Bootstrapping and sensitivity analysis for robust recovery of optical coefficients using time domain diffusion theory from bilayered media

Accurate quantification of tissue absorption coefficients from time-domain diffuse reflectance measurements is essential for advancing optical diagnostics and therapeutic monitoring. Here, we present a comprehensive investigation of absorption coefficient recovery in bilayered tissue models, focusing exclusively on this parameter due to its direct clinical relevance in assessing tissue oxygenation, metabolism, and pathology. We generated temporal point spread functions (TPSF) for 64 bilayered tissue configurations using Monte Carlo simulations at a 2 cm source-detector separation (ρ) across three near-infrared wavelengths (690, 760 and 850 nm). An efficient numerical solver for time domain diffusion theory was utilized for the recovery protocol. We first characterized the robustness of our inverse model against uncertainties in refractive index and superficial layer thickness. Sensitivity analysis using root mean square error (RMSE) revealed that uncertainties in refractive indices to up to 5% and superficial layer thickness to up to 50% do not affect the recovery of the top layer and bottom layer absorption significantly. To address the computational burden of multi-parameter optimization, we developed a bootstrapping strategy that employs semi-infinite diffusion theory to constrain both superficial and deep layer scattering coefficients, effectively reducing the inverse problem from four to two free parameters. This approach achieved absorption coefficient recovery with errors below 0.07 cm−1 for both tissue layers while reducing mean computational time nearly ten fold.