(A.118)

Using the concept in (A.118), the evaluation problem can be solved through an inductiveprocedure with:

• Initialization at instant t = 1:

α1(i) = πibi,k[1] ∀i = 1, . . . , N (A.119)

• Induction for t = 1, . . . , T − 1 (Figure A.12):

αt+1(j) =

{

N∑

i=1

αt(i)ai,j

}

bj,k[t] ∀j = 1, . . . , N (A.120)

• Termination at t = T :

p(Y |Θ) =N∑

j=1

αT (j) (A.121)

Although this ‘forward’ induction based on α’s is sufficient for the evaluation task, a similarand complementary ‘backward’ induction procedure will be useful later on to solve thedecoding and learning problems. Let ‘backward’ variables βt(j) be:

βt(i) = p(

{Yτ = ok[τ ]}Tτ=t+1 |Xt = si; Θ

)

(A.122)

• Initialization at instant t = T :

βT (i) = 1 ∀i = 1, . . . , N (A.123)

• Induction for t = T − 1, . . . , 1 (Figure A.13):

βt(i) =N∑

j=1

ai,jbj,k[t+1]βt+1(j) ∀i = 1, . . . , N (A.124)

177

A.4. Hidden Markov Models

Figure A.12: HMM forward induction for α variables.

Figure A.13: HMM backward induction for β variables.

Figure A.14: HMM forward-backward induction for ξ variables.

178

A. Mathematical foundations

A.4.2 Decoding problem

With HMM’s model parameters Θ being known, this task consists in which sequence ofhidden states X most likely produced a given sequence of observations Y. In this regard,let us define magnitudes γt(i) to represent the probability of a single hidden state si attime t given Y, if considered isolated from all other hidden states at neighbouring instants:

γt(i) = p(Xt = si |Y; Θ) (A.125)

From definitions (A.118), (??) and (A.125) it is derived that γt(i) can be calculated asfollows:

γt(i) =αt(i)βt(i)

p(Y |Θ)=

αt(i)βt(i)∑N

i=1 αt(i)βt(i)(A.126)

Intuitively, the optimization problem could be tackled in a naïve, local manner: choosingfor Xt the individual state that maximizes γt for each instant t. However, such a criteriondoes not take into account transitions between contiguous states in time Xt−1, Xt, Xt+1.Actually, it could occur that two consecutive instants were assigned to correspond to statessi, sj in spite of the fact that the direct transition from one to another may even beinfeasible by definition (i.e. ai,j = 0); hence invalidating the locally optimal solution.Therefore, the correct approach consists in optimizing the overall probability p(X |Y; Θ)for the full sequence of data. To do so, Viterbi’s algorithm should be applied.

A.4.2.1 Viterbi’s algorithm

Let us define auxiliary magnitudes δt(i) as:

δt(i) = maxsj[τ ]

τ=1,...,t−1

{

p(

{

Xτ = sj[τ ]

}t

τ=1;{

Yτ = ok[τ ]

}t

τ=1|Θ)}

(A.127)

where δt(i) represents the highest probability of: a) coming through a certain path{

sj[τ ]

}t−1

τ=1of hidden states, b) reaching hidden state Xt = si at current time t, and c) hav-

ing observed a sequence of symbols{

ok[τ ]

}t

τ=1. In addition, auxiliary variables ψt(i) are

necessary to trace back the most likely pathway of hidden states.

In brief, Viterbi’s algorithm works by induction:

• Initialization at t = 1:{

δ1(i) = πibi,k[1]

ψ1(i) = 0∀i = 1, . . . , N (A.128)

• Induction from t = 1, . . . , T − 1:

δt+1(j) = maxi=1,...,N

δt(i)ai,jbj,k[t+1]

ψt+1(j) = arg maxi=1,...,N

δt(i)ai,j

∀j = 1, . . . , N (A.129)

• Termination at t = T :

s⋆T = arg max

j=1,...,N

δT (j) (A.130)

being s⋆T the hidden state considered as optimal for XT , i.e. at the last time instant.

179

A.4. Hidden Markov Models

• Backtracking of the optimal pathway via the stored ψ variables:

s⋆t = ψt+1(s

⋆t+1) ∀t = T − 1, . . . , 1 (A.131)

where the resulting sequence X⋆ is then formed as follows:

X⋆ = {Xt = s⋆t}

T

t=1 (A.132)

A.4.3 Learning problem

The aim here is to ascertain a set of parameters Θ = {Π, A,B} (i.e. transition and emis-sion matrices A, B plus the vector of initial conditions Π) defining a HMM model whichmaximizes the overall posterior probability of the sequences {X,Y} supplied for training.Contrarily to the two previous tasks, this problem lacks an explicit analytical solution.Hence, this section presents the most commonly used approach, known as Baum-Welch’salgorithm; although other solutions exist, e.g. based on Expectation-Maximization algo-rithms or on gradient-descent search [Rabiner, 1989].

A.4.3.1 Baum-Welch’s algorithm

Let us define auxiliary magnitudes ξt(i, j) to reflect the probability of the pair of consecutivehidden states Xt = si, Xt+1 = sj given the sequence of observations Y:

ξt(i, j) = p(Xt = si, Xt+1 = sj |Y; Θ) =p(Xt = si, Xt+1 = Sj; Y |Θ)

p(Y |Θ)(A.133)

Variables ξ can be calculated by means of a ‘forward-backward’ propagation (Figure A.14):

ξt(i, j) =αt(i)ai,jbj,k[t+1]βt+1(j)

p(Y |Θ)(A.134)

=αt(i)ai,jbj,k[t+1]βt+1(j)

∑Ni=1

∑Nj=1 αt(i)ai,jbj,k[t+1]βt+1(j)

(A.135)

From definitions (A.125) and (A.133), it can be derived [Rabiner, 1989] that:

γt(i) =N∑

j=1

ξt(i, j) (A.136)

Besides, if γt(i) are summed over variable t along the temporal sequence, the resulting valuecan be interpreted as an estimation of the expected number of occasions Ei in which thei-th hidden state si was visited. Or equivalently, excluding instant t = T , it can be thoughtas the number of transitions which occurred departing from si:

Ei =T −1∑

t=1

γt(i) (A.137)

In a similar manner and attending to the definition of auxiliary variables ξt(i, j) in (A.133),a reasonable estimation of the expected number of transitions Ei,j from si to sj would be:

Ei,j =T −1∑

t=1

ξt(i, j) (A.138)

180

A. Mathematical foundations

Using these two concepts (A.137)–(A.138), plus the idea of counting expected occurrencesalong time; Baum-Welch’s algorithm iteratively re-estimates an approximate set of param-eters Θ with:

πi ← γ1(i) ∀i = 1, . . . , N (A.139)

whereas estimations for transitions ai,j would be:

ai,j ←Ei,j

Ei

=

∑T −1t=1 ξt(i, j)∑T −1

t=1 γt(i)∀i, j = 1, . . . , N (A.140)

and with a comparable reasoning:

bj,k ←

∑Tt=1|Yt=ok

γt(j)∑T

t=1 γt(j)

∀j = 1, . . . , N∀k = 1, . . . ,M

(A.141)

To summarize Baum-Welch’s methodology, the currently available best model estimate Θis employed to compute the right-hand sides of equations (A.139)–(A.141), with which

the subsequent estimate Θ gets iteratively re-computed, in the manner of Expectation-Maximization (EM) algorithms. In fact, Baum-Welch’s is essentially an EM algorithm[Rabiner, 1989].

181

A.4. Hidden Markov Models

182

Bibliography

ActiGraph LLC. ActiLife5 Analysis Software Suite for ActiGraph devices (User manual – RevisionH), 2010.

A. J. Ahola, S. Mäkimattila, M. Saraheimo, V. Mikkilä, C. Forsblom, R. Freese, and P.-H. Groop.Many patients with type 1 diabetes estimate their prandial insulin need inappropriately. JDiabetes, 2(3):194–202, Aug 2010. doi:10.1111/j.1753-0407.2010.00086.x.

P. N. Ainslie, T. Reilly, and K. R. Westerterp. Estimating human energy expenditure: A reviewof techniques with particular reference to doubly labelled water. Sports Med, 33(9):683–698,2003. doi:10.2165/00007256-200333090-00004.

B. E. Ainsworth, W. L. Haskell, A. S. Leon, D. R. Jacobs, H. J. Montoye, J. F. Sallis, and R. S. Paf-fenbarger. Compendium of physical activities: classification of energy costs of human physicalactivities. Med Sci Sports Exerc, 25(1):71–80, Jan 1993. doi:10.1249/00005768-199301000-00011.

B. E. Ainsworth, W. L. Haskell, M. C. Whitt, M. L. Irwin, A. M. Swartz, S. J. Strath, W. L.O’Brien, D. R. Bassett, K. H. Schmitz, P. O. Emplaincourt, et al. Compendium of physi-cal activities: an update of activity codes and MET intensities. Med Sci Sports Exerc, 32(Supplement):S498–S516, 2000. doi:10.1097/00005768-200009001-00009.

B. E. Ainsworth, W. L. Haskell, S. D. Herrmann, N. Meckes, D. R. Bassett, C. Tudor-Locke,J. L. Greer, J. Vezina, M. C. Whitt-Glover, and A. S. Leon. 2011 Compendium of phys-ical activities: a second update of codes and MET values. Med Sci Sports Exerc, 43(8):1575–1581, 2011. doi:10.1249/mss.0b013e31821ece12. URL https://sites.google.com/site/

compendiumofphysicalactivities.

F. Albinali, S. Intille, W. Haskell, and M. Rosenberger. Using wearable activity type detectionto improve physical activity energy expenditure estimation. In 12th Int Conf Ubiquitous Comp(UbiComp), 2010. doi:10.1145/1864349.1864396.

A. Albright, M. Franz, G. Hornsby, A. Kriska, D. Marrero, I. Ullrich, and L. S. Verity. AmericanCollege of Sports Medicine position stand: Exercise and type 2 diabetes. Med Sci Sports Exerc,32(7):1345–1360, Jul 2000.

F. R. Allen, E. Ambikairajah, N. H. Lovell, and B. G. Celler. Classification of a known sequenceof motions and postures from accelerometry data using adapted Gaussian Mixture Models.Physiol Meas, 27(10):935–951, Jul 2006. doi:10.1088/0967-3334/27/10/001.

E. Alpaydin. Introduction to Machine Learning. MIT Press, 2014.

M. Altini, J. Penders, R. Vullers, and O. Amft. Estimating energy expenditure using body-wornaccelerometers: A comparison of methods, sensors number and positioning. IEEE J BiomedHealth Inform, 19(1):219–226, Jan 2015. doi:10.1109/jbhi.2014.2313039.

American College of Sports Medicine. ACSM’s Guidelines for Exercise Testing and Prescription.Wolters Kluwer Health, 8 edition, 2011.

American Diabetes Association. Physical activity/exercise and diabetes. Diabetes Care, 27(Supplement1):S58–S62, 2004. doi:10.2337/diacare.27.2007.s58.

