A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media

In this work, development and evaluation of a three-dimensional (3D) finite element model (FEM) based on the diffusion approximation of time-domain (TD) near-infrared fluorescence light transport in biological tissue is presented. This model allows both excitation and fluorescence temporal point-spread function (TPSF) data to be generated for heterogeneous scattering and absorbing media of arbitrary geometry. The TD FEM is evaluated via comparisons with analytical and Monte Carlo (MC) calculations and is shown to provide a quantitative accuracy which has less than 0.72% error in intensity and less than 37 ps error for mean time. The use of the Born-Ratio normalized data is demonstrated to reduce data mismatch between MC and FEM to less than 0.22% for intensity and less than 22 ps in mean time. An image reconstruction framework, based on a 3D FEM formulation, is outlined and simulation results based on a heterogeneous mouse model with a source of fluorescence in the pancreas is presented. It is shown that using early photons (i.e. the photons detected within the first 200 ps of the TPSF) improves the spatial resolution compared to using continuous-wave signals. It is also demonstrated, as expected, that the utilization of two time gates (early and latest photons) can improve the accuracy both in terms of spatial resolution and recovered contrast.