Sassaroli Angelo, Pifferi Antonio, Contini Davide, Torricelli Alessandro, Spinelli Lorenzo, Wabnitz Heidrun, Di Ninni Paola, Zaccanti Giovanni, Martelli Fabrizio
J Opt Soc Am A Opt Image Sci Vis. 2014 Mar 1;31(3):460-9. doi: 10.1364/JOSAA.31.000460.
In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt.18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.
在本文中，在对文献进行批判性综述之后，我们提出了两种正向求解器以及一种新方法，用于描述在扩散介质中嵌入完全吸收性内含物的情况下，时间域和连续波（CW）域中的光子迁移。第一种正向求解器是一种基于应用于扩散方程（DE）的高阶微扰理论的启发式方法[表示为八阶微扰理论（EOPT）]。第二种正向求解器[表示为具有等价关系的八阶微扰理论（EOPTER）]是通过将EOPT求解器与等价关系（ER）的采用相结合而获得的[《生物医学光学杂志》18, 066014 (2013)]。这些正向求解器可能会克服先前方法的一些明显局限性，比如所谓香蕉形区域背后的理论，或者在存在高吸收或完全吸收性内含物时扩散方程的精确解析解。我们还提出了等价关系，以便根据具有有限吸收对比度和重新缩放体积的另一种内含物来重新表述完全吸收性内含物的问题。例如，我们已经展示了这种方法如何确实可以用于用玻恩近似来模拟黑色内含物。通过与蒙特卡罗模拟结果进行比较，我们已经表明EOPTER求解器能够以小于约10%的误差对完全吸收性内含物进行建模，而EOPT求解器的误差小于约20%，其性能大大优于先前提出的求解器所观察到的性能。
