Approximate peak time to time-domain fluorescence diffuse optical tomography for nonzero fluorescence lifetime

TL;DR

This paper develops an approximate peak time equation for fluorescence diffuse optical tomography with nonzero fluorescence lifetime and introduces algorithms for reconstructing multiple target locations, demonstrating robustness and efficiency through numerical experiments.

Contribution

It derives an explicit approximate peak time equation for nonzero fluorescence lifetime and proposes novel algorithms for locating multiple fluorescent targets in FDOT.

Findings

The approximate peak time equation is numerically verified.

The boundary-scan algorithm effectively reconstructs multiple targets.

Algorithms show robustness against noise and artifacts.

Abstract

This paper concerns an inverse problem for fluorescence diffuse optical tomography (FDOT) reconstructing locations of multiple point targets from the measured temporal response functions. The targets are multiple fluorescent point objects with a nonzero fluorescence lifetime at unknown locations. Peak time, when the temporal response function of the fluorescence reaches its maximum, is a robust parameter of the temporal response function in FDOT because it is most less suffered by the artifacts, such as noise, and is easily determined by experiments. We derive an approximate peak time equation based on asymptotic analysis in an explicit way in the case of nonzero fluorescence lifetime when there are single and multiple point targets. The performance of the approximation is numerically verified. Then, we develop a bisection algorithm to reconstruct the location of a single point target from the algorithm proposed in [4] for the case of zero fluorescence lifetime. Moreover, we propose a boundary-scan algorithm for the reconstruction of locations of multiple point targets. Finally, several numerical experiments are implemented to show the efficiency and robustness of the addressed algorithms.