The Ottawa L’HopitalHospital d’OttawaRegional Cancer Centre

John DeMarco1 and Joanna E. Cygler2,3,4

1UCLA Radiation Oncology, David Geffen School of Medicine2The Ottawa Hospital Cancer Centre, Ottawa, Canada3Carleton University Dept. of Physics, Ottawa, Canada

4University of Ottawa, Dept. of Radiology. Ottawa, Canada

Clinical implementation and application of Monte Carlo methods

in photon and electron dose calculation

Part I: Photon beamsPart I: Photon beams

John DeMarco, Ph.D.

UCLA Department of Radiation OncologyDavid Geffen School of Medicine

Los Angeles, CA

OutlineOutline1. Educational review of the physics of the MC method.

2. Factors associated with vendor implementation of the MC dose calculation, such as statistical uncertainties, spatial resolution, variance reduction, CT-number to material density assignments, and reporting of dose-to-medium versus dose-to-water.

3. Review the vendor transport codes currently used for clinical treatment planning.

4. Experimental verification of Photon based MC algorithms.

5. Potential clinical implications of Photon based MC calculated dose distributions.

General Purpose Monte Carlo CodesGeneral Purpose Monte Carlo Codes

Monte Carlo Codes Optimized for Monte Carlo Codes Optimized for Treatment PlanningTreatment Planning

Peregrine (Hartmann-Siantar et. al. 2002) MCDose (Ma et. al. 2002)

DPM (Sempau et. al. 2000) VMC/XVMC (Kawrakov and Fippel)

CMS MonacoCMS Monaco BrainlabBrainlab iPlaniPlanI. Kawrakow, M. Fippel, and K. Friedrich, ‘‘3D electron dose calculation using a Voxel based Monte Carlo algorithm (VMC),’’ Med. Phys. 23, 445–457 (1996).

M. Fippel, “Fast Monte Carlo dose calculation for photon beams based on the VMC electron algorithm”, Med. Phys., 26, 1466-1475 (1999).

C-M Ma, J S Li, T Pawlicki, S B Jiang, J Deng, M C Lee,T Koumrian, M Luxton and S Brain, “A Monte Carlo dose calculation tool for radiotherapy treatment planning”Phys. Med. Biol. 47 (2002) 1671–1689.

Ma C-M, Li JS, Deng J, Fan J. “Implementation of Monte Carlo dose calculationfor CyberKnife treatment planning. J Phys Conf Ser 2008;102

Commercial implementations

AccurayAccuray MultiplanMultiplan

Spatial resolution

Statistical uncertainty

Material Conversion

MLC ModelingiPlan/Brainlab

Chetty et. al. “Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning”, Med. Phys. 34, 4818-4853 (2007).

Linear Accelerator Source Modeling

Phase-space

Virtual source

Virtual Energy Fluence Model

Complete Simulation (target to patient)

M. Fippel, F. Haryanto, O. Dohm, F. Nusslin, and S. Kriesen, “A virtual photon energy fluence model for Monte Carlo dose calculation”, Med. Phys. 30, 301-311, (2003).

Virtual Energy Fluence Model

• Primary photon source and multiple scatter photon sources defined as two-dimensional Gaussian shapes

• Electron contamination source

• Photon energy spectrum derived based upon measured depth dose curves in water

Photon TransportPhoton TransportCollide or Cross?Collide or Cross?

Region 1Region 1 Region 2Region 2

( )μξln−

=x

LLL

• Energy (E)

• Direction

• Position ( )ooo zyxx ,,=v

( ) ( )zyxwvuu θθθ cos,cos,cos,, ==v

Sampling for the photon Sampling for the photon collision typecollision type

0.000

0.107

0.788

1.000

Coherent

IncoherentIncoherent

PhotoElectricRandom Number = 0.532Random Number = 0.532

θθφθθφθθ

coscossinsincoscossincos

======

z

y

x

zyu

φ

θ

(0,0,1)

(u,v,w)

Update Photon Update Photon DirectionDirection

Particle start

Particle end

CT VoxelArray

The transport process is The transport process is repeated across each voxel of a repeated across each voxel of a 3D rectilinear array (based upon 3D rectilinear array (based upon the simulation CT scan).the simulation CT scan).

