Educational Objectives Outline To understand MCMCNP Geometry plotted with Sabrina BEAM Geometry plotted with EGS-Windows Initial Phase Space (Y(E,x,y,u,v)) nAssume ØElectron beam

Monte Carlo for Radiation Therapy Dose CalculationsMonte Carlo Refresher CourseAAPM 2002Jeffrey V. Siebers, VCU

1

This document is the handout for the Monte Carlo Refresher Course presented 44th Annual AAPM Meeting in Montreal, Canada.

Since the AAPM restricts the file size of the hand out to be 1 MB, this hand out does NOT include all slides presented at the meeting. Instead, this hand-out covers major points. A link to the full presentation is available at http://www.radonc.rdo.vcu.edu/AAPM

Monte Carlo for Radiation Therapy Dose Calculations

MC Refresher Course44th Annual AAPM Meeting

Montreal, CanadaJeffrey V. Siebers

Virginia Commonwealth UniversityMedical College of Virginia Hospitals

Richmond, Virginia USA

Educational Objectives

n methodn commissioningn statistical noisen comparison methodsn potential clinical significance

To understand MCOutline

n Historical review of MC methodn Basics of MC transportn Description of an MC system for

patient dose calculationsn Commissioning MC algorithmsØ Determination of initial phase spaceØ Dose normalization

Outline

n Patient calculationsØ Converting CT data to patient materialsØ MC dose grid / CT dose grid differencesØ Dose to material / dose to waterØ Effect of statistical noiseØ Methods to reduce statistical noise

Outline

n MC treatment planningØ Comparing MC with SC and PB for

n 3DCRTn IMRT

Ø Role of MC in IMRT optimization

n MC as a tool for IMRT dosimetric verification


2

Historical Review of Monte Carlo

Early Beginnings

n 1772: Compte de Buffon Ø Uses random sampling to solve mathematical

problem

n 1945: ENIAC Ø First large scale electronic computer (John

Mauchly)

n 1945: Stan Ulam, John van Neumann, Nicholas Metropolis Ø Propose using “computers” to solve neutron

diffusion problemsØ Coined name “Monte Carlo” (Metropolis)

Historical ReviewCompiler Development

n 1954-1957: FortranØ IBM (John Backus)Ø First successful high level language

n 1961: Fortran IVØ Standardized Fortran

Historical ReviewEarly “general purpose” codes

n 1963: MCSØ Precursor to MCNP, general purpose MC code

n 1964: ETRAN (Martin Berger)Ø Condensed history approach

n 1962: O5RØ Predecessor of NTC, NMTC, HETC, LAHET,

MCNP-X intranuclear cascade codes

n 1974: EGS1 (Ford and Nelson)

Historical Review

n EGS3 being used for Med PhysicsØ 1983: Petti, contaminant electron studiesØ 1984: Rogers & BielajewØ 1985: Mohan, energy spectra

n 1985: EGS4 Ø 1986: Rogers and Bielajew publish first Med

Phys papers on EGS4 (Med Phys, 13 5)Ø 256 References in PubMed for EGS4 (6/02)

Historical Review

n 1993: Peregrine Project formed at LLNLØ Radiation Therapy Specific MC code

n 1995: BEAM and DOSXYZØ BEAM: Rogers et al, Med. Phys. 22 5Ø DOSXYZ: Ma et al PIRS-0509b, NRCC, 1995

n Other Therapy Specific MC codesØ 1996: VMC/XVMC/VMC++ (Kawrakow et al)Ø 2000: DPM (Sempau et al)

n 795 “hits” in PubMed with Monte Carlo + radiation + therapy

What is Monte Carlo?


3

What is Monte Carlo?Simple Example

Ø Given, photon of Energy E incident on infinite (water) phantomn Determine interaction probabilities

n Select Random Number (RN (0,1]) to choose interaction distance

total PhotoEffect Compton Pair∑ =∑ +∑ +∑

( )ln totalx RN= − ∑ (cm)

total PhotoEffect Compton∑ =∑ +∑


n Determine which interaction occurred by selecting another random number (RN’)Ø Photo Effect occurs if

Ø Compton Effect occurs otherwise

n Determine interaction products by sampling further distributionsØ Energy and angle (direction) of scattered

photon / electron

' PhotoEffect totalRN < ∑ ∑


n Score quantities of interestØ Energy Deposition (Dose)Ø Fluence

n Follow particles (and secondaries ) until they are no longer of interestØ Particle escapes geometry Ø Particle is absorbedØ Particle drops below energy cut-off

