Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations

We present a finite-element-based algorithm for reconstruction of fluorescence lifetime and yield in turbid media, using frequency-domain data. The algorithm is based on a set of coupled diffusion equations that describe the propagation of both excitation and fluorescent emission light in multiply scattering media. Centered on Newton's iterative method, we implemented our algorithm by using a synthesized scheme of Marquardt and Tikhonov regularizations. A low-pass spatial filter is also incorporated into the algorithm for enhancing image reconstruction. Simulation studies using both noise-free and noisy data have been performed with the nonzero photon density boundary conditions. Our results suggest that quantitative images can be produced in terms of fluorescent lifetime and yield values and location, size, and shape of heterogeneities within a circular background region.