  The gamma-index dose comparison tool has been widely used to compare dose
distributions in cancer radiotherapy. The accurate calculation of gamma-index
requires an exhaustive search of the closest Euclidean distance in the
high-resolution dose-distance space. This is a computational intensive task
when dealing with 3D dose distributions. In this work, we combine a geometric
method with a radial pre-sorting technique , and implement them on computer
graphics processing units (GPUs). The developed GPU-based gamma-index
computational tool is evaluated on eight pairs of IMRT dose distributions. The
GPU implementation achieved 20x~30x speedup factor compared to CPU
implementation and gamma-index calculations can be finished within a few
seconds for all 3D testing cases. We further investigated the effect of various
factors on both CPU and GPU computation time. The strategy of pre-sorting
voxels based on their dose difference values speed up the GPU calculation by
about 2-4 times. For n-dimensional dose distributions, gamma-index calculation
time on CPU is proportional to the summation of gamma^n over all voxels, while
that on GPU is effected by gamma^n distributions and is approximately
proportional to the gamma^n summation over all voxels. We found increasing dose
distributions resolution leads to quadratic increase of computation time on
CPU, while less-than-quadratic increase on GPU. The values of dose difference
(DD) and distance-to-agreement (DTA) criteria also have their impact on
gamma-index calculation time.