Monte Carlo Method

n Follows the path of individual representative particles through accelerator, beam modifiers, and patient to determine dose, fluence, and other distributions in patients and phantoms

n Uses basic physics interaction probabilities (sampled via selection of random numbers) to determine the fate of the representative particles

n Sufficient representative particles are transported to produce a statistically acceptable results (averages)

Monte Carlo MethodItems of Interest

n The particles transported only represent real particles

n Only ~100 Million particles will be used in a patient simulation

n During a 2 Gy fraction ~1016 electrons incident upon the target, ~1014 photons impinging on the patient

n Increasing number of particles transported increases computer time (linearly) but only improves statistics by the square root of the number of particles

Monte Carloe-

e-e

e -

e-

+

Bremsstrahlung

Bremsstrahlung

Compton

Compton

Pair

CSDA

Annihilation

Target Backing

PrimaryCollimator

Flattening Filter

Ion Chamber

Target

Patient

Jaws

MLC

EPID


4

MC Program Flow

Stack empty No

Yes

No

YesElectron Photon

Process photon transport (creates 2ndaries)

Process electrontransport (creates 2ndaries)

Sample next source particle

Put particle on top oflast-in first-out stack

Select particle from top of stack

Terminate history Energy > cutoff & particle in geometry

Electron or photon?

Record events of interest (energy deposition, fluence …)

Why bother with Monte Carlo?

n Current algorithms are accurate enough

n Clinical experience is with current inaccurate algorithms

n Monte Carlo takes too long

Why Monte Carlo?

n Radiation transport is a complex processØ Electron interactions result in

n Photons (Bremsstrahlung + characteristic x-rays)

n Delta-rays (knock on electrons)

Ø Photon interactions result inn Photons (Compton, Pair Production …)

n Secondary electrons (Compton, Photoelectrons)

Why Monte Carlo?

n Accuracy of currently available dose computation models for planning of radiation treatments is limited

n Discrepancies compared to true dose distributions may be clinically significant for many cases

Current methods might have errors!

Why Monte Carlo?

n The discrepancies revealed by accurate predictions of dose can be remedied using different treatment techniques, e.g., use of different margins, beam energies, beam arrangements, and intensity modulation

n High accuracy is now practical and affordable with Monte Carlo simulations of radiation transport

We can do something about it!

n Universal accuracy: all materials, modalities, anatomic geometries, devices, ...

n Can simulate ACTUAL beam delivery (moving MLC’s , dynamic wedges, etc).

n Elimination of laborious trial and error parameterization and refinement of models

n Reduction in time and the amount of measured dose distribution data required for commissioning and validation

Why Monte Carlo?

It might even be easier!


5

Why Monte Carlo?

n Direct prediction of monitor units reducing the probability of human mistakes

n Improvement in consistency of inter-institutional results

n Improvement in quality of dose response data

n Accurate estimation of quantities difficult or impossible to measure

Accurate dose has benefits!

How do we do Monte Carlo dose calculations?

Stage 1: PSD GenerationTransport particles to IC exit

PSD Plane

Stage 2: Patient CalculationsTransport particles through patient dependent devices. (jaws, blocks, mlc, wedges, and patient/phantom)

Target

Vacuum WinCollimator

Flattening FilterIon Chamber

Jaws

Patient / Phantom

MLC

BlocksWedges

Stage 1: Creation of Initial Phase Space

n Method

n Sensitivity to incident electron beam parameters

n Verification and validation

Input Accelerator GeometryMCNP Geometry plotted with Sabrina BEAM Geometry plotted with EGS-Windows

Initial Phase Space(Ψ(E,x,y,u,v) )

n AssumeØ Electron beam is radially symmetric and GaussianØ Geometry specification is correctØ …

n Iterate adjusting E, s E, s R to match profiles and depth dose

n Recent papers on this…Ø D. Sheikh-Bagheri and D. W. Rogers, “Sensitivity of megavoltage photon beam

Monte Carlo simulations to electron beam and other parameters,” Med Phys 29(3), 379 -90 (2002).

Ø G. X. Ding, “Energy spectra, angular spread, fluence profiles an d dose distributions of 6 and 18 MV photon beams: results of Monte Carl o simulations for a Varian 2100EX accelerator,” Phys Med Biol 47, 1025-46 (2002).