Appropriate routines for scoring Appropriate routines for scoring the energy deposition from the energy deposition from secondary electrons.secondary electrons.

Appropriate routines to convert Appropriate routines to convert from HU to mass density and from HU to mass density and material composition on a voxel by material composition on a voxel by voxel basis.voxel basis.

Reproduced from the MCNP users manualReproduced from the MCNP users manual

Accuracy vs. PrecisionAccuracy vs. Precision

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−≈

=

=

∑∑

=

nx

xs

xss

xn

x

i

ir

xr

N

ii

1

1

2

2

1∑

Simulation Efficiency and Simulation Efficiency and Variance ReductionVariance Reduction

Ts21

=ε

•• ““Variance reductionVariance reduction”” techniques seek to increase the efficiency techniques seek to increase the efficiency of the simulation byof the simulation by

•• rayray--tracing tracing

•• photon splittingphoton splitting

•• electron history repetitionelectron history repetition

•• electron and photon cutelectron and photon cut--off energiesoff energies

I. Kawrakow and M. Fippel, “Investigation of variance reduction techniques for Monte Carlo photon dose calculation using XVMC”. Phys. Med. Biol. 45 (2000) 2163–2183.

Particle start

Particle end

Primary photon collision points

Initial rayInitial ray--tracing can be used to tracing can be used to prepre--calculate the collision number calculate the collision number within a voxel for incoming within a voxel for incoming primary photons.primary photons.

Spatial resolution

Statistical uncertainty

Material Conversion

MLC ModelingiPlan/Brainlab

Monte Carlo calculation time as a function Monte Carlo calculation time as a function of the of the axial plane voxel sizeaxial plane voxel size((iPlan/BrainlabiPlan/Brainlab Monte Carlo implementationMonte Carlo implementation))

7-Field IMRT planRPC Lung & Spine phantom

Mean variance = 2%Dose-to-medium

Monte Carlo calculation time as a function Monte Carlo calculation time as a function of the variance setting of the variance setting

((iPlan/BrainlabiPlan/Brainlab Monte Carlo implementationMonte Carlo implementation))

7-Field IMRT planRPC Lung & Spine phantomVoxel resolution = 3 mm

Dose-to-medium

Variance Setting and the Qualitative Assessment Variance Setting and the Qualitative Assessment of the Absorbed Dose Distributionof the Absorbed Dose Distribution

5%5% 2%2% 1%1%

7-Field IMRT planRPC Lung & Spine phantomVoxel resolution = 3 mm

Dose-to-medium

Mean Variance = 5%

Mean Variance = 1%

7-Field IMRT planRPC Lung & Spine phantomVoxel resolution = 3 mm

Dose-to-medium

Mean Variance = 5%

Mean Variance = 1%

7-Field IMRT planRPC Lung & Spine phantomVoxel resolution = 3 mm

Dose-to-medium

J. V. Siebers, P. J. Keall, A. E. Nahum, and R. Mohan, “Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations,” Phys. Med. Biol. 45, 983–995 2000.

DoseDoseww vs. vs. DoseDosemedmed

77--Field IMRT planField IMRT planRPC Lung & Spine phantomRPC Lung & Spine phantom

Clinical Planning Comparison medium vs. water

(γ-setting 3%/3mm)

Dw

Dmed

Dosimetric ValidationDosimetric ValidationChetty et. al. “Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning”, Med. Phys. 34, 4818-4853 (2007).

“Experimental verification of a MC algorithm should include testing to assess the accuracy of: (a) the beam model be it measurement-driven or based on treatment head simulation and (b) the radiation transport algorithm in homogeneous and heterogeneous phantoms. The former is part of routine commissioning of dose calculation algorithms, whereas the latter is likely to have significantly more involvement from developers and vendors.”

• Beam Model

• Multileaf collimator and other beam modifying devices

• Output factors and the normalization condition for conversion to absolute dose

B. Fraass, K. Doppke, M. Hunt, G. Kutcher, G. Starkschall, R. Stern, and J. Van Dyke, “American Association of Physicists in Medicine Radiation Therapy Committee Task Group 53: Quality assurance for clinical radiotherapy treatment planning,” Med. Phys. 25, 1773–1829 1998.

