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Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU

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 Course 44th Annual AAPM Meeting Montreal, Canada

Jeffrey V. Siebers Virginia Commonwealth University Medical College of Virginia Hospitals Richmond, Virginia USA

Educational Objectives

To understand MC

method n commissioning n statistical noise n comparison methods n potential clinical significance

n n

Outline

Historical review of MC method n Basics of MC transport n Description of an MC system for patient dose calculations n Commissioning MC algorithms

Ø Ø

Determination of initial phase space Dose normalization

Outline

n

Outline

n

Patient calculations

Ø Ø Ø Ø Ø

MC treatment planning

Ø

Converting CT data to patient materials MC dose grid / CT dose grid differences Dose to material / dose to water Effect of statistical noise Methods to reduce statistical noise

Comparing MC with SC and PB for

n n

3DCRT IMRT

Ø

Role of MC in IMRT optimization

n

MC as a tool for IMRT dosimetric verification

1

Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU

Historical Review of Monte Carlo

Early Beginnings n

Historical Review

Compiler Development

1772: Compte de Buffon

Ø

Uses random sampling to solve mathematical problem First large scale electronic computer (John Mauchly)

n

1954-1957: Fortran

Ø Ø

n

1945: ENIAC

Ø

IBM (John Backus) First successful high level language Standardized Fortran

n

1945: Stan Ulam, John van Neumann, Nicholas Metropolis

Ø Ø

n

1961: Fortran IV

Ø

Propose using "computers" to solve neutron diffusion problems Coined name "Monte Carlo" (Metropolis)

Historical Review

Early "general purpose" codes n n n

Historical Review

n

1963: MCS

Ø

EGS3 being used for Med Physics

Ø Ø Ø

Precursor to MCNP, general purpose MC code

1964: ETRAN (Martin Berger)

Ø

Condensed history approach

1983: Petti, contaminant electron studies 1984: Rogers & Bielajew 1985: Mohan, energy spectra 1986: Rogers and Bielajew publish first Med Phys papers on EGS4 (Med Phys, 13 5) 256 References in PubMed for EGS4 (6/02)

1962: O5R

Ø

n

1985: EGS4

Ø Ø

Predecessor of NTC, NMTC, HETC, LAHET, MCNP-X intranuclear cascade codes

n

1974: EGS1 (Ford and Nelson)

Historical Review

n n

1993: Peregrine Project formed at LLNL

Ø

Radiation Therapy Specific MC code

1995: BEAM and DOSXYZ

Ø Ø

What is Monte Carlo?

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

n

Other Therapy Specific MC codes

Ø Ø

1996: VMC/XVMC/VMC++ (Kawrakow et al) 2000: DPM (Sempau et al)

n

795 "hits" in PubMed with Monte Carlo + radiation + therapy

2

Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU

What is Monte Carlo?

Simple Example

Ø

What is Monte Carlo?

Simple Example n

Given, photon of Energy E incident on infinite (water) phantom

n

Determine interaction probabilities

Determine which interaction occurred by selecting another random number (RN')

Ø

total =PhotoEffect +Compton +Pair PhotoEffect

n

Photo Effect occurs if

RN ' < PhotoEffect total

Ø

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

Compton Effect occurs otherwise

n

x = - ln ( RN ) total (cm)

Determine interaction products by sampling further distributions

Ø

Energy and angle (direction) of scattered photon / electron

What is Monte Carlo?

Simple Example

n

Monte Carlo Method

Follows the path of individual representative particles through accelerator, beam modifiers, and patient to determine dose, fluence, and other distributions in patients and phantoms Uses basic physics interaction probabilities (sampled via selection of random numbers) to determine the fate of the representative particles Sufficient representative particles are transported to produce a statistically acceptable results (averages)

n

Score quantities of interest

Ø Ø

Energy Deposition (Dose) Fluence

n

n

Follow particles (and secondaries ) until they are no longer of interest

Ø Ø Ø

Particle escapes geometry Particle is absorbed Particle drops below energy cut-off

n

Monte Carlo Method

Items of Interest

e-

Monte Carlo

Target Backing Bremsstrahlung Flattening Filter Ion Chamber Target Primary Collimator

