Arridge S R, Schweiger M, Hiraoka M, Delpy D T
Department of Computer Science, University College London.
Med Phys. 1993 Mar-Apr;20(2 Pt 1):299-309. doi: 10.1118/1.597069.
The use of optical radiation in medical physics is important in several fields for both treatment and diagnosis. In all cases an analytic and computable model of the propagation of radiation in tissue is essential for a meaningful interpretation of the procedures. A finite element method (FEM) for deriving photon density inside an object, and photon flux at its boundary, assuming that the photon transport model is the diffusion approximation to the radiative transfer equation, is introduced herein. Results from the model for a particular case are given: the calculation of the boundary flux as a function of time resulting from a delta-function input to a two-dimensional circle (equivalent to a line source in an infinite cylinder) with homogeneous scattering and absorption properties. This models the temporal point spread function of interest in near infrared spectroscopy and imaging. The convergence of the FEM results are demonstrated, as the resolution of the mesh is increased, to the analytical expression for the Green's function for this system. The diffusion approximation is very commonly adopted as appropriate for cases which are scattering dominated, i.e., where mu s >> mu a, and results from other workers have compared it to alternative models. In this article a high degree of agreement with a Monte Carlo method is demonstrated. The principle advantage of the FE method is its speed. It is in all ways as flexible as Monte Carlo methods and in addition can produce photon density everywhere, as well as flux on the boundary. One disadvantage is that there is no means of deriving individual photon histories.
在医学物理学中，光辐射在治疗和诊断的多个领域都具有重要意义。在所有情况下，辐射在组织中传播的解析且可计算的模型对于有意义地解释这些过程至关重要。本文介绍了一种有限元方法（FEM），用于推导物体内部的光子密度及其边界处的光子通量，假设光子输运模型是辐射传输方程的扩散近似。给出了针对特定情况的模型结果：计算二维圆形（等同于无限圆柱体中的线源）在具有均匀散射和吸收特性的情况下，由狄拉克函数输入所产生的作为时间函数的边界通量。这模拟了近红外光谱和成像中感兴趣的时间点扩散函数。随着网格分辨率的提高，有限元方法的结果收敛于该系统格林函数的解析表达式。对于散射占主导的情况，即μs >> μa，扩散近似被广泛认为是合适的，其他研究人员已将其与其他替代模型进行了比较。本文展示了与蒙特卡罗方法的高度一致性。有限元方法的主要优点是速度快。它在各方面都与蒙特卡罗方法一样灵活，此外还能在各处产生光子密度以及边界处的通量。一个缺点是无法推导单个光子的历史。
