Estrategias de planificación dosimétrica en VMAT · • Las soluciones de clase nos benefician...

Estrategias de planificación dosimétrica en VMAT

TM. Felipe Lucic M.Sc.

Cumplimiento de los objetivos dosimétricos: • Cobertura • Homogeneidad • Conformalidad • Ubicación de puntos calientes • Distribución de las dosis

Éxito de una dosimetría en VMAT

Pero por sobre todo… Un plan que el equipo pueda realizar.

(que pase las pruebas de control dosimétrico, DQA)

• Antes de 5.0 Mónaco fue un sistema de planificación de tratamiento que usa el

algoritmo de Montecarlo XVMC como motor de cálculo. Tiene la posibilidad de poder planificar IMRT/VMAT/DCAT.

• 5.0

Planificación 3D conformacional (con Collapsed Cone ) Planificación de electrones (XVMC MC) Soporta conos para SRS (XVMC MC)

• 5.1

Forward Planning Multiples cursos de tratamiento Planificación con MRI pudiendo ingresar haces no coplanares Importar y recalcular planes DICOM de otros TPS

Mónaco 5.0/5.1 características generales

Templates y Soluciones de Clase

• Mónaco es un TPS que tiene de base los Templates – Templates = ahorran tiempo

• Que significa esto? – Los templates almacenan toda la información relevante de

un plan, que se puede aplicar para crear un plan nuevo en otro paciente.

– Todos los datos desde geometría, parámetros de calculo y restricciones

• Las soluciones de clase son útiles por la siguiente razón: – Las geometrías de los pacientes en una población pueden variar, pero

las relaciones entre los Target(s) y los OARs no varían tanto. – Las restricciones biológicas toman en cuenta todo el volumen del

Target y los OARs por lo que las superposiciones de los volúmenes pueden variar, pero los restricciones no necesariamente.

• Las soluciones de clase nos benefician por: – El uso de un template proporciona una forma mas estandarizada de

planificar, donde el proceso es mas fácil de desarrollar y entender. – Una vez que este se ha usado en varios pacientes este puede ser una

solución de clase para los casos, permitiendo tener una trazabilidad y consistencia en la creación del plan.

Templates y Soluciones de Clase

Estrategias de planificación en Vmat

Dependiendo la zona a tratar y los órganos de riesgo involucrados podemos tener: Estrategias de tipo:

• Geométricas

• Dosimétricas

¿Arco completo o arcos parciales?

En una primera aproximación hay que considerar las

relación de los tamaños del PTV y OARs.

Estrategias Geométricas

V20 < 35% V10 < 45% V5 < 65% Dmed < 20 Gy


¿Arco completo o arcos parciales?


Angulo de colimador

En general es recomendable la angulación de 15° a 20° para disminuir la fuga interláminas (Efecto Tongue & Groove)


Selección de número de sectores de optimización

Este parámetro se relaciona con el tamaño del ángulo del incremento de optimización del haz


•Por lo general se pueden usar un solo arco para lograr una buen resultado dosimétrico. •Pero en algunas situaciones la adición de un segundo arco puede mejorar la homogeneidad y la conformación.

¿Número de arcos?


Mónaco optimiza la 1ra mitad del PTV en el 1er arco

Mónaco optimiza la 2a mitad del PTV en el 2do arco

¿Número de arcos?...


¿Número de arcos?...

Se debe tener en cuenta que aumentarán el numero de segmentos por lo que disminuirá el # de UM por segmento pudiendo provocar: • Detenciones del equipo durante la irradiación y • No pase las pruebas de DQA por falsas fallas en el detector.


•Trabajar con dos arcos independientes para optimizar el PTV y proteger los OARs

Dividir el Target Volume y optimizar con arcos distintos


Estrategias Dosimétricas

¿Que es una Optimización “Restringida”?

Optimización No Restringidas Todas las funciones de costo de los Targets y los OARs compiten por igual.

Optimización Restringida Todos las restricciones de los OARs deben ser reunidas. La prescripción de los Target son secundarios.

•Los objetivos de los targets a veces no pueden ser reunidos.


Optimización de las Restricciones en Dos Etapas

Etapa 1- Optimización de los constrains con la Fluencia de dosis Se optimiza la fluencia basado en la prescripción.

Etapa 2- Optimización de las aperturas (segmentación ) Planes VMAT – Optimiza la forma de las aperturas, posiciones de Gantry y la ponderaciones de los segmentos para crear secuencias de arcos puedan ser entregados por el equipo.


¿Cuales algoritmos de Cálculo ofrece Mónaco?

Pencil Beam Optimizado • Diseñado específicamente para IMRT basado en mini-haces • Bajo consumo de memoria para un cálculo de dosis rápido • El haz primario y las colas de dispersión se representan

eficientemente • El comisionado de Monte Carlo facilita la estrecha concordancia entre

los dos algoritmos XVMC Monte Carlo • Uno de los códigos de Monte Carlo de fotones más rápidos

disponibles • Proporciona los cálculos de dosis más precisos cerca de las

proximidades de las regiones de build-up.


Pestaña de prescripción y definición geométrica


Tabla de restricciones


Priorización de los volúmenes


Propiedades de las estructuras a optimizar


Variación de densidades dentro de PTV

• ¿Por qué limpiar? - Para evitar que el optimizador intente sobrecompensar una región baja densidad, como una cavidad de aire que se ha incluido en la expansión de PTV pero no incluye el tejido que requiere la dosis prescrita.


“Opción Clear All Voxels”


“Opción Fill ED”

•Esta opción afecta los valores de densidad electrónica (ED) para el cálculo de dosis

-Todos los voxles por debajo de la ED especificada son llenados con la ED especificada. -Es útil para llenar los ITV con una densidad tomando en cuenta la posición potencial de la densidad del tumor en el ITV

•Hay que tener en cuenta que se alterará la densidad para el cálculo de dosis final


Propiedades de las estructuras a optimizar Auto Flash margen


Sin Auto Flash sobre Target 1.0 cm Auto Flash sobre Target

Propiedades de las estructuras a optimizar Auto flash margen


Mónaco Funciones de Costo

Funciones de Costo Físicas (basados en la dosis) • Target Penalty • Overdose/Underdose DVH Constraints • Quadratic Overdose/Underdose • Maximum Dose

• Son las comunes a las que tienen todos los sistemas

de planifición de IMRT.

Funciones de Costo Biológicas (basado en la dosis respuesta) • Target (EUD) –Targets • Serial (EUD)/Paralelos – OARs

Son funciones de costo que no tienen los otros sistemas de planificación


¿Que es EUD? EUD = Equivalent Uniform Dose • Para Targets:

• EUD representa una dosis homogénea que cuando es aplicada al volumen blanco, tiene el mismo efecto clínico como si se diera una distribución de dosis heterogénea dentro del volumen blanco.

• EUD permite puntos frios y calientes

• Para OARs: EUD representa una dosis uniforme a la cual puede llevar a la misma probabilidad de daño como una distribución de dosis heterogénea en un OAR.


Formula para las funciones de Costo Biológicas

∑=

=N

iiDfN

EUD1

)(1

)(DfNDi Dose in volume element i of an organ/tumor

Number of volume elements

objective density

Las propiedades de f definen completamente el comportamiento de la función de costo.



Función de Costo- Target EUD • EUD permite puntos fríos y calientes

– Permite al optimizador mucha mas flexibilidad cuando se busca una buena optimización.

**Función de Costo Biológica**

– Puede ser controlado por la sensibilidad celular, aumentándola disminuye el volumen donde se permite estar por debajo de la prescripción, pero no se puede obtener dependiendo de otras restricciones de OARs.

– Usando una restricción Max dose ayudará a una curva mas recta.


Función de Costo – Target Penalty

• Target Penalty – Es una función de costo física – El iso-efecto es un DVH basado

en un parámetro Físico – Resultará en DVH del Target con

mayor pendiente que la función de Costo basado en EUD


Eligiendo la Función de Costo para el Target


•En Resumen

•Target Penalty -Función de Costo Física -Podemos especificar el % del Target a cubrir -Se puede lograr una mejor cobertura -Es un Objetivo menos flexible

•Target EUD (Equivalent Uniform Dose)

-Función de costo Biológica -Mas flexible -No siempre se puede obtener la cobertura mínima al target

Función de Costo- Serial


Serial Cost Function

0 10 20 30 40 50 60

Increasing Dose

Wei

ght (

Pena

lty)

k= 8

k= 12

k=16


Chart4

000

0.50.50.5

111

1.51.51.5

222

2.52.52.5

333

3.53.53.5

444

4.54.54.5

555

5.55.55.5

666

6.56.56.5

777

7.57.57.5

888

8.58.58.5

999

9.59.59.5

101010

10.510.510.5

111111

11.511.511.5

121212

12.512.512.5

131313

13.513.513.5

141414

14.514.514.5

151515

15.515.515.5

161616

16.516.516.5

171717

17.517.517.5

181818

18.518.518.5

191919

19.519.519.5

202020

20.520.520.5

212121

21.521.521.5

222222

22.522.522.5

232323

23.523.523.5

242424

24.524.524.5

252525

25.525.525.5

262626

26.526.526.5

272727

27.527.527.5

282828

28.528.528.5

292929

29.529.529.5

303030

30.530.530.5

313131

31.531.531.5

323232

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33.533.533.5

343434

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36.536.536.5

373737

37.537.537.5

383838

38.538.538.5

393939

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404040

40.540.540.5

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41.541.541.5

424242

42.542.542.5

434343

43.543.543.5

444444

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464646

46.546.546.5

474747

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484848

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54.554.554.5

555555

55.555.555.5

565656

56.556.556.5

575757

57.557.557.5

585858

58.558.558.5

595959

59.559.559.5

606060

k= 8

k= 12

k=16

Increasing Dose

Weight (Penalty)


