生物组织中光场分布的有限元分析

基于对脑组织多层结构特殊性的认识,将有限元方法应用到脑组织的光场分布模拟研究中,即通过区域划分和分片插值确定基函数,并根据变分原理推导了辐射传输方程在边界条件下的泛函,进而得到每个单元的特征式和整个场的联立方程式,可求解联立方程式得到光场分布的模拟结果.最后,进一步讨论了有限元方法的合理性选择问题,给出有限元方法的适用条件是吸收系数远小于散射系数的生物组织.将此方法和蒙特卡罗方法模拟的光场分布进行比较,结果表明,有限元方法对脑组织内的光场分布模拟相当精确,同时模拟所用的时间大大缩短.

Finite Element Analysis of Light Propagation in Tissue

For the specific multi-layer structure of brain tissue, finite element analysis(FEA) is used to simulate light distribution in the brain tissue.By using basis function obtained by finite element division and interpolation in each element,and the extensive function of the diffusion equation with the boundary condition deduced according to variational principles,the eigenfunction of every element and the joint equations of the whole field are obtained.Finally,the reasonable range of FEA application is discussed.A conclusion is that FEA is applicable when tissue absorption coefficient is far less than their scattering coefficient.Then this method is compared with the Monte Carlo(MC) method.Results show that the FEA method has a accurate resolution and the calculation time is greatly decreased.