IAEA-Technical Report Series No. 430: Commissioning and quality assurance of computerized planning systems for radiation treatment of cancer,” in International Atomic Energy Agency, Vienna, 2004

Grofsmid et al. “Dosimetric validation of a commercial Monte Carlo based IMRT planning system”, Med. Phys. 37, 540-549, (2010).

Dosimetric ValidationDosimetric Validation

CMS Monaco

Grofsmid et al. “Dosimetric validation of a commercial Monte Carlo based IMRT planning system”, Med. Phys. 37, 540-549, (2010).

Dosimetric ValidationDosimetric Validation

CMS Monaco

Grofsmid et al. “Dosimetric validation of a commercial Monte Carlo based IMRT planning system”, Med. Phys. 37, 540-549, (2010).

Dosimetric ValidationDosimetric Validation

CMS Monaco

Sharma et al. “Clinical implications of adopting Monte Carlo treatment planning for Cyberknife”, JACMP, 11, (170-175), 2010.

Accuray Multiplan 2.1.0

Retrospective ComparisonRetrospective Comparison

ClinicalClinical PlanningPlanning ComparisonComparisonPencil beam algorithm versus Monte CarloPencil beam algorithm versus Monte Carlo

2.5x2.5x1.5 mm2.5x2.5x1.5 mm33

Monte Carlo Variance setting = 1%Monte Carlo Variance setting = 1%Dose to MediumDose to Medium

88--Field IMRT planField IMRT plan3 x 18 = 54 Gy3 x 18 = 54 Gy

Pencil beamMonte Carlo

The Monte Carlo re-calculated plan predicts a

lower dose (3%-8%) across the axial slice of the PTV

N. van der Voort et al., “Clinical introduction of Monte Carlo treatment planning: A different prescription dose for non-small cell lung cancer according to tumor location and size”, Radiotherapy and Oncology 96 (2010) 55–60.

Clinical Implications for Monte Carlo Clinical Implications for Monte Carlo based Photon Treatment Planningbased Photon Treatment Planning

• Comparison of conventional treatment planning algorithms vs. Monte Carlo

• Modification of prescription dose based upon Monte Carlo recalculation

A. Fogliata, E. Vanetti, D. Albers, C. Brink, A. Clivio, T. Knoos, G. Nicolini, and L. Cozzi, “On the dosimetric behaviour of photon dose calculation algorithms in the presence of simple geometric heterogeneities: comparison with Monte Carlo calculations” Phys. Med. Biol. 52 (2007) 1363–1385.

Clinical Implications for Monte Carlo based Clinical Implications for Monte Carlo based Photon Treatment PlanningPhoton Treatment Planning

Photon energy, field size, and the heterogeneous nature of the treatment area will determine the dosimetric impact of a Monte Carlo treatment planning algorithm.

Part II: Electron beams

Joanna E. Cygler, Ph.D., FCCPM, FAAPM

The Ottawa Hospital Cancer Centre, Ottawa, CanadaCarleton University Dept. of Physics, Ottawa, Canada

University of Ottawa, Dept. of Radiology, Ottawa, Canada

Outline

• Rationale for MC dose calculations for electron beams

• Commercially available Monte Carlo based electron treatment planning systems

• Clinical implementation of MC-based TPS• Issues to pay attention to when using MC based

system • Timing comparisons of major vendor MC codes in

the clinical setting.

Rationale for Monte Carlo dose calculation for electron beams

• Difficulties of commercial pencil beam based algorithms– Monitor unit calculations for arbitrary

SSD values – large errors*– Dose distribution in inhomogeneous media

has large errors for complex geometries

* can be circumvented by entering separate virtual machines for each SSD – labour consuming

-10 -5 0 5 100

5

10

15

6.2 cm

9 MeV

depth = 7 cm

depth = 6.2 cm

98-10-21/tex/E TP /abs/X TS K 09S .OR G

Measured Pencil beam Monte Carlo

Rela

tive

Dose

Horizontal Position /cm

Rationale for Monte Carlo dose calculation for electron beams

Ding, G. X., et al, Int. J. Rad. Onc. Biol Phys. (2005) 63:622-633

Commercial implementations• MDS Nordion (now Nucletron) 2001

- First commercial Monte Carlo treatment planning for electron beams

– Kawrakow’s VMC++ Monte Carlo dose calculation algorithm (2000)– Handles electron beams from all clinical linacs

