Inverse Models for Diffuse Optical Molecular Tomography

In this article, we will present fundamental concepts and mathematical formulations of optical molecular tomography with a focus on bioluminescence tomography (BLT) and fluorescence molecular tomography (FMT). BLT employs a light-emitting marker called luciferases that emit light when certain biochemical environments are encountered, while FMT uses fluorophores that absorb light and reemit it at longer wavelength. Both BLT and FMT recover a spatial distribution of light-emitting biomarkers such as bioluminescent or fluorescent probes inside tissue from measurements of transmitted and/or back-reflected light intensities on the tissue surface. Thus, these two modalities can be used to target and image specific molecules and their pathways associated with diseases or drug effects. State-of-the-art image reconstruction codes for this type of molecular tomography employ a so-called model-based iterative image reconstruction scheme in which a light propagation model in tissue such as the equation of radiative transfer and its diffusion approximation is needed. Depending on how the forward and inverse variables are treated, existing methods can be classified into one of two groups: unconstrained or partial differential equations (PDE)-constrained. In both BLT and FMT, the PDE-constrained approach is similar to the unconstrained approach in terms of accuracy, impact of noise, and robustness to initial guess, but it outperforms its competitor in terms of reconstruction speed. As compared to the unconstrained method, the PDE-constrained approach can increase the speed of an image reconstruction process by a factor of up to 20 or greater, depending on the character of a problem under consideration, thus enabling accurate and fast imaging of the spatial distribution of light-emitting probes inside living organisms or tissue.