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

n

Compton eBremsstrahlung Compton CSDA Annihilation e+ ePair e-

Jaws

MLC

Patient

EPID

3

MC Program Flow

Sample next source particle Yes Put particle on top of last-in first-out stack No Select particle from top of stack Energy > cutoff & particle in geometry Yes Electron Electron or photon? Photon

Why bother with Monte Carlo?

n

Stack empty

Current algorithms are accurate enough Clinical experience is with current inaccurate algorithms Monte Carlo takes too long

Terminate history

No

n

Process electron transport (creates 2nd aries)

Process photon transport (creates 2nd aries)

n

Record events of interest (energy deposition, fluence ...)

Why Monte Carlo?

n

Why Monte Carlo?

n

Radiation transport is a complex process

Ø

Electron interactions result in

n n

Accuracy of currently available dose computation models for planning of radiation treatments is limited Discrepancies compared to true dose distributions may be clinically significant for many cases

Current methods might have errors!

Photons (Bremsstrahlung + characteristic x-rays) Delta-rays (knock on electrons) Photons (Compton, Pair Production ...) Secondary electrons (Compton, Photoelectrons)

n

Ø

Photon interactions result in

n n

Why Monte Carlo?

n

Why Monte Carlo?

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

We can do something about it!

n

n

Universal accuracy: all materials, modalities, anatomic geometries, devices, ... Can simulate ACTUAL beam delivery (moving MLC's , dynamic wedges, etc). Elimination of laborious trial and error parameterization and refinement of models Reduction in time and the amount of measured dose distribution data required for commissioning and validation

It might even be easier!

4

Why Monte Carlo?

n

n n

n

Direct prediction of monitor units reducing the probability of human mistakes Improvement in consistency of interinstitutional results Improvement in quality of dose response data Accurate estimation of quantities difficult or impossible to measure

Accurate dose has benefits!

How do we do Monte Carlo dose calculations?

Target Collimator Vacuum Win Flattening Filter Ion Chamber

PSD Plane

Stage 1: PSD Generation Transport particles to IC exit

Jaws

Stage 1: Creation of Initial Phase Space

n

MLC Blocks Wedges

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

Method Sensitivity to incident electron beam parameters Verification and validation

n

Patient / Phantom

n

Input Accelerator Geometry

MCNP Geometry plotted with Sabrina BEAM Geometry plotted with EGS-Windows

Initial Phase Space ((E,x,y,u,v) )

n

Assume

Ø Ø Ø

Electron beam is radially symmetric and Gaussian Geometry specification is correct ...

n n

Iterate adjusting E, s E, s R to match profiles and depth dose Recent papers on this...

Ø 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). 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).

5

Initial Phase Space

Dependence of Depth Dose on Energy

1.8 1.6 1.4

Initial Phase Space

Dependence of lateral profile on energy

1.02

Measurement Monte Carlo E = 5.6 MeV Monte Carlo E = 6.4 MeV

Relative dose

1.2 1.0 0.8 0.6 0.4 0.2 0 10 20 30 1.8 1.6 1.4

Relative dose

1.00 1.02

Measurement Monte Carlo E = 17.0 MeV Monte Carlo E = 19.0 MeV

0.98

Relative dose

1.2 1.0

0.96

Measurement Monte Carlo E = 5.6 MeV Monte Carlo E = 6.4 MeV

5 10

Relative dose

1.00

40 0.8 0.6 0.4 0.2 0 1 0 20 30 40

Depth (cm)

X (cm)

15 0.98

Measurement Monte Carlo E = 17.0 MeV Monte Carlo E = 19.0 MeV

0.96 5 10 15

Depth (cm)

X (cm)

Monte Carlo dose per particle to dose per MU

n n

Target Collimator Vacuum Win Flattening Filter Ion Chamber

PSD Plane

Save Initial Phase Space for Future Use

n

Jaws

Normalize to a point or Integrate measured and MC 10×10 inphantom depth dose curves between 5 and 15 cm

