Radiative transport theory for optical molecular imaging

We study the inverse fluorescent source problem for optical molecular imaging. In particular, we recover key properties of a fluorescent source inside a halfspace composed of a uniform absorbing and scattering medium from angularly resolved measurements at the boundary plane. We use the radiative transport equation to model the multiple scattering of light in tissues. Using Green’s function, given as an analytical expansion in plane wave solutions, we subtract contributions from the measured angular data due to surface sources yielding a quantity that depends only on the interior fluorescent source. We analyse this reduced problem and obtain explicit solutions for a point source and a voxel source. Using the point source and voxel source solutions, we estimate the location, size and total strength of a general source. We perform numerical studies to validate this theory as well as investigate modelling errors due to incorrectly assumed optical properties of the medium.