A direct voxel tracking method for four-dimensional Monte Carlo dose calculations in deforming anatomy

In this work we present a method of calculating dose in deforming anatomy where the position and shape of each dose voxel is tracked as the anatomy changes. The EGSnrc/DOSXYZnrc Monte Carlo code was modified to calculate dose in voxels that are deformed according to deformation vectors obtained from a nonlinear image registration algorithm. The defDOSXYZ code was validated by consistency checks and by comparing calculations against DOSXYZnrc calculations. Calculations in deforming phantoms were compared with a dose remapping method employing trilinear interpolation. Dose calculations with the deforming voxels agree with DOSXYZnrc calculations within 1%. In simple deforming rectangular phantoms the trilinear dose remapping method was found to underestimate the dose by up to 29% for a 1.0 cm voxel size within the field, with larger discrepancies in regions of steep dose gradients. The agreement between the two calculation methods improved with smaller voxel size and deformation magnitude. A comparison of dose remapping from Inhale to Exhale in an anatomical breathing phantom demonstrated that dose deformations are underestimated by up to 16% in the penumbra and 8% near the surface with trilinear interpolation.