Quantitative photoacoustic tomography: modeling and inverse problems.

Significance: Quantitative photoacoustic tomography (QPAT) exploits the photoacoustic effect with the aim of estimating images of clinically relevant quantities related to the tissue's optical absorption. The technique has two aspects: an acoustic part, where the initial acoustic pressure distribution is estimated from measured photoacoustic time-series, and an optical part, where the distributions of the optical parameters are estimated from the initial pressure. Aim: Our study is focused on the optical part. In particular, computational modeling of light propagation (forward problem) and numerical solution methodologies of the image reconstruction (inverse problem) are discussed. Approach: The commonly used mathematical models of how light and sound propagate in biological tissue are reviewed. A short overview of how the acoustic inverse problem is usually treated is given. The optical inverse problem and methods for its solution are reviewed. In addition, some limitations of real-life measurements and their effect on the inverse problems are discussed. Results: An overview of QPAT with a focus on the optical part was given. Computational modeling and inverse problems of QPAT were addressed, and some key challenges were discussed. Furthermore, the developments for tackling these problems were reviewed. Although modeling of light transport is well-understood and there is a well-developed framework of inverse mathematics for approaching the inverse problem of QPAT, there are still challenges in taking these methodologies to practice. Conclusions: Modeling and inverse problems of QPAT together were discussed. The scope was limited to the optical part, and the acoustic aspects were discussed only to the extent that they relate to the optical aspect.