Inverse Problems of Combined Photoacoustic and Optical Coherence Tomography

TL;DR

This paper develops a unified mathematical model for combined photoacoustic and optical coherence tomography, demonstrating that joint imaging provides additional information enabling the reconstruction of optical parameters, which is not possible with individual modalities.

Contribution

It introduces a new mathematical model based on Maxwell's equations for dual PAT and OCT experiments and shows that combined imaging allows for feasible reconstruction of optical parameters.

Findings

Unified Maxwell's equations model for dual imaging

Additional information enables optical parameter reconstruction

Joint modality improves inverse problem feasibility

Abstract

Optical coherence tomography (OCT) and photoacoustic tomography (PAT) are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform PAT and OCT imaging at once. In this paper we present a mathematical model describing the dual experiment. Since OCT is mathematically modelled by Maxwell's equations or some simplifications of it, whereas the light propagation in quantitative photoacoustics is modelled by (simplifications of) the radiative transfer equation, the first step in the derivation of a mathematical model of the dual experiment is to obtain a unified mathematical description, which in our case are Maxwell's equations. As a by-product we therefore derive a new mathematical model of photoacoustic tomography based on Maxwell's equations. It is well known by now, that without additional assumptions on the medium, it is not possible to uniquely reconstruct all optical parameters from either one of these modalities alone. We show that in the combined approach one has additional information, compared to a single modality, and the inverse problem of reconstruction of the optical parameters becomes feasible.