183

Bibliography

American Diabetes Association. Diagnosis and classification of diabetes mellitus. Diabetes Care,33(Supplement1):S62–S69, 2010. doi:10.2337/dc10-s062.

American Diabetes Association. Standards of medical care in diabetes 2014. Diabetes Care, 37(Supplement1):S14–S80, 2014. doi:10.2337/dc14-S014.

V. Arutchelvam, T. Heise, S. Dellweg, B. Elbroend, I. Minns, and P. D. Home. Plasma glucoseand hypoglycaemia following exercise in people with type 1 diabetes: a comparison of threebasal insulins. Diabet Med, 26(10):1027–1032, Oct 2009. doi:10.1111/j.1464-5491.2009.02807.x.

L. Atallah, J. J. H. Leong, B. Lo, and G.-Z. Yang. Energy expenditure predictionusing a miniaturized ear-worn sensor. Med Sci Sports Exerc, 43(7):1369–1377, 2011.doi:10.1249/mss.0b013e3182093014.

E. Atlas, R. Nimri, S. Miller, E. A. Grunberg, and M. Phillip. MD-logic artificial pancreassystem: A pilot study in adults with type 1 diabetes. Diabetes Care, 33(5):1072–1076, Feb2010. doi:10.2337/dc09-1830.

J. A. Baecke, J. Burema, and J. E. Frijters. A short questionnaire for the measurement of habitualphysical activity in epidemiological studies. Am J Clin Nutr, 36(5):936–942, Nov 1982.

L. Bao and S. S. Intille. Activity recognition from user-annotated acceleration data. In 2nd IntConf Pervasive Comp, pages 1–17. Springer, 2004. doi:10.1007/978-3-540-24646-6_1.

D. R. Bassett, B. E. Ainsworth, S. A. M., S. J. Strath, W. L. O’Brien, and G. A. King. Validityof four motion sensors in measuring moderate intensity physical activity. Med Sci Sports Exerc,32(Supplement):S471–S480, 2000. doi:10.1097/00005768-200009001-00006.

D. R. Bassett, A. Rowlands, and S. G. Trost. Calibration and validation of wearable monitors.Med Sci Sports Exerc, 44:S32–S38, Jan 2012. doi:10.1249/mss.0b013e3182399cf7.

R. Basu, B. Di Camillo, G. Toffolo, A. Basu, P. Shah, A. Vella, R. Rizza, and C. Cobelli. Useof a novel triple-tracer approach to assess postprandial glucose metabolism. Am J Physiol-Endocrinol Metab, 284(1):E55–E69, Jan 2003. doi:10.1152/ajpendo.00190.2001.

R. Basu, M. L. Johnson, Y. C. Kudva, and A. Basu. Exercise, hypoglycemia, and type 1 diabetes.Diabetes Technol Ther, 16(6):331–337, Jun 2014. doi:10.1089/dia.2014.0097.

P. J. Benito, C. Neiva, P. S. González-Quijano, R. Cupeiro, E. Morencos, and A. B. Peinado.Validation of the SenseWear armband in circuit resistance training with different loads. Eur JAppl Physiol, 112(8):3155–3159, Dec 2011. doi:10.1007/s00421-011-2269-5.

P. J. Benito Peinado, M. Álvarez Sánchez, V. Díaz Molina, A. B. Peinado Lozano, andF. J. Calderón Montero. Aerobic energy expenditure and intensity prediction during a spe-cific circuit weight training: a pilot study. J Hum Sport Exerc, 5(2):134–145, May 2010.doi:10.4100/jhse.2010.52.04.

R. N. Bergman, Y. Z. Ider, C. R. Bowden, and C. Cobelli. Quantitative estimation of insulinsensitivity. Am J Physiol, 236(6):E667–E677, Jun 1979.

A. G. Bonomi, A. H. C. Goris, B. Yin, and K. R. Westerterp. Detection of type, duration, andintensity of physical activity using an accelerometer. Med Sci Sports Exerc, 41(9):1770–1777,2009. doi:10.1249/mss.0b013e3181a24536.

R. Borg, J. C. Kuenen, B. Carstensen, H. Zheng, D. M. Nathan, R. J. Heine, J. Nerup,K. Borch-Johnsen, and D. R. Witte. Associations between features of glucose exposure andA1c: The A1c-Derived Average Glucose (ADAG) study. Diabetes, 59(7):1585–1590, Apr 2010.doi:10.2337/db09-1774.

J. Bort-Roig, N. D. Gilson, A. Puig-Ribera, R. S. Contreras, and S. G. Trost. Measuring andinfluencing physical activity with smartphone technology: A systematic review. Sports Med, 44(5):671–686, Feb 2014. doi:10.1007/s40279-014-0142-5.

184

Bibliography

C. Bouchard, A. Tremblay, C. Leblanc, G. Lortie, R. Savard, and G. Theriault. A method toassess energy expenditure in children and adults. Am J Clin Nutr, 37(3):461–467, Mar 1983.

S. Brage, N. Brage, P. Franks, U. Ekelund, M.-Y. Wong, et al. Branched equation model-ing of simultaneous accelerometry and heart rate monitoring improves estimate of directlymeasured physical activity energy expenditure. J Appl Physiol, 96(1):343–351, Aug 2004.doi:10.1152/japplphysiol.00703.2003.

S. Brage, N. Brage, P. W. Franks, U. Ekelund, and N. J. Wareham. Reliability and validity ofthe combined heart rate and movement sensor Actiheart. Eur J Clin Nutr, 59(4):561–570, Feb2005. doi:10.1038/sj.ejcn.1602118.

M. D. Breton. Physical activity – the major unaccounted impediment to closed loop control. JDiabetes Sci Technol, 2(1):169–174, Jan 2008. doi:10.1177/193229680800200127.

M. D. Breton, S. A. Brown, C. H. Karvetski, L. Kollar, K. A. Topchyan, S. M. Anderson, and B. P.Kovatchev. Adding heart rate signal to a control-to-range artificial pancreas system improvesthe protection against hypoglycemia during exercise in type 1 diabetes. Diabetes Technol Ther,16(8):506–511, Aug 2014. doi:10.1089/dia.2013.0333.

V. J. Briscoe, D. B. Tate, and S. N. Davis. Type 1 diabetes: exercise and hypoglycemia. ApplPhysiol Nutr Metab, 32(3):576–582, Mar 2007. doi:10.1139/h07-025.

C. J. Burges. A tutorial on Support Vector Machines for pattern recognition. Data Mining andKnowledge Discovery, 2(2):121–167, 1998. doi:10.1023/a:1009715923555.

V. Bussau, L. Ferreira, T. Jones, and P. Fournier. The 10-s maximal sprint: A novel approachto counter an exercise-mediated fall in glycemia in individuals with type 1 diabetes. DiabetesCare, 29(3):601–606, 2006. doi:10.2337/diacare.29.03.06.dc05-1764.

V. Bussau, L. Ferreira, T. Jones, and P. Fournier. A 10-s sprint performed prior to moderate-intensity exercise prevents early post-exercise fall in glycaemia in individuals with type 1 dia-betes. Diabetologia, 50(9):1815–1818, 2007. doi:10.1007/s00125-007-0727-8.

N. M. Byrne. Metabolic equivalent: one size does not fit all. J Appl Physiol, 99(3):1112–1119,Sep 2005. doi:10.1152/japplphysiol.00023.2004.

D. Callejas, C. J. Mann, E. Ayuso, R. Lage, I. Grifoll, C. Roca, A. Andaluz, R. Ruiz-de Gopegui,J. Montané, S. Muñoz, et al. Treatment of diabetes and long-term survival after insulin andglucokinase gene therapy. Diabetes, 62(5):1718–1729, Feb 2013. doi:10.2337/db12-1113.

I. Capel, M. Rigla, G. García-Sáez, A. Rodríguez-Herrero, B. Pons, D. Subías, F. García-García,M. Gallach, M. Aguilar, C. Pérez-Gandía, et al. Artificial pancreas using a personalized rule-based controller achieves overnight normoglycemia in patients with type 1 diabetes. DiabetesTechnol Ther, 16(3):172–179, Mar 2014. doi:10.1089/dia.2013.0229.

E. R. Carson, C. Cobelli, and L. Finkelstein. The Mathematical Modeling of Metabolic andEndocrine Systems: Model Formulation, Identification, and Validation. Wiley, New York, 1edition, 1983. ISBN 9780471086604.

P. Casale, O. Pujol, and P. Radeva. Human activity recognition from accelerometer data using awearable device. In 5th Iberian Conf IbPRIA, pages 289–296. Springer, 2011. doi:10.1007/978-3-642-21257-4_36.

K.-h. Chang, M. Y. Chen, and J. Canny. Tracking free-weight exercises. In 9th Int Conf UbiquitousComp (UbiComp), pages 19–37. Springer, 2007. doi:10.1007/978-3-540-74853-3_2.

L. J. Chassin, M. E. Wilinska, and R. Hovorka. Intense exercise in type 1 diabetes: Exploringthe role of continuous glucose monitoring. J Diabetes Sci Technol, 1(4):570–573, Jul 2007.doi:10.1177/193229680700100415.

N. Chavannes, J. J. H. Vollenberg, C. P. van Schayck, and E. F. M. Wouters. Effects of physicalactivity in mild to moderate COPD: a systematic review. Br J Gen Pract, 52(480):574–578,Jul 2002.

185

Bibliography

K. Y. Chen and D. R. Bassett. The technology of accelerometry-based activity mon-itors: Current and future. Med Sci Sports Exerc, 37(Supplement):S490–S500, 2005.doi:10.1249/01.mss.0000185571.49104.82.

M. Chimen, A. Kennedy, K. Nirantharakumar, T. T. Pang, R. Andrews, and P. Narendran.What are the health benefits of physical activity in type 1 diabetes mellitus? A literaturereview. Diabetologia, 55(3):542–551, 2012. doi:10.1007/s00125-011-2403-2.

K. Chokkalingam, K. Tsintzas, L. Norton, K. Jewell, I. A. Macdonald, and P. I. Mansell. Ex-ercise under hyperinsulinaemic conditions increases whole-body glucose disposal without af-fecting muscle glycogen utilisation in type 1 diabetes. Diabetologia, 50(2):414–421, Nov 2006.doi:10.1007/s00125-006-0520-0.

L. Chu, J. Hamilton, and M. C. Riddell. Clinical management of the physically active patientwith type 1 diabetes. Phy Sportsmed, 39(2):64–77, May 2011. doi:10.3810/psm.2011.05.1896.

W. L. Clarke, S. Anderson, M. Breton, S. Patek, L. Kashmer, and B. Kovatchev. Closed-loop ar-tificial pancreas using subcutaneous glucose sensing and insulin delivery and a model predictivecontrol algorithm: the Virginia experience. J Diabetes Sci Technol, 3(5):1031–1038, Sep 2009.

A. H. Clemens, P. H. Chang, and R. W. Myers. The development of Biostator, a glucose controlledinsulin infusion system (GCIIS). Horm Metab Res, Suppl 7:23–33, 1977.