• Varian Eclipse eMC 2004– Neuenschwander’s MMC dose calculation algorithm (1992)

– Handles electron beams from Varian linacs only (23EX)

– work in progress to include linacs from other vendors

• CMS XiO eMC for electron beams 2010– Based on XVMC (Kawrakow, Fippel, Friedrich, 1996)

– Handles electron beams from all clinical linacs

Nucletron Electron Monte Carlo Dose Calculation Module

•Originally released as part of Theraplan Plus

•Currently sold as part of Oncentra Master Plan

•Fixed applicator with optional, arbitrary inserts, or variable size fields defined by the applicator like DEVA

•Calculates absolute dose per monitor unit (Gy/MU)

•User can change the number of particle histories used in calculation (in terms of particle #/cm2)

•Data base of 22 materials

•Dose-to-water is calculated in Oncentra

•Dose-to-water or dose-to-medium can be calculatedin Theraplan Plus MC DCM

•Nucletron performs beam modeling

510(k) clearance (June 2002)

Varian Macro Monte Carlotransport model in Eclipse

• An implementation of Local-to-Global (LTG) Monte Carlo:– Local: Conventional MC simulations of electron transport performed

in well defined local geometries (“kugels” or spheres).• Monte Carlo with EGSnrc Code System - PDF for “kugels”• 5 sphere sizes (0.5-3.0 mm)• 5 materials (air, lung, water, Lucite and solid bone)• 30 incident energy values (0.2-25 MeV)• PDF table look-up for “kugels”

This step is performed off-line.

– Global: Particle transport through patient modeled as a series of macroscopic steps, each consisting of one local geometry (“kugel”)

C. Zankowski et al “Fast Electron Monte Carlo for Eclipse”

Varian Macro Monte Carlotransport model in Eclipse

• Global geometry calculations– CT images are pre-processed to

user defined calculation grid

– HU in CT image are converted to mass density

– The maximum sphere radius and material at the center of each voxel is determined

• Homogenous areas → large spheres

• In/near heterogeneous areas →small spheres

C. Zankowski et al “Fast Electron Monte Carlo for Eclipse”

Varian Eclipse Monte Carlo

• User can control– Total number of particles per simulation

– Required statistical uncertainty

– Random number generator seed

– Calculation voxel size

– Isodose smoothing on / off• Methods: 2-D Median, 3-D Gaussian

• Levels: Low, Medium, Strong

• Dose-to-medium is calculated

CMS XiO Monte Carlo system• XiO eMC module is based on VMC*

– simulates electron (or photon) transport through voxelizedmedia

• The beam model and electron air scatter functions were developed by CMS

• The user can specify– the number of histories – voxel size – dose-to-medium or dose-to-water – random seed– the total number of particle histories – or the goal Mean Relative Statistical Uncertainty (MRSU)

• CMS performs the beam modeling

*Kawrakow, Fippel, Friedrich, Med. Phys. 23 (1996) 445-457*Fippel, Med. Phys. 26 (1999) 1466–1475

User input data for MC based TPS

• Position and thickness of jaw collimators and MLC

• For each applicator scraper layer:ThicknessPositionShape (perimeter and edge)Composition

• For inserts:ThicknessShapeComposition

Treatment unit specifications:

No head geometry details required for Eclipse, since at this time it only works for Varian linac configuration

User input data for MC TPS contDosimetric data for beam characterization, as

specified in User Manual

• Beam profiles without applicators:-in-air profiles for various field sizes–in-water profiles

–central axis depth dose for various field sizes–some lateral profiles

• Beam profiles with applicators:– Central axis depth dose and profiles in water – Absolute dose at the calibration point

Dosimetric data for verification

– Central axis depth doses and profiles for various field sizes

Clinical implementation of MC treatment planning software

• Beam data acquisition and fitting• Software commissioning tests*

• Clinical implementation– procedures for clinical use– possible restrictions– staff training

*should include tests specific to Monte Carlo

A physicist responsible for TPS implementation should have a thorough understanding of how the system works.

