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。

It is highly necessary to study the phenomenon of photon migration in the knee joint for the non-invasive near-infrared optical early diagnosis of the osteoarthritis of the knee. We investigate the migration trace and distribution rule of the photons in knee layered structure, which are simulated by the Monte-Carlo modeling. The proportion of photons which collide with bone tissue then migrate out of the muscle tissue and photons directly migrate out of muscle tissue is calculated. For analyzing the signal-to-noise ratio to determine the accurate position of the detector, we perform quantitative evaluations of distribution of photons, as well as qualitative assessments of the distribution of photons.

The accuracy of the background optical properties has a considerable effect on the quality of reconstructed images in near-infrared functional brain imaging based on continuous wave diffuse optical tomography (CW-DOT). We propose a region stepwise reconstruction method in CW-DOT scheme for reconstructing the background absorption and reduced scattering coefficients of the two-layered slab sample with the known geometric information. According to the relation between the thickness of the top layer and source–detector separation, the conventional measurement data are divided into two groups and are employed to recon-struct the top and bottom background optical properties, respectively. The numerical simulation results demonstrate that the proposed method can reconstruct the background optical properties of two-layered slab sample effectively. The region-of-interest reconstruction results are better than those of the conventional simultaneous reconstruction method.

Laminar optical tomography (LOT) is a new mesoscopic functional optical imaging technique. Currently, the forward problem of LOT image reconstruction is generally solved on the basis of Monte-Carlo (MC) methods. However, considering the nonlinear nature of the image reconstruction in LOT with the increasing number of source positions, methods based on MC take too much computation time. This letter develops a fast image reconstruction algorithm based on perturbation MC (pMC) for reconstructing the absorption or scattering image of a slab medium, which is suitable for LOT or other functional optical tomography system with narrow source-detector separation and dense sampling. To calculate the pMC parameters, i.e., the path length passed by a photon and the collision numbers experienced in each voxel with only one baseline MC simulation, we propose a scheme named as the trajectory translation and target voxel regression (TT&TVR) based on the reciprocity principle. To further speed up the image reconstruction procedure, the weighted average of the pMC parameters for all survival photons is adopted and the region of interest (ROI) is extracted from the raw data to save as the prior information of the image reconstruction. The method is applied to the absorption reconstruction of the layered inhomogeneous media. Results demonstrate that the reconstructing time is less than 20 s with the X-Y section of the sample subdivided into 50 \times 50 voxels, and the target size quantitativeness ratio can be obtained in a satisfying accuracy in the source-detector separations of 0.4 and 1.25 mm, respectively.

Monte Carlo (MC) method is a statistical method for simulating photon propagation in media in the optical molecular imaging field. However, obtaining an accurate result using the method is quite time-consuming, especially because the boundary of the media is complex. A voxel classification method is proposed to reduce the computation cost. All the voxels generated by dividing the media are classified into three types (outside, boundary, and inside) according to the position of the voxel. The classified information is used to determine the relative position of the photon and the intersection between photon path and media boundary in the MC method. The influencing factors and effectiveness of the proposed method are analyzed and validated by simulation experiments.

The Monte Carlo code MCML (Monte Carlo modeling of light transport in multi-layered tissue) has been the gold standard for simulations of light transport in multi-layer tissue, but it is ineffective in the presence of three-dimensional (3D) heterogeneity. New techniques have been attempted to resolve this problem, such as MCLS, which is derived from MCML, and tMCimg, which draws upon image datasets. Nevertheless, these approaches are insufficient because of their low precision or simplistic modeling. We report on the development of a novel model for photon migration in voxelized media (MCVM) with 3D heterogeneity. Voxel crossing detection and refractive-index-unmatched boundaries were considered to improve the precision and eliminate dependence on refractive-index-matched tissue. Using a semi-infinite homogeneous medium, steady-state and time-resolved simulations of MCVM agreed well with MCML, with high precision (～100%) for the total diffuse reflectance and total fractional absorption compared to those of tMCimg (<70%). Based on a refractive-index-matched heterogeneous skin model, the results of MCVM were found to coincide with those of MCLS. Finally, MCVM was applied to a two-layered sphere with multi-inclusions, which is an example of a 3D heterogeneous media with refractive-index-unmatched boundaries. MCVM provided a reliable model for simulation of photon migration in voxelized 3D heterogeneous media, and it was developed to be a flexible and simple software tool that delivers high-precision results.

To provide a computational efficient forward model with moderate accuracy for rapid 3D optical tomography in small volumes, radiative transport in the delta-P1 approximation combined with the approximation of the reciprocity was examined. Perturbations of optical signals caused by absorption and fluorescence heterogeneities submerged in a resin-based liquid phantom with background parameters close to rat brain tissues were measured using a recently constructed laminar optical tomography system. These measured perturbations were used to examine the theoretically calculated fluence perturbations based on the delta-P1 approximation and the reciprocity approximation. Results show that the errors between the predicted and measured data are acceptable, especially for fluorescence perturbations.

Monte Carlo algorithm and Stokes-Mueller formalism are used to simulate the propagation behavior of polarized light in turbid media. The influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media is discussed. Single and double scattering photons form the major part of backscattered polarization patterns, while multiple scattering photons present more likely as background. Further quantitative analyses show that single scattering approximation and double scattering approximation are quite accurate when discussing the polarization patterns near the incident point.

A new method of Monte Carlo simulation is developed to simulate the photon migration path in a scattering medium after an ultrashort-pulse laser beam comes into the medium. The most probable trajectory of photons at an instant can be obtained with this method. How the photon migration paths are affected by the optical parameters of the scattering medium is analyzed. It is also concluded that the absorption coefficient has no effect on the most probable trajectory of photons.

Our preliminary results on two-dimensional (2D) optical tomographic imaging of hemodynamic changes in a preterm infant brain are reported. We use the established 16-channel time-correlated single photon counting system for the detection and generalized pulse spectrum technique based algorithm for the image reconstruction. The experiments demonstrate that diffuse optical tomography may be a potent means for investigating brain functions and neural development of infant brains in the perinatal period.