Sassaroli Angelo, Blaney Giles, Martelli Fabrizio, Fantini Sergio
Department of Biomedical Engineering, Tufts University, 4 Colby Street, Medford, MA, 02155, USA.
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Florence, Italy.
Sci Rep. 2024 Dec 28;14(1):31266. doi: 10.1038/s41598-024-82682-3.
We propose an overview of the Rytov approximation in diffuse optics of biological tissues, for the inverse and forward problems. First, we show a physical interpretation of the Rytov approximation as a type of partial pathlength (named fluence rate partial pathlength) which is distinct from the usual partial pathlength for reflectance measurements. Second, we study the accuracy of the Rytov approximation for the calculation of Jacobians considering absorption perturbations and reflectance measurements. For higher absorption and lower reduced scattering values the discrepancy between the true Jacobian (i.e., the reflectance partial pathlength) and that obtained with the Rytov approximation (i.e., the fluence rate partial pathlength) can be up to about 70% for diffusion theory calculations and up to about 25% for Monte Carlo simulations. For higher reduced scattering values, the discrepancies become less than 10%. Third, we propose a calibration method that can circumvent numerical inaccuracies when the calculation of Jacobians is carried out in presence of highly absorbing layers. Finally, fourth, we also propose an original formula derived from the Rytov approximation for reflectance measurements, and we show how it performs for the forward problem, when we consider defects with large absorption contrast with respect to the background.
我们针对生物组织漫射光学中的逆问题和正向问题，对里托夫近似进行了概述。首先，我们展示了里托夫近似的一种物理解释，即将其视为一种与用于反射率测量的常规部分光程不同的部分光程（称为fluence率部分光程）。其次，我们研究了在考虑吸收扰动和反射率测量的情况下，里托夫近似用于计算雅可比矩阵的准确性。对于较高的吸收和较低的约化散射值，在扩散理论计算中，真实雅可比矩阵（即反射率部分光程）与通过里托夫近似获得的矩阵（即fluence率部分光程）之间的差异可达约70%，在蒙特卡罗模拟中可达约25%。对于较高的约化散射值，差异小于10%。第三，我们提出了一种校准方法，当在存在高吸收层的情况下进行雅可比矩阵计算时，该方法可以规避数值不准确性。最后，第四，我们还提出了一个从里托夫近似推导得出的用于反射率测量的原始公式，并展示了在考虑相对于背景具有大吸收对比度的缺陷时，该公式在正向问题中的表现。
