Analytical solutions of radiative transfer equation for analysis of medical hyperspectral images*

Hyperspectral imaging (HIS) is an optical technique providing both spectral and spatial information in one measurement. A big challenge in the medical HIS (diagnostics and surgery) is effective processing of a huge amount of data and extraction of relevant parameters.

An analytical solution of the 2D radiative transfer equation (RTE) was derived for a multi layered biological tissue. The solution represents reflectance from the tissue surface. Each tissue layer was specified by a set of optical properties including refractive index. The solution served as an azimuthal single scattering approximate inverse light transport model for analyzing HSI.

Hyperspectral images of a human forearm were recorded in the 400–1000 nm spectral range. A cuff test was performed to simulate hypo-, hyper- and normoxia of the skin. The inverse RTE was used to determine physiological parameters of the skin (e.g., oxygenation, hemoglobin concentration). A good agreement with the parameters reported in the literature was obtained.

The RTE solutions can be effectively used to analyze medical HSI. The RTE is as accurate but significantly less computationally demanding as the alternative Monte Carlo approach.