Estrategias de planificación dosimétrica en VMAT · • Las soluciones de clase nos benefician...
Transcript of Estrategias de planificación dosimétrica en VMAT · • Las soluciones de clase nos benefician...
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Estrategias de planificación dosimétrica en VMAT
TM. Felipe Lucic M.Sc.
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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)
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• 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
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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
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• 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
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Estrategias de planificación en Vmat
Dependiendo la zona a tratar y los órganos de riesgo involucrados podemos tener: Estrategias de tipo:
• Geométricas
• Dosimétricas
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¿Arco completo o arcos parciales?
En una primera aproximación hay que considerar las
relación de los tamaños del PTV y OARs.
Estrategias Geométricas
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V20 < 35% V10 < 45% V5 < 65% Dmed < 20 Gy
Estrategias Geométricas
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¿Arco completo o arcos parciales?
Estrategias Geométricas
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Angulo de colimador
En general es recomendable la angulación de 15° a 20° para disminuir la fuga interláminas (Efecto Tongue & Groove)
Estrategias Geométricas
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Selección de número de sectores de optimización
Este parámetro se relaciona con el tamaño del ángulo del incremento de optimización del haz
Estrategias Geométricas
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•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?
Estrategias Geométricas
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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?...
Estrategias Geométricas
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¿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.
Estrategias Geométricas
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•Trabajar con dos arcos independientes para optimizar el PTV y proteger los OARs
Dividir el Target Volume y optimizar con arcos distintos
Estrategias Geométricas
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Estrategias Dosimétricas
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¿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.
Estrategias Dosimétricas
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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.
Estrategias Dosimétricas
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¿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.
Estrategias Dosimétricas
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Pestaña de prescripción y definición geométrica
Estrategias Dosimétricas
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Tabla de restricciones
Estrategias Dosimétricas
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Priorización de los volúmenes
Estrategias Dosimétricas
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Propiedades de las estructuras a optimizar
Estrategias Dosimétricas
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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.
Estrategias Dosimétricas
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“Opción Clear All Voxels”
Estrategias Dosimétricas
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“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
Estrategias Dosimétricas
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Propiedades de las estructuras a optimizar Auto Flash margen
Estrategias Dosimétricas
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Sin Auto Flash sobre Target 1.0 cm Auto Flash sobre Target
Propiedades de las estructuras a optimizar Auto flash margen
Estrategias Dosimétricas
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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
Estrategias Dosimétricas
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¿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.
Estrategias Dosimétricas
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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.
Estrategias Dosimétricas
Estrategias Dosimétricas
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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.
Estrategias Dosimétricas
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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
Estrategias Dosimétricas
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Eligiendo la Función de Costo para el Target
Estrategias Dosimétricas
•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
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Función de Costo- Serial
**Función de Costo Biológica**
Serial Cost Function
0 10 20 30 40 50 60
Increasing Dose
Wei
ght (
Pena
lty)
k= 8
k= 12
k=16
Estrategias Dosimétricas
Chart4
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k= 8
k= 12
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Increasing Dose
Weight (Penalty)
Serial Cost Function
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
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0.1068900077
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0.123410307
0.0614424574
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0.2855807421
0.1526136491
0.0815563603
0.2992179271
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0.0895313679
0.3134215541
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0.201417238
0.118067087
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0.2469904036
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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
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)
Serial Cost Function
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
**Función de Costo Biológica**
Estrategias Dosimétricas
-
Visualización de los Voxel de la Variación de la Función de Costo Serial
Dose
Volu
me
Estrategias Dosimétricas
-
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**
Estrategias Dosimétricas
-
Función de Costo - Paralelo
Parallel Cost FunctionDref =20
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
Parallel Cost FunctionDref =20
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
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49.5471858477
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13.6388926482
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11.7391036919
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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