0.16777216

0.0687194767

0.0281474977

0.1763465806

0.0740543483

0.0310981165

0.1853020189

0.0797664431

0.0343368382

0.1946528962

0.0858798555

0.03788975

0.2044140859

0.0924200563

0.0417851185

0.2146009244

0.0994139621

0.0460535568

0.2252292232

0.1068900077

0.050728203

0.2363152801

0.1148782221

0.0558449116

0.2478758911

0.123410307

0.0614424574

0.259928363

0.1325197193

0.0675627539

0.272490525

0.1422417571

0.0742510862

0.2855807421

0.1526136491

0.0815563603

0.2992179271

0.1636746477

0.0895313679

0.3134215541

0.1754661268

0.0982330706

0.3282116715

0.1880316822

0.1077229013

0.3436089158

0.201417238

0.118067087

0.3596345248

0.2156711558

0.1293369914

0.376310352

0.2308443494

0.141609481

0.3936588806

0.2469904036

0.1549673143

0.4117032378

0.2641656981

0.1694995561

0.43046721

0.2824295365

0.1853020189

0.449975257

0.3018442801

0.2024777319

0.4702525276

0.3224754874

0.2211374397

0.4913248752

0.3443920589

0.241400133

0.5132188731

0.3676663877

0.2633936117

0.5359618307

0.3923745159

0.287255084

0.5595818097

0.4185962975

0.3131318017

0.5841076403

0.446415567

0.3411817355

0.6095689385

0.4759203148

0.3715742908

0.6359961228

0.5072028697

0.4044910682

0.6634204313

0.5403600877

0.4401266687

0.6918739397

0.575493548

0.4786895484

0.721389579

0.6127097573

0.5204029247

0.7520011535

0.6521203607

0.5655057348

0.7837433594

0.693842361

0.6142536535

0.8166518037

0.7379983458

0.6669201684

0.8507630226

0.7847167237

0.7237977206

0.8861145015

0.8341319683

0.7851989098

0.9227446944

0.8863848717

0.8514577711

0.9606930436

0.9416228069

0.922931124

1

1

1

1.0407070439

1.0616778119

1.0830711513

1.0828567056

1.1268250301

1.1725786449

1.1264925866

1.1956181715

1.2689855477

1.171659381

1.2682417946

1.3727857051

1.2184028975

1.3448888242

1.4845056207

1.2667700814

1.4257608868

1.6047064391

1.316809037

1.5110686573

1.7339860398

1.3685690504

1.6010322186

1.8729812457

1.4221006128

1.6958814328

2.022370153

1.4774554438

1.795856326

2.1828745884

1.534686515

1.9012074858

2.3552626993

1.5938480745

2.0121964718

2.5403516847

1.6549956713

2.1290962415

2.739010672

1.7181861798

2.252191589

2.9521637486

1.7834778256

2.381779599

3.1807931543

1.8509302103

2.5181701168

3.4259426433

1.9206043381

2.6616862324

3.6887210235

1.9925626417

2.8126647818

3.9703058811

2.066869009

2.9714568642

4.2719475002

2.14358881

3.1384283767

4.5949729864

2.2227889246

3.3139605657

4.9407906031

2.3045377697

3.4984505969

5.3108943321

2.3889053281

3.6923121434

5.7068686665

2.4759631763

3.8959759925

6.1303936504

2.565784514

4.1098906729

6.583250172

2.6584441929

4.3345231002

7.0673255268

2.754018747

4.5703592449

7.5846192587

2.8525864221

4.8179048198

8.1372492954

2.9542272066

5.0776859902

8.7274583883

3.0590228625

5.3502501055

9.3576208735

3.1670569566

5.6361664541

10.0302497662

3.278414892

5.9360270418

10.748004204

3.3931839407

6.2504473939

11.5136972552

3.5114532758

6.580067382

12.3303041081

3.6333140048

6.9255520766

13.2009706574

3.7588592027

7.2875926251

14.1290225055

3.888183946

7.6669071568

15.117974398

4.0213853472

8.0642417152

16.1715401104

4.158562589

8.4803712184

17.2936428064

4.29981696

8.9161004483

18.4884258895

4.4452518901

9.3722650689

19.7602643661

4.5949729864

9.8497326758

21.1137767454

4.7490880699

10.3494038758

22.5538374961

4.9077072127

10.8722133987

24.0855900859

5.0709427749

11.4191312421

25.7144606263

5.2389094428

11.9911638487

27.4461721501

5.4117242674

12.5893553192

29.2867595465

5.589506703

13.2147886588

31.2425851826

5.7723786465

13.8685870612

33.3203552387

5.9604644775

14.5519152284

35.527136788

6.1538910984

15.2659807287

37.8703756505

6.3527879748

16.0120353934

40.3579150534

6.5572871777

16.7913767536

42.9980151305

6.7675234241

17.6053495162

45.7993732958

6.9836341202

18.4553470835

48.7711455254

7.2057594038

19.3428131138

51.9229685853

7.4340421873

20.2692431263

55.2649832432

7.6686282021

21.2361861505

58.8078585026

7.9096660424

22.2452464217

62.5628169017

8.15730721

23.2980851225

66.5416609183

8.4117061601

24.3964221731

70.7568005247

8.6730203469

25.5420380699

75.2212819378

8.9414102697

26.7367757751

79.9488176119

9.2170395205

27.9825426565

84.9538175225

9.5000748308

29.281312481

90.2514217915

9.7906861202

30.6351274611

95.8575347049

10.0890465446

32.0461003567

101.7888601794

10.3953325454

33.5164166334

108.0629387305

10.7097238994

35.0483366774

114.6981860024

11.0324037688

36.6441980706

121.7139329176

11.363558752

38.3064179246

129.1304675093

11.7033789351

40.0374952772

136.9690784992

12.0520579441

41.8400135514

145.2521006873

12.4097929968

43.7166430787

154.0029622226

12.7767849565

45.6701436883

163.2462338235

13.1532383854

47.7033673637

173.0076800225

13.539361599

49.8192609675

183.3143125097

13.9353667212

52.0208690373

194.1944456534

14.3414697391

54.3113366525

205.6777542778

14.75789056

56.6939123753

217.7953337809

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78.578.5

78.878.8

79.179.1

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81.581.5

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82.782.7

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100.4100.4

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150.3439192978

0.0087642482

145.9005849787

0.0081309742

141.5885710347

0.0075434583

137.4039963621

0.0069983943

133.3430945613

0.0064927148

129.4022105466

0.0060235738

125.5777972562

0.0055883314

121.8664124602

0.005184538

118.2647156616

0.0048099214

114.7694650901

0.0044623733

111.3775147845

0.0041399377

108.0858117603

0.0038408003

104.8913932628

0.0035632774

101.7913840995

0.0033058074

98.7829940531

0.0030669413

95.8635153694

0.0028453348

93.0303203205

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90.2808588396

0.0024490024

87.6126562258

0.002272046

85.0233109167

0.0021078759

82.5104923266

0.0019555681

80.0719387492

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77.7054553218

0.0016831731

75.4089120494

0.0015615529

73.180241888

0.0014487205

71.0174388843

0.001344041

68.9185563693

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66.8817052072

0.0011568268

64.9050520944

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62.9868179098

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61.125276113

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59.3187511907

0.0008569984

57.5656171487

0.0007950747

55.8642960479

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54.2132565846

0.0006843271

52.6110127116

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51.0561223014

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49.5471858477

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48.0828452058

0.000506962

46.6617823703

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45.2827182887

0.0004363462

43.9444117102

0.0004048174

42.6456580686

0.0003755667

41.3852883979

0.0003484295

40.1621682803

0.0003232532

38.9751968253

0.0002998961

37.8233056783

0.0002782266

36.7054580595

0.000258123

35.6206478307

0.0002394719

34.5678985894

0.0002221685

33.5462627903

0.0002061154

32.554820892

0.0001912222

31.5926805302

0.0001774051

30.6589757133

0.0001645865

29.7528660442

0.000152694

28.8735359628

0.0001416609

28.0201940129

0.000131425

27.192072129

0.0001219286

26.3884249455

0.0001131185

25.6085291257

0.000104945

24.8516827108

0.000097362

24.1172044879

0.000090327

23.4044333769

0.0000838003

22.7127278359

0.0000777451

22.041465283

0.0000721275

21.3900415368

0.0000669159

20.7578702718

0.0000620808

20.1443824912

0.000057595

19.5490260147

0.0000534334

18.9712649812

0.0000495725

18.4105793668

0.0000459906

17.8664645165

0.0000426674

17.3384306904

0.0000395844

16.8260026222

0.0000367242

16.3287190922

0.0000340706

15.8461325116

0.0000316088

15.3778085199

0.0000293249

14.9233255939

0.000027206

14.4822746683

0.0000252402

14.0542587674

0.0000234164

13.6388926482

0.0000217244

13.235802453

0.0000201547

12.8446253734

0.0000186984

12.4650093238

0.0000173473

12.0966126239

0.0000160938

11.7391036919

0.0000149309

11.3921607457

0.0000138521

11.0554715131

0.0000128512

10.7287329512

0.0000119226

10.4116509731

0.0000110611

10.1039401837

0.0000102619

9.8053236225

0.0000095204

9.5155325145

0.0000088325

9.234306028

0.0000081943

8.9613910403

0.0000076022

8.6965419094

0.0000070529

8.4395202533

0.0000065433

8.1900947351

0.0000060705

7.9480408551

0.0000056318

7.7131407483

0.0000052249

7.4851829888

0.0000048474

7.2639623992

0.0000044971

7.0492798662

0.0000041722

6.8409421609

0.0000038707

6.6387617653

0.000003591

6.4425567034

0.0000033315

6.2521503775

0.0000030908

6.0673714089

0.0000028675

5.8880534841

0.0000026603

5.714035205

0.0000024681

5.5451599432

0.0000022897

5.3812756997

0.0000021243

5.2222349676

0.0000019708

5.0678945994

0.0000018284

4.9181156785

0.0000016963

4.7727633937

0.0000015737

4.6317069181

0.00000146

4.4948192914

0.0000013545

4.3619773054

0.0000012566

4.2330613935

0.0000011658

4.1079555225

0.0000010816

Poisson

XRhoAlphaXRhoAlphaXRhoAlpha

100.175100.2575100.1375

652.7182818285150.34391929786512.18249396070.0087642482653.669296667621.3900415368

65.32.6379444594145.900584978765.311.30222941930.008130974265.33.528948672220.5718876167

65.62.5599814183141.588571034765.610.48556972470.007543458365.63.39396888819.7850275038

65.92.4843225334137.403996362165.99.72791901260.006998394365.93.264151984819.0282642323

66.22.4108997064133.343094561366.29.02501349940.006492714866.23.139300486218.3004466192

