RTE-based bioluminescence tomography: A theoretical study

Abstract

Molecular imaging has become a rapidly developing area in biomedical imaging. Bioluminescence tomography (BLT) is an emerging and promising molecular imaging technology. Light propagation within biological media is accurately described by the radiative transfer equation (RTE). However, due to the difficulties in theoretical investigation and numerical simulations, so far, the study of BLT problems has been largely based on a diffusion approximation of the RTE. In this article, we provide a rigorous theoretical foundation for the study of the RTE-based BLT. After a discussion of the forward problem of the RTE and its numerical approximation, we establish a comprehensive mathematical framework for the RTE-based BLT problem through Tikhonov regularization. We show the solution existence, uniqueness and continuous dependence on the data for the regularized formulation. We then introduce stable numerical methods for the BLT reconstruction and show convergence of the numerical solutions. Finally, we present simulation results from a numerical example to demonstrate that reasonable numerical results can be expected from solving the RTE-based BLT problem via regularization.