A general framework for integration of bioluminescence tomography and diffuse optical tomography

Abstract

Diffuse optical tomography (DOT) and bioluminescence tomography (BLT) are different but complementary modalities in optical molecular imaging. The goal of DOT is to reconstruct optical parameters of a medium from surface measurements induced by external sources, whereas that of BLT is to reconstruct running a bioluminescent source distribution in the medium from surface measurements induced by internal bioluminescent sources. A pre-requisite for BLT reconstruction is knowledge on the distribution of optical parameters within the medium, which is the output of DOT. In this paper, we propose a mathematical model integrating BLT and DOT at the fundamental level; that is, performing the two types of reconstructions simultaneously instead of doing them sequentially. The model is introduced through minimizing the difference between predicted quantities and boundary measurements, as well as incorporating regularization terms. In practice, the optical parameters are assumed to be piecewise constants or piecewise smooth functions. Hence, we seek the optical parameters in the space of functions with bounded variation (BV). For the BV-regularized data-fitting functional and its discretized approximations, we demonstrate the existence of minima and show convergence of the minima of the discretized functionals to that of the non-discretized one. We also present numerical results to illustrate the strength of our proposed model.