漫射近似在测量生物组织光学性质中的适用范围

漫射近似理论经常被用来作为测量生物组织光学特性参数实验和方法的理论基础,但是漫射近似理论只是一种对辐射传输理论的近似结果,在一定条件下有其特定的适用范围.为了确定漫射近似理论在活体非侵入式无损测量要求下的适用范围,本文采用Monte Carlo模拟校验的方法,对漫射近似理论和Monte Carlo模拟计算的结果进行了比较,给出了基于单散射反照率a和各向异性因子g的漫射近似理论适用范围数值标准.这一标准为漫射理论的应用提供了参考依据.     

光学相关论题 生物光学

Q63 2005032397 漫射近似在测量生物组织光学性质中的适用范围=Valid- ity of the diffusion approximation in determining the optical properties of biological tissus[刊,中]／李剑平(山东大学信 息科学与工程学院．山东,济南(250100)),陈冰泉∥应用 光学．-2005,26(1).-20-24 采用Monte Carlo模拟校验的方法,对漫射近似理论 和Monte Carlo模拟计算的结果进行了比较,给出了基于     

基于有限元模拟的圆柱边界介质中的光传输

应用有限元模拟方法,在外推边界条件下研究圆柱介质中的光传输问题,讨论了不同光学参数条件下圆柱表面空间分辨反射率和穿透深度的规律,并且与有限元分析、Monte Carlo模拟和解析解方法的结果进行比较.结果表明:有限元模拟的结果与Monte Carlo模拟的结果吻合度很好,其空间反射率在光学参数满足漫射近似条件μ′s/μa≥5时误差小于10%,在非近源区甚至小于5%;穿透深度的值随μ′s/μa值增大而增大.但比Monte Carlo模拟的穿透深度略小,误差不超过7%,且μ′s/μa的值越大时该误差越小.有限元模拟结果比解析解方法的结果误差要更小,解析解方法在μ′s/μa≥5时,其误差在非近源区接近10%,在近源区会超过15%.此外比较了三种方法的计算速度.单次运算有限元模拟用时约385s,甚至比通常用于快速计算的解析解方法(单次运算耗时416s)更快,而Monte Carlo模拟单次运算耗时8~9h.考虑到有限元模拟方法的介质模型构建简便,计算速度快,且模拟结果有着不错的精度,该方法对圆柱边界乃至一般具有曲率的复杂介质中光子辐射传输问题具有非常好的应用前景.     

漫射近似理论的有效使用范围分析

利用蒙特卡罗方法模拟了半无限大生物组织内部深度分辨的光能流率的分布情况。分析了漫射近似理论的有效使用范围。当组织厚度大于 3/ 2个光子的平均自由程时 ,应用漫射近似理论能得到很好的结果 ,反之 ,漫射理论不能使用。也就是说 ,当组织厚度z >0 1875cm时 ,应用漫射理论能得到很好的结果 ;当组织厚度z <0 1875cm时 ,漫射理论不能使用     

基于P3近似的空间分辨漫反射研究

光源附近组织的空间分辨漫反射是近年来生物医学光子学领域的一个研究热点,其目的是发展一种能够测定活体生物组织光学参量的新技术。漫射近似理论研究光源附近组织的空间分辨漫反射具有很大局限性。P3近似理论考虑了相函数的三阶矩,能较准确地描述光源附近组织的光辐射分布。研究了基于P3近似的空间分辨漫反射,从输运理论的PN方程组出发,导出了P3近似方程组和P3近似的格林函数解;阐述了漫射近似与P1近似的关系,给出了外推边界条件下,准直光束近似后的P3近似漫反射率的完整表示,讨论了相函数二阶参量对P3近似漫反射的影响,并与漫射近似和蒙特卡罗模拟结果进行了比较,指出了P3近似的应用范围。     

