Efficient implementation of the 3D-DDA ray traversal algorithm on GPU and its application in radiation dose calculation

The three-dimensional digital differential analyzer (3D-DDA) algorithm is a widely used ray traversal method, which is also at the core of many convolution∕superposition (C∕S) dose calculation approaches. However, porting existing C∕S dose calculation methods onto graphics processing unit (GPU) has brought challenges to retaining the efficiency of this algorithm. In particular, straightforward implementation of the original 3D-DDA algorithm inflicts a lot of branch divergence which conflicts with the GPU programming model and leads to suboptimal performance. In this paper, an efficient GPU implementation of the 3D-DDA algorithm is proposed, which effectively reduces such branch divergence and improves performance of the C∕S dose calculation programs running on GPU.

The main idea of the proposed method is to convert a number of conditional statements in the original 3D-DDA algorithm into a set of simple operations (e.g., arithmetic, comparison, and logic) which are better supported by the GPU architecture. To verify and demonstrate the performance improvement, this ray traversal method was integrated into a GPU-based collapsed cone convolution∕superposition (CCCS) dose calculation program.

The proposed method has been tested using a water phantom and various clinical cases on an NVIDIA GTX570 GPU. The CCCS dose calculation program based on the efficient 3D-DDA ray traversal implementation runs 1.42 ∼ 2.67× faster than the one based on the original 3D-DDA implementation, without losing any accuracy.

The results show that the proposed method can effectively reduce branch divergence in the original 3D-DDA ray traversal algorithm and improve the performance of the CCCS program running on GPU. Considering the wide utilization of the 3D-DDA algorithm, various applications can benefit from this implementation method.