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The normalized Born ratio of steady-state fluorescence measurements in a concave or convex-shaped medium geometry is investigated by analytical and numerical methods. The “concave” geometry refers to a scattering-dominant medium enclosed by a long circular cylindrical applicator, and the “convex” geometry refers to a scattering-dominant medium enclosing a long circular cylindrical applicator. The numerical investigation uses finite element- method, and the corresponding analytical evaluation is based upon a recently developed method of treating steady-state photon diffusion in both concave and convex geometries. The steady-state Born ratio associated with a source and a detector located on the medium-applicator interface is examined for the medium to have a homogeneous distribution of fluorophore, and for the source and detector aligning either azimuthally or longitudinally in both concave and convex geometries. At a given set of optical properties and the line-of-sight source-detector distance, the normalized Born ratio is always smaller in concave and greater in convex geometry respectively when comparing to that in semi-infinite geometry. At a given set of optical properties, the rate of increase of the normalized Born ratio versus the line-of-sight source-detector distance is the greatest along the azimuthal direction in convex geometry among the studied cases. The change of the normalized Born ratio caused by containing a target of either positive or negative contrast of fluorophore in the otherwise homogeneous background of fluorophore is also investigated numerically. The results for both homogenous and heterogeneous fluorophore distribution demonstrate that the normalized Born ratio is a geometry-specific parameter that imposes geometrically-specific sensitivity in measurements.
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