Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator V Steady-state fluorescence

Abstract

As Part V in our series, this paper examines steady-state fluorescence photon diffusion in a homogenous medium that contains a homogenous distribution of fluorophores, and is enclosed by a "concave" circular cylindrical applicator or is enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to predict by analytics and examine with the finite-element method the changing characteristics of the fluorescence-wavelength photon-fluence rate and the ratio (sometimes called the Born ratio) of it versus the excitation-wavelength photon-fluence rate, with respect to the source-detector distance. The analysis is performed for a source and a detector located on the medium-applicator interface and aligned either azimuthally or longitudinally in both concave and convex geometries. When compared to its steady-state counterparts on a semi-infinite medium-applicator interface with the same line-of-sight source-detector distance, the fluorescence-wavelength photon-fluence rate reduces faster along the longitudinal direction and slower along the azimuthal direction in the concave geometry, and conversely in the convex geometry. However, the Born ratio increases slower in both azimuthal and longitudinal directions in the concave geometry and faster in both directions in the convex geometry, respectively, when compared to that in the semi-infinite geometry.