C. Cobelli and E. R. Carson. Introduction to modeling methodology for physiology and medicine.Elsevier, 2008.

C. Cobelli, C. Dalla Man, G. Sparacino, L. Magni, G. De Nicolao, and B. Kovatchev.Diabetes: Models, signals, and control. IEEE Rev Biomed Eng, 2:54–96, 2009.doi:10.1109/rbme.2009.2036073.

C. Cobelli, E. Renard, and B. Kovatchev. Artificial pancreas: Past, present, future. Diabetes, 60(11):2672–2682, Oct 2011. doi:10.2337/db11-0654.

J. Cohen. Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum Assoc. Inc.,2 edition, 1988.

S. R. Colberg. Diabetic athlete’s handbook. Human Kinetics, 2009.

S. R. Colberg, R. J. Sigal, B. Fernhall, J. G. Regensteiner, B. J. Blissmer, R. R. Rubin, L. Chasan-Taber, A. L. Albright, and B. Braun. Exercise and type 2 diabetes: The American College ofSports Medicine and the American Diabetes Association: Joint position statement. DiabetesCare, 33(12):e147–e167, Nov 2010. doi:10.2337/dc10-9990.

M. H. Coletti and H. L. Bleich. Medical Subject Headings used to search the biomedical literature.J Am Med Inform Assoc, 8(4):317–323, Jul 2001. doi:10.1136/jamia.2001.0080317.

P. Concannon, H. A. Erlich, C. Julier, G. Morahan, J. Nerup, F. Pociot, J. A. Todd, and S. S. Rich.Type 1 diabetes: Evidence for susceptibility loci from four genome-wide linkage scans in 1,435multiplex families. Diabetes, 54(10):2995–3001, Sep 2005. doi:10.2337/diabetes.54.10.2995.

K. Corder, S. Brage, N. J. Wareham, and U. Ekelund. Comparison of PAEE from combined andseparate heart rate and movement models in children. Med Sci Sports Exerc, 37(10):1761–1767,2005. doi:10.1249/01.mss.0000176466.78408.cc.

C. L. Craig, A. L. Marshall, M. Sjostrom, A. E. Bauman, M. L. Booth, B. E. Ainsworth,M. Pratt, U. Ekelund, A. Yngve, J. F. Sallis, et al. International physical activity ques-tionnaire: 12-country reliability and validity. Med Sci Sports Exerc, 35(8):1381–1395, 2003.doi:10.1249/01.mss.0000078924.61453.fb.

S. E. Crouter, J. R. Churilla, and D. R. Bassett. Estimating energy expenditure using accelerom-eters. Eur J Appl Physiol, 98(6):601–612, Oct 2006. doi:10.1007/s00421-006-0307-5.

P. E. Cryer. Exercise-related hypoglycemia-associated autonomic failure in diabetes. Diabetes, 58(9):1951–1952, Aug 2009. doi:10.2337/db09-0834.

186

Bibliography

F. A. da Cunha, P. d. T. V. Farinatti, and A. W. Midgley. Methodological and practical applicationissues in exercise prescription using the heart rate reserve and oxygen uptake reserve methods.J Sci Med Sport, 14(1):46–57, Jan 2011. doi:10.1016/j.jsams.2010.07.008.

DAFNE Study Group. Training in flexible, intensive insulin management to enable dietary free-dom in people with type 1 diabetes: dose adjustment for normal eating (DAFNE) randomisedcontrolled trial. BMJ, 325(7367):746–746, Oct 2002. doi:10.1136/bmj.325.7367.746.

C. Dalla Man, M. Camilleri, and C. Cobelli. A system model of oral glucose absorption:Validation on gold standard data. IEEE Trans Biomed Eng, 53(12):2472–2478, Dec 2006.doi:10.1109/tbme.2006.883792.

C. Dalla Man, R. A. Rizza, and C. Cobelli. Meal simulation model of the glucose-insulin system.IEEE Trans Biomed Eng, 54(10):1740–1749, Oct 2007. doi:10.1109/tbme.2007.893506.

C. Dalla Man, M. D. Breton, and C. Cobelli. Physical activity into the meal glucose-insulinmodel of type 1 diabetes: In silico studies. J Diabetes Sci Technol, 3(1):56–67, Jan 2009.doi:10.1177/193229680900300107.

T. Danne, C. Tsioli, O. Kordonouri, S. Blaesig, K. Remus, A. Roy, B. Keenan, S. W. Lee, and F. R.Kaufman. The PILGRIM study: In silico modeling of a predictive low glucose managementsystem and feasibility in youth with type 1 diabetes during exercise. Diabetes Technol Ther, 16(6):338–347, Jun 2014. doi:10.1089/dia.2013.0327.

R. J. Davey, W. Howe, N. Paramalingam, L. D. Ferreira, E. A. Davis, P. A. Fournier, andT. W. Jones. The effect of midday moderate-intensity exercise on postexercise hypoglycemiarisk in individuals with type 1 diabetes. J Clin Endocrinol Metab, 98(7):2908–2914, Jul 2013.doi:10.1210/jc.2013-1169.

DCCT Research Group. Factors in development of diabetic neuropathy: baseline analysis ofneuropathy in feasibility phase of the diabetes control and complications trial (DCCT). Diabetes,37(4):476–481, Apr 1988. doi:10.2337/diab.37.4.476.

DCCT Research Group. The effect of intensive treatment of diabetes on the development andprogression of long-term complications in insulin-dependent diabetes mellitus. N Engl J Med,329(14):977–986, Sep 1993. doi:10.1056/nejm199309303291401.

DCCT Research Group. Effect of intensive diabetes management on macrovascular events andrisk factors in the diabetes control and complications trial (DCCT). Am J Cardiol, 75(14):894–903, May 1995a. doi:10.1016/s0002-9149(99)80683-3.

DCCT Research Group. Effect of intensive therapy on the development and progression of diabeticnephropathy in the diabetes control and complications trial (DCCT). Kidney Int, 47(6):1703–1720, Jun 1995b.

DCCT Research Group. Progression of retinopathy with intensive versus conventional treatmentin the diabetes control and complications trial (DCCT). Ophthalmology, 102(4):647–661, Apr1995c. doi:10.1016/s0161-6420(95)30973-6.

DCCT Research Group. Hypoglycemia in the diabetes control and complications trial (DCCT).Diabetes, 46(2):271–286, Feb 1997.

H. de Kort, E. J. de Koning, T. J. Rabelink, J. A. Bruijn, and I. M. Bajema. Islet transplantationin type 1 diabetes. BMJ, 342:d217–d217, Jan 2010. doi:10.1136/bmj.d217.

A. de Leiva and M. E. Hernando. Telemedical artificial pancreas: PARIS (Pancreas ArtificialTelemedico Inteligente) research project. Diabetes Care, 32(Suppl. 2):S211–S216, Oct 2009.doi:10.2337/dc09-s313.

S. I. de Vries, F. G. Garre, L. H. Engbers, V. H. Hildebrandt, and S. van Buuren. Evaluation ofneural networks to identify types of activity using accelerometers. Med Sci Sports Exerc, 43(1):101–107, Jan 2011. doi:10.1249/mss.0b013e3181e5797d.

187

Bibliography

DiaMond Project Group. Incidence and trends of childhood type 1 diabetes worldwide 1990–1999.Diabet Med, 23(8):857–866, Aug 2006.

C. Ding and H. Peng. Minimum redundancy feature selection from microarray gene expressiondata. J Bioinform Comput Biol, 03(02):185–205, Apr 2005. doi:10.1142/s0219720005001004.

DirecNet Study Group. Impact of exercise on overnight glycemic control in children with type 1diabetes mellitus. J Pediatr, 147(4):528–534, Oct 2005. doi:10.1016/j.jpeds.2005.04.065.

M.-C. Dubé, S. Weisnagel, D. Prud’homme, and C. Lavoie. Exercise and newer insulins: Howmuch glucose supplement to avoid hypoglycemia? Med Sci Sports Exerc, 37(8):1276–1282, 2005.doi:10.1249/01.mss.0000174950.25188.36.

M.-C. Dubé, S. Weisnagel, D. Prud’homme, and C. Lavoie. Is early and late post-meal exerciseso different in type 1 diabetic lispro users? Diabetes Res Clin Pract, 72(2):128–134, 2006.doi:10.1016/j.diabres.2005.09.017.

M.-C. Dubé, C. Lavoie, I. Galibois, and S. J. Weisnagel. Nutritional strategies to prevent hy-poglycemia at exercise in diabetic adolescents. Med Sci Sports Exerc, 44(8):1427–1432, 2012.doi:10.1249/mss.0b013e3182500a35.

M.-C. Dubé, C. Lavoie, and S. J. Weisnagel. Glucose or intermittent high-intensity ex-ercise in glargine/glulisine users with T1DM. Med Sci Sports Exerc, 45(1):3–7, 2013.doi:10.1249/MSS.0b013e31826c6ad3.

R. O. Duda, P. E. Hart, and D. G. Stork. Pattern Classification. Wiley, 2000.

G. S. Eisenbarth. Type I diabetes mellitus. a chronic autoimmune disease. N Engl J Med, 314(21):1360–1368, May 1986. doi:10.1056/NEJM198605223142106.

F. H. El-Khatib, J. Jiang, and E. R. Damiano. Adaptive closed-loop control provides blood-glucose regulation using dual subcutaneous insulin and glucagon infusion in diabetic swine. JDiabetes Sci Technol, 1(2):181–192, Mar 2007. doi:10.1177/193229680700100208.

F. H. El-Khatib, J. Jiang, and E. R. Damiano. A feasibility study of bihormonal closed-loop bloodglucose control using dual subcutaneous infusion of insulin and glucagon in ambulatory diabeticswine. J Diabetes Sci Technol, 3(4):789–803, Jul 2009. doi:10.1177/193229680900300428.

F. H. El-Khatib, S. J. Russell, D. M. Nathan, R. G. Sutherlin, and E. R. Damiano. A bihor-monal closed-loop artificial pancreas for type 1 diabetes. Sci Transl Med, 2(27):27, Apr 2010.doi:10.1126/scitranslmed.3000619.

D. Elleri, J. M. Allen, J. Harris, K. Kumareswaran, M. Nodale, L. Leelarathna, C. L. Acerini,A. Haidar, M. E. Wilinska, N. Jackson, A. M. Umpleby, M. L. Evans, D. B. Dunger, andR. Hovorka. Absorption patterns of meals containing complex carbohydrates in type 1 diabetes.Diabetologia, 56(5):1108–1117, 2013a. doi:10.1007/s00125-013-2852-x.

D. Elleri, J. M. Allen, K. Kumareswaran, L. Leelarathna, M. Nodale, K. Caldwell, P. Cheng,C. Kollman, A. Haidar, H. R. Murphy, and et al. Closed-loop basal insulin delivery over 36hours in adolescents with type 1 diabetes: Randomized clinical trial. Diabetes Care, 36(4):838–844, 2013b. doi:10.2337/dc12-0816.

