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. Monte Carlo for Radiation Therapy Dose Calculations 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 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 Outline To understand MC method n commissioning n statistical noise n comparison methods n potential clinical significance n Historical review of MC method n Basics of MC transport n Description of an MC system for patient dose calculations n Commissioning MC algorithms n Ø Ø Determination of initial phase space Dose normalization Outline n Patient calculations Ø Ø Ø Ø 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 Outline n MC treatment planning Ø Comparing MC with SC and PB for n n Ø n 3DCRT IMRT Role of MC in IMRT optimization 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 Historical Review Compiler Development Early Beginnings 1772: Compte de Buffon n Ø Uses random sampling to solve mathematical problem n Ø 1945: ENIAC n Ø First large scale electronic computer (John Mauchly) 1945: Stan Ulam, John van Neumann, Nicholas Metropolis n Ø Ø 1954-1957: Fortran Ø n IBM (John Backus) First successful high level language 1961: Fortran IV Ø Standardized Fortran Propose using “computers” to solve neutron diffusion problems Coined name “Monte Carlo” (Metropolis) Historical Review Historical Review Early “general purpose” codes n 1963: MCS Ø n 1964: ETRAN (Martin Berger) n 1962: O5R Ø Ø n n Precursor to MCNP, general purpose MC code Ø Ø Ø Condensed history approach Predecessor of NTC, NMTC, HETC, LAHET, MCNP-X intranuclear cascade codes 1974: EGS1 (Ford and Nelson) EGS3 being used for Med Physics n 1983: Petti, contaminant electron studies 1984: Rogers & Bielajew 1985: Mohan, energy spectra 1985: EGS4 Ø Ø 1986: Rogers and Bielajew publish first Med Phys papers on EGS4 (Med Phys, 13 5) 256 References in PubMed for EGS4 (6/02) Historical Review n 1993: Peregrine Project formed at LLNL n 1995: BEAM and DOSXYZ Ø Ø Ø n What is Monte Carlo? BEAM: Rogers et al, Med. Phys. 22 5 DOSXYZ: Ma et al PIRS-0509b, NRCC, 1995 Other Therapy Specific MC codes Ø Ø n Radiation Therapy Specific MC code 1996: VMC/XVMC/VMC++ (Kawrakow et al) 2000: DPM (Sempau et al) 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? What is Monte Carlo? Simple Example Simple Example Ø Given, photon of Energy E incident on infinite (water) phantom n n Determine interaction probabilities Determine which interaction occurred by selecting another random number (RN’) ∑total =∑PhotoEffect PhotoEffect +∑Compton +∑Pair n Select Random Number (RN (0,1]) to choose interaction distance Ø Photo Effect occurs if Ø Compton Effect occurs otherwise RN ' < ∑ PhotoEffect ∑total 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? Monte Carlo Method Simple Example n Score quantities of interest Ø Ø n n Energy Deposition (Dose) Fluence Follow particles (and secondaries ) until they are no longer of interest n Particle escapes geometry Particle is absorbed Particle drops below energy cut-off n Ø Ø Ø 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) Monte Carlo Monte Carlo Method Items of Interest 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 Target Backing Target e- Primary Collimator Bremsstrahlung n Flattening Filter Ion Chamber Compton Jaws eBremsstrahlung Compton MLC CSDA Annihilation e+ ePair e- Patient EPID 3 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU MC Program Flow Why bother with Monte Carlo? Sample next source particle Yes Stack empty Terminate history Put particle on top of last-in first-out stack No n Current algorithms are accurate enough n Clinical experience is with current inaccurate algorithms n Monte Carlo takes too long Select particle from top of stack No Energy > cutoff & particle in geometry Yes Electron Electron or photon? Process electron transport (creates 2nd aries) Photon Process photon transport (creates 2nd aries) Record events of interest (energy deposition, fluence …) Why Monte Carlo? n Radiation transport is a complex process Ø Ø 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 Electron interactions result in n Photons (Bremsstrahlung + characteristic x-rays) n Delta-rays (knock on electrons) Photon interactions result in n Photons (Compton, Pair Production …) n Secondary electrons (Compton, Photoelectrons) Current methods might have errors! Why Monte Carlo? 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 n n 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, ... 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 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU 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 How do we do Monte Carlo dose calculations? Accurate dose has benefits! Target Collimator Vacuum Win Flattening Filter Ion Chamber PSD Plane Stage 1: PSD Generation Transport particles to IC exit Stage 1: Creation of Initial Phase Space Jaws MLC Stage 2: Patient Calculations Transport particles through patient dependent devices. (jaws, blocks, mlc, wedges, and patient/phantom) Blocks Wedges Patient / Phantom n Method n Sensitivity to incident electron beam parameters n Verification and validation Initial Phase Space (Ψ(E,x,y,u,v) ) Input Accelerator Geometry MCNP Geometry plotted with Sabrina BEAM Geometry plotted with EGS-Windows n Assume Ø Ø Ø n n Electron beam is radially symmetric and Gaussian Geometry specification is correct … 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 