球谐函数法解点源辐射传输方程的P3近似及其在生物组织中的应用

计算物理 ›› 2009, Vol. 26 ›› Issue (1): 101-106.

球谐函数法解点源辐射传输方程的P3近似及其在生物组织中的应用

柴成钢

华中农业大学理学院, 湖北武汉 430070

收稿日期:2007-07-25 修回日期:2008-01-25 出版日期:2009-01-25 发布日期:2009-01-25
作者简介:柴成钢(1966-),男,湖南临湘,博士生,从事激光与组织相互作用机理研究.
基金资助:
华中农业大学科技创新基金(52204-010025)资助项目

P3 Approximation in Spherical Harmonics Method for Radiative Transfer Equation and Application in Biological Tissues

CHAI Chenggang

Science College, Huazhong Agricultural University, Wuhan 430070, China

Received:2007-07-25 Revised:2008-01-25 Online:2009-01-25 Published:2009-01-25

摘要/Abstract

摘要： 辐射传输方程在球坐标下的P3近似是一个非线性微分方程组,其齐次解为球Bessel函数.需要将球Bessel函数分解为指数函数,才能用参数变异法求出它的特解.由于球Bessel函数在r=0的奇异性,无法利用Marshak和其它近似边界条件,因此直接利用能量守恒,和当介质的吸收系数比约化散射系数小得多时P3近似等于P1近似这个特点,确定全解中的常数.比较Monte Carolo模拟和P3近似理论的解析解发现,P3近似能处理约化散射系数与吸收系数之比介于2~10之间的生物组织.

关键词: 辐射传输方程, P3近似, 参数变异法, 球Bessel函数

Abstract: P3 approximation of raditive transfer equation in spherical coordinate results nonlinear differential equations.Their solution are spherical Bessel functions. Particular solutions are obtained with variation of parameters in exponenital representation of spherical Bessel functions.Approximation boundary condition of Marshak and others can not be satisfied due to solution discontinuity at r=0.It is solved by energy conservation with approximation of P3 by P1 as absorption coefficient is much lower than reduced scattering coefficient.Compared with Monte Carlo and analytic solutions of P3 approximation,it is found that P3 approximation deals with biological tissues with ratios of reduced scattering coefficient to absorption coefficient from 2 to 10.

Key words: radiative transfer equation, P3 approximation, method of variation of parameters, spherical Bessel function

中图分类号:

Q682

柴成钢. 球谐函数法解点源辐射传输方程的P3近似及其在生物组织中的应用[J]. 计算物理, 2009, 26(1): 101-106.

CHAI Chenggang. P3 Approximation in Spherical Harmonics Method for Radiative Transfer Equation and Application in Biological Tissues[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(1): 101-106.