D. Elleri, G. Maltoni, J. M. Allen, M. Nodale, K. Kumareswaran, L. Leelarathna, H. Thabit,K. Caldwell, M. E. Wilinska, P. Calhoun, et al. Safety of closed-loop therapy during reductionor omission of meal boluses in adolescents with type 1 diabetes: a randomized clinical trial.Diabetes Obes Metab, 16(11):1174–1178, Jul 2014. doi:10.1111/dom.12324.

M. Ermes, J. Parkka, J. Mantyjarvi, and I. Korhonen. Detection of daily activities and sports withwearable sensors in controlled and uncontrolled conditions. IEEE Trans Inf Technol Biomed,12(1):20–26, Jan 2008. doi:10.1109/titb.2007.899496.

A. C. Ertl and S. N. Davis. Evidence for a vicious cycle of exercise and hypoglycemia in type 1diabetes mellitus. Diabetes Metab Res Rev, 20(2):124–130, Mar 2004. doi:10.1002/dmrr.450.

188

Bibliography

EURODIAB ACE Study Group. Variation and trends in incidence of childhood diabetes inEurope. The Lancet, 355(9207):873–876, Mar 2000. doi:10.1016/s0140-6736(99)07125-1.

A. B. Evert, J. L. Boucher, M. Cypress, S. A. Dunbar, M. J. Franz, E. J. Mayer-Davis, J. J.Neumiller, R. Nwankwo, C. L. Verdi, P. Urbanski, et al. Nutrition therapy recommenda-tions for the management of adults with diabetes. Diabetes Care, 36(11):3821–3842, Oct 2013.doi:10.2337/dc13-2042.

M. Fogelholm. Physical activity, fitness and fatness: relations to mortality, morbidity and diseaserisk factors. a systematic review. Obes Rev, 11(3):202–221, Mar 2010. doi:10.1111/j.1467-789x.2009.00653.x.

G. Forman and M. Scholz. Apples-to-apples in cross-validation studies. SIGKDD Explor Newsl,12(1):49, Nov 2010. doi:10.1145/1882471.1882479.

D. Fradkin and I. Muchnik. Support vector machines for classification. DIMACS Series in DiscreteMathematics and Theoretical Computer Science, 62H30:1–9, 2000.

P. S. Freedson and K. Miller. Objective monitoring of physical activity using motion sensors andheart rate. Res Q Exerc Sport, 71(2 Suppl):S21–S29, Jun 2000.

P. S. Freedson, E. Melanson, and J. Sirard. Calibration of the Computer Science and Applica-tions, Inc. accelerometer. Med Sci Sports Exerc, 30(5):777–781, 1998. doi:10.1097/00005768-199805000-00021.

P. S. Freedson, K. Lyden, S. Kozey-Keadle, and J. Staudenmayer. Evaluation of artifi-cial neural network algorithms for predicting METs and activity type from accelerometerdata: validation on an independent sample. J Appl Physiol, 111(6):1804–1812, Sep 2011.doi:10.1152/japplphysiol.00309.2011.

Y. Freund and R. E. Schapire. A decision-theoretic generalization of on-line learning and an ap-plication to Boosting. J Comput Syst Sci, 55(1):119–139, Aug 1997. doi:10.1006/jcss.1997.1504.

Y. Freund and R. E. Schapire. A short introduction to boosting. J Jap Soc Artif Intell, 14(5):771–780, Sep 1999.

T. Fujimoto, J. Kemppainen, K. K. Kalliokoski, P. Nuutila, M. Ito, and J. Knuuti. Skeletal muscleglucose uptake response to exercise in trained and untrained men. Med Sci Sports Exerc, 35(5):777–783, 2003. doi:10.1249/01.mss.0000065070.49295.c0.

I. W. Gallen. Hypoglycemia associated with exercise in people with type 1 diabetes. DiabeticHypoglycemia, 7(1):3–10, 2014.

C. E. Garber, B. Blissmer, M. R. Deschenes, B. A. Franklin, M. J. Lamonte, I.-M. Lee, D. C.Nieman, and D. P. Swain. Quantity and quality of exercise for developing and maintainingcardiorespiratory, musculoskeletal, and neuromotor fitness in apparently healthy adults. MedSci Sports Exerc, 43(7):1334–1359, 2011. doi:10.1249/mss.0b013e318213fefb.

S. E. Gaskill, C. Bouchard, T. Rankinen, D. Rao, J. H. Wilmore, A. S. Leon, and J. S. Skinner.%Heart Rate reserve is better related to %VO2max than to %VO2 reserve: The HERITAGEfamily study. Med Sci Sports Exerc, 36(5):S3, May 2004.

D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 1989. ISBN 9780201157673.

R. Golubic, A. M. May, K. Benjaminsen Borch, K. Overvad, M.-A. Charles, M. J. T. Diaz,P. Amiano, D. Palli, E. Valanou, M. Vigl, et al. Validity of electronically administered recentphysical activity questionnaire (RPAQ) in ten European countries. PLoS ONE, 9(3):e92829,Mar 2014. doi:10.1371/journal.pone.0092829.

E. Gómez, M. Hernando Pérez, T. Vering, M. Rigla Cros, O. Bott, G. García-Sáez, P. Pretschner,E. Brugués, O. Schnell, C. Patte, et al. The INCA system: A further step towards atelemedical artificial pancreas. IEEE Trans Inf Technol Biomed, 12(4):470–479, Jul 2008.doi:10.1109/titb.2007.902162.

189

Bibliography

Á. L. González Martín. Desarrollo de un asistente personal para la monitorización de la actividadfísica y promoción de estilos de vida saludables en plataformas iOS [Development of a personalassisstant for the monitoring of physical activity and the promotion of healthy lifestyles in iOSplatforms]. Master’s thesis, ETSI Telecomunicación, Technical University of Madrid, 2013.

L. A. Gotshalk, R. A. Berger, and W. J. Kraemer. Cardiovascular responses to a high-volumecontinuous circuit resistance training protocol. J Strength Cond Res, 18(4):760–764, Nov 2004.doi:10.1519/14954.1.

A. Green, E. A. Gale, and C. C. Patterson. Incidence of childhood-onset insulin-dependentdiabetes mellitus: the EURODIAB ACE study. The Lancet, 339(8798):905–909, Apr 1992.

B. Grosman, E. Dassau, H. C. Zisser, L. Jovanovic, and F. J. Doyle, 3rd. Zone model predictivecontrol: a strategy to minimize hyper- and hypoglycemic events. J Diabetes Sci Technol, 4(4):961–975, Jul 2010.

L. Guariguata, D. Whiting, I. Hambleton, J. Beagley, U. Linnenkamp, and J. Shaw. Globalestimates of diabetes prevalence for 2013 and projections for 2035. Diabetes Res Clin Pract,103(2):137–149, Feb 2014. doi:10.1016/j.diabres.2013.11.002.

K. Guelfi, T. Jones, and P. Fournier. Intermittent high-intensity exercise does not increase therisk of early postexercise hypoglycemia in individuals with type 1 diabetes. Diabetes Care, 28(2):416–418, 2005a. doi:10.2337/diacare.28.2.416.

K. Guelfi, T. Jones, and P. Fournier. The decline in blood glucose levels is less with intermittenthigh-intensity compared with moderate exercise in individuals with type 1 diabetes. DiabetesCare, 28(6):1289–1294, 2005b. doi:10.2337/diacare.28.6.1289.

K. J. Guelfi, T. W. Jones, and P. A. Fournier. New insights into managing the risk of hypogly-caemia associated with intermittent high-intensity exercise in individuals with type 1 diabetesmellitus. Sports Med, 37(11):937–946, 2007. doi:10.2165/00007256-200737110-00002.

I. Guyon and A. Elisseeff. An introduction to variable and feature selection. J Mach Learn Res,3:1157–1182, 2003.

J. R. Guyton, R. O. Foster, J. S. Soeldner, M. H. Tan, C. B. Kahn, L. Koncz, and R. E.Gleason. A model of glucose-insulin homeostasis in man that incorporates the heteroge-neous fast pool theory of pancreatic insulin release. Diabetes, 27(10):1027–1042, Oct 1978.doi:10.2337/diab.27.10.1027.

I. C. Gyllensten and A. G. Bonomi. Identifying types of physical activity with a single accelerom-eter: Evaluating laboratory-trained algorithms in daily life. IEEE Trans Biomed Eng, 58(9):2656–2663, Sep 2011. doi:10.1109/tbme.2011.2160723.

A. Haidar, D. Elleri, J. M. Allen, J. Harris, K. Kumareswaran, M. Nodale, C. L. Acerini, M. E.Wilinska, N. Jackson, A. M. Umpleby, et al. Validity of triple- and dual-tracer techniquesto estimate glucose appearance. Am J Physiol -Endocrinol Metab, 302(12):E1493–E1501, Mar2012. doi:10.1152/ajpendo.00581.2011.

S. A. Ham, J. P. Reis, S. J. Strath, K. D. Dubose, and B. E. Ainsworth. Discrepancies betweenmethods of identifying objectively determined physical activity. Med Sci Sports Exerc, 39(1):52–58, Jan 2007. doi:10.1249/01.mss.0000235886.17229.42.

C. Hayes and A. Kriska. Role of physical activity in diabetes management and prevention. J AmDiet Assoc, 108(4):S19–S23, Apr 2008. doi:10.1016/j.jada.2008.01.016.

J. He, H. Li, and J. Tan. Real-time daily activity classification with wireless sensor networksusing Hidden Markov Model. In 29th Annual Internat Conf IEEE Eng Med Biol Soc (EMBS),2007. doi:10.1109/iembs.2007.4353008.

L. Heinemann and J. H. Anderson. Measurement of insulin absorption and insulin action. DiabetesTechnol Ther, 6(5):698–718, Oct 2004. doi:10.1089/dia.2004.6.698.

190

Bibliography

D. Hendelman, K. Miller, C. Baggett, E. Debold, and P. Freedson. Validity of accelerometry forthe assessment of moderate intensity physical activity in the field. Med Sci Sports Exerc, 32(Supplement):S442–S449, 2000. doi:10.1097/00005768-200009001-00002.

A. Herbst, R. Bachran, T. Kapellen, and R. W. Holl. Effects of regular physical activity on controlof glycemia in pediatric patients with type 1 diabetes mellitus. Arch Pediatr Adolesc Med, 160(6):573, Jun 2006. doi:10.1001/archpedi.160.6.573.

B. J. Hering. Single-donor, marginal-dose islet transplantation in patients with type 1 diabetes.JAMA, 293(7):830–835, Feb 2005. doi:10.1001/jama.293.7.830.

R. Hermann, M. Knip, R. Veijola, O. Simell, A.-P. Laine, H. K. Akerblom, P.-H. Groop, C. Fors-blom, K. Pettersson-Fernholm, and J. Ilonen. Temporal changes in the frequencies of HLAgenotypes in patients with type 1 diabetes–indication of an increased environmental pressure?Diabetologia, 46(3):420–425, Mar 2003.