MCMGP3三维多群P3近似蒙特卡罗中子输运程序基准检验

三维多群P3近似Monte Carlo中子输运程序MCMGP3是为反应堆临界安全计算设计的,它是从连续点截面中－－光孙耦合输运Monte Carlo程序MCNP发展而来,程序用多群截面代替了MCNP程序的连续点截面,但保留了MCNP程序的几何处理能力,计数能力和降低方差技巧及图形功能。能群数可扩展,使用宏观截面或微观截面均可,中子解分布采用P3近似和广义Gaussia求积。多个基准问题结果显示,MCMGP3程序结果与其它方法计算结果符合很好,计算还表明在同样计算精度下,MCMGP3程序的计处时间较MCNP程序少得多。此外,MCMGP3程序还实验了与WIMS程序的连算,可作反应堆全数值模拟。     

矩形微槽道气体流动的速度分布

矩形微槽道的各个流向截面可以局部近似为平面Poiseuille流动,应用信息保存(IP)方法和直接模拟Monte Carlo(DSMC)方法计算了从连续介质区到自由分子流区的平面Poiseuille流动,利用其结果对Beskok-Karniadadis公式和质量流率动理论因子进行修正和重新拟合,给出在整个稀薄气体流动领域都适用的微槽道气体流动速度分布.     

边界条件对生物组织漫射光时域模拟计算的影响

采用蒙特卡洛方法与漫射近似相结合的杂合算法,在不同的边界条件下(零边界条件、外延边界条件、部分流边界条件),对板状生物组织模型的漫射光的时域分布进行了计算,计算结果表明:采用外延边界条件,在保证计算精度的基础上,和单纯的蒙特卡洛方法相比,较大地提高了运算速度.     

两层生物组织光学特性参数无损测量的模拟研究

生物组织的光学特性参数是与疾病的无损光诊断有关的重要的光学参数，一般的测量所应用的模型是假设生物组织为半无限厚的均匀结构。为了更能反映生物组织的真实特性，本文应用两层结构模型，即假设第一层为有限厚的均匀组织，第二层为半无限厚，由漫射方程经过傅立叶变换得到传输方程的漫射解。为检验漫射解的准确性，将漫射解的表面漫射光分布与Monte Carlo模拟结果进行了比较，结果表明两者符合得很好。为了研究由漫射解是否可以获得两层组织的光学特性参数，将漫射解与Monte Carlo模拟数据进行了非线性拟合，反演获得组织的光学特性参数，结果表明，由漫射解可以获得两层组织的有效散射系数和吸收系数。     

有限宽光束在生物组织中传输的蒙特卡罗方法

基于光在生物组织中的传输理论,研究有限宽光束在生物组织中的传输特性.利用入射光强与格林函数进行卷积计算,推导了有限宽光束在圆柱坐标系下的光传输过程,给出了有限宽光束的光传输方程.以高斯光源和平圆光源为例,进一步给出了两种光源的有限宽光束在生物组织中的光传输方程.介绍了Monte Carlo方法原理及模拟光在多层生物组织中的传输过程.给出了典型三层生物组织的散射系数、吸收系数和折射率等光学参数.利用Monte Carlo方法模拟了有限宽光束在三层生物组织中的传输特性,对比研究了高斯光源和平圆光源有限宽光束在三层生物组织传输时光学参数漫透射率、漫反射率和光能流率的变化规律.这些参数的变化规律可为光在生物组织传输的实际应用提供理论指导.     

Alternative boundary conditions for solving optical diffusion equations by a finite difference time domain analysis in three-dimensional scattering medium

Alternative boundary conditions for solving optical diffusion equations in three-dimensional (3-D) scattering medium by a finite difference time domain (FDTD) analysis formulated by the author are proposed. The previous boundary conditions were defined only by fluence rate, which, although essential, is only one factor needed to solve approximated diffusion equations for fluence rate. In this paper, alternative boundary conditions defined both by fluence rate and radiant flux have been proposed for use in the FDTD analysis, which is derived from the two coupled differential equations for fluence rate and radiant flux. It has been become clear that these boundary conditions are almost equivalent to the previous boundary conditions in the FDTD analysis for sufficiently fine grid spacing. For the analysis with coarser grid spacing, the proposed boundary conditions suppress analytical errors, especially in intensity of time-resolved reflectance and transmittance.     

