摘要
传统的漫射方程均假设生物组织在纵向上是半无限厚的,横向上是无限大的。针对某些在横向上不是无限大的生物组织(如前臂和手指),建立了一个任意多层矩形生物组织漫射模型,该模型假设生物组织在纵向上是半无限厚的、多层的,在横向上是个矩形。在矩形边界条件下,根据光在生物介质中传播的漫射方程,结合外推边界条件,建立并给出了光在半无限厚稳态多层矩形介质中的漫射方程的精确解,利用建立的模型计算了空间分辨漫反射,同时编写相应的蒙特卡罗模拟程序,验证方程的正确性。建立的方程不但能解决横向上是矩形的介质问题,还能解决横向上无限大、纵向上半无限厚的介质问题,更能解决在横向上x或y轴之一是无限大、另一个轴是有限大小的组织问题。
The assumption that biological tissues are semi-infinite in the longitudinal direction and infinite in the transverse direction is applied in traditional diffusion equations. Aiming at the biological tissues, e.g. forearms and fingers, that are not infinite in the transverse direction, a diffusion model for random multi- layer rectangular biological tissues is established. It is assumed that biological tissues are semi-infinite and multi-layered in the longitudinal direction, and are rectangular in the transverse direction. Under the rectangular boundary conditions, exact solution of the diffusion equation for light in semi-infinite multi-layer rectangular media in steady-state is provided based on the diffusion equation of light propagating in biological media and by combining with the extrapolated boundary conditions. The spatially resolved diffusion is calculated using the established model, and corresponding Monte Carlo simulation is programmed to demonstrate correctness of the equation. The established equation does not only solve the problem of rectangular media in the transverse direction, but also the problem of media that are infinite in the transverse direction and semi-infinite in the longitudinal direction, even the problem of tissues that are infinite in the transverse x or y axial direction and finite in the other axial direction.
出处
《光学学报》
EI
CAS
CSCD
北大核心
2016年第3期167-172,共6页
Acta Optica Sinica
关键词
生物光学
光子迁移
漫射方程
蒙特卡罗模拟
稳态
biotechnology
photon migration
diffusion equation
Monte Carlo simulation
steady-state