J. Higgins and S. Green. Cochrane Handbook for Systematic Reviews of Interventions. TheCochrane Collaboration, 2011. URL www.cochrane-handbook.org. Version 5.1.0 [updatedMarch 2011].

I. B. Hirsch. Realistic expectations and practical use of continuous glucose monitoring for theendocrinologist. J Clin Endocrinol Metab, 94(7):2232–2238, Jul 2009. doi:10.1210/jc.2008-2625.

M. D. Holmes. Physical activity and survival after breast cancer diagnosis. JAMA, 293(20):2479,May 2005. doi:10.1001/jama.293.20.2479.

R. Hovorka. Closed-loop insulin delivery: from bench to clinical practice. Nat Rev Endocrinol, 7:385–395, Feb 2011. doi:10.1038/nrendo.2011.32.

R. Hovorka and P. Vicini. Parameter estimation. In E. Carson and C. Cobelli, editors, ModelingMethodology for Physiology and Medicine, pages 107–151. Academic Press, 2001.

R. Hovorka, F. Shojaee-Moradie, P. V. Carroll, L. J. Chassin, I. J. Gowrie, N. C. Jackson, R. S.Tudor, A. M. Umpleby, and R. H. Jones. Partitioning glucose distribution/transport, disposal,and endogenous production during IVGTT. Am J Physiol -Endocrinol Metab, 282(5):E992–1007, May 2002. doi:10.1152/ajpendo.00304.2001.

R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. O. Federici, T. R.Pieber, H. C. Schaller, L. Schaupp, T. Vering, and M. E. Wilinska. Nonlinear model predictivecontrol of glucose concentration in subjects with type 1 diabetes. Physiol Meas, 25(4):905–920,Jul 2004. doi:10.1088/0967-3334/25/4/010.

R. Hovorka, H. Jayatillake, E. Rogatsky, V. Tomuta, T. Hovorka, and D. T. Stein. Calculatingglucose fluxes during meal tolerance test: a new computational approach. Am J Physiol -Endocrinol Metab, 293(2):E610–E619, May 2007. doi:10.1152/ajpendo.00546.2006.

R. Hovorka, D. Elleri, H. Thabit, J. M. Allen, L. Leelarathna, R. El-Khairi, K. Kumareswaran,K. Caldwell, P. Calhoun, C. Kollman, et al. Overnight closed-loop insulin delivery in youngpeople with type 1 diabetes: A free-living, randomized clinical trial. Diabetes Care, 37(5):1204–1211, Apr 2014. doi:10.2337/dc13-2644.

K. J. Hunt and K. L. Schuller. The increasing prevalence of diabetes in pregnancy. Obstet GynecolClin North Am, 34(2):173–99, Jun 2007. doi:10.1016/j.ogc.2007.03.002.

International Diabetes Federation. IDF Diabetes Atlas, 6th edition. International Diabetes Fed-eration, 2013.

International Diabetes Federation. IDF Diabetes Atlas, 6th edition - 2014 update. InternationalDiabetes Federation, 2014.

K. Iscoe and M. Riddell. Continuous moderate-intensity exercise with or without intermittenthigh-intensity work: Effects on acute and late glycaemia in athletes with type 1 diabetes mel-litus. Diabet Med, 28(7):824–832, 2011. doi:10.1111/j.1464-5491.2011.03274.x.

191

Bibliography

J. M. Jakicic, M. Marcus, K. I. Gallagher, C. Randall, E. Thomas, F. L. Goss, and R. J. Robertson.Evaluation of the SenseWear Pro armband to assess energy expenditure during exercise. MedSci Sports Exerc, 36(5):897–904, 2004.

Z. Jankovec, M. Krcma, J. Gruberova, J. Komorousova, J. Tomesova, M. Zourek, and Z. Rusavy.Influence of physical activity on metabolic state within a 3-h interruption of continuous sub-cutaneous insulin infusion in patients with type 1 diabetes. Diabetes Technol Ther, 13(12):1234–1239, 2011. doi:10.1089/dia.2011.0121.

S. Jenni, C. Oetliker, S. Allemann, M. Ith, L. Tappy, S. Wuerth, A. Egger, C. Boesch, P. Schneiter,P. Diem, et al. Fuel metabolism during exercise in euglycaemia and hyperglycaemia in patientswith type 1 diabetes mellitus – a prospective single-blinded randomised crossover trial. Dia-betologia, 51(8):1457–1465, May 2008. doi:10.1007/s00125-008-1045-5.

C. Jiménez, M. Santiago, M. Sitler, G. Boden, and C. Homko. Insulin-sensitivity response to asingle bout of resistive exercise in type 1 diabetes mellitus. J Sport Rehabil, 18(4):564–571, Nov2009.

J. A. Johnstone, P. A. Ford, G. Hughes, T. Watson, and A. T. Garrett. Bioharness™ multivariablemonitoring device: Part I validity. J Sports Sci Med, 11(3):400–408, 2012a.

J. A. Johnstone, P. A. Ford, G. Hughes, T. Watson, and A. T. Garrett. Bioharness™ multivariablemonitoring device: Part II reliability. J Sports Sci Med, 11(3):409–417, 2012b.

J. A. Johnstone, P. A. Ford, G. Hughes, T. Watson, A. C. S. Mitchell, and A. T. Garrett. Fieldbased reliability and validity of the Bioharness™ multivariable monitoring device. J Sports SciMed, 11(4):643–652, 2012c.

K. Jungheim and T. Koschinsky. Glucose monitoring at the arm: Risky delays ofhypoglycemia and hyperglycemia detection. Diabetes Care, 25(6):956–960, Jun 2002.doi:10.2337/diacare.25.6.956.

M. Karvonen, M. Pitkäniemi, J. Pitkäniemi, K. Kohtamäki, N. Tajima, and J. Tuomilehto. Sexdifference in the incidence of insulin-dependent diabetes mellitus: an analysis of the recentepidemiological data. Diabetes Metab Rev, 13(4):275–291, Dec 1997. doi:10.1002/(sici)1099-0895(199712)13:4<275::aid-dmr197>3.0.co;2-v.

M. Karvonen, M. Viik-Kajander, E. Moltchanova, I. Libman, R. LaPorte, and J. Tuomilehto.Incidence of childhood type 1 diabetes worldwide. Diabetes Mondiale (DiaMond) project group.Diabetes Care, 23(10):1516–1526, Oct 2000.

S. Kaski. Data exploration using self-organizing maps. Acta Polytech Sc Ma, 82:X1–56, 1997.

A. Kennedy, K. Nirantharakumar, M. Chimen, T. T. Pang, K. Hemming, R. C. Andrews, andP. Narendran. Does exercise improve glycaemic control in type 1 diabetes? A systematic reviewand meta-analysis. PLoS ONE, 8(3):e58861, Mar 2013. doi:10.1371/journal.pone.0058861.

R. Kohavi and G. H. John. Wrappers for feature subset selection. Artif Intell, 97(1–2):273–324,Dec 1997. doi:10.1016/s0004-3702(97)00043-x.

T. Kohonen. The self-organizing map. Proceedings of the IEEE, 78(9):1464–1480, 1990.doi:10.1109/5.58325.

L. Kovács and B. Paláncz. Glucose-insulin control of type1 diabetic patients in H2/H∞ space viacomputer algebra. Algebraic Biology, 4545:95–109, 2007. doi:10.1007/978-3-540-73433-8_8.

B. P. Kovatchev, M. Breton, C. Dalla Man, and C. Cobelli. In silico preclinical trials: A proof ofconcept in closed-loop control of type 1 diabetes. J Diabetes Sci Technol, 3(1):44–55, Jan 2009.doi:10.1177/193229680900300106.

A. Krause, D. Siewiorek, A. Smailagic, and J. Farringdon. Unsupervised, dynamic identificationof physiological and activity context in wearable computing. In 7th IEEE Int Symp WearableComp, 2003. doi:10.1109/iswc.2003.1241398.

192

Bibliography

H. Kumahara, K. Ishii, and H. Tanaka. Physical activity monitoring for health management:Practical techniques and methodological issues. Int J Sport Health Sci, 4:380–393, 2006.doi:10.5432/ijshs.4.380.

K. Kumareswaran, D. Elleri, J. M. Allen, K. Caldwell, M. Nodale, M. E. Wilinska, S. A.Amiel, R. Hovorka, and H. R. Murphy. Accuracy of continuous glucose monitoring duringexercise in type 1 diabetes pregnancy. Diabetes Technol Ther, 15(3):223–229, Mar 2013a.doi:10.1089/dia.2012.0292.

K. Kumareswaran, H. Thabit, L. Leelarathna, K. Caldwell, D. Elleri, J. M. Allen, M. Nodale,M. E. Wilinska, M. L. Evans, and R. Hovorka. Feasibility of closed-loop insulin delivery intype 2 diabetes: A randomized controlled study. Diabetes Care, 37(5):1198–1203, Sep 2013b.doi:10.2337/dc13-1030.

H.-Y. Lau, K.-Y. Tong, and H. Zhu. Support Vector Machine for classification of walking con-ditions using miniature kinematic sensors. Med Biol Eng Comput, 46(6):563–573, Mar 2008.doi:10.1007/s11517-008-0327-x.

A. Laurenzi, A. M. Bolla, G. Panigoni, V. Doria, A. Uccellatore, E. Peretti, A. Saibene, G. Galim-berti, E. Bosi, and M. Scavini. Effects of carbohydrate counting on glucose control and qualityof life over 24 weeks in adult patients with type 1 diabetes on continuous subcutaneous insulininfusion: A randomized, prospective clinical trial (GIOCAR). Diabetes Care, 34(4):823–827,Mar 2011. doi:10.2337/dc10-1490.

G. C. Le Masurier and C. Tudor-Locke. Comparison of pedometer and accelerome-ter accuracy under controlled conditions. Med Sci Sports Exerc, 35(5):867–871, 2003.doi:10.1249/01.mss.0000064996.63632.10.

I.-M. Lee. Physical activity and cancer prevention, data from epidemiologic studies. Med SciSports Exerc, 35(11):1823–1827, 2003. doi:10.1249/01.mss.0000093620.27893.23.

L. Leelarathna, S. W. English, H. Thabit, K. Caldwell, J. M. Allen, K. Kumareswaran, M. E.Wilinska, M. Nodale, J. Mangat, M. L. Evans, et al. Feasibility of fully automated closed-loop glucose control using continuous subcutaneous glucose measurements in critical illness: arandomized controlled trial. Crit Care, 17(4):R159, 2013. doi:10.1186/cc12838.

L. Leelarathna, S. Dellweg, J. K. Mader, J. M. Allen, C. Benesch, W. Doll, M. Ellmerer, S. Hart-nell, L. Heinemann, H. Kojzar, et al. Day and night home closed-loop insulin delivery in adultswith type 1 diabetes: Three-center randomized crossover study. Diabetes Care, 37(7):1931–1937,Jun 2014. doi:10.2337/dc13-2911.