K = 5 Dmeasured ( z) dz 5 Dcomputed ( z )dz Dose Fluence MU = Dose MU Fluence

15 15

Phase Space Files

Ø

MLC Blocks Wedges

Phase space particles from BEAM simulations of upstream beam line

n

Patient / Phantom

n

Single MU calibration factor used for all fields

Phase Space Models

Phase Space References

n

Commissioning / Acceptance testing

n

n

n

n

n

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 2 6 (7), 1196-211 (1999) 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) 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 Med Biol 45 (2), 411- 27 (2000) I. Chetty, J. J. DeMarco, and T. D. Solberg, "A virtual source model for Monte Carlo modeling of arbitrary intensity distributions," Med Phys 2 7 (1), 166-72 (2000) 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) 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 4 6 (5), 1407 -27 (2001)

n

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

Ø Ø

Depth Dose (open and wedged, various field sizes) Lateral Profiles (open and wedged, various field sizes)

n

Dose profile comparisons in specific materials / interfaces

6

Commissioning / Acceptance testing

n

Standard Tx planning tests (TG-53)

Ø Ø

Orientation, device selection, ... Calculation verification

CT number to material conversion n Users will likely perform additional confidence building tests

n

Dosimetric Verification of a PSD (LLNL Peregrine)

Dosimetric Verification References

n

Stage 2: Patient Simulation

Conversion of patient CT image for MC transport n The MC run n Effect of patient noise n Dose to water conversion n Plan comparisons

n

n

n

n

n

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," 2 8 (7), 1322-37 (2001). 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) 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) L. Wang, M. Lovelock, and C. S. Chui, "Experimental verification of a CT -based Monte Carlo dose-calculation method in heterogeneous phantoms," Med Phys 2 6 (12), 2626- 34 (1999) M. Fippel, W. Laub, B. Huber, and F. Nusslin, "Experimental investigation of a fast Monte Carlo photon beam dose calculation algorithm," Phys Me d Biol 44 (12), 3039- 54 (1999) 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 Med Biol 45 (10), 2969- 85 (2000)

CT to Material Conversion

n

ctcreate blending of voxels

ctcreate (BEAM distribution)

Ø Ø

uses mean CT number in dose grid voxel to assign density and material uses dose grid voxels for particle transport

n

52 materials in CT-to-density conversion

Ø Ø Ø

covers density from 0-2.0 g/cm2 most materials from ICRU-46 to minimize error in dose-to-material conversion

7

Voxel Blending

n

Patient Simulations

An example of MC integration into commercial TPS n Effect of MC Noise n Dose to ? n Plan Comparisons

Reduces resolution n Homogenizes patient n May impact dose at interfaces

n n

Note: CT data itself is homogenization...

Example Monte Carlo Code Implementation

Ø Ø

Breast Case Comparison

4 field

Ø

Ø Ø

Ø

MCV developed interface to NRCC EGS4 BEAM / DOSXYZ code BEAM used for transport through treatment head (Jaws, wedges, etc) Internal MC routines used for MLC and EPID simulations DOSXYZ for patient / phantom simulation Interfaced to Pinnacle treatment planning system Unix workstations (multi -processor,multi computer)

Pinnacle

MCV

Dose/FX (cGy)

Breast

Dose Difference: MCV-Pinnacle

Effect of Statistical Noise

n n

MCV-Pinnacle

Each dose point has statistical uncertainty Effect on plan evaluation

Ø Ø Ø

Dose Difference (cGy)

Isodose DVH TCP / NTCP / EUD

n n

Effect on prescription Methods to reduce noise

8

Patient Prescriptions

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

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).

Consequence Unacceptable: Point Dose Prescriptions Prescribe 200 cGy per fraction to 90% of maximum dose Acceptable: Regional or Dose (MU) based prescriptions Prescribe 200 cGy per fraction to 98% of the tumor volume

n

Removing from DVH

Ø

Ø

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). 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

Example of denoising...

