Generalized Beer-Lambert model for near-infrared light propagation in thick biological tissues.

The attenuation of near-infrared (NIR) light intensity as it propagates in a turbid medium like biological tissue is described by modified the Beer–Lambert law (MBLL). The MBLL is generally used to quantify the changes in tissue chromophore concentrations for NIR spectroscopic data analysis. Even though MBLL is effective in terms of providing qualitative comparison, it suffers from its applicability across tissue types and tissue dimensions.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation.

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part I: zero and extrapolated boundary conditions.

The mathematical model for diffuse fluorescence spectroscopy/imaging is represented by coupled partial differential equations (PDEs), which describe the excitation and emission light propagation in soft biological tissues. The generic closed-form solutions for these coupled PDEs are derived in this work for the case of regular geometries using the Green's function approach using both zero and extrapolated boundary conditions. The specific solutions along with the typical data types, such as integrated intensity and the mean time of flight, for various regular geometries were also derived for both time- and frequency-domain cases.