Zołek Norbert S, Liebert Adam, Maniewski Roman
Institute of Biocybernetics and Biomedical Engineering PAS, 02-109 Warsaw, ul. Ks. Trojdena 4, Poland.
Comput Methods Programs Biomed. 2006 Oct;84(1):50-7. doi: 10.1016/j.cmpb.2006.07.007. Epub 2006 Sep 7.
The Monte Carlo method is frequently used to simulate light transport in turbid media because of its simplicity and flexibility, allowing to analyze complicated geometrical structures. Monte Carlo simulations are, however, time consuming because of the necessity to track the paths of individual photons. The time consuming computation is mainly associated with the calculation of the logarithmic and trigonometric functions as well as the generation of pseudo-random numbers. In this paper, the Monte Carlo algorithm was developed and optimized, by approximation of the logarithmic and trigonometric functions. The approximations were based on polynomial and rational functions, and the errors of these approximations are less than 1% of the values of the original functions. The proposed algorithm was verified by simulations of the time-resolved reflectance at several source-detector separations. The results of the calculation using the approximated algorithm were compared with those of the Monte Carlo simulations obtained with an exact computation of the logarithm and trigonometric functions as well as with the solution of the diffusion equation. The errors of the moments of the simulated distributions of times of flight of photons (total number of photons, mean time of flight and variance) are less than 2% for a range of optical properties, typical of living tissues. The proposed approximated algorithm allows to speed up the Monte Carlo simulations by a factor of 4. The developed code can be used on parallel machines, allowing for further acceleration.
蒙特卡罗方法因其简单性和灵活性而经常用于模拟浑浊介质中的光传输，它能够分析复杂的几何结构。然而，由于需要追踪单个光子的路径，蒙特卡罗模拟耗时较长。耗时的计算主要与对数函数和三角函数的计算以及伪随机数的生成有关。在本文中，通过对对数函数和三角函数进行近似，开发并优化了蒙特卡罗算法。这些近似基于多项式函数和有理函数，且这些近似的误差小于原始函数值的1%。通过对几个源探测器间距下的时间分辨反射率进行模拟，验证了所提出的算法。将使用近似算法的计算结果与通过精确计算对数函数和三角函数得到的蒙特卡罗模拟结果以及扩散方程的解进行了比较。对于一系列典型的生物组织光学特性，光子飞行时间模拟分布的矩（光子总数、平均飞行时间和方差）的误差小于2%。所提出的近似算法能够将蒙特卡罗模拟加速4倍。所开发的代码可在并行机器上使用，从而实现进一步加速。
