Majaron Boris, Milanič Matija, Premru Jan
J Biomed Opt. 2015 Jan;20(1):015002. doi: 10.1117/1.JBO.20.1.015002.
In three-dimensional (3-D) modeling of light transport in heterogeneous biological structures using the Monte Carlo (MC) approach, space is commonly discretized into optically homogeneous voxels by a rectangular spatial grid. Any round or oblique boundaries between neighboring tissues thus become serrated, which raises legitimate concerns about the realism of modeling results with regard to reflection and refraction of light on such boundaries. We analyze the related effects by systematic comparison with an augmented 3-D MC code, in which analytically defined tissue boundaries are treated in a rigorous manner. At specific locations within our test geometries, energy deposition predicted by the two models can vary by 10%. Even highly relevant integral quantities, such as linear density of the energy absorbed by modeled blood vessels, differ by up to 30%. Most notably, the values predicted by the customary model vary strongly and quite erratically with the spatial discretization step and upon minor repositioning of the computational grid. Meanwhile, the augmented model shows no such unphysical behavior. Artifacts of the former approach do not converge toward zero with ever finer spatial discretization, confirming that it suffers from inherent deficiencies due to inaccurate treatment of reflection and refraction at round tissue boundaries.
在使用蒙特卡罗（MC）方法对异质生物结构中的光传输进行三维（3-D）建模时，空间通常通过矩形空间网格离散为光学均匀的体素。相邻组织之间的任何圆形或倾斜边界因此都会变得参差不齐，这引发了人们对在此类边界上光的反射和折射建模结果的真实性的合理担忧。我们通过与一个增强的3-D MC代码进行系统比较来分析相关影响，在该代码中，对解析定义的组织边界进行了严格处理。在我们测试几何形状中的特定位置，两种模型预测的能量沉积可能相差10%。即使是高度相关的积分量，如模拟血管吸收的能量的线密度，也相差高达30%。最值得注意的是，传统模型预测的值随空间离散化步长和计算网格的微小重新定位而强烈且相当不稳定地变化。同时，增强模型没有表现出这种非物理行为。前一种方法的伪像不会随着空间离散化越来越精细而趋近于零，这证实了它由于在圆形组织边界处对反射和折射的处理不准确而存在固有缺陷。
