University of Latvia, Institute of Atomic Physics and Spectroscopy, Biophotonics Laboratory, Riga, Latvia.
J Biomed Opt. 2021 Oct;26(10). doi: 10.1117/1.JBO.26.10.100901.
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.
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.
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.
Modified expressions of the BLL suitable for several specific cases of living tissue characterization are presented and discussed.
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.
比尔-朗伯定律（BLL）是一种广泛用于接触和远程确定各种介质（包括活体组织）中吸收体浓度的工具。该定律最初在 18 世纪提出，是一个简单的指数表达式，经过多次修改和更新得以保留。该定律的基本假设在实际测量条件下可能无法得到满足。这可能导致错误或误解的结果。特别是，在组织测量中需要额外考虑的效应包括各向异性、散射、荧光、化学平衡、干扰、二色性、光谱带宽差异、杂散光和仪器效应。
我们回顾了使用比尔-朗伯定律进行远程组织诊断的最新技术和主要限制。描述了通过考虑特定附加因素（如漫反射中的光散射和光子路径长度）来更新该定律的历史发展，同时强调了在解释测量数据时需要考虑的主要风险。
收集和分析了与组织评估和特定组织分子浓度估计相关的扩展和修改比尔-朗伯定律的文献数据。这里的主要重点是放在活体组织发色团浓度的光学测量和生理参数的估计上，例如血氧饱和度。
提出并讨论了适合几种特定活体组织特性的修正比尔-朗伯定律表达式。
针对特定测量条件的更新/修正比尔-朗伯定律（MBLL）的应用有助于获得有关目标组织生理状态和生化含量的更可靠数据。以多种方式考虑散射作用的扩展 MBLL 和 BLL 似乎是一种成功的方法。扩展的 MBLL 和时间域中的 BLL 可以提供更准确的结果，但这需要花费更多的时间资源。