66.52.3396468519129.402210546666.58.37289748810.006023573866.53.019224468817.6004675137

66.82.2704998375125.577797256266.87.76790110630.005588331466.82.903741273916.9272621126

67.12.2033964263121.866412460267.17.20661965380.00518453867.12.792675229416.2798063407

67.42.1382762205118.264715661667.46.68589444230.004809921467.42.685857382315.6571152929

67.72.0750806077114.769465090167.76.20279501910.004462373367.72.583125242115.0582417362

682.0137527075111.3775147845685.7546026760.0041399377682.484322533414.4822746683

68.31.9542373206108.085811760368.35.33879514910.003840800368.32.389298958213.9283379323

68.61.8964808793104.891393262868.64.95303242440.003563277468.62.297909967413.3955888836

68.91.8404313988101.791384099568.94.59514356930.003305807468.92.210016540712.8832171082

69.21.786038430898.782994053169.24.26311451520.003066941369.22.125484975312.3904431899

69.51.733253017995.863515369469.53.95507672290.002845334869.52.044186682311.9165175245

69.81.682027649793.030320320569.83.66929666760.002639740869.81.965997991311.4607191798

70.11.6323162290.280858839670.13.40416608280.002449002470.11.890799962311.0223547985

70.41.58407398587.612656225870.43.15819290970.00227204670.41.818478204610.6007575439

70.71.537257523585.023310916770.72.92999290050.002107875970.71.748922702810.1952860853

711.491824697682.5104923266712.71828182850.0019555681711.68202764979.8053236225

71.31.447734614780.071938749271.32.52186826040.001814265671.31.61769128499.4302769474

71.61.404947590677.705455321871.62.33964685190.001683173171.61.55581574049.0695755416

71.91.363425114175.408912049471.92.17059212720.001561552971.91.49630689178.7226707088

72.21.323129812373.18024188872.22.01375270750.001448720572.21.43907421428.3890347398

72.51.284025416771.017438884372.51.86824595740.00134404172.51.3840306468.0681601101

72.81.246076730668.918556369372.81.73325301790.001246925372.81.33109245537.7595587074

73.11.209249597766.881705207273.11.60801419750.001156826873.11.28017911287.4627610895

73.41.17351087164.905052094473.41.49182469760.001073238573.41.23121316957.17731577

73.71.138828383362.986817909873.71.3840306460.000995690173.71.18412013896.9027885316

741.105170918161.125276113741.28402541670.000923745741.13882838336.6387617653

74.31.072508181359.318751190774.31.19124621660.000856998474.31.09526900536.3848338356

74.61.040810774257.565617148774.61.10517091810.000795074774.61.05337574256.1406184692

74.91.010050167155.864296047974.91.02531512050.000737625374.91.01308486745.9057441674

75.20.980198673354.213256584675.20.95122942450.000684327175.20.97433508965.679853641

75.50.951229424552.611012711675.50.88249690260.0006348875.50.93706746345.4626032671

75.80.923116346451.056122301475.80.81873075310.000589005875.80.90122529745.2536625659

76.10.895834135349.547185847776.10.75957212320.000546446376.10.86675406895.0527136984

76.40.869358235448.082845205876.40.70468808970.00050696276.40.83360134044.8594509825

76.70.843664816646.661782370376.70.65376978510.000470330776.70.80171668034.6735804285

770.818730753145.2827182887770.60653065970.0004363462770.77105158584.4948192914

77.30.794533602543.944411710277.30.56270486880.000404817477.30.74155940944.3228956409

77.60.771051585842.645658068677.60.52204577680.000375566777.60.71319528794.1575479482

77.90.748263567641.385288397977.90.4843245690.000348429577.90.68591607393.9985246875

78.20.726149037140.162168280378.20.44932896410.000323253278.20.65968027053.8455839538

78.50.704688089738.975196825378.50.41686201970.000299896178.50.63444796793.6984930946

78.80.683861409237.823305678378.80.38674102350.000278226678.80.61018078313.5570283565

79.10.663650250136.705458059579.10.35879646540.00025812379.10.58684180083.4209745443

79.40.644036421135.620647830779.40.33287108370.000239471979.40.56439551813.290124694

79.70.625002268334.567898589479.70.30881897970.000222168579.70.54280778983.1642797576

800.606530659733.5462627903800.28650479690.0002061154800.52204577683.0432483008

80.30.588604969732.55482089280.30.26580295910.000191222280.30.5020778962.9268462114

80.60.571209063831.592680530280.60.24659696390.000177405180.60.48287377252.8148964194

80.90.554327284730.658975713380.90.2287787270.000164586580.90.46440419322.7072286275

81.20.537944437629.752866044281.20.21224797380.00015269481.20.44664106212.6036790524

81.50.522045776828.873535962881.50.19691167520.000141660981.50.42955735822.504090175

81.80.506616992428.020194012981.80.18268352410.00013142581.80.41312709392.4083105016

82.10.491644197527.19207212982.10.16948344950.000121928682.10.39732527552.3161943327

82.40.477113915526.388424945582.40.15723716630.000113118582.40.38212786552.227601542

82.70.463013068325.608529125782.70.14587575690.00010494582.70.36751174562.1423973627

830.449328964124.8516827108830.13533528320.000097362830.3534546822.0604521829

83.30.436049286324.117204487983.30.12555642750.00009032783.30.3399352911.9816413481

83.60.423162082323.404433376983.60.11648415780.000083800383.60.32693300721.9058449718

83.90.410655752822.712727835983.90.10806741860.000077745183.90.31442805151.8329477531

84.20.398519041122.04146528384.20.10025884370.000072127584.20.30240140151.7628388014

84.50.386741023521.390041536884.50.09301448920.000066915984.50.29083476241.6954114673

84.80.375311098920.757870271884.80.08629358650.000062080884.80.2797105391.630563181

85.10.364218979620.144382491285.10.08005831280.00005759585.10.26901180921.5681952957

85.40.35345468219.549026014785.40.07427357820.000053433485.40.25872229831.5082129377

85.70.343008517418.971264981285.70.06890682840.000049572585.70.24882635381.4505248624

860.332871083718.4105793668860.06392786120.0000459906860.23930892221.395043315

86.30.323033256417.866464516586.30.05930865680.000042667486.30.23015552571.3416838975

86.60.313486180917.338430690486.60.05502322010.000039584486.60.221352241.2903654399

86.90.304221264116.826002622286.90.0510474340.000036724286.90.21288567381.2410098768

87.20.295230166916.328719092287.20.04735892440.000034070687.20.20474294781.1935421291

87.50.286504796915.846132511687.50.04393693360.000031608887.50.19691167521.1478899891

87.80.278037300515.377808519987.80.0407622040.000029324987.80.18937994331.103984011

88.10.269820056414.923325593988.10.03781686920.00002720688.10.18213629471.0617574055

88.40.261845668614.482274668388.40.03508435410.000025240288.40.17516971061.0211459377

88.70.254106959614.054258767488.70.0325492810.000023416488.70.16846959340.9820878297

890.246596963913.6388926482890.03019738340.0000217244890.16202575090.9445236666

89.30.239308922213.23580245389.30.02801542580.000020154789.30.15582838090.9083963062

89.60.232236274712.844625373489.60.02599112880.000018698489.60.14986805580.8736507917

89.90.225372655512.465009323889.90.02411310040.000017347389.90.14413570890.8402342684

90.20.21871188712.096612623990.20.02237077190.000016093890.20.13862262030.8080959035

90.50.212247973811.739103691990.50.02075433790.000014930990.50.13332040340.7771868083

90.80.205975098211.392160745790.80.01925470180.000013852190.80.12822099250.747459964

91.10.199887614111.055471513191.10.01786342420.000012851291.10.12331663040.7188701504

91.40.193980042310.728732951291.40.01657267540.000011922691.40.11859985680.691373877

91.70.188247065610.411650973191.70.01537519170.000011061191.70.11406349640.6649293164

920.182683524110.1039401837920.01426423390.0000102619920.10970064850.6394962416

92.30.177284419.805323622592.30.01323355010.000009520492.30.10550467650.6150359639

92.60.17204486389.515532514592.60.01227733990.000008832592.60.10146919740.5915112744

92.90.16696016979.23430602892.90.01139022210.000008194392.90.09758807260.5688863876

93.20.16202575098.961391040393.20.01056720440.000007602293.20.0938553980.5471268867

93.50.15723716638.696541909493.50.0098036550.000007052993.50.09026549560.5261996713

93.80.15259010588.439520253393.80.00909527710.000006543393.80.08681290440.506072907

94.10.14808038668.190094735194.10.00843808410.000006070594.10.08349237240.4867159772

94.40.14370394987.948040855194.40.00782837750.000005631894.40.08029884830.4680994362

94.70.13945685627.713140748394.70.00726272630.000005224994.70.07722747430.4501949648

950.13533528327.4851829888950.0067379470.0000048474950.07427357820.4329753266

95.30.13133552117.263962399295.30.00625108640.000004497195.30.07143266650.4164143274

95.60.12745396997.049279866295.60.00579940470.000004172295.60.06870041770.4004867747

95.90.12368713586.840942160995.90.005380360.000003870795.90.06607267540.3851684396

96.20.12003162856.638761765396.20.00499159390.00000359196.20.06354544240.3704360199

96.50.11648415786.442556703496.50.00463091870.000003331596.50.06111487430.3562671048

96.80.11304153066.252150377596.80.00429630470.000003090896.80.05877727370.3426401407

97.10.10970064856.067371408997.10.00398586870.000002867597.10.05652908470.3295343983

97.40.10645850445.888053484197.40.00369786370.000002660397.40.05436688730.3169299413

97.70.10331218015.71403520597.70.0034306690.000002468197.70.05228739240.3048075958

980.10025884375.5451599432980.00318278080.0000022897980.05028743670.2931489214

98.30.09729574715.381275699798.30.00295280420.000002124398.30.04836397790.281936183

98.60.09442022325.222234967698.60.00273944480.000001970898.60.04651409010.2711523239

98.90.09162968395.067894599498.90.00254150210.000001828498.90.04473495910.2607809398

99.20.08892161754.918115678599.20.0023578620.000001696399.20.04302387860.2508062538

99.50.08629358654.772763393799.50.00218749110.000001573799.50.04137824580.2412130925

