Investigation of Nonuniform Dose Voxel Geometry in Monte Carlo Calculations

The purpose of this work is to investigate the efficacy of using multi-resolution nonuniform dose voxel geometry in Monte Carlo (MC) simulations. An in-house MC code based on the dose planning method MC code was developed in C++ to accommodate the nonuniform dose voxel geometry package since general purpose MC codes use their own coupled geometry packages. We devised the package in a manner that the entire calculation volume was first divided into a coarse mesh and then the coarse mesh was subdivided into nonuniform voxels with variable voxel sizes based on density difference. We name this approach as multi-resolution subdivision (MRS). It generates larger voxels in small density gradient regions and smaller voxels in large density gradient regions. To take into account the large dose gradients due to the beam penumbra, the nonuniform voxels can be further split using ray tracing starting from the beam edges. The accuracy of the implementation of the algorithm was verified by comparing with the data published by Rogers and Mohan. The discrepancy was found to be 1% to 2%, with a maximum of 3% at the interfaces. Two clinical cases were used to investigate the efficacy of nonuniform voxel geometry in the MC code. Applying our MRS approach, we started with the initial voxel size of 5 × 5 × 3 mm(3), which was further divided into smaller voxels. The smallest voxel size was 1.25 × 1.25 × 3 mm(3). We found that the simulation time per history for the nonuniform voxels is about 30% to 40% faster than the uniform fine voxels (1.25 × 1.25 × 3 mm(3)) while maintaining similar accuracy.