Local analysis for locating a single point target in time-domain fluorescence diffuse optical tomography

Abstract

The time-domain fluorescence diffuse optical tomography (FDOT) problem is to recover the distribution of fluorophores in biological tissue from the time-domain measurement on the boundary. The measurement is conducted by several pairs (S-D pairs) of a point source and a point detector. In this paper, we identify the location of the distribution of fluorophores over a point, refer as a point target. We first express a solution for the forward problem in a dimensionless form and consider its asymptotic expansion. Then, we theoretically investigate the minimal number of S-D pairs to determine the point target location, analyzing the sensitivity matrix. Finally, we numerically verify the invertibility of the matrix and demonstrate the local solvability for locating well-separated multiple point targets.