^{1,a)}, Michael J. Price

^{1}, John L. Horton Jr.

^{1}, Todd A. Wareing

^{2}and Firas Mourtada

^{3,b)}

### Abstract

The goal of this work was to calculate the dose distribution around a high dose-ratebrachytherapy source using a multi-group discrete ordinates code and then to compare the results with a Monte Carlo calculated dose distribution. The unstructured tetrahedral mesh discrete ordinates code Attila™ version 6.1.1 was used to calculate the photon kerma rate distribution in water around the Nucletron microSelectron mHDRv2 source. MCNPX 2.5.c was used to compute the Monte Carlo water photon kerma rate distribution. Two hundred million histories were simulated, resulting in standard errors of the mean of less than overall. The number of energy groups, (angular order), (scattering order), and mesh elements were varied in addition to the method of analytic ray tracing to assess their effects on the deterministic solution. Water photon kerma rate matrices were exported from both codes into an in-house data analysis software. This software quantified the percent dose difference distribution, the number of points within and , and the mean percent difference between the two codes. The data demonstrated that a 5 energy-group cross-section set calculated results to within of a 15 group cross-section set. was sufficient to resolve the solution in angle. expansion of the scattering cross-section was necessary to compute accurate distributions. A computational mesh with 55 064 tetrahedral elements in a 30 cm diameter phantom resolved the solution spatially. An efficiency factor of 110 with the above parameters was realized in comparison to MC methods. The Attila™ code provided an accurate and efficient solution of the Boltzmann transport equation for the mHDRv2 source.

The authors are grateful to Scientific Publications and Steven M. Kirsner, M.S., for their help in editing and reviewing this manuscript.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. DM code and the LBTE method of solution

II.A.1. Ray-tracing technique for mitigation of ray-effects

II.B. Monte Carlo code

II.C. source design, simulation geometry modeling, and radiation transport

II.C.1. Attila™ transport geometry and simulation

II.C.2. MCNPXtransport geometry and simulation

II.C.3. Data analysis and comparisons

III. RESULTS AND DISCUSSION

III.A. Energy groups

III.B. order

III.C. Scattering order

III.D. Ray-tracing style

III.E. Mesh refinement

IV. CONCLUSIONS

### Key Topics

- Monte Carlo methods
- 41.0
- Photons
- 19.0
- Dosimetry
- 10.0
- Brachytherapy
- 5.0
- Electron scattering
- 5.0

## Figures

The left-hand diagram is the MCNPX and Attila™ model of the mHDRv2 source. The origin is at the center of the active source core. The right-hand diagram is the Attila™ unstructured tetrahedral mesh of the source core, stainless steel shell and 2 mm segment of cable. All units are in millimeters.

The left-hand diagram is the MCNPX and Attila™ model of the mHDRv2 source. The origin is at the center of the active source core. The right-hand diagram is the Attila™ unstructured tetrahedral mesh of the source core, stainless steel shell and 2 mm segment of cable. All units are in millimeters.

Percent difference distributions between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) (left) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (b) (right) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. This figure demonstrates that using a higher order mitigates ray-effects.

Percent difference distributions between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) (left) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (b) (right) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. This figure demonstrates that using a higher order mitigates ray-effects.

Percent difference distribution between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (b) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (c) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh.

Percent difference distribution between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (b) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh. (c) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the medium mesh.

Percent difference distribution between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the coarse mesh. (b) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the fine mesh.

Percent difference distribution between Attila™ and MCNPX dose calculations for the mHDRv2 source. (a) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the coarse mesh. (b) is the 5 energy group, , , trace to quadrature points-quadratic simulation on the fine mesh.

## Tables

Statistics related to the Attila™ and MCNPX calculations for 15 and 5 energy groups, and order, ray-tracing style, and mesh size. TQr indicates trace to quadrature points-quartic, TC indicates trace to quadrature points-cubic, TQ indicates trace to quadrature points-quadratic, and TL indicates trace to quadrature points-linear. Fine indicates the 92 235 element mesh, Medium indicates the 55 064 element mesh, Coarse indicates the 41 072 element mesh, and time.

Statistics related to the Attila™ and MCNPX calculations for 15 and 5 energy groups, and order, ray-tracing style, and mesh size. TQr indicates trace to quadrature points-quartic, TC indicates trace to quadrature points-cubic, TQ indicates trace to quadrature points-quadratic, and TL indicates trace to quadrature points-linear. Fine indicates the 92 235 element mesh, Medium indicates the 55 064 element mesh, Coarse indicates the 41 072 element mesh, and time.

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