基于自然边界条件求解辐射传输方程的方法  

A Finite Difference Method to Solve Radiative Transfer Equation with Natural Boundary Condition

作　　者：金蒙[1] 高峰[1,2] 马文娟[1] 杨芳[1] 赵会娟[1,2] 

机构地区：[1]天津大学精密仪器与光电子工程学院,天津300072 [2]天津市生物医学检测技术与仪器重点实验室,天津300072

出　　处：《天津大学学报》2011年第9期816-822,共7页Journal of Tianjin University(Science and Technology)

基　　金：国家自然科学基金资助项目(30870657;30970775);国家重点基础研究发展计划(973计划)资助项目(2006CB705700);国家高技术研究发展计划(863计划)资助项目(2009AA02Z413);天津市自然科学基金资助项目(09JCZDJC18200;10JCZDJC17300)

摘　　要：基于零内向流边界条件的辐射传输方程是目前被广泛采用的描述有限组织体中光子传播过程的模型.由于生物组织体及其周围介质之间折射率的差异,零内向流边界条件无法准确模拟光子到达边界时的传播过程,从而导致了实际应用中对光学参数的重建存在明显误差.为解决这一问题,建立了考虑边界内反射效应的自然边界条件下的辐射传输方程模型,发展了一种结合立体角元离散法和有限差分法的自然边界条件稳态辐射传输方程求解算法,并通过与蒙特卡洛模拟结果的对比验证了该算法的正确性.The radiative transfer equation （RTE） with the inflow-zero boundary condition is currently increasingly adopted as a universally applicable photon-migration model in the tissues. However, since biological tissues have normally different refractive indexes from the surroundings such as air, this inflow-zero boundary condition can not accurately model the behavior of photons that hit the boundary, leading to large errors in retrieval or image reconstruction of the optical properties. To overcome the limitations, the natural boundary condition that takes into account the internal reflection effect should be considered. A joint discrete-ordinate and finite-difference solution to the steadystate RTE with the natural boundary condition is proposed and validated by comparison with the Monte-Carlo simula- tions.

关 键 词：辐射传输方程 有限差分方法 边界条件 扩散光学层析成像 

分 类 号：Q63[生物学—生物物理学]