99.80.08374322564.631706918199.80.00202943060.0000014699.80.03979555720.2319868627

100.10.08126823924.4948192914100.10.00188279110.0000013545100.10.03827340540.2231135298

100.40.07886639984.3619773054100.40.00174674710.0000012566100.40.03680947480.2145795955

100.70.07653554544.2330613935100.70.00162053330.0000011658100.70.03540153850.2063720781

1010.07427357824.10795552251010.00150343920.00000108161010.03404745470.1984784925

Poisson

Cell Sen. =0.1

Cell Sen. =0.25

Cell Sen. =0.4

Prescription Dose

Penalty

Poisson Cell Kill Cost FunctionPrescribed Dose = 75

Serial

Cell Sen.=0.1

Cell Sen.=0.13

Cell Sen.=2.5

Dose (cGY)

Increasing Penalty for Cold Spots

Poisson Cell Kill Cost Function

Parallel

Xk Vol Eff Parmd RefXk Vol Eff Parmd RefXk Vol Eff Parmd Ref

85012501650

0400.16777216400.0687194767400.0281474977

0.540.250.176346580640.250.074054348340.250.0310981165

140.50.185302018940.50.079766443140.50.0343368382

1.540.750.194652896240.750.085879855540.750.03788975

2410.2044140859410.0924200563410.0417851185

2.541.250.214600924441.250.099413962141.250.0460535568

341.50.225229223241.50.106890007741.50.050728203

3.541.750.236315280141.750.114878222141.750.0558449116

4420.2478758911420.123410307420.0614424574

4.542.250.25992836342.250.132519719342.250.0675627539

542.50.27249052542.50.142241757142.50.0742510862

5.542.750.285580742142.750.152613649142.750.0815563603

6430.2992179271430.1636746477430.0895313679

6.543.250.313421554143.250.175466126843.250.0982330706

743.50.328211671543.50.188031682243.50.1077229013

7.543.750.343608915843.750.20141723843.750.118067087

8440.3596345248440.2156711558440.1293369914

8.544.250.37631035244.250.230844349444.250.141609481

944.50.393658880644.50.246990403644.50.1549673143

9.544.750.411703237844.750.264165698144.750.1694995561

10450.43046721450.2824295365450.1853020189

10.545.250.44997525745.250.301844280145.250.2024777319

1145.50.470252527645.50.322475487445.50.2211374397

11.545.750.491324875245.750.344392058945.750.241400133

12460.5132188731460.3676663877460.2633936117

12.546.250.535961830746.250.392374515946.250.287255084

1346.50.559581809746.50.418596297546.50.3131318017

13.546.750.584107640346.750.44641556746.750.3411817355

14470.6095689385470.4759203148470.3715742908

14.547.250.635996122847.250.507202869747.250.4044910682

1547.50.663420431347.50.540360087747.50.4401266687

15.547.750.691873939747.750.57549354847.750.4786895484

16480.721389579480.6127097573480.5204029247

16.548.250.752001153548.250.652120360748.250.5655057348

1748.50.783743359448.50.69384236148.50.6142536535

17.548.750.816651803748.750.737998345848.750.6669201684

18490.8507630226490.7847167237490.7237977206

18.549.250.886114501549.250.834131968349.250.7851989098

1949.50.922744694449.50.886384871749.50.8514577711

19.549.750.960693043649.750.941622806949.750.922931124

20501501501

20.550.251.040707043950.251.061677811950.251.0830711513

2150.51.082856705650.51.126825030150.51.1725786449

21.550.751.126492586650.751.195618171550.751.2689855477

22511.171659381511.2682417946511.3727857051

22.551.251.218402897551.251.344888824251.251.4845056207

2351.51.266770081451.51.425760886851.51.6047064391

23.551.751.31680903751.751.511068657351.751.7339860398

24521.3685690504521.6010322186521.8729812457

24.552.251.422100612852.251.695881432852.252.022370153

2552.51.477455443852.51.79585632652.52.1828745884

25.552.751.53468651552.751.901207485852.752.3552626993

26531.5938480745532.0121964718532.5403516847

26.553.251.654995671353.252.129096241553.252.739010672

2753.51.718186179853.52.25219158953.52.9521637486

27.553.751.783477825653.752.38177959953.753.1807931543

28541.8509302103542.5181701168543.4259426433

28.554.251.920604338154.252.661686232454.253.6887210235

2954.51.992562641754.52.812664781854.53.9703058811

29.554.752.06686900954.752.971456864254.754.2719475002

30552.14358881553.1384283767554.5949729864

30.555.252.222788924655.253.313960565755.254.9407906031

3155.52.304537769755.53.498450596955.55.3108943321

31.555.752.388905328155.753.692312143455.755.7068686665

32562.4759631763563.8959759925566.1303936504

32.556.252.56578451456.254.109890672956.256.583250172

3356.52.658444192956.54.334523100256.57.0673255268

33.556.752.75401874756.754.570359244956.757.5846192587

34572.8525864221574.8179048198578.1372492954

34.557.252.954227206657.255.077685990257.258.7274583883

3557.53.059022862557.55.350250105557.59.3576208735

35.557.753.167056956657.755.636166454157.7510.0302497662

36583.278414892585.93602704185810.748004204

36.558.253.393183940758.256.250447393958.2511.5136972552

3758.53.511453275858.56.58006738258.512.3303041081

37.558.753.633314004858.756.925552076658.7513.2009706574

38593.7588592027597.28759262515914.1290225055

38.559.253.88818394659.257.666907156859.2515.117974398

3959.54.021385347259.58.064241715259.516.1715401104

39.559.754.15856258959.758.480371218459.7517.2936428064

40604.29981696608.91610044836018.4884258895

40.560.254.445251890160.259.372265068960.2519.7602643661

4160.54.594972986460.59.849732675860.521.1137767454

41.560.754.749088069960.7510.349403875860.7522.5538374961

42614.90770721276110.87221339876124.0855900859

42.561.255.070942774961.2511.419131242161.2525.7144606263

4361.55.238909442861.511.991163848761.527.4461721501

43.561.755.411724267461.7512.589355319261.7529.2867595465

44625.5895067036213.21478865886231.2425851826

44.562.255.772378646562.2513.868587061262.2533.3203552387

4562.55.960464477562.514.551915228462.535.527136788

45.562.756.153891098462.7515.265980728762.7537.8703756505

46636.35278797486316.01203539346340.3579150534

46.563.256.557287177763.2516.791376753663.2542.9980151305

4763.56.767523424163.517.605349516263.545.7993732958

47.563.756.983634120263.7518.455347083563.7548.7711455254

48647.20575940386419.34281311386451.9229685853

48.564.257.434042187364.2520.269243126364.2555.2649832432

4964.57.668628202164.521.236186150564.558.8078585026

49.564.757.909666042464.7522.245246421764.7562.5628169017

50658.157307216523.29808512256566.5416609183

50.565.258.411706160165.2524.396422173165.2570.7568005247

5165.58.673020346965.525.542038069965.575.2212819378

51.565.758.941410269765.7526.736775775165.7579.9488176119

52669.21703952056627.98254265656684.9538175225

52.566.259.500074830866.2529.28131248166.2590.2514217915

5366.59.790686120266.530.635127461166.595.8575347049

53.566.7510.089046544666.7532.046100356766.75101.7888601794

546710.39533254546733.516416633467108.0629387305

54.567.2510.709723899467.2535.048336677467.25114.6981860024

5567.511.032403768867.536.644198070667.5121.7139329176

55.567.7511.36355875267.7538.306417924667.75129.1304675093

566811.70337893516840.037495277268136.9690784992

56.568.2512.052057944168.2541.840013551468.25145.2521006873

5768.512.409792996868.543.716643078768.5154.0029622226

57.568.7512.776784956568.7545.670143688368.75163.2462338235

586913.15323838546947.703367363769173.0076800225

58.569.2513.53936159969.2549.819260967569.25183.3143125097

5969.513.935366721269.552.020869037369.5194.1944456534

59.569.7514.341469739169.7554.311336652569.75205.6777542778

607014.757890567056.693912375370217.7953337809

Parallel

k= 8

k= 12

k=16

Increasing Dose

Weight (Penalty)


Quad Overdose

Xk Response Steepnessd RefXk Response Steepnessd RefXk Response Steepnessd RefXk Response Steepnessd RefXk Response Steepnessd RefXk Response Steepnessd Ref

1202.5203.9202.5202.5402.560

000000000000

0.60.05825242720.60.00031172060.60.00000230040.60.00031172060.60.0000551120.60.0000199998

1.20.11320754721.20.00176207881.20.0000343411.20.00176207881.20.00031172061.20.0001131307

1.80.16513761471.80.00484821881.80.0001669321.80.00484821881.80.00085876581.80.0003117206

2.40.21428571432.40.00992709332.40.00051253742.40.00992709332.40.00176207882.40.0006397953

30.260869565230.017277862130.00122326430.017277862130.003076200630.0011174093

3.60.30508474583.60.02711952253.60.00248915493.60.02711952253.60.00484821883.60.0017620788

4.20.3471074384.20.03961767774.20.0045362724.20.03961767774.20.00711958194.20.0025894792

4.80.38709677424.80.05488742374.80.00762421434.80.05488742374.80.00992709334.80.003613845

5.40.42519685045.40.07299486065.40.01204275145.40.07299486065.40.0133035015.40.0048482188

60.461538461560.093958379260.018107272560.093958379260.017277862160.0063046184

6.60.49624060156.60.11775031636.60.02615278236.60.11775031636.60.02187577376.60.0079941505

7.20.52941176477.20.14429928747.20.03652623067.20.14429928747.20.02711952257.20.0099270933

7.80.56115107917.80.1734933297.80.04957705947.80.1734933297.80.03302818187.80.0121129545

8.40.59154929588.40.20518385868.40.06564598838.40.20518385868.40.03961767778.40.0145605153

90.620689655290.239190369390.08505223690.239190369390.046900836690.0172778621

9.60.64864864869.60.275305719.60.10807958999.60.275305719.60.05488742379.60.0202724105

10.20.675496688710.20.313301758410.20.134961961310.20.313301758410.20.063584179810.20.023550923

10.80.701298701310.80.35293527410.80.165869276110.80.35293527410.80.072994860610.80.0271195225

