The Steady-State Spatially Resolved Reflectance of a Three-Layered Mismatched Medium

Near-IR radiation is often utilized to detect the properties in tissues, up to now, a semi-infinite medium photon migration model and a two-layered turbid medium model are applied widely. In this paper, we set up the steady-state photon diffusion model of three-layered mismatched medium. We utilize the diffuse equation to solve a three-layered mismatched medium and obtain the accurate solution of a three-layered mismatched medium of the steady state in tissue. We find that the solution of a three-layered mismatched medium diffusion equation not only accord with the Monte-Carlo simulation, but can still solve the problems of a two-layered turbid medium model.     

平稳状态下匹配介质三层漫射方程的空间分辨漫反射

如果应用漫射方程分析和确定生物表面组织的光学特性,就能够确定生物活体是否发生病变,实现生物活体的无损探测。目前,光在生物体内传播常用的基本模型是半无限厚模型和两层介质模型。而实际上,人体组织为多层介质。根据漫射方程理论,在平稳状态条件下,使用外推边界条件,精确给出了匹配介质中平稳状态下三层体系光的漫射方程格林函数的解。通过此解,可以算出空间分辨漫反射。使用蒙特卡罗方法来验证三层体系的漫射方程,发现我们给出的理论解,不仅可以包括与Kienle的结论一致的两层体系模型的空间分辨漫反射的解,而且三层体系漫射方程的空间分辨漫反射解和蒙特卡罗方法基本一致。     

不匹配介质三层漫射方程的时间分辨漫反射

生物体的表面组织是一个不匹配的多层介质,大多数研究人员研究匹配介质的漫射方程,将组织表面看作折射率相同的介质。为更好的理解光在生物体内的传播,建立了不匹配条件的三层半无限厚频域方程的解;并对频域进行傅里叶变换,计算出时域的时间分辨漫反射。为了验证此的理论,使用蒙特卡罗方法进行仿真研究,结果表明该理论研究不仅和蒙特卡罗方法高度一致,而且还可以解决两层不匹配介质模型。     

The Infrared Ray Transport in an N-Layered Matched Skin

Infrared ray (IR) has great potential in medical diagnosis and therapy. In order to detect tumor in skin, we set up the steady-state and time domain IR diffusion model of an n-layered matched medium with an infinitely thick. We utilize the diffuse equation to solve a five-layered infinite matched medium and obtain the accurate solution of a matched medium of the steady state and time domain in tissue. We compare the steady-state spatially resolved reflectance calculated with Monte-Carlo simulations. The Monte-Carlo simulation shows that the solution is valid. Our equation can be used to obtain the tumor information in medical diagnosis and therapy.     

Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

The paper focuses on the determination of statistical characteristics of photon distributions in a semi-infinite turbid medium, specifically the photon average trajectory and the root-mean-square deviation of photons from the average trajectory, with an approach based on the diffusion approximation to the radiative transfer equation. We show that the Dirichlet and Robin boundary conditions used for this purpose give close results. We derive exact analytical expressions for the case of the Dirichlet boundary condition. To demonstrate the practical value of our results we consider approximate solution of the inverse problem of time-domain diffuse optical tomography with the flat layer transmission geometry. The problem is solved with the method of photon average trajectories which are constructed with analytical expressions derived for a semi-infinite medium.     

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.     

Photon-transport forward model for imaging in turbid media

A photon-transport forward model for image reconstruction in turbid media is derived that treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation. This model can conveniently replace the commonly used diffusion approximation in optical tomography. An analytical expression of the background Green's function is obtained from the cumulant solution of the Boltzmann equation. Our model provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. Numerical comparisons between this model and the standard and center-moved diffusion models are presented.     

Modeling of Raman-Scattering Signals in Biological Tissues by Direct and Two-Step Approaches

A search for an effective method of modelling of the Raman-spectroscopy problem in turbid (scattering) media has been performed taking into account the corresponding parameters of the detector and sample volume. A solution of the radiative-transfer equation by Monte-Carlo method underlies the proposed model. Two fundamental approaches to numerical modeling of Raman scattering are considered: the direct transport problem of Rayleigh and Raman photons at each point of the medium and the two-step model, in which a photon flux in the medium is calculated in the first stage, followed by generation of the corresponding number of Raman photons at each point.     

