Implementation of the equation of radiative transfer on block-structured grids for modeling light propagation in tissue.
Implementation of the equation of radiative transfer on block-structured grids for modeling light propagation in tissue.
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DOI：
10.1364/boe.1.000861
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发表时间：
2010-09-14
影响因子：
3.4
通讯作者：
Hielscher AH
中科院分区：
文献类型：
--
作者：
Montejo LD;Klose AD;Hielscher AH
提出了求解三维块结构笛卡尔网格(BSG)频域辐射传递方程(ERT)的第一种算法。与目前可用的结构网格算法相比，该算法能够以更快的速度准确地模拟任意形状的介质中的光在边界处的折射率失配的情况下的传播。为了准确地模拟任意形状的几何图形，该算法生成的BSG只在物理边界附近进行精细离散，因此密度低于精细网格。我们使用迎风步长方法和离散坐标(SN)近似相结合的方法来离散FD-ERT。采用源迭代法求解。当在粗网格和细网格区域之间遍历时，我们实现了一阶内插。利用数值模型(圆形、圆柱形和任意形状)以及改变吸收和散射系数、调制频率和折射率来评估几何和光学参数对算法性能的影响。在三层BSG上得到的解比在单细网格上得到的解快4.2倍，数值误差增加最小(小于5%)。
We present the first algorithm for solving the equation of radiative transfer (ERT) in the frequency domain (FD) on three-dimensional block-structured Cartesian grids (BSG). This algorithm allows for accurate modeling of light propagation in media of arbitrary shape with air-tissue refractive index mismatch at the boundary at increased speed compared to currently available structured grid algorithms. To accurately model arbitrarily shaped geometries the algorithm generates BSGs that are finely discretized only near physical boundaries and therefore less dense than fine grids. We discretize the FD-ERT using a combination of the upwind-step method and the discrete ordinates (SN) approximation. The source iteration technique is used to obtain the solution. We implement a first order interpolation scheme when traversing between coarse and fine grid regions. Effects of geometry and optical parameters on algorithm performance are evaluated using numerical phantoms (circular, cylindrical, and arbitrary shape) and varying the absorption and scattering coefficients, modulation frequency, and refractive index. The solution on a 3-level BSG is obtained up to 4.2 times faster than the solution on a single fine grid, with minimal increase in numerical error (less than 5%).