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Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues

Kuan Peng, Xinbo Gao, Xiaochao Qu, Nunu Ren, Xueli Chen, Xiaowei He, Xiaorei Wang, Jimin Liang, Jie Tian
School of Electronic Engineering, Xidian University, Xi’an, Shaanxi 710071, China
Applied Optics, Vol. 50, No. 21. (20 July 2011), pp. 3808-3823.

@article{peng2011graphics,

   title={Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues},

   author={Peng, K. and Gao, X. and Qu, X. and Ren, N. and Chen, X. and He, X. and Wang, X. and Liang, J. and Tian, J.},

   journal={Applied Optics},

   volume={50},

   number={21},

   pages={3808–3823},

   year={2011},

   publisher={Optical Society of America}

}

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As a widely used numerical solution for the radiation transport equation (RTE), the discrete ordinates can predict the propagation of photons through biological tissues more accurately relative to the diffusion equation. The discrete ordinates reduce the RTE to a serial of differential equations that can be solved by source iteration (SI). However, the tremendous time consumption of SI, which is partly caused by the expensive computation of each SI step, limits its applications. In this paper, we present a graphics processing unit (GPU) parallel accelerated SI method for discrete ordinates. Utilizing the calculation independence on the levels of the discrete ordinate equation and spatial element, the proposed method reduces the time cost of each SI step by parallel calculation. The photon reflection at the boundary was calculated based on the results of the last SI step to ensure the calculation independence on the level of the discrete ordinate equation. An element sweeping strategy was proposed to detect the calculation independence on the level of the spatial element. A GPU parallel frame called the compute unified device architecture was employed to carry out the parallel computation. The simulation experiments, which were carried out with a cylindrical phantom and numerical mouse, indicated that the time cost of each SI step can be reduced up to a factor of 228 by the proposed method with a GTX 260 graphics card.
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