11.40.726114649711.40.393953712111.40.200894716911.40.393953712111.40.083120282811.40.0309837024

120.75120.4361008001120.2400444045120.4361008001120.0939583792120.0351483351

12.60.77300613512.60.479121696612.60.283230563212.60.479121696612.60.10550426512.60.0396176777

13.20.795180722913.20.522767600113.20.330269030113.20.522767600113.20.117750316313.20.0443953779

13.80.816568047313.80.566799705213.80.380881649213.80.566799705213.80.130686261813.80.0494844788

14.40.837209302314.40.610992453614.40.434703667114.40.610992453614.40.144299287414.40.0548874237

150.8571428571150.6551360629150.4912957788150.6551360629150.1585741543150.0606060606

15.60.876404494415.60.699038348915.60.550160015215.60.699038348915.60.17349332915.60.0666416481

16.20.895027624316.20.742525888216.20.610758306616.20.742525888216.20.189037125716.20.0729948606

16.80.913043478316.80.785444584816.80.672532331916.80.785444584816.80.205183858616.80.0796657953

17.40.930481283417.40.827659718717.40.734923220617.40.827659718717.40.221910003817.40.0866539795

180.9473684211180.8690555611180.7973897932180.8690555611180.2391903693180.0939583792

18.60.963730569918.60.909534641818.60.85942428318.60.909534641818.60.256998270318.60.1015774083

19.20.979591836719.20.949016749319.20.920564823419.20.949016749319.20.2753057119.20.1095089397

19.80.994974874419.80.987437741119.80.980404353819.80.987437741119.80.294083562819.80.1177503163

20.41.009900990120.41.024748229720.41.038595941320.41.024748229720.40.313301758420.40.126298365

211.0243902439211.0609122029211.0948547913211.0609122029210.3329294657210.1351494097

21.61.038461538521.61.095905624821.61.14895742221.61.095905624821.60.35293527421.60.1442992874

22.21.052132701422.21.129715056522.21.20073858322.21.129715056522.20.373287370322.20.153743364

22.81.065420560722.81.162336325822.81.250086529122.81.162336325822.80.393953712122.80.163476552

23.41.078341013823.41.193773266623.41.296937234623.41.193773266623.40.41490219323.40.173493329

241.0909090909241.2240365437241.3412680585241.2240365437240.4361008001240.1837877569

24.61.103139013524.61.253142571124.61.383091280424.61.253142571124.60.457517763724.60.1943535025

25.21.115044247825.21.281112527925.21.422447828925.21.281112527925.20.479121696625.20.2051838586

25.81.126637554625.81.307971474225.81.459401425725.81.307971474225.80.500881723825.80.2162717656

26.41.137931034526.41.333747562726.41.494033290526.41.333747562726.40.522767600126.40.2276098344

271.1489361702271.3584713439271.5264374791271.3584713439270.5447498185270.2391903693

27.61.159663865527.61.382175157727.61.55671687727.61.382175157727.60.566799705227.60.2510053914

28.21.170124481328.21.404892607128.21.584979832628.21.404892607128.20.588889504928.20.2630466627

28.81.180327868928.81.426658104828.81.61133738828.81.426658104828.80.610992453628.80.27530571

29.41.190283400829.41.447506488329.41.635901050629.41.447506488329.40.633082841429.40.2877738492

301.2301.4674726944301.6587810417301.4674726944300.6551360629300.3004422096

30.61.20948616630.61.48659148830.61.680084956330.61.48659148830.60.677128659430.60.3133017584

31.21.2187531.21.504897237931.21.699916770631.21.504897237931.20.699038348931.20.3263433243

31.81.227799227831.81.522423734531.81.718376138831.81.522423734531.80.720844048831.80.3395576217

32.41.236641221432.41.539204043732.41.73555792532.41.539204043732.40.742525888232.40.352935274

331.2452830189331.5552703919331.751551926331.5552703919330.7640652134330.3664668368

33.61.253731343333.61.570654078333.61.76644274333.61.570654078333.60.785444584833.60.3801428205

34.21.261992619934.21.585385409534.21.780309769534.21.585385409534.20.806647768134.20.3939537121

34.81.270072992734.81.599493654934.81.79322726834.81.599493654934.80.827659718734.80.407889997

35.41.277978339435.41.613007016735.41.805264510935.41.613007016735.40.848466560535.40.4219421788

361.2857142857361.6259526156361.8164859679361.6259526156360.8690555611360.4361008001

36.61.293286219136.61.63835648636.61.826951525836.61.63835648636.60.889415101236.60.4503564608

37.21.300699300737.21.650243582437.21.836716726537.21.650243582437.20.909534641837.20.4646998367

37.81.307958477537.81.661637791737.81.845833016937.81.661637791737.80.929404687837.80.4791216966

38.41.315068493238.41.672561952838.41.854348001338.41.672561952838.40.949016749338.40.4936129188

391.3220338983391.6830378804391.8623056924391.6830378804390.9683633012390.508164506

39.61.328859060439.61.693086392739.61.869746756639.61.693086392739.60.987437741139.60.5227676001

40.21.335548172840.21.70272734240.21.876708750240.21.70272734240.21.006234346140.20.5374134958

40.81.342105263240.81.711979646840.81.883226346540.81.711979646840.81.024748229740.80.5520936523

41.41.34853420241.41.720861326141.41.889331549441.41.720861326141.41.042975297441.40.5667997052

421.3548387097421.7293895338421.8950538969421.7293895338421.0609122029420.5815234767

42.61.361022364242.61.737580593642.61.900420649942.61.737580593642.61.078556305242.60.5962569853

43.21.367088607643.21.745450034143.21.905456970143.21.745450034143.21.095905624843.20.6109924536

43.81.373040752443.81.753012623943.81.910186084743.81.753012623943.81.112958802343.80.6257223165

44.41.378881987644.41.76028240544.41.914629439644.41.76028240544.41.129715056544.40.6404392272

451.3846153846451.7672727273451.9188068413451.7672727273451.1461741453450.6551360629

45.61.390243902445.61.773996280245.61.922736587345.61.773996280245.61.162336325845.60.66980593

46.21.395770392746.21.780465124946.21.926435587546.21.780465124946.21.178202317646.20.6844421671

46.81.401197604846.81.786690725146.81.929919475346.81.786690725146.81.193773266646.80.6990383489

47.41.406528189947.41.792683975847.41.933202709647.41.792683975847.41.2090507147.40.7135882882

481.4117647059481.7984552325481.9362986694481.7984552325481.2240365437480.7280860371

48.61.41690962148.61.804014337748.61.939219739648.61.804014337748.61.238732990848.60.7425258882

49.21.421965317949.21.809370647449.21.941977391249.21.809370647449.21.253142571149.20.7569023747

49.81.426934097449.81.814533055849.81.944582253249.81.814533055849.81.267268073349.80.7712102695

50.41.431818181850.41.819510018950.41.9470441850.41.819510018950.41.281112527950.40.7854445848

511.4366197183511.8243095776511.9493723126511.8243095776511.2946791817510.7996005698

51.61.441340782151.61.828939378451.61.951575134551.61.828939378451.61.307971474251.60.8136737088

52.21.445983379552.21.833406694852.21.953660523652.21.833406694852.21.320993014952.20.8276597187

52.81.450549450552.81.837718446252.81.95563579952.81.837718446252.81.333747562752.80.8415545456

53.41.455040871953.41.841881216153.41.95750776553.41.841881216153.41.346239005853.40.8553543617

541.4594594595541.8459012704541.9592827504541.8459012704541.3584713439540.8690555611

54.61.463806970554.61.849784573354.61.960966644854.61.849784573354.61.370448670554.60.8826547559

55.21.468085106455.21.853536803455.21.96256493355.21.853536803455.21.382175157755.20.8961487714

55.81.472295514555.81.857163368255.81.964082724755.81.857163368255.81.393655041355.80.9095346418

56.41.476439790656.41.860669418756.41.965524783556.41.860669418756.41.404892607156.40.9228096051

571.4805194805571.8640598624571.9668955525571.8640598624571.4158921784570.9359710977

57.61.484536082557.61.86733937657.61.968199178257.61.86733937657.61.426658104857.60.9490167493

58.21.488491048658.21.870512417458.21.969439532558.21.870512417458.21.437194751158.20.9619443777

58.81.492385786858.81.873583236958.81.970620232958.81.873583236958.81.447506488358.80.9747519828

59.41.496221662559.41.87655588859.41.971744661159.41.87655588859.41.457597683859.40.9874377411

601.5601.8794342375601.9728159798601.8794342375601.4674726944601

60.61.503722084460.61.882221974860.61.97383714960.61.882221974860.61.477135858160.61.0124372722

61.21.507389162661.21.884922621461.21.9748109461.21.884922621461.21.48659148861.21.0247482297

61.81.51100244561.81.887539539161.81.975739948961.81.887539539161.81.495843866161.81.036931698

62.41.514563106862.41.89007593862.41.976626609262.41.89007593862.41.504897237962.41.0489866506

631.5180722892631.8925348847631.9774732029631.8925348847631.5137558078631.0609122029

63.61.521531100563.61.894919308763.61.978281871363.61.894919308763.61.522423734563.61.0727076068

64.21.524940617664.21.8972320164.21.979054624364.21.8972320164.21.530905127664.21.0843722449

64.81.528301886864.81.899475665164.81.979793349964.81.899475665164.81.539204043764.81.0959056248

65.41.531615925165.41.901652833265.41.980499822165.41.901652833265.41.547324484165.41.1073073741

661.5348837209661.9037659623661.981175709661.9037659623661.5552703919661.1185772345

66.61.538106235666.61.905817394166.61.981822579266.61.905817394166.61.563045649866.61.1297150565

67.21.541284403767.21.907809369867.21.982441909367.21.907809369867.21.570654078367.21.1407207947

67.81.544419134467.81.909744034567.81.983035089467.81.909744034567.81.578099434267.81.1515945022

68.41.547511312268.41.911623442168.41.983603428968.41.911623442168.41.585385409568.41.1623363258

691.5505617978691.9134495599691.9841481619691.9134495599691.5925156301691.1729465012

69.61.553571428669.61.915224272169.61.984670451969.61.915224272169.61.599493654969.61.1834253483

70.21.5565410270.21.916949384670.21.985171396470.21.916949384670.21.606322975870.21.1937732666