J. Lester, T. Choudhury, G. Kern, N. Borriello, and B. Hannaford. A hybrid discrimina-tive/generative approach for modeling human activities. In 19th Int Joint Conf Artif Intell(IJCAI), pages 766–772, 2005.

J. Lester, T. Choudhury, and G. Borriello. A practical approach to recognizing physical activities.In 4th Int Conf Pervasive Comp, pages 1–16. Springer, 2006. doi:10.1007/11748625_1.

C. Lévy-Marchal, C. C. Patterson, and A. Green. Geographical variation of presentation atdiagnosis of type I diabetes in children: the EURODIAB study. Diabetologia, 44(S3):B75–B80,Oct 2001. doi:10.1007/pl00002958.

M. Li, V. Rozgic, G. Thatte, S. Lee, A. Emken, M. Annavaram, U. Mitra, D. Spruijt-Metz, and S. Narayanan. Multimodal physical activity recognition by fusing temporaland cepstral information. IEEE Trans Neural Syst Rehabil Eng, 18(4):369–380, Aug 2010.doi:10.1109/tnsre.2010.2053217.

C. B. Liden, M. Wolowicz, J. Stivoric, A. Teller, C. Kasabach, S. Vishnubhatla, R. Pelletier,J. Farringdon, and S. Boehmke. Characterization and implications of the sensors incorporatedinto the SenseWear armband for energy expenditure and activity detection. Technical report,BodyMedia, 2002.

193

Bibliography

C.-W. Lin, Y.-T. C. Yang, J.-S. Wang, and Y.-C. Yang. A wearable sensor module with a neural-network-based activity classification algorithm for daily energy expenditure estimation. IEEETrans Inf Technol Biomed, 16(5):991–998, Sep 2012. doi:10.1109/titb.2012.2206602.

S. Liu, R. X. Gao, D. John, J. Staudenmayer, and P. S. Freedson. SVM-based multi-sensor fusionfor free-living physical activity assessment. In 33rd Annual Internat Conf IEEE Eng Med BiolSoc (EMBS), pages 3188–3191, 2011. doi:10.1109/iembs.2011.6090868.

S. Liu, R. X. Gao, D. John, J. W. Staudenmayer, and P. S. Freedson. Multisensor data fu-sion for physical activity assessment. IEEE Trans Biomed Eng, 59(3):687–696, Mar 2012.doi:10.1109/tbme.2011.2178070.

A. N. Lumb and I. W. Gallen. Diabetes management for intense exercise. Curr Opin EndocrinolDiabetes Obes, 16(2):150–155, 2009. doi:10.1097/med.0b013e328328f449.

K. Lyden, S. L. Kozey, J. W. Staudenmeyer, and P. S. Freedson. A comprehensive evaluation ofcommonly used accelerometer energy expenditure and MET prediction equations. Eur J ApplPhysiol, 111(2):187–201, Sep 2010. doi:10.1007/s00421-010-1639-8.

D. M. Maahs, N. A. West, J. M. Lawrence, and E. J. Mayer-Davis. Epidemiology of type 1 dia-betes. Endocrinol Metab Clin North Am, 39(3):481–497, Sep 2010. doi:10.1016/j.ecl.2010.05.011.

L. Magni, D. M. Raimondo, C. Dalla Man, G. De Nicolao, B. Kovatchev, and C. Cobelli. Modelpredictive control of glucose concentration in subjects with type 1 diabetes: an in silico trial.In 17th IFAC World Congress. Elsevier, 2008. doi:10.3182/20080706-5-kr-1001.00714.

L. Magni, M. Forgione, C. Toffanin, C. Dalla Man, B. Kovatchev, G. De Nicolao, and C. Cobelli.Run-to-run tuning of model predictive control for type 1 diabetes subjects: in silico trial. JDiabetes Sci Technol, 3(5):1091–1098, Sep 2009.

M. Malavolti, A. Pietrobelli, M. Dugoni, M. Poli, E. Romagnoli, P. De Cristofaro, andN. C. Battistini. A new device for measuring resting energy expenditure (REE) in healthysubjects. Nutrition, Metabolism and Cardiovascular Diseases, 17(5):338–343, Jun 2007.doi:10.1016/j.numecd.2005.12.009.

A. Mannini and A. M. Sabatini. Accelerometry-based classification of human activities usingMarkov modeling. Comput Intell Neurosci, 2011:1–10, 2011. doi:10.1155/2011/647858.

A. Maran, P. Pavan, B. Bonsembiante, E. Brugin, A. Ermolao, A. Avogaro, and M. Zaccaria.Continuous glucose monitoring reveals delayed nocturnal hypoglycemia after intermittent high-intensity exercise in nontrained patients with type 1 diabetes. Diabetes Technol Ther, 12(10):763–768, 2010. doi:10.1089/dia.2010.0038.

G. Marchetti, M. Barolo, L. Jovanovic, H. Zisser, and D. E. Seborg. An improved PID switch-ing control strategy for type 1 diabetes. IEEE Trans Biomed Eng, 55(3):857–865, Mar 2008.doi:10.1109/tbme.2008.915665.

E. B. Marliss and M. Vranic. Intense exercise has unique effects on both insulin release and itsroles in glucoregulation: Implications for diabetes. Diabetes, 51(Supplement1):S271–S283, Feb2002. doi:10.2337/diabetes.51.2007.s271.

C. D. Mathers and D. Loncar. Projections of global mortality and burden of disease from 2002to 2030. PLoS Med, 3(11):e442, 2006. doi:10.1371/journal.pmed.0030442.

MathWorks Documentation. MATLAB R2014b fitctree, 2015. URL http://es.mathworks.com/

help/stats/fitctree.html. [Online; accessed 25-February-2015].

J. McGarrigle and J. Oberholzer. Human islet transplantation: Current status and future direc-tion. Micro Nanosys, 5(3):156–161, 2013.

S. K. McMahon, L. D. Ferreira, N. Ratnam, R. J. Davey, L. M. Youngs, E. A. Davis, P. A.Fournier, and T. W. Jones. Glucose requirements to maintain euglycemia after moderate-intensity afternoon exercise in adolescents with type 1 diabetes are increased in a biphasicmanner. J Clin Endocrinol Metab, 92(3):963–968, Mar 2007. doi:10.1210/jc.2006-2263.

194

Bibliography

K. L. Mehers and K. M. Gillespie. The genetic basis for type 1 diabetes. Br Med Bull, 88(1):115–129, Dec 2008. doi:10.1093/bmb/ldn045.

D. Moher, A. Liberati, J. Tetzlaff, and D. G. Altman. Preferred reporting items for systematicreviews and meta-analyses: The PRISMA statement. PLoS Med, 6(7):e1000097, Jul 2009.doi:10.1371/journal.pmed.1000097.

P. G. Montgomery, D. J. Green, N. Etxebarria, D. B. Pyne, P. U. Saunders, and C. L. Minahan.Validation of heart rate monitor-based predictions of oxygen uptake and energy expenditure. JStrength Cond Res, 23(5):1489–1495, 2009. doi:10.1519/jsc.0b013e3181a39277.

E. Munguia Tapia, S. S. Intille, W. Haskell, K. Larson, J. Wright, A. King, and R. Fried-man. Real-time recognition of physical activities and their intensities using wireless ac-celerometers and a heart rate monitor. In 11th IEEE Int Symp Wearable Comp, 2007.doi:10.1109/iswc.2007.4373774.

H. R. Murphy, D. Elleri, J. M. Allen, J. Harris, D. Simmons, G. Rayman, R. Temple, D. B. Dunger,A. Haidar, M. Nodale, et al. Closed-loop insulin delivery during pregnancy complicated by type1 diabetes. Diabetes Care, 34(2):406–411, Jan 2011. doi:10.2337/dc10-1796.

D. Nagi. Exercise and Sport in Diabetes. John Wiley & Sons, 2006. ISBN 9780470022078.

A. Nguyen, D. Moore, and I. McCowan. Unsupervised clustering of free-living human activi-ties using ambulatory accelerometry. In 29th Annual Internat Conf IEEE Eng Med Biol Soc(EMBS), 2007. doi:10.1109/iembs.2007.4353437.

T. O’Brien. Gene therapy for type 1 diabetes moves a step closer to reality. Diabetes, 62(5):1396–1397, Apr 2013. doi:10.2337/db13-0348.

R. R. Pate. Physical activity and public health. JAMA, 273(5):402, Feb 1995.doi:10.1001/jama.1995.03520290054029.

C. Patterson, L. Guariguata, G. Dahlquist, G. Soltész, G. Ogle, and M. Silink. Diabetes in theyoung – a global view and worldwide estimates of numbers of children with type 1 diabetes.Diabetes Res Clin Pract, 103(2):161–175, Feb 2014. doi:10.1016/j.diabres.2013.11.005.

C. C. Patterson, G. G. Dahlquist, E. Gyürüs, A. Green, and G. Soltész. Incidence trendsfor childhood type 1 diabetes in Europe during 1989–2003 and predicted new cases 2005–20: a multicentre prospective registration study. The Lancet, 373(9680):2027–2033, Jun 2009.doi:10.1016/s0140-6736(09)60568-7.

H. Peng, F. Long, and C. Ding. Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Machine Intell, 27(8):1226–1238, Aug 2005. doi:10.1109/tpami.2005.159.

C. Perrone, O. Laitano, and F. Meyer. Effect of carbohydrate ingestion on the glycemic responseof type 1 diabetic adolescents during exercise. Diabetes Care, 28(10):2537–2538, Sep 2005.doi:10.2337/diacare.28.10.2537.

R. Peter, S. Luzio, G. Dunseath, A. Miles, B. Hare, K. Backx, V. Pauvaday, and D. Owens. Effectsof exercise on the absorption of insulin glargine in patients with type 1 diabetes. Diabetes Care,28(3):560–565, 2005. doi:10.2337/diacare.28.3.560.

G. Plasqui and K. R. Westerterp. Accelerometry and heart rate as a measure ofphysical fitness: Proof of concept. Med Sci Sports Exerc, 37(5):872–876, 2005.doi:10.1249/01.mss.0000161805.61893.c0.

G. Plasqui and K. R. Westerterp. Accelerometry and heart rate as a measure of physical fitness.Med Sci Sports Exerc, 38(8):1510–1514, 2006. doi:10.1249/01.mss.0000228942.55152.84.

G. Plasqui and K. R. Westerterp. Physical activity assessment with accelerometers: An evaluationagainst doubly labeled water. Obesity, 15(10):2371–2379, Oct 2007. doi:10.1038/oby.2007.281.

195

Bibliography

D. M. Pober, J. Staudenmayer, C. Raphael, and P. S. Freedson. Development of novel techniquesto classify physical activity mode using accelerometers. Med Sci Sports Exerc, 38(9):1626–1634,2006. doi:10.1249/01.mss.0000227542.43669.45.

S. Preece, J. Goulermas, L. Kenney, and D. Howard. A comparison of feature extraction methodsfor the classification of dynamic activities from accelerometer data. IEEE Trans Biomed Eng,56(3):871–879, Mar 2009a. doi:10.1109/tbme.2008.2006190.

