GPU-based fast gamma index calculation

The γ-index dose comparison tool has been widely used to compare dose distributions in cancer radiotherapy. The accurate calculation of γ-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 (Ju et al 2008 Med. Phys. 35 879-87) with a radial pre-sorting technique (Wendling et al 2007 Med. Phys. 34 1647-54) and implement them on computer graphics processing units (GPUs). The developed GPU-based γ-index computational tool is evaluated on eight pairs of IMRT dose distributions. The γ-index calculations can be finished within a few seconds for all 3D testing cases on one single NVIDIA Tesla C1060 card, achieving 45-75× speedup compared to CPU computations conducted on an Intel Xeon 2.27 GHz processor. 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 speeds up the GPU calculation by about 2.7-5.5 times. For n-dimensional dose distributions, γ-index calculation time on CPU is proportional to the summation of γ(n) over all voxels, while that on GPU is affected by γ(n) distributions and is approximately proportional to the γ(n) summation over all voxels. We found that increasing the resolution of dose distributions leads to a quadratic increase of computation time on CPU, while less-than-quadratic increase on GPU. The values of dose difference and distance-to-agreement criteria also have an impact on γ-index calculation time.