Software commissioning tests: goals

• Setting user control parameters in the TPS to achieve optimum results (acceptable statistical noise, accuracy vs. speed of calculations)– Number of histories– Voxel size– Smoothing

• Understand differences between water tank and real patient anatomy based monitor unit values

Software commissioning tests• Criteria for acceptability

– Van Dyk et al, Int. J. Rad. Oncol. Biol. Phys., 26, 261-273,1993; – Fraass, et al, AAPM TG 53: Quality assurance for clinical radiotherapy

treatment planning,” Med. Phys. 25, 1773–1829 1998

• Homogeneous water phantom• Inhomogeneous phantoms (1D, 2D, 3D, complex)

– Cygler et al, Phys. Med. Biol., 32, 1073, 1987 – Ding G.X.et al, Med. Phys., 26, 2571-2580, 1999– Shiu et al, Med.Phys. 19, 623—36, 1992; – Boyd et al, Med. Phys., 28, 950-8, 2001

• Measurements, especially in heterogeneous phantoms, should done with a high (1 mm) resolution

Lateral profiles at various depths, SSD=100cm, Nucletron TPS

9 MeV, 10x10cm2 applicator, SSD=100cm. Homogeneous water phantom,cross-plane profiles at various depths. MC

with 10k/cm2.

0

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-10 -5 0 5 10

Off - axis / cm

Dos

e / c

Gy

meas.@2cm

calc.@2cm

meas.@3.0cm

calc.@3.0cm

meas.@4.0cm

calc.@4.0cm

20 MeV, 10x10cm2 applicator, SSD=100cm. Homogeneous water phantom. Cross-plane profiles at

various depths. MC with 10k and 50k/cm2.

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meas.@d=3cmcalc.@d=3cmcalc.@d=3cm,50kmeas.@d=7.8cmcalc.@d=7.8cmcalc.@d=7.8cm,50kmeas.@d=9cmcalc.@d=9cmcalc.@d=9cm,50k

CMS: Cut-out factors

Vandervoort and Cygler, COMP 56th Annual Scientific Meeting, Ottawa June 2010

Cutout Output Factors: 9 MeV

0.350

0.450

0.550

0.650

0.750

0.850

0.950

1.050

1 2 3 4 5 6 7 8 9

Square Cutout Length (cm)

Out

put F

acto

r (cG

y/M

U)

ExperimentalXiO Calculated

Cutout Output Factors: 17 MeV

0.600

0.650

0.700

0.750

0.800

0.850

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0.950

1.000

1.050

1 2 3 4 5 6 7 8 9

Square Cutout Length (cm)

Out

put F

acto

r (cG

y/M

U)

ExperimentalXiO Calculated

SSD=100 cm

SSD=115 cm

SSD=100 cm

SSD=115 cm

-6 -4 -2 0 2 4 60

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depth = 4.7 cm

Bone

Off-axis Y position /cm

Rel

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ose

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Measured eMC

Off-axis X position /cm-6 -4 -2 0 2 4 6

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depth = 7.7 cm

depth = 4.7 cm

Air Air

Bone

Relat

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ose

Measured eMC

18 MeV

Eclipse eMC no smoothingVoxel size = 2 mm

Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.

Eclipse eMCEffect of voxel size and smoothing

-6 -4 -2 0 2 4 60

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2 mm and no smoothing

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depth = 4.9 cm

Bone

Off-axis Y position /cm

Relat

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18 MeV

Off-axis X position /cm-6 -4 -2 0 2 4 6

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2 mm and no smoothing

depth = 4.9 cm

Air Air

Bone

Relat

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18 MeV

Ding, G X., et al (2006). Phys. Med. Biol. 51 (2006) 2781-2799.

CMS: 9 MeV - Trachea and spine

Bone

Air

Bone Bone Bone Film Film

Air

Vandervoort and Cygler, COMP 56th Annual Scientific Meeting, Ottawa June 2010

DoseDose--toto--water vs. dosewater vs. dose--toto--mediummedium

Ding, G X., et al Phys. Med. Biol. 51 (2006) 2781-2799.

