摘要
为了提取生物组织的光学特性,需要建立光在生物组织中传输的方程。P3方程是对波尔兹曼传输方程的三阶近似,相比一阶近似的扩散方程,P3方程更加准确。本文基于多层扩散方程,建立了在任意多层半无限厚介质中光传输的P3方程的稳态解和时域解,并提供了空间分辨漫反射和时间分辨漫反射的计算方法。与光在多层介质中传播的蒙特卡罗模拟进行比较,结果显示,P3方程的稳态和时域解正确地描述了光在混浊介质中的传输。对比P3稳态方程和扩散稳态方程,在吸收系数较小时,发现在近光源处,P3稳态方程比扩散方程更加准确,远离光源处,P3方程与扩散方程结果一致。在吸收系数较大时,P3方程精度更高。对比P3时域方程和扩散时域方程,多层介质的P3方程在峰值附近比扩散时域方程更接近蒙特卡罗模拟。这表明多层介质的P3方程为研究更加复杂的生物组织的正向和逆向问题奠定了基础。
Objective In tissue optics,the optical characteristics and parameters of tissues can be obtained by utilizing the diffused light from the tissue surface,which can also predict the characteristic parameters of tissue structure.This can help understand the tissue pathology degree and changes in physiological properties.Various models have been studied in light transmission modeling to describe the light transmission behavior in tissues.Common theoretical models include the Boltzmann equation,diffusion equation,and P3 equation,where the diffusion equation is a first-order approximation of the Boltzmann equation,and the P3 equation is a third-order approximation.We aim to investigate the light transmission behavior in multi-layered media and provide the P3 steady-state equation for light transmission in multi-layered biological tissues with semi-infinite thicknesses.Meanwhile,this equation is extended to the frequency domain equation and transformed into the time domain equation by Fourier transforms at different frequencies,which serves as a third-order approximation of the radiation transfer theory.Our objective is to evaluate the P3 equation accuracy compared to the firstorder diffusion equation in complex multi-layered biological tissues,and thus validate the accuracy by comparisons with different parameter settings.Methods Based on the study of the diffusion equation describing the light transmission in multi-layered media with semiinfinite thicknesses,we combine it with the P3 equation for single-layered media to successfully build the steady-state model of the P3 equation applicable to light transmission in multi-layered biological tissues,and elucidate the boundary conditions.By adopting Fourier transforms and extrapolated boundary conditions,we obtain the functional solution of the P3 steady-state model for light transmission in multi-layered biological tissues.To validate this model,we employ Monte Carlo simulation as a standard non-experimental verification method.Additionally,we calculate and compare the
作者
王喜昌
Wang Xichang(School of Physics and Electronic Information,Yantai University,Yantai 264005,Shandong,China)
出处
《光学学报》
EI
CAS
CSCD
北大核心
2024年第11期169-178,共10页
Acta Optica Sinica
关键词
生物医学光学
P3方程
辐射传输方程
扩散方程
蒙特卡罗模拟
biomedical optics
P3 equation
radiation transfer equation
diffusion equation
Monte Carlo simulation
