Photon Beam Transport in a Voxelized Human Phantom Model: Discrete Ordinates vs Monte Carlo R. A. Lillie, D. E. Peplow, M. L. Williams, B. L. Kirk, M. P. Langer †, T. L. Nichols ††, and Y. Y. Azmy ††† Oak Ridge National Laboratory † Indiana University School of Medicine †† University of Tennessee Medical Center ††† The Pennsylvania State University The ANS 14 th Biennial Topical Meeting of the Radiation Protection and Shielding Division, Carlsbad NM, April 3-6, 2006

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 2 Introduction  Background  NIH Proposal  Assess accuracy of 3-D coupled electron-photon transport calculations performed with existing discrete-ordinates transport codes  Establish a plan to develop a new deterministic code system optimized for voxel geometries to be used in Radiation Treatment Planning  Presentation  3-D Photon only comparisons – TORT vs EGSnrc (preliminary study for NIH proposal)  Total flux and Energy Deposition  Local (point by point) and Global agreement  1-D Coupled electron-photon comparisons - ANISN vs EGSnrc and MCNP (first portion of NIH proposal)  Investigated effect of mesh size and quadrature order  Did not investigate effect of Legendre Order

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 3 Important Calculation Parameters in 3-D TORT vs EGSnrc Comparisons  Voxel size (TORT mesh size) = 4 mm  Number of voxels = 124 x 62 x 75 =  All voxels contained water (densities = shifted CT number / 1000)  Number of material zones = 1991 (number of different densities)  TORT space mesh and EGSnrc geometry built from reformated CT Scan data obtained from the Department of Radiation Oncology at UNC Chapel Hill

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 4 Important Calculation Parameters in 3-D TORT vs EGSnrc Comparisons  All TORT calculations were performed using:  Fully symmetric S12 quadrature (196 directions)  Optimal xyz nodal flux extrapolation in space  Maximum of 20 inner iterations per group  Space flux convergence criterion of (not all groups converged)  FSD of 0.5 % in isocenter voxel targeted in EGSnrc calculations  Photon cross sections used in TORT taken from Vitamin-B6 fine group library (ENDF/B-VI based)  40 energy groups below 12 MeV  P5 scattering  Photon cross sections used in EGSnrc processed from continuous cross section data supplied with EGSnrc

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 5 Photon Beam Parameters  Photon beam approximated by employing two point sources positioned 100 cm from CT scan isocenter  Collimated component  Isotropic within solid angle subtended by 10 by 10 cm square centered at CT scan isocenter  Normalized to 0.77 photons  Scattered component  Isotropic over cm radius disc also centered at CT scan isocenter  Normalized to 0.23 photons  Energy distribution derived from previously calculated phase space data supplied by Dept. of Radiation Oncology at UNC Chapel Hill

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 6 Photon Beam Parameters

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 7 P3 Scattering Produces More Beam Spread than P5 Scattering and EGSnrc Energy Deposited Sagittal Profiles EGSnrc TORT (p3 scattering) TORT (p5 scattering) blue: 0.1-1%, green: 1-10%, yellow: 10-50%, orange: 50-90%, and red: % of max

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 8 Discrete Ordintates vs Monte Carlo Flux Transverse Profiles Voxel Number Mid-plane Coronal Slice halfway between CT Isocenter and Beam Exit  TORT Calculations  P5 (full) agrees very well with EGSnrc  P5 (2 iter) agrees fairly well  P5 (1 iter) underestimates flux outside beam edge  P3 (full) overestimates flux outside beam edge  P3 (2 iter) better agreement  P3 (1 iter) slightly better agreement  P3 (1 and 2 iter) better agreement purely fortuitous  P5 (2 iter) agreement could result in less computational time – further study required

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 9 Discrete Ordintates vs Monte Carlo Energy Deposited Transverse Profiles Voxel Number Mid-plane Coronal Slice halfway between CT Isocenter and Beam Exit  TORT Calculations (similar agreement)  P5 (full) agrees very well with EGSnrc  P5 (2 iter) agrees fairly well  P5 (1 iter) underestimates energy deposited outside beam edge  P3 (full) overestimates energy deposited outside beam edge  P3 (2 iter) better agreement  P3 (1 iter) slightly better agreement  Again P3 (1 and 2 iter) better agreement purely fortuitous

