Quantitative Fluorescence Photoacoustic Tomography

Fluorescence photoacoustic tomography (fPAT) is a multimodality biomedical imaging technique that combines high-resolution ultrasound imaging with high-contrast fluorescence optical tomography. In the first step of fPAT, one utilizes the photoacoustic effect to recover the total absorbed energy map inside the media with ultrasound tomography. In the second step, called quantitative fPAT (QfPAT), one uses interior absorbed energy data to recover either the quantum efficiency or the concentration distribution or both of the fluorophores inside the media. The objective of this work is to derive the mathematical model for QfPAT and to study the corresponding inverse problems. We derive some uniqueness and stability results on these inverse problems and propose a few (often explicit) reconstruction algorithms. Numerical simulations based on synthetic data are presented to verify the theory and algorithms proposed.