  Quantitative photoacoustic tomography (qPAT) is an imaging technique aimed at
estimating chromophore concentrations inside tissues from photoacoustic images,
which are formed by combining optical information and ultrasonic propagation.
The application of qPAT as a transcranial imaging modality is complicated by
shear waves that can be produced when ultrasound waves travel from soft tissue
to bone. Because of this, the estimation of chromophores distributions near the
skull can be problematic. In this paper, we take steps towards compensating for
aberrations of the recorded photoacoustic signals caused by elastic wave
propagation. With photoacoustic data simulated in a coupled elastic-acoustic
domain, we conduct inversions in a purely acoustic domain. Estimation of the
posterior density of the initial pressure is achieved by inversion under the
Bayesian framework. We utilize the Bayesian approximation error approach to
compensate for the modelling errors arising from approximating a coupled
elastic-acoustic domain with a purely fluid domain. The resulting
reconstructions and corresponding uncertainty estimates are then used to
evaluate the posterior density of the optical absorption parameter. In the
sense of the posterior uncertainty, the results show that the Bayesian
approximation error approach yields a more feasible estimate for the posterior
model of the initial pressure which, in turn, yields a more feasible estimate
for the posterior model of the absorption coefficient.