6

Initial Phase SpaceDependence of Depth Dose on Energy

Depth (cm)0 10 20 30 40

Rel

ativ

e do

se

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

MeasurementMonte Carlo E = 5.6 MeVMonte Carlo E = 6.4 MeV

Depth (cm)0 10 20 30 40

Rel

ativ

e do

se

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8


Initial Phase SpaceDependence of lateral profile on energy

X (cm)5 10 15

Rel

ativ

e do

se

0.96

0.98

1.00

1.02


X (cm)5 10 15

Rel

ativ

e do

se

0.96

0.98

1.00

1.02


Monte Carlo dose per particle to dose per MU

n Normalize to a point orn Integrate measured and MC 10×10 in-

phantom depth dose curves between 5 and 15 cm

n Single MU calibration factor used for all fields

∫∫= 15

5

15

5 )()( dzzDdzzDK computedmeasured

=

FluenceDose

MUDoseMUFluence

Save Initial Phase Space for Future Use

n Phase Space FilesØ Phase space particles

from BEAM simulations of upstream beam line

n Phase Space Models

PSD Plane

Target

Vacuum WinCollimator

Flattening FilterIon Chamber

Jaws

Patient / Phantom

MLC

BlocksWedges

Phase Space References

n A. E. Schach von Wittenau, L. J. Cox, P. M. Bergstrom, Jr., W. P. Chandler, C. L.Hartmann Siantar, and R. Mohan, “Correlated histogram representation of Monte Carlo derived medical accelerator photon- output phase space,” Med Phys 26 (7), 1196-211 (1999)

n J. V. Siebers, P. J. Keall, B. Libby, and R. Mohan, “Comparison of EGS4 and MCNP4b Monte Carlo codes for generation of photon phase space distributions for a Varian 2100C,” Phys Med Biol 44 (12), 3009- 26 (1999)

n J. Deng, S. B. Jiang, A. Kapur, J. Li, T. Pawlicki, and C. M. Ma, “Photon beam characterization and modelling for Monte Carlo treatment planning,” Phys MedBiol 45 (2), 411- 27 (2000)

n I. Chetty, J. J. DeMarco, and T. D. Solberg, “A virtual source model for Monte Carlo modeling of arbitrary intensity distributions,” Med Phys 27 (1), 166-72 (2000)

n M. K. Fix, H. Keller, P. Ruegsegger, and E. J. Born, “Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy,” Med Phys 27 (12), 2739-47 (2000)

n M. K. Fix, M. Stampanoni, P. Manser, E. J. Born, R. Mini, and P. Ruegsegger, “A multiple source model for 6 MV photon beam dose calculations using Monte Carlo,” Phys Med Biol 46 (5), 1407 -27 (2001)

Commissioning / Acceptance testing

n Set acceptance criteria for dose profile (2%, 2mm) and output agreement (1%)

n Water phantom comparisonsØ Depth Dose (open and wedged, various field sizes)

Ø Lateral Profiles (open and wedged, various field sizes)

n Dose profile comparisons in specific materials / interfaces


7

Commissioning / Acceptance testing

n Standard Tx planning tests (TG-53)Ø Orientation, device selection, …Ø Calculation verification

n CT number to material conversionn Users will likely perform additional

confidence building tests

Dosimetric Verification of

a PSD(LLNL

Peregrine)

Dosimetric Verification References

n C. L. Hartmann Siantar, R. S. Walling, T. P. Daly, B. Faddegon, N. Albright, P. Bergstrom, A. F. Bielajew, C. Chuang, D. Garrett, R. K. House, D. Knapp, D. J.Wieczorek, and L. J. Verhey, “Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom,” 28 (7), 1322-37 (2001).

n C. M. Ma, E. Mok, A. Kapur, T. Pawlicki, D. Findley, S. Brain, K. Korster, and A. L. Boyer, “Clinical implementation of a Monte Carlo treatment pl anning system,” Med Phys 26 (10), 2133 -43 (1999)

n E. Spezi, D. G. Lewis, and C. W. Smith, “Monte Carlo simulation and dosimetric verification of radiotherapy beam modifiers,” Phys Med Biol 46 (11), 3007- 29 (2001)

n L. Wang, M. Lovelock, and C. S. Chui, “Experimental verification of a CT -based Monte Carlo dose-calculation method in heterogeneous phantoms,” Med Phys 26(12), 2626- 34 (1999)

n M. Fippel, W. Laub, B. Huber, and F. Nusslin, “Experimental investigation of a fast Monte Carlo photon beam dose calculation algorithm,” Phys Med Biol 44(12), 3039- 54 (1999)

n J. S. Li, T. Pawlicki, J. Deng, S. B. Jiang, E. Mok, and C. M. Ma, “Validation of a Monte Carlo dose calculation tool for radiotherapy treatment pla nning,” Phys MedBiol 45 (10), 2969- 85 (2000)

Stage 2: Patient Simulation

n Conversion of patient CT image for MC transport

n The MC runn Effect of patient noisen Dose to water conversionn Plan comparisons

