J. Tinslay 1, B. Faddegon 2, J. Perl 1 and M. Asai 1 (1) Stanford Linear Accelerator Center, Menlo Park, CA, (2) UC San Francisco, San Francisco, CA Verification of Bremsstrahlung Splitting in Geant4 for Radiotherapy Quality Beams

Purpose To evaluate the impact of applying the uniform bremsstrahlung splitting with charged secondary Russian Roulette variance reduction technique, on a Geant4 based thick target bremsstrahlung benchmark Monte Carlo simulation.

Method and Materials (1) Thick target bremsstrahlung benchmark simulation runs were carried out using recent versions of the Geant4 simulation toolkit. The primary electrons were generated at energies in the range MeV. Target materials of lead, aluminum and beryllium were used. The low energy physics list along with a 0.1 mm range cut was used.

Method and Materials (2) To speed up the simulation, the efficiency change with the following splitting configurations was estimated: Splitting at all generations Splitting at first generation only Splitting at all generations with Russian Roulette played at all generations A splitting factor of 100 was used throughout. The effect on photon fluence was investigated.

1. A.F. Bielajew et al., SLAC-PUB-6499 (1994) Bremsstrahlung Splitting (1) The uniform bremsstrahlung splitting variance reduction technique was first developed as an improvement to the EGS4 Monte Carlo code by Bielajew et al. 1. The method involves doing regular electron transport until a bremsstrahlung interaction occurs. Then, instead of generating one secondary photon, the energy and angular distributions are sampled N times to generate N unique secondary photons.

Bremsstrahlung Splitting (2) The secondaries are assigned a weight, W: Where W e is the weight of the parent electron. The energy of the electron is reduced by the energy of just one photon. To further increase the efficiency of the Monte Carlo, unnecessary electron transport can be avoided by playing Russian Roulette with the charged secondaries produced by pair production, photoelectric effect and Compton scattering.

Bremsstrahlung Splitting (3) When Russian Roulette is applied, 1/N charged secondaries will be kept, with their weight increased by a factor of N and the rest discarded. The net effect is that all photons have a relative weight of 1/N, while all electrons have the same weight.

Splitting factor = 100No splitting Scoring Geometry Uniform Bremsstrahlung Splitting

Efficiency Results (1) The efficiency is estimated by comparing the CPU time taken to generate 10 million unbiased events to 0.1 million biased events with a brem-splitting factor of 100. In general, the efficiency drops off as a function of atomic number as more of the bremsstrahlung photons interact in the higher atomic number material. Splitting at all generations without also playing Russian Roulette can result in a degradation of the efficiency for high atomic number materials.

BerylliumAluminumLead Splitting all generations Splitting first generation only Splitting all generations + Russian Roulette Table showing estimated efficiency relative to unbiased Monte Carlo Efficiency Results (2)

2. B.A.Faddegon, C. K. Ross, and D. W. O. Rogers. "Angular Distributions of Bremsstrahlung from 15 MeV Electrons Incident on Thick Targets of Be, Al and Pb", Med Phys 18(4):727 (1991). Fluence Results The following plots show fluence comparisons as a function of angle and energy, along with a comparison to data 2, for both bremsstrahlung splitting and bremsstrahlung splitting with Russian Roulette. The results indicate the photon fluence and energy and angular distributions are properly calculated when using both bremsstrahlung splitting and bremsstrahlung splitting with Russian Roulette.

Conclusions Reasonable speedup can be achieved through the use of uniform bremsstrahlung splitting with charged secondary Russian Roulette in Geant4. It is more efficient to use bremsstrahlung splitting with charged secondary Russian Roulette, rather than bremsstrahlung splitting alone. Photon fluence and energy and angular distributions are properly calculated with bremsstrahlung splitting and bremsstrahlung splitting with Russian Roulette.