S. J. Preece, J. Y. Goulermas, L. P. J. Kenney, D. Howard, K. Meijer, and R. Crompton. Activityidentification using body-mounted sensors – a review of classification techniques. Physiol Meas,30(4):R1–R33, Apr 2009b. doi:10.1088/0967-3334/30/4/r01.

M. G. Priebe, R. E. Wachters-Hagedoorn, J. A. J. Heimweg, A. Small, T. Preston, H. Elzinga,F. Stellaard, and R. J. Vonk. An explorative study of in vivo digestive starch characteristicsand postprandial glucose kinetics of wholemeal wheat bread. Eur J Nutr, 47(8):417–423, Oct2008. doi:10.1007/s00394-008-0743-6.

C. Purdon, M. Brousson, S. L. Nyveen, P. D. Miles, J. B. Halter, M. Vranic, and E. B. Marliss.The roles of insulin and catecholamines in the glucoregulatory response during intense exerciseand early recovery in insulin-dependent diabetic and control subjects. J Clin Endocrinol Metab,76(3):566–573, Mar 1993. doi:10.1210/jcem.76.3.8445012.

R. Rabasa-Lhoret, J. Bourque, F. Ducros, and J.-L. Chiasson. Guidelines for premeal insulindose reduction for postprandial exercise of different intensities and durations in type 1 diabeticsubjects treated intensively with a basal-bolus insulin regimen (ultralente-lispro). Diabetes Care,24(4):625–630, 2001. doi:10.2337/diacare.24.4.625.

L. Rabiner. A tutorial on Hidden Markov Models and selected applications in speech recognition.Proceedings of the IEEE, 77(2):257–286, 1989. doi:10.1109/5.18626.

A. Reiss and D. Stricker. Aerobic activity monitoring: towards a long-term approach. Univ AccessInf Soc, 13(1):101–114, Mar 2013. doi:10.1007/s10209-013-0292-5.

A. C. Rencher and W. F. Christensen. Methods of Multivariate Analysis. John Wiley & Sons,2012. ISBN 9781118391655.

RevMan. Review Manager (RevMan) [computer program]. Copenhagen: The Nordic CochraneCentre, The Cochrane Collaboration, 2012. Version 5.2.

D. A. Reynolds. Speaker identification and verification using Gaussian mixture speaker models.Speech Commun, 17(1-2):91–108, Aug 1995. doi:10.1016/0167-6393(95)00009-d.

M. C. Riddell. The endocrine response and substrate utilization during exercise in children andadolescents. J Appl Physiol, 105(2):725–733, Apr 2008. doi:10.1152/japplphysiol.00031.2008.

M. C. Riddell and J. Burr. Evidence-based risk assessment and recommendations for physicalactivity clearance: diabetes mellitus and related comorbidities. Appl Physiol Nutr Metab, 36(S1):S154–S189, Jul 2011. doi:10.1139/h11-063.

M. C. Riddell and B. A. Perkins. Type 1 diabetes and vigorous exercise: Applications of exercisephysiology to patient management. Canadian Journal of Diabetes, 30(1):63–71, Jan 2006.doi:10.1016/s1499-2671(06)01010-0.

J. Rosenblatt, D. Chinkes, M. Wolfe, and R. R. Wolfe. Stable isotope tracer analysis by GC-MS,including quantification of isotopomer effects. Am J Physiol, 263(3 Pt 1):E584–E596, Sep 1992.

M. P. Rothney, M. Neumann, A. Beziat, and K. Y. Chen. An artificial neural network model ofenergy expenditure using nonintegrated acceleration signals. J Appl Physiol, 103(4):1419–1427,Oct 2007. doi:10.1152/japplphysiol.00429.2007.

A. Rotstein and Y. Meckel. Estimation of %VO2reserve from heart rate during arm exercise andrunning. Eur J Appl Physiol, 83(6):545–550, Dec 2000. doi:10.1007/s004210000308.

196

Bibliography

E. A. Ryan, B. W. Paty, P. A. Senior, D. Bigam, E. Alfadhli, N. M. Kneteman, J. R. Lakey, andA. J. Shapiro. Five-year follow-up after clinical islet transplantation. Diabetes, 54(7):2060–2069,Jun 2005. doi:10.2337/diabetes.54.7.2060.

J. E. Sasaki, D. John, and P. S. Freedson. Validation and comparison of ActiGraph activitymonitors. J Sci Med Sport, 14(5):411–416, Sep 2011. doi:10.1016/j.jsams.2011.04.003.

SEARCH for Diabetes in Youth Study Group. The burden of diabetes mellitus among US youth:Prevalence estimates from the SEARCH for diabetes in youth study. Pediatrics, 118(4):1510–1518, Oct 2006. doi:10.1542/peds.2006-0690.

A. J. Shapiro, J. R. Lakey, E. A. Ryan, G. S. Korbutt, E. Toth, G. L. Warnock, N. M. Kneteman,and R. V. Rajotte. Islet transplantation in seven patients with type 1 diabetes mellitus usinga glucocorticoid-free immunosuppressive regimen. N Engl J Med, 343(4):230–238, Jul 2000.doi:10.1056/nejm200007273430401.

K. A. Shaw, H. C. Gennat, P. O’Rourke, and C. del Mar. Exercise for overweight or obesity.Cochrane Database Syst Rev, 4:1–85, 1996. doi:10.1002/14651858.cd003817.pub3.

M. Z. Shrayyef and J. E. Gerich. Principles of Diabetes Mellitus, chapter Normal Glucose Home-ostasis, pages 19–35. Springer Science, Nov 2009. doi:10.1007/978-0-387-09841-8_2.

R. J. Sigal, S. J. Fisher, J. B. Halter, M. Vranic, and E. B. Marliss. Glucoregulation during andafter intense exercise: Effects of β-adrenergic blockade in subjects with type 1 diabetes mellitus.J Clin Endocrinol Metab, 84(11):3961–3971, Nov 1999. doi:10.1210/jcem.84.11.6116.

R. J. Sigal, S. J. Fisher, A. Manzon, J. A. Morais, J. B. Halter, M. Vranic, and E. B. Marliss.Glucoregulation during and after intense exercise: Effects of α-adrenergic blockade. Metabolism,49(3):386–394, Mar 2000. doi:10.1016/s0026-0495(00)90374-3.

P. Siirtola, P. Laurinen, E. Haapalainen, J. Roning, and H. Kinnunen. Clustering-based activityclassification with a wrist-worn accelerometer using basic features. In IEEE Symp Comput IntellData Mining, 2009. doi:10.1109/cidm.2009.4938635.

G. E. Sonnenberg, F. W. Kemmer, and M. Berger. Exercise in type 1 (insulin-dependent) diabeticpatients treated with continuous subcutaneous insulin infusion. Diabetologia, 33(11):696–703,Nov 1990. doi:10.1007/bf00400572.

K. Soo, S. Furler, K. Samaras, A. Jenkins, L. Campbell, and D. Chisholm. Glycemic responsesto exercise in IDDM after simple and complex carbohydrate supplementation. Diabetes Care,19(6):575–579, 1996.

G. B. Spurr, A. M. Prentice, P. R. Murgatroyd, G. R. Goldberg, J. C. Reina, and N. T. Christ-man. Energy expenditure from minute-by-minute heart-rate recording: comparison with indi-rect calorimetry. Am J Clin Nutr, 48(3):552–559, 1988.

J. Staudenmayer, D. Pober, S. Crouter, D. Bassett, and P. Freedson. An artificial neural networkto estimate physical activity energy expenditure and identify physical activity type from an ac-celerometer. J Appl Physiol, 107(4):1300–1307, Jul 2009. doi:10.1152/japplphysiol.00465.2009.

J.-L. Steimer, A. Mallet, J.-L. Golmard, and J.-F. Boisvieux. Alternative approaches to estimationof population pharmacokinetic parameters: Comparison with the nonlinear mixed-effect model.Drug Metab Rev, 15(1–2):265–292, Jan 1984. doi:10.3109/03602538409015066.

M. Stenerson, F. Cameron, S. R. Payne, S. L. Payne, T. T. Ly, D. M. Wilson, and B. A. Bucking-ham. The impact of accelerometer use in exercise-associated hypoglycemia prevention in type1 diabetes. J Diabetes Sci Technol, 9(1):80–85, Jan 2015. doi:10.1177/1932296814551045.

S. J. Strath, D. R. Bassett, A. M. Swartz, and D. L. Thompson. Simultaneous heart rate-motionsensor technique to estimate energy expenditure. Med Sci Sports Exerc, 33(12):2118–2123, 2001.doi:10.1097/00005768-200112000-00022.

197

Bibliography

S. J. Strath, D. R. Bassett, D. L. Thompson, and A. M. Swartz. Validity of the simultaneousheart rate-motion sensor technique for measuring energy expenditure. Med Sci Sports Exerc,34(5):888–894, 2002. doi:10.1097/00005768-200205000-00025.

S. J. Strath, S. Brage, and U. Ekelund. Integration of physiological and accelerometer data toimprove physical activity assessment. Med Sci Sports Exerc, 37(Supplement):S563–S571, 2005.doi:10.1249/01.mss.0000185650.68232.3f.

A. M. Swartz, S. J. Strath, D. R. Bassett, W. L. O’Brien, G. A. King, and B. E. Ainsworth.Estimation of energy expenditure using CSA accelerometers at hip and wrist sites. Med SciSports Exerc, 32(9 Suppl):S450–S456, Sep 2000.

H. Thabit, A. Lubina-Solomon, M. Stadler, L. Leelarathna, E. Walkinshaw, A. Pernet, J. M.Allen, A. Iqbal, P. Choudhary, K. Kumareswaran, et al. Home use of closed-loop insulindelivery for overnight glucose control in adults with type 1 diabetes: a 4-week, multicentre,randomised crossover study. The Lancet Diabetes and Endocrinology, 2(9):701–709, Sep 2014.doi:10.1016/s2213-8587(14)70114-7.

P. D. Thompson, D. Buchner, I. L. Piña, G. J. Balady, M. A. Williams, B. H. Marcus, K. Berra,et al. Exercise and physical activity in the prevention and treatment of atherosclerotic car-diovascular disease: A statement from the Council on Clinical Cardiology (subcommittee onExercise, rehabilitation, and prevention) and the Council on Nutrition, Physical Activity, andMetabolism (subcommittee on Physical activity). Circulation, 107(24):3109–3116, Jun 2003.doi:10.1161/01.cir.0000075572.40158.77.

A. Thorell, M. F. Hirshman, J. Nygren, L. Jorfeldt, J. F. Wojtaszewski, S. D. Dufresne, E. S.Horton, O. Ljungqvist, and L. J. Goodyear. Exercise and insulin cause GLUT-4 translocationin human skeletal muscle. Am J Physiol, 277(4 Pt 1):E733–E741, Oct 1999.

