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

Transport of light in biological tissues is commonly modelled by solving radiative transfer equation (RTE). In the past only indirect or approximate solutions of RTE were used. Recently, analytical solutions of RTE for specific geometries emerged, yet without a thorough evaluation of convergence and accuracy.

We developed a full analytical framework for solving 2D radiative transfer equation (RTE) in a multilayered system, each layer characterized by its own set of optical properties. The analytical solution in infinite medium was combined with mode matching techniques and transfer matrix approach of solving equations. The intention was to improve the precision and the speed of calculations in comparison to the Monte-Carlo approach (MC), which is the golden standard in the field. The derived framework was thoroughly tested against MC and a complete agreement for a broad range of optical properties and number of layers was obtained.

The developed framework provides significantly faster and accurate alternative to MC. It can be used to facilitate study of light-tissue interactions and to develop novel spectral-spatial algorithms for analysis of biomedical hyperspectral images.