MLDT: an open-source multilayer diffusion theory Python implementation

Diffuse reflectance spectroscopy and imaging are powerful noninvasive tools for quantifying tissue biomarkers such as hemoglobin, melanin, and water. A theoretical model of light propagation is required to interpret these reflectance measurements and translate them into quantitative biomarker concentrations. Although Monte Carlo (MC) simulations offer the gold-standard in accuracy, their high computational burden renders them impractical for real-time iterative inverse solving. Conversely, standard analytical approximations can be efficient but often oversimplify tissue as a semi-infinite homogeneous medium, leading to significant errors when analyzing layered structures.

We aim to develop a generalized, computationally efficient forward model capable of rapidly predicting light transport in complex, multilayered tissue structures.

We present a generalized derivation and open-source Python implementation of the P1 diffusion approximation for predicting diffuse reflectance from tissue with an arbitrary number of layers. This framework utilizes a vectorized banded matrix approach to solve the fluence rate equations efficiently. The model was validated against 400 randomized MC simulations encompassing architectures ranging from one to eight layers.

Diffuse reflectance spectra predicted by the generalized multilayer diffusion theory model show strong agreement with MC simulations in the diffusion regime ( ${\mu }_a\ll {\mu }_s^{\text{'}}$ ), achieving a median spectral root mean square error of 0.0145 across the validation set. Computation times were over 5 orders of magnitude faster than GPU-accelerated MC, yielding a mean calculation time of 0.0087 s to generate a single predicted diffuse reflectance spectrum given a set of input optical properties and a speedup of $\sim 277,607\times$ . Notably, validation results demonstrated that numerical error does not scale with structural complexity, indicating that multilayer architectures maintained high stability.

We provide an accurate, computationally efficient, and generalized tool for modeling light transport in stratified media. By combining the ability of MC modeling to simulate complex tissue structures, with the speed of analytical diffusion methods, this tool facilitates real-time, depth-resolved quantitative tissue profiling. The full source code is made freely available to the community.