聚焦光束在半无限大生物组织内传播的Monte Carlo模拟

分析了聚焦光束在介质中的传播情况,利用VC++语言编制了一套平圆光束聚焦在半无限大生物组织内传播的Monte Carlo模拟程序,对几种不同参数值的情况进行了模拟,通过对模拟结果的分析,得出了平圆光束聚焦在半无限大生物组织内传播的规律。     

连续光在生物组织中能流率分布的漫射近似和模拟

分析了半无限大介质漫射近似不同边界条件的镜像光源结构,用镜像光源的方法给出了连续光入射时稳态能流率分布的漫射近似表达式,并用Monte Carlo方法对能流率分布进行模拟,分析了两种模型能流率分布的特点及其形成的机理;用Monte Carlo模拟结果检验了能流率分布漫射近似的精度,结果表明:漫射近似采用EBC边界条件的结果有较高的精度和计算较简单等优点,为能流率分布的快速准确计算提供了依据.     

二维稳态辐射传输方程的有限差分求解法

针对扩散光学层析在小动物成像中的应用问题并基于混浊介质空间光子三维散射的实际物理效应,提出的二维稳态辐射传输方程的有限差分数值求解新方法.在此基础上,研究了不同的空间剖分网格和角度离散密度对求解准确度的影响,并通过将所提方法与蒙特卡洛模拟进行比对,验证方法的正确性.研究表明：在均匀组织体内,当离散角度达到一定数量时,由辐射传输方程的有限差分解获得的透射面和侧面的光子密度对空间网格大小并不敏感,而在反射面上光子密度计算则需要较密的空间网格才能够达到一定准确度.本研究为发展基于辐射传输方程的扩散光学层析理论奠定了基础.     

在多层结构的生物组织中近红外光子迁移的研究

在无损近红外光学诊断领域中,研究光子在多层生物组织中的迁移十分重要。本文以猪的脂肪和肌肉组成的两层结构作为研究的样品。将近红外光源和检测器置于脂肪的表面,由光源发出被两层组织反射的光子的一部分由检测器所接收。本文给出了光电流与光源到检测器的距离的关系以及光电流与脂肪厚度的关系。为了分析实验结果,用蒙特卡罗仿真计算光子在均匀介质中迁移轨迹,用菲涅耳定律来决定光子包在脂肪和肌肉边界处的折射分量和反射分量。结果表明,仿真数据与实验符合得很好。结论是：本文中所提供的实验和仿真方法对于分析光子在生物组织中的迁移以及优化传感器设计十分有用。     

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.     

Nonuniqueness in optical tomography: relevance of the P1 approximation

The question of whether a unique distribution of the absorption coefficient, the scattering coefficient, and the refractive index of a turbid medium can be reconstructed by optical tomography is considered. A recent publication [Opt. Lett. 23, 882 (1998)] established that such reconstruction is not possible when photon transport is well modeled by the diffusion equation. A simple proof is offered that, when measurements at high modulation frequencies are included, the more exact P1 model of light transport suggests that this reconstruction may be possible.     

Light transport model in a n-layered mismatched tissue

The steady-state and time-domain analytical solutions of the diffusion equation for photon migration through a highly scattering n-layered mismatched medium have been obtained. The effect of the refractive-index mismatch is taken into account, and the extrapolated boundary condition has been considered. A Monte Carlo code for photon migration through an n-layered mismatched medium has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the photon migration, while reflectance is observed.     

A Model of Irradiance Distribution for a Directed Point Source in an Infinite Weakly Absorbing Turbid Medium

We propose simple models describing the irradiance distributions for a unidirectional point source in an infinite weakly absorbing turbid medium and also for a narrow light beam obliquely incident on the boundary of a semi-infinite turbid medium. These models involve the same optical parameters of the medium as the formulas of the diffusion approximation of radiation-transport theory. At the same time, the condition of weak anisotropy of the radiation field does not limit the applicability of our models.     

光在多层匹配生物组织中的时域传输模型

建立了匹配介质的n层半无限厚频域方程的解,并对频域进行傅里叶变换,计算出时域方程的时间分辨漫反射（Time-resolved Reflectance）.为检验漫射模型的准确性,将时间分辨漫反射与蒙特卡罗（Monte Carlo）模拟结果进行了比较,结果表明两者符合得很好.研究表明：该时域漫射模型可以判断生物组织和病变的光学特性.     

Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.     

Discrete Green's Function for Lattice Random Walk

A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue.