Bouza Domínguez Jorge, Bérubé-Lauzière Yves
Laboratoire TomOptUS, Département de Génie Electrique et de Génie Informatique, Faculté de Génie, Université de Sherbrooke, 2500 boulevard Université, Sherbrooke, Québec J1K 2R1, Canada.
Appl Opt. 2010 Mar 10;49(8):1414-29. doi: 10.1364/AO.49.001414.
We present a simplified spherical harmonics approximation for the time-domain radiative transfer equation including the source-divergence effect. This leads to a set of coupled partial differential equations (PDEs) of the parabolic type that model diffuse light propagation in biological-tissue-like media. We introduce a finite element approach for solving these PDEs, thereby obtaining the time-dependent spatial profile of the fluence. We compare the results with the diffusion equation and Monte Carlo simulations. The fluence obtained via our model is shown to reproduce well the Monte Carlo results in all cases and improves on the solution of the diffusion equation in homogeneous diffusive-defying media. Our solution also shows more sensitivity than the diffusion equation to changes in the absorption coefficient of small inclusions.
我们提出了一种简化的球谐函数近似，用于包含源发散效应的时域辐射传输方程。这导致了一组抛物型的耦合偏微分方程（PDE），用于模拟类似生物组织介质中的漫射光传播。我们引入了一种有限元方法来求解这些PDE，从而获得通量随时间变化的空间分布。我们将结果与扩散方程和蒙特卡罗模拟进行了比较。通过我们的模型获得的通量在所有情况下都能很好地再现蒙特卡罗结果，并且在均匀的抗扩散介质中比扩散方程的解有所改进。我们的解对小内含物吸收系数的变化也比扩散方程表现出更高的敏感性。