CT to Material Conversion

n ctcreate (BEAM distribution)Ø uses mean CT number in dose grid voxel to

assign density and material Ø uses dose grid voxels for particle transport

n 52 materials in CT-to-density conversionØ covers density from 0-2.0 g/cm2

Ø most materials from ICRU-46Ø to minimize error in dose-to-material

conversion

ctcreate blending of voxels


8

Voxel Blending

n Reduces resolutionn Homogenizes patientn May impact dose at interfaces

n Note: CT data itself is homogenization…

Patient Simulations

n An example of MC integration into commercial TPS

n Effect of MC Noisen Dose to ?n Plan Comparisons

Example Monte Carlo Code

ImplementationØ MCV developed interface to NRCC EGS4

BEAM / DOSXYZ codeØ BEAM used for transport through treatment

head (Jaws, wedges, etc)Ø Internal MC routines used for MLC and EPID

simulationsØ DOSXYZ for patient / phantom simulationØ Interfaced to Pinnacle treatment planning

systemØ Unix workstations (multi -processor,multi -

computer)

Breast Case Comparison4 field

Pinnacle MCV

Dose/FX (cGy)

BreastDose Difference: MCV-Pinnacle

MCV-Pinnacle

Dose Difference (cGy)

Effect of Statistical Noise

n Each dose point has statistical uncertainty

n Effect on plan evaluationØ IsodoseØ DVHØ TCP / NTCP / EUD

n Effect on prescriptionn Methods to reduce noise


9

Patient Prescriptions

Prescribe 200 cGy per fraction to 90% of maximum dose

Unacceptable: Point Dose Prescriptions

Acceptable: Regional or Dose (MU) based prescriptions

Prescribe 200 cGy per fraction to 98% of the tumor volume

As the number of points in a dose distribution increases, so does the maximum deviation from the mean

Consequence

Effect of Statistical Noise

n Acceptable level (~2%)Ø P. J. Keall, J. V. Siebers, R. Jeraj, and R. Mohan, “The effect of

dose calculation uncertainty on the evaluation of radiotherapy plans,” Med Phys 27 (3), 478-84 (2000).

n Removing from DVHØ J. Sempau and A. F. Bielajew, “Towards the elimination of Monte

Carlo statistical fluctuation from dose volume histograms for radiotherapy treatment planning,” Phys Med Biol 45 (1), 131-57 (2000).

Ø S. B. Jiang, T. Pawlicki , and C. M. Ma, “Removing the effect of statistical uncertainty on dose-volume histograms from Monte Carlo dose calculations,” Phys Med Biol 45 (8), 2151-61 (2000).

Methods to reduce statistical noise

n Denoising / SmoothingØ J. O. Deasy, “Denoising of electron beam Monte Carlo dose

distributions using digital filtering techniques,” Phys Med Biol 45 (7), 1765-79 (2000).

Ø WE-D-517D-2: Miao et al: “3-D Anisotropic Diffusion and Wavelet Filtering of Monte Carlo Dose Distribution”

Ø WE-D-517D-4: Kawrakow: “Smoothing Monte Carlo Calculated Dose Distributions for Radiation Treatment Planning”

Example of denoising…

Example of denoising… Example of denoising…


10

Example of denoising…Denoising

n Can reduce MC dose calculation time by factor of ~8

n Can introduce artifactsn Must be applied carefully

(see papers and posters)

How to compare with MC? Absorbed Dose to Water

Statement of the problem

n Measurements are typically in terms of Dwater

n Current clinical experience in radiation therapy is based upon Dwater

n “Conventional” algorithms compute Dwater

n Monte Carlo dose algorithms most accurate when they compute Dmedium

n To compare, need a method to convert Dwater to Dmedium .

Dose to water or dose to water?

n Method of conversionØ 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 (4), 983- 95 (2000).

n AAPM Point / CounterpointØ H. H. Liu, “Dm rather than Dw should be used in Monte Carlo treatment

planning. For the proposition,” Med Phys 29 (5), 922-3 (2002).Ø Dm rather than Dw should be used in Monte Carlo treatment planning.