0 1 2 3 4 50

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BEAM/dosxyz simulation

Bone cylinder is replaced by water-like medium but with bone density

depth in water /cm

Dose

Central Axis Depth /cm

0 1 2 3 4 51.10

1.11

1.12

1.13

1.14

9 MeV

Water/Bone stopping-power ratios

SPR

01 cm diameter and 1 cm length

Hard bone cylinder 2 cm

Dm - energy absorbed in a medium voxel divided by the mass of the medium element.

Dw - energy absorbed in a small cavity of water divided by the mass of that cavity.

Voxel of medium

w

mmw

SDD ⎟⎠

⎞⎜⎝

⎛=

ρ

Small volume of water

Voxel of medium

Good clinical practice

• Murphy’s Law of computer software (including

Monte Carlo)

“All software contains at least one bug”• Independent checks

MU MC vs. hand calculations

Monte CarloMonte Carlo Hand CalculationsHand Calculations

Real physical dose Real physical dose calculated on a patient calculated on a patient anatomy anatomy

Rectangular water Rectangular water tanktank

Inhomogeneity Inhomogeneity correction includedcorrection included

No inhomogeneity No inhomogeneity correctioncorrection

Arbitrary beam angleArbitrary beam anglePerpendicular beam Perpendicular beam incidence onlyincidence only

9 MeV, full scatter phantom(water tank)

RDR=1 cGy/MU

Lateral scatter missing

Real contour / Water tank =

=234MU / 200MU=1.17

MU real patient vs.water tank

MC / Water tank= 292 / 256=1.14

MU-real patient vs. water tankImpact on DVH

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% v

olum

e

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PTV-MU-WT

LT eye-MU-MC

LT eye-MU-WT

RT eye-MU-MC

RT eye-MU-WT

Posterior cervical lymph node irradiation - impact on DVH

0.0

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PTV

/ cm

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conventional

customized

Jankowska et al, Radiotherapy & Oncology, 2007

Internal mammary nodes

MC / Water tank= 210 / 206=1.019

Timing – Pinnacle3

dual processor 1.6 GHz Sun workstation, 16 GB RAM.

Fragoso et al.: Med. Phys. 35, 1028-1038, 2008

24.55.2x108134.54.7x10832.11.1x1074 (face)

5.41.5x10829.91.4x1077.13.3x1063 (breast)

1.57.1x1078.1 6.5x1062.11.7x1062 (ear)

3.91.6x108201.4x1074.83.4x1061(cheek)

CPU time(h)

# historiesCPU time(min)

# histories

CPU time(min)

# histories

Patient

2% 1% 0.5%

Overall uncertainty

Timing – Nucletron TPSOncentra 4.0

4 MeV Timer Results:Init = 0.321443 secondsCalc = 42.188 secondsFini = 0.00158201 secondsSum = 42.5111 seconds

20 MeV Timer Results:Init = 0.311014 secondsCalc = 110.492 secondsFini = 0.00122603 secondsSum = 110.805 seconds

Anatomy - 201 CT slicesVoxels 3 mm3

10x10 cm2 applicator50k histories/cm2

Faster than pencil beam!

Timing – Varian Eclipse

Eclipse MMC, Varian single CPU Pentium IV

XEON, 2.4 GHz

10x10 cm2, applicator, water phantom,

cubic voxels of 5.0 mm sides

6, 12, 18 MeV electrons,

3, 4, 4 minutes, respectively

Chetty et al.: AAPM Task Group Report No. 105: Monte Carlo-based treatment planning, Med. Phys. 34, 4818-4853, 2007

Conclusions• Commercial MC based TP system are available

– fairly easy to implement and use– MC specific testing required

• Fast and accurate 3-D dose calculations• Single virtual machine for all SSDs• Large impact on clinical practice

– Accuracy improved– More attention to technical issues needed– Dose-to-medium calculated– MU based on real patient anatomy (including contour

irregularities and tissue heterogeneities)

• Requirement for well educated physics staff

AcknowledgementsGeorge X. Ding Indrin ChettyGeorge Daskalov Margarida FragosoGordon Chan Charlie MaRobert Zohr Eric Vandervoort Ekaterina Tchistiakova David W.O. Rogers

In the past I have received research support from Nucletron and Varian

TOHCC has a research agreement with Elekta

Thank You