# Presentation: 281815

## 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**

## 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**

## 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 = 576600**
**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**

## 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 10-3 (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

## 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 35.35 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**

## Photon Beam Parameters

## 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: 90-100% of max**

## 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**

## 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**

## Fractional 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**

## Fractional 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 ?**

##  Comparison of CPU Times: TORT vs EGSnrc

## 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**

## Position of Voxels used in 1-D Model indicated on CT Images

**Position of Voxels used in 1-D Model indicated on CT Images**

## 1-D Model Density as a Function of Depth

## 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)**

## 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**

## 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 56 - 60 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**

## 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 **

## 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 ?**