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 10 F ractional Frequency Distribution of Voxel Flux Differences in MC Standard Deviations MC Standard Deviations  TORT Calculations  P5 (full) tightly clustered at 0 MC SD’s  P5 (2 iter) clustered at -5 MC SD’s  P5 (1 iter) much larger spread at -15 MC SD’s  P3 (full) slightly less clustered at 0 MC SD’s  P3 (2 iter) slightly less clustered at -5 MC SD’s  P3 (1 iter) similar to P5 (1 iter) distribution  Small number of iters results in less scattering – therefore less particles of all energies outside beam resulting smaller total tracklengths

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 11 F ractional Frequency Distribution of Voxel Energy Deposited Differences in MC Standard Deviations MC Standard Deviations  TORT Calculations  P5 (full) tightly clustered at 0 MC SD’s  P5 (2 iter) also tightly clustered at -5 MC SD’s  P5 (1 iter) clustered less at ~ -2 MC SD’s  P3 (full) larger spread at ~ - 5 MC SD’s  P3 (2 iter) similar to P3 (full)  P3 (1 iter) slightly less clustered than P3(2 iter) and P3(1 iter)  Again less scattering – however high energy particles contribute more to energy deposition thus effect of less scattering is reduced  P5 (2 iter) may be adequate ?

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 12 Comparison of CPU Times: TORT vs EGSnrc

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 13 Recent 1-D Coupled Photon-Electron Calculations  Isotropic photon source in 1 cm interval at entrance to phantom  ANISN photon cross sections  40 group P5 Vitamin-B6 (same as used in TORT)  40 group P15 (same group structure as Vitamin-B6) generated by CEPXS  Both sets of photon cross sections produced similar results  ANISN electron cross sections  40 group (linear energy grid) P15 from CEPXS-BFP (Russian modified version of CEPXS)  Original CEPXS – smooth component of scattering adjusted using diamond difference approximation on CSD term to relate group boundary fluxes and group fluxes (as expected ANISN would not run with these cross sections)  Modified CEPXS (CEPXS-BFP) – smooth component adjusting using double 2-step approximation to relate fluxes  Photon and electron cross sections used in EGSnrc and MCNP processed from continuous cross section data supplied with both codes

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 14 Position of Voxels used in 1-D Model indicated on CT Images

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 15 1-D Model Density as a Function of Depth

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 16 Comparison of 1-D Calculated Total Photon Flux vs Depth in Phantom  Large differences in first 7 voxels is artificial and due to low density (void)  MCNP and EGSnrc total photon fluxes are almost identical  ANISN total photon flux approximately 4 percent lower in all non void voxels  ANISN calculated same total photon fluxes using both Vitamin-B6 and CEPXS cross sections  Reason for 4 % difference not known (under investigation)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 17 Comparison of 1-D Calculated Total Electron Flux vs Depth in Phantom  Again large differences in first 7 voxels is artificial and due to low density  EGSnrc total electron flux is approximately 5 % lower than MCNP total electron flux in non void voxels  Reason for difference is unknown  ANISN total electron flux lies between MCNP and EGSnrc values - closer to MCNP except around voxels 37 and 56

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 18 Mesh Size has Little Effect on ANISN Calculated Total Electron Flux  Reduce mesh from 4 mm to 2 mm to 1 mm since  Density in voxels 35 – 40 approximately 4 times higher than surrounding voxels  Density in voxels approximately 10 times higher than surrounding voxels  Decreasing mesh size  Improves agreement with MCNP around voxel 56  Produces little change around voxel 37  Similar changes occur using S32 and S64 quadratures  Overall effect minimal

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 19 Higher Order Quadratures Improve ANISN Total Electron Flux  ANISN total electron flux agrees very well with MCNP total electron flux with S32 and S64 quadratures  Very little difference between S32 and S64 quadratures  S20 (next higher order quadrature above S16) also improved agreement with MCNP  Although not shown, agreement with MCNP also improves between voxels 15 and 27  Note: All the ANISN results were obtained using double Pl quadratures – similar results were obtained using fully symmetric quadratures

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 20 Closing Remarks  Photon Only Calculations  3-D deterministic transport codes (TORT)  can yield accurate dose distributions in anatomical voxel based models when compared to MC codes  with less computational cost (than MC codes), and  possibly much less cost if few collisions are required  Coupled Electron-Photon Calculations  1-D deterministic transport codes (ANISN) using currently available cross sections  can yield reasonable agreement with MC codes  with significantly less computational cost  Further Effort  Investigate photon discrepancy between ANISN and MC codes (possibly due to poor choice of model)  Investigate electron flux MC discrepancies (MCNP vs EGSnrc) – MC calculated energy deposited agreed very well  Similar couple electron-photon calculation with TORT (1-D, 2-D, and 3-D)  Boltzmann-Fokker-Planck equation needed ?