Implementierung und Anwendung analytischer und numerischer Verfahren zur Lösung der Maxwellgleichungen für die Untersuchung der Lichtausbreitung in biologischem Gewebe

Abstract

The comprehension of light propagation in biological tissue is of particular importance for the development of optical applications in biomedical diagnostics and therapy. Typically, solutions of the radiative transfer or the diffusion theory are used for this purpose whereas the exact theory in the sense of classical physics is given by Maxwell"s equations. The aim of this work is the investigation of the light propagation in biological tissue based on solutions of Maxwell"s equations. With the presented analytical and numerical solution methods it is possible to calculate the light propagation including all effects due to the wave nature of light and considering the microstructure of the tissue. Starting from single scattering and advancing to multiple scattering calculations, the propagation of light is systematically examined using simple idealized tissue models. Besides the usually calculated far field results, emphasis is put in particular on the investigation of the near fields. Based on the simulation of the scattering by individual particles shadowing and focusing effects are identified in the near field, which are taken into account to explain some phenomena of multiple scattering. In addition, a model is presented which allows to study the coupling between the radiative transfer and the Maxwell theory and to examine the validity of the radiative transfer theory for selected problems quantitatively.