70.81.559471365670.81.918626628170.81.985652031270.81.918626628170.81.613007016770.81.2039907306

71.41.562363238571.41.920257661771.41.986113334271.41.920257661771.41.619549133971.41.2140782856

721.5652173913721.9218440768721.9865562289721.9218440768721.6259526156721.2240365437

Quad Overdose

k=1

k=2.5

k=3.9

Pivot point

Reference Dose

Penalty

Parallel Cost FunctionDref =20

Quad Underdose

Dref =20

Dref =40

Dref =60

Pivot pt 20

Pivot pt 40

Pivot pt 60

Reference Dose

Penalty

Parallel Cost Functionk = 2.5

Max Dose

XIntervalDoseWeightPower

0.5703002.5

5000

50.500

5100

51.500

5200

52.500

5300

53.500

5400

54.500

5500

55.500

5600

56.500

5700

57.500

5800

58.500

5900

59.500

6000

60.500

6100

61.500

6200

62.500

6300

63.500

6400

64.500

6500

65.500

6600

66.500

6700

67.500

6800

68.500

6900

69.500

7000

70.50.750.1767766953

7131

71.56.752.7556759606

72125.6568542495

72.518.759.882117688

732715.5884572681

73.536.7522.917651494

744832

74.560.7542.9567369571

757555.9016994375

75.590.7570.9425383673

7610888.1816307402

76.5126.75107.7167872246

77147129.6418142422

77.5168.75154.0469692983

78192181.0193359838

78.5216.75210.6431372013

79243243

79.5270.75278.169181884

80300316.2277660168

80.5330.75357.2508309997

81363401.311599633

81.5396.75448.4815701342

82432498.8306325798

82.5468.75552.427172802

83507609.3381655534

83.5546.75669.6292584334

84588733.3648478077

84.5630.75800.6081477539

85675871.4212528967

85.5720.75945.8651958657

867681024

86.5816.751105.8847278311

878671191.5775258035

87.5918.751281.1356656303

889721374.6155826266

88.51026.751472.0729113227

8910831573.5625186182

89.51140.751679.1385347106

9012001788.8543819998

90.51260.751902.7628021511

9113232020.9158814755

91.51386.752143.3650747714

9214522270.1612277545

92.51518.752401.3545981904

9315872536.9948758324

93.51656.752677.1312012582

9417282821.8121836862

94.51800.752971.0859178506

9518753125

95.51950.753283.601543085

9620283446.9371911887

96.52106.753615.0531332541

9721873787.9951161531

97.52268.753965.8084571434

9823524148.5380557493

98.52436.754336.2284051062

9925234528.9236028001

99.52610.754726.6673612335

10027004929.5030175465

100.52790.755137.4735431192

10128835350.6215526797

101.52976.755568.9893130397

10230725792.6187514802

102.53168.756021.5514638048

10332676255.8287220799

103.53366.756495.4914820782

10434686740.5803904412

104.53570.756991.1357915756

10536757247.197734297

105.53780.757508.8059782332

10638887776

106.53996.758048.8189991607

10741078327.3019039783

107.54218.758611.4873769721

10843328901.4138202872

108.54446.759197.119380885

10945639498.641955564

109.54680.759806.0191958179

110480010119.2885125388

Max Dose

Maximum Dose

Penalty

Quadratic Overdose

DVH Overdose

X0DoseInterval

0700.5

50400

50.5380.25

51361

51.5342.25

52324

52.5306.25

53289

53.5272.25

54256

54.5240.25

55225

55.5210.25

56196

56.5182.25

57169

57.5156.25

58144

58.5132.25

59121

59.5110.25

60100

60.590.25

6181

61.572.25

6264

62.556.25

6349

63.542.25

6436

64.530.25

6525

65.520.25

6616

66.512.25

679

67.56.25

684

68.52.25

691

69.50.25

700

70.50

710

71.50

720

72.50

730

73.50

740

74.50

750

75.50

760

76.50

770

77.50

780

78.50

790

79.50

800

80.50

810

81.50

820

82.50

830

83.50

840

84.50

850

85.50

860

86.50

870

87.50

880

88.50

890

89.50

900

90.50

910

91.50

920

92.50

930

93.50

940

94.50

950

95.50

960

96.50

970

97.50

980

98.50

990

99.50

1000

100.50

1010

101.50

1020

102.50

1030

103.50

1040

104.50

1050

105.50

1060

106.50

1070

107.50

1080

108.50

1090

109.50

1100

DVH Overdose

Minimum Dose

Penalty

Quadratic Underdose

DVH Underdose

XIntervalDoseWeight

0.570300

5000

50.500

5100

51.500

5200

52.500

5300

53.500

5400

54.500

5500

55.500

5600

56.500

5700

57.500

5800

58.500

5900

59.500

6000

60.500

6100

61.500

6200

62.500

6300

63.500

6400

64.500

6500

65.500

6600

66.500

6700

67.500

6800

68.500

6900

69.500

7000

7000.75

7003

7006.75

70012

70018.75

70027

70036.75

70048

70060.75

70075

70090.75

700108

700126.75

700147

700168.75

700192

700216.75

700243

700270.75

700300

700330.75

700363

700396.75

700432

700468.75

700507

700546.75

700588

700630.75

700675

700720.75

700768

700816.75

700867

700918.75

700972

7001026.75

7001083

7001140.75

7001200

7001260.75

7001323

7001386.75

7001452

7001518.75

7001587

7001656.75

7001728

7001800.75

7001875

7001950.75

7002028

7002106.75

7002187

7002268.75

7002352

7002436.75

7002523

7002610.75

7002700

7002790.75

7002883

7002976.75

7003072

7003168.75

7003267

7003366.75

7003468

7003570.75

7003675

7003780.75

7003888

7003996.75

7004107

7004218.75

7004332

7004446.75

7004563

7004680.75

7004800

DVH Underdose

Maximum Dose

Penalty

Maximum Dose

Como la Función de Costo Serial controla la curva de DVH

Función de Costo- Serial



Visualización de los Voxel de la Variación de la Función de Costo Serial

Dose

Volu

me


Ejemplo sobre Estudio Planificación sobre la médula espinal

EUD 32 Gy EUD 36 Gy EUD 40 Gy

PTV 70 Gy

(k = 12 for this example) Estrategias Dosimétricas

Función de Costo - Serial OAR Serial

Valores comunes de k Recto 12 Vejiga 8 Médula espinal 12 Tronco cerebral 12 Nervio Óptico 16 Corazón 6

