Three-dimensional Scheme for Time-domain Fluorescence Molecular Tomography Based on Laplace Transforms with Noise-robust Factors

As a visualizing and quantitative method, Fluorescence Molecular Tomography (FMT) has many potential applications in biomedical field and its three-dimensional (3D) implementation is needed in both theory and practice. In this paper, we propose a 3D scheme for time-domain FMT within the normalized Born-ratio formulation. A finite element method solution to the Laplace transformed time-domain coupled diffusion equations is employed as the forward model, and the resultant linear inversions at two distinct transform-factors are solved with an algebraic reconstruction technique to separate fluorescent yield and lifetime images. The algorithm is validated using simulated data for 3D cylinder phantoms, and the spatial resolution and quantitativeness of the reconstruction assessed. We demonstrate that the proposed approach can accurately retrieve the positions and shapes of the targets with high spatial resolution and quantitative accuracy, and tolerate a signal-to-noise ratio down to 25dB by appropriately choosing the transform factors.