Title:
A correction scheme for a simplified analytical random walk model algorithm of proton dose calculation in distal Bragg peak regions.

Abstract:
The lateral homogeneity assumption is used in most analytical algorithms for proton dose, such as the pencil-beam algorithms and our simplified analytical random walk model. To improve the dose calculation in the distal fall-off region in heterogeneous media, we analyzed primary proton fluence near heterogeneous media and propose to calculate the lateral fluence with voxel-specific Gaussian distributions. The lateral fluence from a beamlet is no longer expressed by a single Gaussian for all the lateral voxels, but by a specific Gaussian for each lateral voxel. The voxel-specific Gaussian for the beamlet of interest is calculated by re-initializing the fluence deviation on an effective surface where the proton energies of the beamlet of interest and the beamlet passing the voxel are the same. The dose improvement from the correction scheme was demonstrated by the dose distributions in two sets of heterogeneous phantoms consisting of cortical bone, lung, and water and by evaluating distributions in example patients with a head-and-neck tumor and metal spinal implants. The dose distributions from Monte Carlo simulations were used as the reference. The correction scheme effectively improved the dose calculation accuracy in the distal fall-off region and increased the gamma test pass rate. The extra computation for the correction was about 20% of that for the original algorithm but is dependent upon patient geometry.