Beer–Lambert law for optical tissue diagnostics: current state of the art and the main limitations

Abstract

Significance: Beer–Lambert law (BLL) is a widely used tool for contact and remote determination of absorber concentration in various media, including living tissues. Originally proposed in the 18th century as a simple exponential expression, it has survived numerous modifications and updates. The basic assumptions of this law may not be fulfilled in real measurement conditions. This can lead to mistaken or misinterpreted results. In particular, the effects to be additionally taken into account in the tissue measurements include anisotropy, scattering, fluorescence, chemical equilibria, interference, dichroism, spectral bandwidth disagreements, stray radiation, and instrumental effects. Aim: We review the current state of the art and the main limitations of remote tissue diagnostics using the BLL. Historical development of updating this law by taking into account specific additional factors such as light scattering and photon pathlengths in diffuse reflectance is described, along with highlighting the main risks to be considered by interpreting the measured data. Approach: Literature data related to extension and modification of the BLL related to tissue assessment and concentration estimation of specific tissue molecules are collected and analyzed. The main emphasis here is put on the optical measurements of living tissue chromophore concentrations and estimation of physiological parameters, e.g., blood oxygen saturation. Results: Modified expressions of the BLL suitable for several specific cases of living tissue characterization are presented and discussed. Conclusions: Applications of updated/modified Beer–Lambert law (MBLL) with respect to particular measurement conditions are helpful for obtaining more reliable data on the target tissue physiological state and biochemical content. MBLL accounting for the role of scattering in several ways appears to be a successful approach. Extended MBLL and BLL in the time domain form could provide more accurate results, but this requires more time resources to be spent.