k = 0.15 x Dref **Función de Costo Biológica**


Función de Costo - Paralelo


0 20 40 60

Reference Dose

Incr

easi

ng C

ompl

icat

ion

Prob

abili

ty

k=2

k=3

k=4

Inflectionpoint

**Función de Costo Biológica** Estrategias Dosimétricas

Chart2

00020.4

0.60.60.6

1.21.21.2

1.81.81.8

2.42.42.4

333

3.63.63.6

4.24.24.2

4.84.84.8

5.45.45.4

666

6.66.66.6

7.27.27.2

7.87.87.8

8.48.48.4

999

9.69.69.6

10.210.210.2

10.810.810.8

11.411.411.4

121212

12.612.612.6

13.213.213.2

13.813.813.8

14.414.414.4

151515

15.615.615.6

16.216.216.2

16.816.816.8

17.417.417.4

181818

18.618.618.6

19.219.219.2

19.819.819.8

20.420.420.4

212121

21.621.621.6

22.222.222.2

22.822.822.8

23.423.423.4

242424

24.624.624.6

25.225.225.2

25.825.825.8

26.426.426.4

272727

27.627.627.6

28.228.228.2

28.828.828.8

29.429.429.4

303030

30.630.630.6

31.231.231.2

31.831.831.8

32.432.432.4

333333

33.633.633.6

34.234.234.2

34.834.834.8

35.435.435.4

363636

36.636.636.6

37.237.237.2

37.837.837.8

38.438.438.4

393939

39.639.639.6

40.240.240.2

40.840.840.8

41.441.441.4

424242

42.642.642.6

43.243.243.2

43.843.843.8

44.444.444.4

454545

45.645.645.6

46.246.246.2

46.846.846.8

47.447.447.4

484848

48.648.648.6

49.249.249.2

49.849.849.8

50.450.450.4

515151

51.651.651.6

52.252.252.2

52.852.852.8

53.453.453.4

545454

54.654.654.6

55.255.255.2

55.855.855.8

56.456.456.4

575757

57.657.657.6

58.258.258.2

58.858.858.8

59.459.459.4

606060

60.660.660.6

61.261.261.2

61.861.861.8

62.462.462.4

636363

63.663.663.6

64.264.264.2

64.864.864.8

65.465.465.4

666666

66.666.666.6

67.267.267.2

67.867.867.8

68.468.468.4

696969

69.669.669.6

70.270.270.2

70.870.870.8

71.471.471.4

727272

k=2

k=3

k=4

Inflection point

Reference Dose

Increasing Complication Probability


0

0

0

1.0296952079

0.0017983815

0.0000539985

0.00000162

0.007174173

0.0004319067

0.0000259197

0.0160698343

0.0014569379

0.0001312114

0.0283911672

0.0034500383

0.000414634

0.04400978

0.0067272954

0.0010119877

0.0627663696

0.01159637

0.0020973183

0.0844746672

0.0183520417

0.0038820701

0.1089258699

0.0272710056

0.0066135777

0.1358933731

0.0386061158

0.0105726327

0.1651376147

0.0525803311

0.0160698343

0.1964108576

0.069380667

0.023440435

0.2294617564

0.0891525009

0.0330374182

0.2640395799

0.1119945928

0.0452226213

0.2998979939

0.1379551769

0.0603558301

0.3367983368

0.1670294421

0.0787819478

0.3745123537

0.1991586469

0.1008165577

0.412824379

0.2342310209

0.1267304503

0.4515329823

0.2720844882

0.1567339449

0.4904521096

0.3125111269

0.1909620627

0.5294117647

0.3552631579

0.2294617564

0.5682582862

0.4000601577

0.2721824282

0.606854277

0.4465971156

0.3189708444

0.6450782467

0.4945529161

0.3695712562

0.6828240253

0.5435988256

0.4236311065

0.72

0.5934065934

0.4807121662

0.7565282268

0.6436558358

0.5403064025

0.7923434575

0.6940404495

0.6018554036

0.8273921201

0.7442738889

0.6647718533

0.8616312824

0.7940932274

0.7284614159

0.8950276243

0.8432620012

0.7923434575

0.9275564373

0.8915719007

0.8558692827

0.9592006661

0.9388434242

0.9185369345

0.9899500025

0.9849256382

0.979902035

1.0198000392

1.0296952079

1.0395845596

1.0487514863

1.0730548636

1.0972717861

1.0768094535

1.1149314603

1.1527179182

1.1039827965

1.1552737737

1.2057410341

1.1302835276

1.1940501559

1.2562180616

1.1557262865

1.2312461538

1.3040784645

1.1803278689

1.2668621701

1.349297241

1.2041068089

1.3009112273

1.3918877356

1.2270830113

1.3334168784

1.4318946436

1.2492774295

1.3644112907

1.4693874793

1.2707117853

1.3939335169

1.504454675

1.291408326

1.4220279594

1.5371984016

1.3113896158

1.4487430238

1.5677301347

1.3306783575

1.4741299546

1.5961669467

1.349297241

1.4982418394

1.6226284766

1.3672688158

1.52113277

1.6472345097

1.3846153846

1.5428571429

1.6701030928

1.4013589153

1.563469085

1.6913491086

1.4175209692

1.5830219898

1.7110832354

1.4331226439

1.6015681481

1.7294112252

1.4481845271

1.6191584621

1.7464334393

1.4627266622

1.6358422286

1.7622445894

1.4767685224

1.6516669825

1.7769336391

1.4903289926

1.6666783885

1.7905838282

1.5034263581

1.6809201752

1.8032727885

1.5160782985

1.6944341019

1.8150727269

1.5283018868

1.7072599532

1.826050654

1.5401135919

1.7194355548

1.8362686437

1.5515292851

1.7309968075

1.8457841095

1.5625642484

1.7419777329

1.8546500897

1.5732331854

1.7524105311

1.8629155326

1.5835502343

1.7623256436

1.8706255779

1.5935289814

1.771751823

1.8778218283

1.6031824765

1.780716205

1.884542611

1.6125232486

1.7892443821

1.8908232257

1.6215633219

1.7973604784

1.8966961786

1.6303142329

1.8050872235

1.9021914016

1.6387870469

1.8124460255

1.9073364581

1.646992375

1.8194570423

1.9121567324

1.654940391

1.8261392508

1.9166756074

1.6626408474

1.8325105133

1.9209146273

1.6701030928

1.8385876419

1.9248936482

1.6773360867

1.8443864594

1.9286309773

1.6843484162

1.8499218581

1.9321434995

1.6911483106

1.8552078549

1.9354467953

1.6977436564

1.8602576444

1.9385552476

1.7041420118

1.8650836481

1.9414821403

1.7103506206

1.8696975622

1.9442397486

1.7163764252

1.8741104011

1.9468394209

1.7222260802

1.8783325402

1.9492916551

1.7279059643

1.8823737541

1.9516061673

1.7334221926

1.8862432546

1.9537919549

1.738780628

1.8899497246

1.9558573549

1.7439868921

1.8935013513

1.9578100963

1.7490463762

1.8969058561

1.959657349

1.753964251

1.9001705237

1.961405768

1.7587454765

1.9033022289

1.9630615339

1.7633948112

1.9063074613

1.9646303901

1.7679168214

1.9091923495

1.9661176769

1.7723158889

1.9119626824

1.9675283626

1.77659622

1.9146239304

1.9688670723

1.7807618526

1.9171812643

1.970138114

1.7848166638

1.9196395738

1.9713455026

1.7887643772

1.922003484

1.9724929821

1.7926085694

1.9242773714

1.9735840457

1.7963526764

1.9264653786

1.9746219549

1.8

1.9285714286

1.9756097561

1.8035537133

1.9305992371

1.9765502965

1.8070168667

1.9325523252

1.9774462387

1.8103923929

1.9344340308

1.9783000742

1.8136831122

1.9362475188

1.9791141351

1.8168917372

1.9379957915

1.9798906062

1.8200208776

1.9396816979

1.9806315347

1.8230730443

1.9413079425

1.9813388406

1.826050654

1.9428770934

1.9820143247

1.8289560331

1.9443915902

1.9826596778

1.8317914214

1.945853751

1.9832764873

1.8345589756

1.9472657794

1.9838662451

1.8372607733

1.9486297711

1.9844303535

1.8398988161

1.9499477191

1.9849701314

1.8424750323

1.9512215204

1.9854868199

1.8449912808

1.9524529805

1.9859815874

1.8474493532

1.9536438184

1.9864555345

1.8498509771

1.9547956718

1.9869096981

1.8521978184

1.955910101

1.9873450559

1.8544914841

1.9569885934

1.9877625301

1.8567335244

1.9580325667

1.9881629909

xx

6565

65.365.3

65.665.6

65.965.9

66.266.2

66.566.5

66.866.8

67.167.1

67.467.4

67.767.7

6868

68.368.3

68.668.6

68.968.9

69.269.2

69.569.5

69.869.8

70.170.1

70.470.4

70.770.7

7171

71.371.3

71.671.6

71.971.9

72.272.2

72.572.5

72.872.8

73.173.1

73.473.4

73.773.7

7474

74.374.3

74.674.6

74.974.9

75.275.2

75.575.5

75.875.8

76.176.1

76.476.4

76.776.7

7777

77.377.3

77.677.6

77.977.9

78.278.2

78.578.5

78.878.8

79.179.1

79.479.4

79.779.7

8080

80.380.3

80.680.6

80.980.9

81.281.2

81.581.5

81.881.8

82.182.1

82.482.4

82.782.7

8383

83.383.3

83.683.6

83.983.9

84.284.2

84.584.5

84.884.8

85.185.1

85.485.4

85.785.7

8686

86.386.3

86.686.6

86.986.9

87.287.2

87.587.5

87.887.8

88.188.1

88.488.4

88.788.7

8989

89.389.3

89.689.6

89.989.9

90.290.2

90.590.5

90.890.8

91.191.1

91.491.4

91.791.7

9292

92.392.3

92.692.6

92.992.9

93.293.2

93.593.5

93.893.8

94.194.1

94.494.4

94.794.7

9595

95.395.3

95.695.6

95.995.9

96.296.2

96.596.5

96.896.8

97.197.1

97.497.4

97.797.7

9898

98.398.3

98.698.6

98.998.9

99.299.2

99.599.5

99.899.8

100.1100.1

100.4100.4

100.7100.7

101101

0.1

0.25

150.3439192978

0.0087642482

145.9005849787

0.0081309742

141.5885710347

0.0075434583

137.4039963621

0.0069983943

133.3430945613

0.0064927148

129.4022105466

0.0060235738

125.5777972562

0.0055883314

121.8664124602

0.005184538

118.2647156616

0.0048099214

114.7694650901

0.0044623733

111.3775147845

0.0041399377

108.0858117603

0.0038408003

104.8913932628

0.0035632774

101.7913840995

0.0033058074

98.7829940531

0.0030669413

95.8635153694

0.0028453348

93.0303203205

0.0026397408

90.2808588396

0.0024490024

87.6126562258

0.002272046

85.0233109167

0.0021078759

82.5104923266

0.0019555681

80.0719387492

0.0018142656

77.7054553218

0.0016831731

75.4089120494

0.0015615529

73.180241888

0.0014487205

71.0174388843

0.001344041

68.9185563693

0.0012469253

66.8817052072

0.0011568268

64.9050520944

0.0010732385

62.9868179098

0.0009956901

61.125276113

0.000923745

59.3187511907

0.0008569984

57.5656171487

0.0007950747

55.8642960479

0.0007376253

54.2132565846

0.0006843271

52.6110127116

0.00063488

51.0561223014

0.0005890058

49.5471858477

0.0005464463

48.0828452058

0.000506962

46.6617823703

0.0004703307

45.2827182887

0.0004363462

43.9444117102

0.0004048174

42.6456580686

0.0003755667

41.3852883979

0.0003484295

40.1621682803

0.0003232532

38.9751968253

0.0002998961

37.8233056783

0.0002782266

36.7054580595

0.000258123

35.6206478307

0.0002394719

34.5678985894

0.0002221685

33.5462627903

0.0002061154

32.554820892

0.0001912222

31.5926805302

0.0001774051

30.6589757133

0.0001645865

29.7528660442

0.000152694

28.8735359628

0.0001416609

28.0201940129

0.000131425

27.192072129

0.0001219286

26.3884249455

0.0001131185

25.6085291257

0.000104945

24.8516827108

0.000097362

24.1172044879

0.000090327

23.4044333769

0.0000838003

22.7127278359

0.0000777451

22.041465283

0.0000721275

21.3900415368

0.0000669159

20.7578702718

0.0000620808

20.1443824912

0.000057595

19.5490260147

0.0000534334

18.9712649812

0.0000495725

18.4105793668

0.0000459906

17.8664645165

0.0000426674

17.3384306904

0.0000395844

16.8260026222

0.0000367242

16.3287190922

0.0000340706

15.8461325116

0.0000316088

15.3778085199

0.0000293249

14.9233255939

0.000027206

14.4822746683

0.0000252402

14.0542587674

0.0000234164

13.6388926482

0.0000217244

13.235802453

0.0000201547

12.8446253734

0.0000186984

12.4650093238

0.0000173473

12.0966126239

0.0000160938

11.7391036919

0.0000149309

11.3921607457

0.0000138521

11.0554715131

0.0000128512

10.7287329512

0.0000119226

10.4116509731

0.0000110611

10.1039401837

0.0000102619

9.8053236225

0.0000095204

9.5155325145

0.0000088325

9.234306028

0.0000081943

8.9613910403

0.0000076022

8.6965419094

0.0000070529

8.4395202533

0.0000065433

8.1900947351

0.0000060705

7.9480408551

0.0000056318

7.7131407483

0.0000052249

7.4851829888

0.0000048474

7.2639623992

0.0000044971

7.0492798662

0.0000041722

6.8409421609

0.0000038707

6.6387617653

0.000003591

6.4425567034

0.0000033315

6.2521503775

0.0000030908

6.0673714089

0.0000028675

5.8880534841

0.0000026603

5.714035205

0.0000024681

5.5451599432

0.0000022897

5.3812756997

0.0000021243

5.2222349676

0.0000019708

5.0678945994

0.0000018284

4.9181156785

0.0000016963

4.7727633937

0.0000015737

4.6317069181

0.00000146

4.4948192914

0.0000013545

4.3619773054

0.0000012566

4.2330613935

0.0000011658

4.1079555225

0.0000010816

Poisson

XRhoAlphaXRhoAlphaXRhoAlpha

100.175100.2575100.1375

652.7182818285150.34391929786512.18249396070.0087642482653.669296667621.3900415368