G. Toffolo, C. Dalla Man, C. Cobelli, and A. L. Sunehag. Glucose fluxes during OGTT inadolescents assessed by a stable isotope triple tracer method. J Pediatr Endocrinol Metab, 21(1):31–45, Jan 2008.

C. Tonoli, E. Heyman, B. Roelands, L. Buyse, S. S. Cheung, S. Berthoin, and R. Meeusen. Effectsof different types of acute and chronic (training) exercise on glycaemic control in type 1 diabetesmellitus. Sports Med, 42(12):1059–1080, Dec 2012. doi:10.1007/bf03262312.

S. G. Trost, W.-K. Wong, K. A. Pfeiffer, and Y. Zheng. Artificial neural networks to predictactivity type and energy expenditure in youth. Med Sci Sports Exerc, 44(9):1801–1809, 2012.doi:10.1249/mss.0b013e318258ac11.

E. Tsalikian, N. Mauras, R. W. Beck, W. V. Tamborlane, K. F. Janz, H. P. Chase, T. Wysocki,S. A. Weinzimer, B. A. Buckingham, C. Kollman, D. Xing, and K. J. Ruedy. Impact of exerciseon overnight glycemic control in children with type 1 diabetes mellitus. J Pediatr, 147(4):528–534, 2005. doi:10.1016/j.jpeds.2005.04.065.

E. Tsalikian, C. Kollman, W. B. Tamborlane, R. W. Beck, R. Fiallo-Scharer, L. Fox, K. F. Janz,K. J. Ruedy, D. Wilson, D. Xing, and S. A. Weinzimer. Prevention of hypoglycemia duringexercise in children with type 1 diabetes by suspending basal insulin. Diabetes Care, 29(10):2200–2204, Oct 2006. doi:10.2337/dc06-0495.

K. Turksoy, E. S. Bayrak, L. Quinn, E. Littlejohn, and A. Cinar. Multivariable adaptive closed-loop control of an artificial pancreas without meal and activity announcement. Diabetes TechnolTher, 15(5):386–400, May 2013. doi:10.1089/dia.2012.0283.

E. M. Valanou, C. Bamia, and A. Trichopoulou. Methodology of physical-activity and energy-expenditure assessment: a review. J Public Health, 14(2):58–65, Mar 2006. doi:10.1007/s10389-006-0021-0.

T. L. van Belle, K. T. Coppieters, and M. G. von Herrath. Type 1 diabetes: Eti-ology, immunology, and therapeutic strategies. Physiol Rev, 91(1):79–118, Jan 2011.doi:10.1152/physrev.00003.2010.

198

Bibliography

A. C. van Bon, E. Verbitskiy, G. von Basum, J. B. L. Hoekstra, and J. H. de Vries. Exercisein closed-loop control: A major hurdle. J Diabetes Sci Technol, 5(6):1337–1341, Nov 2011.doi:10.1177/193229681100500604.

V. N. Vapnik. Statistical Learning Theory. Wiley, 1998. ISBN 9780471030034.

K. Vehik, R. F. Hamman, D. Lezotte, J. M. Norris, G. J. Klingensmith, M. Rewers, and D. Dabe-lea. Trends in high-risk HLA susceptibility genes among Colorado youth with type 1 diabetes.Diabetes Care, 31(7):1392–1396, Mar 2008. doi:10.2337/dc07-2210.

M. von Herrath, S. Sanda, and K. Herold. Type 1 diabetes as a relapsing-remitting disease? NatRev Immunol, 7(12):988–994, Dec 2007. doi:10.1038/nri2192.

R. E. Wachters-Hagedoorn, M. G. Priebe, J. A. J. Heimweg, A. M. Heiner, K. N. Englyst, J. J.Holst, F. Stellaard, and R. J. Vonk. The rate of intestinal glucose absorption is correlated withplasma glucose-dependent insulinotropic polypeptide concentrations in healthy men. J Nutr,136(6):1511–1516, Jun 2006.

R. E. Wachters-Hagedoorn, M. G. Priebe, J. A. J. Heimweg, A. M. Heiner, H. Elzinga, F. Stel-laard, and R. J. Vonk. Low-dose acarbose does not delay digestion of starch but reduces itsbioavailability. Diabet Med, 24(6):600–606, Jun 2007. doi:10.1111/j.1464-5491.2007.02115.x.

A. Wald and J. Wolfowitz. On a test whether two samples are from the same population. AnnMath Stat, 11(2):147–162, 1940.

M. Wallymahmed, C. Morgan, G. Gill, and I. MacFarlane. Does hypoglycaemic avoidance be-haviour contribute to increased HbA1c levels in physically active people with type 1 diabetes?Pract Diabetes Internat, 24(8):418–421, 2007. doi:10.1002/pdi.1167.

Y. Wang, E. Dassau, H. Zisser, L. Jovanovic, and F. J. Doyle. Automatic bolus and adaptivebasal algorithm for the artificial pancreatic β-cell. Diabetes Technol Ther, 12(11):879–887, Nov2010. doi:10.1089/dia.2010.0029.

J. H. Ward. Hierarchical grouping to optimize an objective function. J Am Stat Assoc, 58(301):236–244, Mar 1963. doi:10.1080/01621459.1963.10500845.

D. H. Wasserman and B. Zinman. Exercise in individuals with IDDM. Diabetes Care, 17(8):924–937, Aug 1994. doi:10.2337/diacare.17.8.924.

K. Wasserman, J. E. Hansen, D. Y. Sue, B. J. Whipp, and R. Casaburi. Principles of exercisetesting and interpretation. Lippincott Williams & Wilkins, 2 edition, 1994.

G. J. Welk, J. A. Schaben, and J. R. J. Morrow. Reliability of accelerometry-based activitymonitors: a generalizability study. Med Sci Sports Exerc, 36(9):1637–1645, Sep 2004.

G. J. Welk, J. J. McClain, J. C. Eisenmann, and E. E. Wickel. Field validation of the MTIActiGraph and BodyMedia armband monitor using the IDEEA monitor. Obesity, 15(4):918–928, Apr 2007. doi:10.1038/oby.2007.624.

D. J. West, R. D. Morton, S. C. Bain, J. W. Stephens, and R. M. Bracken. Blood glucose responsesto reductions in pre-exercise rapid-acting insulin for 24 h after running in individuals with type1 diabetes. J Sports Sci, 28(7):781–788, May 2010. doi:10.1080/02640411003734093.

D. J. West, J. W. Stephens, S. C. Bain, L. P. Kilduff, S. Luzio, R. Still, and R. M. Bracken.A combined insulin reduction and carbohydrate feeding strategy 30 min before running bestpreserves blood glucose concentration after exercise through improved fuel oxidation in type 1diabetes mellitus. J Sports Sci, 29(3):279–289, Feb 2011. doi:10.1080/02640414.2010.531753.

K. R. Westerterp. Diet induced thermogenesis. Nutr Metab, 1(1):5, 2004. doi:10.1186/1743-7075-1-5.

K. R. Westerterp. Assessment of physical activity: a critical appraisal. Eur J Appl Physiol, 105(6):823–828, Feb 2009. doi:10.1007/s00421-009-1000-2.

199

Bibliography

M. Wilinska, L. Chassin, H. Schaller, L. Schaupp, T. Pieber, and R. Hovorka. Insulin kineticsin type-1 diabetes: Continuous and bolus delivery of rapid acting insulin. IEEE Trans BiomedEng, 52(1):3–12, Jan 2005. doi:10.1109/tbme.2004.839639.

M. E. Wilinska, E. S. Budiman, M. B. Taub, D. Elleri, J. M. Allen, C. L. Acerini, D. B. Dunger,and R. Hovorka. Overnight closed-loop insulin delivery with model predictive control: assess-ment of hypoglycemia and hyperglycemia risk using simulation studies. J Diabetes Sci Technol,3(5):1109–1120, Sep 2009.

M. E. Wilinska, L. J. Chassin, C. L. Acerini, J. M. Allen, D. B. Dunger, and R. Hovorka.Simulation environment to evaluate closed-loop insulin delivery systems in type 1 diabetes. JDiabetes Sci Technol, 4(1):132–144, Jan 2010. doi:10.1177/193229681000400117.

D. A. Winter, A. O. Quanbury, and G. D. Reimer. Instantaneous energy and power flow in normalhuman gait. Biomechanics, pages 334–340, 1976.

World Health Organization. Diabetes – fact sheet 312, January 2015. URL http://www.who.

int/mediacentre/factsheets/fs312/en/. [Online; accessed 25-February-2015].

K. Yamanouchi, R. Abe, A. Takeda, Y. Atsumi, M. Shichiri, and Y. Sato. The effect of walkingbefore and after breakfast on blood glucose levels in patients with type 1 diabetes treatedwith intensive insulin therapy. Diabetes Res Clin Pract, 58(1):11–18, 2002. doi:10.1016/S0168-8227(02)00099-2.

J. Yardley, G. Kenny, B. Perkins, M. Riddell, J. Malcolm, P. Boulay, F. Khandwala, and R. Sigal.Effects of performing resistance exercise before versus after aerobic exercise on glycemia in type1 diabetes. Diabetes Care, 35(4):669–675, 2012. doi:10.2337/dc11-1844.

J. E. Yardley, G. P. Kenny, B. A. Perkins, M. C. Riddell, N. Balaa, J. Malcolm, P. Boulay,F. Khandwala, and R. J. Sigal. Resistance versus aerobic exercise: acute effects on glycemia intype 1 diabetes. Diabetes Care, 36(3):537–542, 2013a. doi:10.2337/dc12-0963.

J. E. Yardley, R. J. Sigal, G. P. Kenny, M. C. Riddell, L. E. Lovblom, and B. A. Perkins.Point accuracy of interstitial continuous glucose monitoring during exercise in type 1 diabetes.Diabetes Technol Ther, 15(1):46–49, Jan 2013b. doi:10.1089/dia.2012.0182.

I. Zakeri, A. L. Adolph, M. R. Puyau, F. A. Vohra, and N. F. Butte. Application of cross-sectionaltime series modeling for the prediction of energy expenditure from heart rate and accelerometry.J Appl Physiol, 104(6):1665–1673, Apr 2008. doi:10.1152/japplphysiol.01163.2007.

A. G. Zapico, P. J. Benito, M. González-Gross, A. B. Peinado, E. Morencos, B. Romero, M. A.Rojo-Tirado, R. Cupeiro, B. Szendrei, J. Butragueño, et al. Nutrition and physical activityprograms for obesity treatment (PRONAF study): methodological approach of the project.BMC Public Health, 12(1):1100, 2012. doi:10.1186/1471-2458-12-1100.

H. Zisser, L. Robinson, W. Bevier, E. Dassau, C. Ellingsen, F. J. Doyle, and L. Jovanovic. Boluscalculator: a review of four ’smart’ insulin pumps. Diabetes Technol Ther, 10(6):441–444, Dec2008. doi:10.1089/dia.2007.0284.

N. Zumel and J. Mount. Practical Data Science with R. Manning Publications Co., 2014. ISBN1617291560.

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