650nm光在Intralipid-10%中分布的测量和分析

本文提出一种用光纤测定光在生物组织模型Iitralipid内部光分布的方法并测定了650nm激光在Iitralipid 10%中的分布,该方法与各向同性球形光纤探头探测组织内光分布是一种互补的方法。实验结果揭示了在生物组织模型中不同方向散射光的分布规律,表明了不同的组织光学参数和不同直径的入射光束与光分布之间的关系;采用外推边界条件的漫射方程解拟合前向散射光的测量数据确定了组织模型的散射系数和吸收系数并得到较好的结果,所测量的光学参数与公开发表的结果比较其差别在2 35%以内。     

Analytical methods of solution of the relaxational equations

The master equations system for rotational, vibrational and chemical kinetics in nonuniform gas flows with the sources is studied. Two approximate analytical methods of its solution for the arbitrary rate constants are developed for the case of the smooth distributions. The first method is based on the introduction of slow variables to the discrete equations. The second one uses WKB solution for diffusion approximation in Fokker-Planck form. The particular cases of harmonic and weakly anharmonic oscillators relaxation are examined.     

Multiple scattering of light in superdiffusive media

Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method. Truncated step length distributions and complex boundary conditions are considered. The profile of a coherent backscattering cone is calculated in the superdiffusion approximation.     

Finite element approximation of the Fokker-Planck equation for diffuse optical tomography

In diffuse optical tomography, light transport theory is used to describe photon propagation inside turbid medium. A commonly used simplification for the radiative transport equation is the diffusion approximation due to computational feasibility. However, it is known that the diffusion approximation is not valid close to the sources and boundary and in low-scattering regions. Fokker-Planck equation describes light propagation when scattering is forward-peaked. In this article a numerical solution of the Fokker-Planck equation using finite element method is developed. Approach is validated against Monte Carlo simulation and compared with the diffusion approximation. The results show that the Fokker-Planck equation gives equal or better results than the diffusion approximation on the boundary of a homogeneous medium and in turbid medium containing a low-scattering region when scattering is forward-peaked.     

短脉冲激光与介质相互作用的扩散模型

推导了扩散近似方程,通过半无限大均匀介质计算,用扩散理论分析解验证了数值方法的有效性.模拟了光在非均匀介质内的传输过程,给出了介质内光通量随时间变化的空间分布.结果表明,该基于扩散模型的数值方法能够模拟短脉冲光在强散射介质中的传播过程以及漫散射光的时间变化特性,并且借助于光通量空间分布能够准确模拟非均匀介质内内含物的位置.     

Image reconstruction in diffuse optical tomography using the coupled radiative transport-diffusion model

The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.     

A new complex variable meshless method for advection–diffusion problems

In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, an improved complex variable meshless method (ICVMM) for two-dimensional advection-diffusion problems is developed. The equivalent functional of two-dimensional advection-diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented. Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper. It is shown that the ICVMM is very effective for advection-diffusion problems, and has good convergent character, accuracy, and computational efficiency.     

Model calculation of ion collection in the presence of sputtering

This paper presents a zero order approximation of ion collection during sputtering. Neglecting diffusion, range shortening and knock-on effects and assuming a constant sputtering yield general analytical results are developed which allow a comparison with experimental data. The accumulation of implantation profiles and the build-up of surface concentrations and collected quantities are described in detail for Gaussian range distributions. A thorough discussion of available experimental results indicates that the model is suitable for a variety of projectile-target combinations, in particular for medium mass noble gas atoms collected in high melting point targets. Application to sputtering experiments presents further evidence of a strong fluence dependence of the silicon sputtering yield. Some comments are devoted to recently reported analytical and numerical treatments of ion collection during sputtering.