65.32.6379444594145.900584978765.311.30222941930.008130974265.33.528948672220.5718876167

65.62.5599814183141.588571034765.610.48556972470.007543458365.63.39396888819.7850275038

65.92.4843225334137.403996362165.99.72791901260.006998394365.93.264151984819.0282642323

66.22.4108997064133.343094561366.29.02501349940.006492714866.23.139300486218.3004466192

66.52.3396468519129.402210546666.58.37289748810.006023573866.53.019224468817.6004675137

66.82.2704998375125.577797256266.87.76790110630.005588331466.82.903741273916.9272621126

67.12.2033964263121.866412460267.17.20661965380.00518453867.12.792675229416.2798063407

67.42.1382762205118.264715661667.46.68589444230.004809921467.42.685857382315.6571152929

67.72.0750806077114.769465090167.76.20279501910.004462373367.72.583125242115.0582417362

682.0137527075111.3775147845685.7546026760.0041399377682.484322533414.4822746683

68.31.9542373206108.085811760368.35.33879514910.003840800368.32.389298958213.9283379323

68.61.8964808793104.891393262868.64.95303242440.003563277468.62.297909967413.3955888836

68.91.8404313988101.791384099568.94.59514356930.003305807468.92.210016540712.8832171082

69.21.786038430898.782994053169.24.26311451520.003066941369.22.125484975312.3904431899

69.51.733253017995.863515369469.53.95507672290.002845334869.52.044186682311.9165175245

69.81.682027649793.030320320569.83.66929666760.002639740869.81.965997991311.4607191798

70.11.6323162290.280858839670.13.40416608280.002449002470.11.890799962311.0223547985

70.41.58407398587.612656225870.43.15819290970.00227204670.41.818478204610.6007575439

70.71.537257523585.023310916770.72.92999290050.002107875970.71.748922702810.1952860853

711.491824697682.5104923266712.71828182850.0019555681711.68202764979.8053236225

71.31.447734614780.071938749271.32.52186826040.001814265671.31.61769128499.4302769474

71.61.404947590677.705455321871.62.33964685190.001683173171.61.55581574049.0695755416

71.91.363425114175.408912049471.92.17059212720.001561552971.91.49630689178.7226707088

72.21.323129812373.18024188872.22.01375270750.001448720572.21.43907421428.3890347398

72.51.284025416771.017438884372.51.86824595740.00134404172.51.3840306468.0681601101

72.81.246076730668.918556369372.81.73325301790.001246925372.81.33109245537.7595587074

73.11.209249597766.881705207273.11.60801419750.001156826873.11.28017911287.4627610895

73.41.17351087164.905052094473.41.49182469760.001073238573.41.23121316957.17731577

73.71.138828383362.986817909873.71.3840306460.000995690173.71.18412013896.9027885316

741.105170918161.125276113741.28402541670.000923745741.13882838336.6387617653

74.31.072508181359.318751190774.31.19124621660.000856998474.31.09526900536.3848338356

74.61.040810774257.565617148774.61.10517091810.000795074774.61.05337574256.1406184692

74.91.010050167155.864296047974.91.02531512050.000737625374.91.01308486745.9057441674

75.20.980198673354.213256584675.20.95122942450.000684327175.20.97433508965.679853641

75.50.951229424552.611012711675.50.88249690260.0006348875.50.93706746345.4626032671

75.80.923116346451.056122301475.80.81873075310.000589005875.80.90122529745.2536625659

76.10.895834135349.547185847776.10.75957212320.000546446376.10.86675406895.0527136984

76.40.869358235448.082845205876.40.70468808970.00050696276.40.83360134044.8594509825

76.70.843664816646.661782370376.70.65376978510.000470330776.70.80171668034.6735804285

770.818730753145.2827182887770.60653065970.0004363462770.77105158584.4948192914

77.30.794533602543.944411710277.30.56270486880.000404817477.30.74155940944.3228956409

77.60.771051585842.645658068677.60.52204577680.000375566777.60.71319528794.1575479482

77.90.748263567641.385288397977.90.4843245690.000348429577.90.68591607393.9985246875

78.20.726149037140.162168280378.20.44932896410.000323253278.20.65968027053.8455839538

78.50.704688089738.975196825378.50.41686201970.000299896178.50.63444796793.6984930946

78.80.683861409237.823305678378.80.38674102350.000278226678.80.61018078313.5570283565

79.10.663650250136.705458059579.10.35879646540.00025812379.10.58684180083.4209745443

79.40.644036421135.620647830779.40.33287108370.000239471979.40.56439551813.290124694

79.70.625002268334.567898589479.70.30881897970.000222168579.70.54280778983.1642797576

800.606530659733.5462627903800.28650479690.0002061154800.52204577683.0432483008

80.30.588604969732.55482089280.30.26580295910.000191222280.30.5020778962.9268462114

80.60.571209063831.592680530280.60.24659696390.000177405180.60.48287377252.8148964194

80.90.554327284730.658975713380.90.2287787270.000164586580.90.46440419322.7072286275

81.20.537944437629.752866044281.20.21224797380.00015269481.20.44664106212.6036790524

81.50.522045776828.873535962881.50.19691167520.000141660981.50.42955735822.504090175

81.80.506616992428.020194012981.80.18268352410.00013142581.80.41312709392.4083105016

82.10.491644197527.19207212982.10.16948344950.000121928682.10.39732527552.3161943327

82.40.477113915526.388424945582.40.15723716630.000113118582.40.38212786552.227601542

82.70.463013068325.608529125782.70.14587575690.00010494582.70.36751174562.1423973627

830.449328964124.8516827108830.13533528320.000097362830.3534546822.0604521829

83.30.436049286324.117204487983.30.12555642750.00009032783.30.3399352911.9816413481

83.60.423162082323.404433376983.60.11648415780.000083800383.60.32693300721.9058449718

83.90.410655752822.712727835983.90.10806741860.000077745183.90.31442805151.8329477531

84.20.398519041122.04146528384.20.10025884370.000072127584.20.30240140151.7628388014

84.50.386741023521.390041536884.50.09301448920.000066915984.50.29083476241.6954114673

84.80.375311098920.757870271884.80.08629358650.000062080884.80.2797105391.630563181

85.10.364218979620.144382491285.10.08005831280.00005759585.10.26901180921.5681952957

85.40.35345468219.549026014785.40.07427357820.000053433485.40.25872229831.5082129377

85.70.343008517418.971264981285.70.06890682840.000049572585.70.24882635381.4505248624

860.332871083718.4105793668860.06392786120.0000459906860.23930892221.395043315

86.30.323033256417.866464516586.30.05930865680.000042667486.30.23015552571.3416838975

86.60.313486180917.338430690486.60.05502322010.000039584486.60.221352241.2903654399

86.90.304221264116.826002622286.90.0510474340.000036724286.90.21288567381.2410098768

87.20.295230166916.328719092287.20.04735892440.000034070687.20.20474294781.1935421291

87.50.286504796915.846132511687.50.04393693360.000031608887.50.19691167521.1478899891

87.80.278037300515.377808519987.80.0407622040.000029324987.80.18937994331.103984011

88.10.269820056414.923325593988.10.03781686920.00002720688.10.18213629471.0617574055

88.40.261845668614.482274668388.40.03508435410.000025240288.40.17516971061.0211459377

88.70.254106959614.054258767488.70.0325492810.000023416488.70.16846959340.9820878297

890.246596963913.6388926482890.03019738340.0000217244890.16202575090.9445236666

89.30.239308922213.23580245389.30.02801542580.000020154789.30.15582838090.9083963062

89.60.232236274712.844625373489.60.02599112880.000018698489.60.14986805580.8736507917

89.90.225372655512.465009323889.90.02411310040.000017347389.90.14413570890.8402342684

90.20.21871188712.096612623990.20.02237077190.000016093890.20.13862262030.8080959035

90.50.212247973811.739103691990.50.02075433790.000014930990.50.13332040340.7771868083

90.80.205975098211.392160745790.80.01925470180.000013852190.80.12822099250.747459964

91.10.199887614111.055471513191.10.01786342420.000012851291.10.12331663040.7188701504

91.40.193980042310.728732951291.40.01657267540.000011922691.40.11859985680.691373877

91.70.188247065610.411650973191.70.01537519170.000011061191.70.11406349640.6649293164

920.182683524110.1039401837920.01426423390.0000102619920.10970064850.6394962416

92.30.177284419.805323622592.30.01323355010.000009520492.30.10550467650.6150359639

92.60.17204486389.515532514592.60.01227733990.000008832592.60.10146919740.5915112744

92.90.16696016979.23430602892.90.01139022210.000008194392.90.09758807260.5688863876

93.20.16202575098.961391040393.20.01056720440.000007602293.20.0938553980.5471268867

93.50.15723716638.696541909493.50.0098036550.000007052993.50.09026549560.5261996713

93.80.15259010588.439520253393.80.00909527710.000006543393.80.08681290440.506072907

94.10.14808038668.190094735194.10.00843808410.000006070594.10.08349237240.4867159772

94.40.14370394987.948040855194.40.00782837750.000005631894.40.08029884830.4680994362

94.70.13945685627.713140748394.70.00726272630.000005224994.70.07722747430.4501949648

950.13533528327.4851829888950.0067379470.0000048474950.07427357820.4329753266

95.30.13133552117.263962399295.30.00625108640.000004497195.30.07143266650.4164143274

95.60.12745396997.049279866295.60.00579940470.000004172295.60.06870041770.4004867747

95.90.12368713586.840942160995.90.005380360.000003870795.90.06607267540.3851684396

96.20.12003162856.638761765396.20.00499159390.00000359196.20.06354544240.3704360199

Estrategias de planificación dosimétrica en VMAT · • Las soluciones de clase nos benefician...

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