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Initial Phase Space Initial Phase Space Dependence of Depth Dose on Energy Dependence of lateral profile on energy 1.8 1.2 1.8 1.0 Measurement Monte Carlo E = 17.0 MeV Monte Carlo E = 19.0 MeV 1.6 0.8 0.4 0.2 0 10 20 Depth (cm) 30 Relative dose 1.4 0.6 1.00 1.02 0.98 Measurement Monte Carlo E = 5.6 MeV Monte Carlo E = 6.4 MeV 1.2 1.0 0.96 40 5 0.8 10 X (cm) Relative dose Relative dose 1.4 Relative dose 1.02 Measurement Monte Carlo E = 5.6 MeV Monte Carlo E = 6.4 MeV 1.6 1.00 15 0.98 Measurement Monte Carlo E = 17.0 MeV Monte Carlo E = 19.0 MeV 0.6 0.4 0.96 0.2 0 10 20 30 40 5 Monte Carlo dose per particle to dose per MU 10 15 X (cm) Depth (cm) Target Collimator Vacuum Win Flattening Filter Ion Chamber PSD Plane Save Initial Phase Space for Future Use Jaws n n Normalize to a point or Integrate measured and MC 10×10 inphantom depth dose curves between 5 and 15 cm n Ø Blocks Wedges K = ∫ 5 Dmeasured ( z) dz ∫ 5 Dcomputed ( z )dz Dose Fluence MU = Dose MU Fluence 15 n 15 n Single MU calibration factor used for all fields 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) Phase space particles from BEAM simulations of upstream beam line Phase Space Models Patient / Phantom Commissioning / Acceptance testing Phase Space References n Phase Space Files MLC n n n Set acceptance criteria for dose profile (2%, 2mm) and output agreement (1%) Water phantom comparisons Ø Depth Dose (open and wedged, various field sizes) Ø Lateral Profiles (open and wedged, various field sizes) Dose profile comparisons in specific materials / interfaces 6 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU 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 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 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 ctcreate blending of voxels ctcreate (BEAM distribution) Ø Ø n Stage 2: Patient Simulation uses mean CT number in dose grid voxel to assign density and material uses dose grid voxels for particle transport 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 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Patient Simulations Voxel Blending An example of MC integration into commercial TPS n Effect of MC Noise n Dose to ? n Plan Comparisons n 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 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) Breast Case Comparison 4 field Pinnacle MCV Dose/FX (cGy) Breast Dose Difference: MCV-Pinnacle MCV-Pinnacle Effect of Statistical Noise n n Each dose point has statistical uncertainty Effect on plan evaluation Ø Ø Ø Dose Difference (cGy) n n Isodose DVH TCP / NTCP / EUD Effect on prescription Methods to reduce noise 8 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Effect of Statistical Noise Patient Prescriptions As the number of points in a dose distribution increases, so does the maximum deviation from the mean Consequence Unacceptable: Point Dose Prescriptions n Acceptable level (~2%) Ø n Removing from DVH Ø 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 Methods to reduce statistical noise n 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). 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). 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). Ø 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 Example of denoising… Example of denoising… 9 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Example of denoising… Denoising Can reduce MC dose calculation time by factor of ~8 n Can introduce artifacts n Must be applied carefully n (see papers and posters) How to compare with MC? Dose to water or dose to water? Absorbed Dose to Water Statement of the problem n n n n 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 . Water-to-Material Stopping Power Ratios n Method of conversion Ø n 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). 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) Patient Plan Comparisons 10 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Breast Case Breast Case Isodose Comparison Dose Difference Display Pinnacle Dmaterial Dwater MCV - Pinnacle MCV - Pinnacle MCV +10 +5 +3 +2 +1 -1 -2 -3 -5 -10 Breast Dose Difference: MCV-Pinnacle Dwater Lung Case MCV MCV - Pinnacle MCV - Pinnacle MCV-Pinnacle MCV - Pinnacle Dose Difference (%) Dose Difference (%) Relevant Papers for MC Comparisons Head and Neck Case n MCV MCV - Pinnacle n Pinnacle MCV n 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) 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) Dose Difference (%) 11 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU Head and Neck Case Monte Carlo and IMRT MCV - Pinnacle n n n n n Impact for IMRT??? n n IMRT Consequences of inaccuracy n Consequences of inaccuracy 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 n Convergence error Ø 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 Can be avoided by optimization with an accurate algorithm Ø IMRT Comparison between Film and SC on Flat Phantom (a) (b) 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) VCU IMRT Case (c) 12 Monte Carlo for Radiation Therapy Dose Calculations Monte Carlo Refresher Course AAPM 2002 Jeffrey V. Siebers, VCU IMRT Comparison between Film and SC on Flat Phantom (a) (b) (c) 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)? What is the statistical uncertainty at that quoted speed? n n n 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