The Inverse Source Problem in Fluorescence and Bioluminescence Tomography

Bioluminescence tomography (BLT) and fluorescence molecular tomography (FMT) are novel optical reporter probe imaging modalities for studying disease-associated processes on a molecular and cellular level in small animals prior to the development of macroscopic tissue changes. Since biological tissue is highly scattering, direct imaging of optical reporter probes is almost impossible and computational techniques for image reconstruction need to be employed. The underlying mathematical model of these tomographic reconstruction approaches is an ill-posed inverse source problem. The inverse source problem can be solved with local and global optimization methods, which minimize chi squared. The predicted fluorescent and bioluminescent light intensities are calculated by solving the equation of radiative transfer (ERT) with finite-difference discrete-ordinate techniques, or by solving the simplified spherical harmonics (SPN) equations.

Numerical techniques for image reconstruction in FMT and BLT will be presented, which include different light propagation models based on the ERT, gradient-based optimization techniques for minimizing the error function in FMT, an adjoint differentiation technique for calculation the search directions, and an evolution strategy for finding the bioluminescent source distributions in BLT. Image reconstruction results of three-dimensional mouse models will be shown as well.