二维稳态辐射传输方程的有限差分求解法  

A Finite-Difference-Method Solution to Two-dimensional Steady-State Radiative Transfer Equation

作　　者：金蒙[1] 高峰[1] 李娇[1] 赵会娟[1] 

机构地区：[1]天津大学精密仪器与光电子工程学院,天津300072

出　　处：《光子学报》2010年第9期1594-1601,共8页Acta Photonica Sinica

基　　金：国家自然科学基金(30870657;30978049);国家重点基础研究发展计划(2006CB705700);国家高技术研究发展计划(2009AA02Z413);天津市自然科学基金(09JCYBJC06600)资助

摘　　要：针对扩散光学层析在小动物成像中的应用问题并基于混浊介质空间光子三维散射的实际物理效应,提出的二维稳态辐射传输方程的有限差分数值求解新方法.在此基础上,研究了不同的空间剖分网格和角度离散密度对求解准确度的影响,并通过将所提方法与蒙特卡洛模拟进行比对,验证方法的正确性.研究表明:在均匀组织体内,当离散角度达到一定数量时,由辐射传输方程的有限差分解获得的透射面和侧面的光子密度对空间网格大小并不敏感,而在反射面上光子密度计算则需要较密的空间网格才能够达到一定准确度.本研究为发展基于辐射传输方程的扩散光学层析理论奠定了基础.A novel finite difference method （FDM） solution to the 2-dimensional time-independent radiative transfer equation （RTE） is proposed for small-animal imaging applications, which is based on the real physics of 3-dimensional scattering of a photon in turbid medium. The influences of the angular discretization and the spatially meshing grids on the accuracy of FDM-RTE solution are investigated and a comparison is made between the FDM-RTE calculations to the relevant Monte-Carlo simulation ones for a validation of the proposed method. The comparison shows that, as the number of the discretized solid angles is over 80, the accuracy of the FDM-RTE calculated forward photon density is insensitive to the spatially meshing grids on the transmission and side surfaces but on the reflection surface. This study provides a viable methodology to the development of the RTE-based Diffuse Optical Tomography（DOT） technology.

关 键 词：辐射传输方程 有限差分方法 扩散光学层析 正向问题 

分 类 号：Q63[生物学—生物物理学]