Against the proposition,” Med Phys 29 (5), 923- 4 (2002)

Water-to-Material Stopping Power Ratios

Patient Plan Comparisons


11

Breast CaseIsodose Comparison

Pinnacle MCV

Breast CaseDose Difference Display

Dwater

MCV - Pinnacle MCV - Pinnacle

Dmaterial

+10 +5 +3 +2 +1 -1 -2 -3 -5 -10

BreastDose Difference: MCV-Pinnacle

MCV - Pinnacle

DwaterMCV - Pinnacle

Dose Difference (%)

Lung Case MCV

MCV-Pinnacle

MCV - Pinnacle

Dose Difference (%)

Head and Neck Case

MCV

MCV - Pinnacle

Pinnacle

MCV

Dose Difference (%)

Relevant Papers for MC Comparisons

n P. Francescon, C. Cavedon, S. Reccanello, and S. Cora, “Photon dose calculation of a three -dimensional treatment planning system compared to the Monte Carlo code BEAM,” Med Phys 27 (7), 1579- 87 (2000)

n C. M. Ma, E. Mok, A. Kapur, T. Pawlicki, D. Findley, S. Brain, K. Korster, and A. L. Boyer, “Clinical implementation of a Monte Carlo treatment pl anning system,” Med Phys 26 (10), 2133 -43 (1999)

n M. Miften, M. Wiesmeyer, A. Kapur, and C. M. Ma, “Comparison of RTP dose distributions in heterogeneous phantoms with the BEAM Monte Carlo simulation system,” J Appl Clin Med Phys 2 (1), 21- 31 (2001)

n L. Wang, E. Yorke, G. Desobry, and C. S. Chui, “Dosimetric advantage of using 6 MV over 15 MV photons in conformal therapy of lung cancer: MonteCarlo studies in patient geometries,” J Appl Clin Med Phys 3 (1), 51-9 (2002)


12

Head and Neck CaseMCV - Pinnacle

Impact for IMRT???

Monte Carlo and IMRTn R. Jeraj and P. J. Keall, “The effect of statistical uncertainty on inverse treatment

planning based on Monte Carlo dose calculation,” Phys Med Biol 45 (12), 3601-13. (2000)

n R. Jeraj, P. J. Keall, and J. V. Siebers, “The effect of dose calculation accuracy oninverse treatment planning,” Phys Med Biol 47 (3), 391-407 (2002)

n C. M. Ma, T. Pawlicki, S. B. Jiang, J. S. Li, J. Deng, E. Mok, A. Kapur, L. Xing, L. Ma, and A. L. Boyer, “Monte Carlo verification of IMRT dose distributions from a commercial treatment planning optimization system,” Phys Med Biol 45 (9), 2483- 95 (2000)

n T. Pawlicki and C. M. Ma, “Monte Carlo simulation for MLC-based intensity-modulated radiotherapy,” Med Dosim 26 (2), 157- 68 (2001)

n W. U. Laub, A. Bakai, and F. Nusslin, “Intensity modulated irradiation of a thorax phantom: comparisons between measurements, Monte Carlo calculations and pencil beam calculations,” Phys Med Biol 46 (6), 1695- 706 (2001)

n W. Laub, M. Alber, M. Birkner, and F. Nusslin, “Monte Carlo dose computation for IMRT optimization,” Phys Med Biol 45 (7), 1741-54 (2000)

n J. V. Siebers, M. Lauterbach, S. Tong, Q. Wu, and R. Mohan, “Reducing dose calculation time for accurate iterative IMRT planning,” Med Phys 29 (2), 231- 7 (2002)

IMRTConsequences of inaccuracy

n Systematic errorØ For a given intensity distribution, dose

predicted differs from that actually delivered to the patient/phantom

Ø Can be avoided by performing final calculation with accurate algorithm

Consequences of inaccuracy

n Convergence errorØ Consequence of systematic error during optimization

Ø Optimization with an inaccurate algorithm results in different intensities than those predicted by an accurate algorithm

Ø Actual dose is not optimal, a better solution exists Ø Can be avoided by optimization with an accurate

algorithm

IMRTComparison between Film and SC on Flat Phantom

(a) (b) (c)

VCU IMRT Case


13

(a) (b) (c)

Points with a dose difference <2% or a DTA <2 mm are considered dosimetrically equivalent. For the MC computation, 97% of the points fall in that category

IMRTComparison between Film and SC on Flat Phantom

Questions to ask your MC vendor / developer?

n What is the acceptance criteria (systematic errors)?

n How fast is the Code (field size, voxel size, Tx volume)?n What is the statistical uncertainty at that quoted speed?

n How much $$ must I spend on computers?n Does it compute Dwater so I can compare results with

other algorithms and relate to my clinical experience?

Summary

n MC Historyn Basics of MCn Commissioning of MCn Patient Calculationsn MC and IMRT

Documents

Educational Objectives Outline To understand MCMCNP Geometry plotted with Sabrina BEAM Geometry plotted with EGS-Windows Initial Phase Space (Y(E,x,y,u,v)) nAssume ØElectron beam