A gradient-based method for quantitative photoacoustic tomography using the radiative transfer equation

Abstract

Quantitative photoacoustic tomography (QPAT) offers the possibility of high-resolution molecular imaging by quantifying molecular concentrations in biological tissue. QPAT comprises two inverse problems: (1) the construction of a photoacoustic image from surface measurements of photoacoustic wave pulses over time, and (2) the determination of the optical properties of the imaged region. The first is a well-studied area for which a number of solution methods are available, while the second is, in general, a nonlinear, ill-posed inverse problem. Model-based inversion techniques to solve (2) are usually based on the diffusion approximation to the radiative transfer equation (RTE) and typically assume the acoustic inversion step has been solved exactly. Here, neither simplification is made: the full RTE is used to model the light propagation, and the acoustic propagation and image reconstruction are included in the simulations of measured data. Since Hessian- and Jacobian-based minimizations are computationally expensive for the large data sets typically encountered in QPAT, gradient-based minimization schemes provide a practical alternative. The acoustic pressure time series were simulated using a k-space, pseudo-spectral time domain model, and a time-reversal reconstruction algorithm was used to form a set of photoacoustic images corresponding to four illumination positions. A regularized, adjoint-assisted gradient inversion using a finite element model of the RTE was then used to determine the optical absorption and scattering coefficients.