Denoising / Smoothing

Ø

J. O. Deasy, "Denoising of electron beam Monte Carlo dose distributions using digital filtering techniques," Phys Med Biol 45 (7), 1765-79 (2000). WE-D-517D-2: Miao et al: "3-D Anisotropic Diffusion and Wavelet Filtering of Monte Carlo Dose Distribution" WE-D-517D-4: Kawrakow: "Smoothing Monte Carlo Calculated Dose Distributions for Radiation Treatment Planning"

Ø Ø

Example of denoising...

Example of denoising...

9

Example of denoising...

n

Denoising

Can reduce MC dose calculation time by factor of ~8 n Can introduce artifacts n Must be applied carefully

(see papers and posters)

How to compare with MC?

Absorbed Dose to Water

Statement of the problem

n n n n n

Dose to water or dose to water?

n

Measurements are typically in terms of Dwater Current clinical experience in radiation therapy is based upon Dwater "Conventional" algorithms compute Dwater Monte Carlo dose algorithms most accurate when they compute Dmedium To compare, need a method to convert Dwater to Dmedium .

Method of conversion

Ø

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 4 5 (4), 983- 95 (2000).

n

AAPM Point / Counterpoint

Ø Ø

H. H. Liu, "Dm rather than Dw should be used in Monte Carlo treatment planning. For the proposition," Med Phys 2 9 (5), 922-3 (2002). 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

10

Breast Case

Isodose Comparison

Dmaterial

Breast Case

Dose Difference Display

Dwater

MCV - Pinnacle Pinnacle MCV

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

MCV - Pinnacle

-2

-3

-5

-10

Breast

Dose Difference: MCV-Pinnacle MCV

Lung Case

Dwater

MCV - Pinnacle

MCV - Pinnacle

MCV-Pinnacle MCV - Pinnacle

Dose Difference (%)

Dose Difference (%)

Head and Neck Case

n

Relevant Papers for MC Comparisons

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) 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) 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) 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)

MCV Pinnacle MCV

MCV - Pinnacle

n

n

n

Dose Difference (%)

11

Head and Neck Case

MCV - Pinnacle

n n

Monte Carlo and IMRT

R. Jeraj and P. J. Keall, "The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation," Phys Med Biol 4 5 (12), 3601-13. (2000) R. Jeraj, P. J. Keall, and J. V. Siebers, "The effect of dose calculation accuracy on inverse treatment planning," Phys Med Biol 47 (3), 391-407 (2002) 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) T. Pawlicki and C. M. Ma, "Monte Carlo simulation for MLC-based intensitymodulated radiotherapy," Med Dosim 26 (2), 157- 68 (2001) 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 4 6 (6), 1695- 706 (2001) W. Laub, M. Alber, M. Birkner, and F. Nusslin, "Monte Carlo dose computation for IMRT optimization," Phys Med Biol 45 (7), 1741-54 (2000) 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)

n

n

n

Impact for IMRT???

n

n

IMRT Consequences of inaccuracy

n

Consequences of inaccuracy

n

Systematic error

Ø

Ø

For a given intensity distribution, dose predicted differs from that actually delivered to the patient/phantom Can be avoided by performing final calculation with accurate algorithm

Convergence error

Ø Ø

Consequence of systematic error during optimization Optimization with an inaccurate algorithm results in different intensities than those predicted by an accurate algorithm Actual dose is not optimal, a better solution exists Can be avoided by optimization with an accurate algorithm

Ø Ø

IMRT Comparison between Film and SC on Flat Phantom

(a) (b) (c)

VCU IMRT Case

12

IMRT Comparison between Film and SC on Flat Phantom

(a) (b) (c)

n n n n n

Questions to ask your MC vendor / developer?

What is the acceptance criteria (systematic errors)? How fast is the Code (field size, voxel size, Tx volume)? What is the statistical uncertainty at that quoted speed? How much $$ must I spend on computers? Does it compute D water so I can compare results with other algorithms and relate to my clinical experience?

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

Summary

MC History n Basics of MC n Commissioning of MC n Patient Calculations n MC and IMRT

n

13

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