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Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical parameter estimation is an ill-posed inverse problem, and thus it is sensitive to measurement and modeling errors. In this work, we propose a novel way to solve the inverse problem of quantitative photoacoustic tomography based on the perturbation Monte Carlo method. Monte Carlo method for light propagation is a stochastic approach for simulating photon trajectories in a medium with scattering particles. It is widely accepted as an accurate method to simulate light propagation in tissues. Furthermore, it is numerically robust and easy to implement. Perturbation Monte Carlo maintains this robustness and enables forming gradients for the solution of the inverse problem. We validate the method and apply it in the framework of Bayesian inverse problems. The simulations show that the perturbation Monte Carlo method can be used to estimate spatial distributions of both absorption and scattering parameters simultaneously. These estimates are qualitatively good and quantitatively accurate also in parameter scales that are realistic for biological tissues. [ABSTRACT FROM AUTHOR]

• Bayesian framework enables accurate estimates and reliability assessment. • Modeling errors can be compensated using Bayesian methods. • Modeling of the errors improves the reliability of the credibility estimates. In quantitative photoacoustic tomography, the aim is to reconstruct distributions of optical parameters of an imaged target from an initial pressure distribution obtained from ultrasound measurements. In order to obtain accurate and quantitative information on the optical parameters, modeling light transport in the target is required. Utilizing an approximative model for light transport would be favorable to reduce the computational cost, but the modeling errors of the approximative model can result in significant errors in the reconstructions. In this work, we approach the image reconstruction problem of quantitative photoacoustic tomography in the Bayesian framework. We utilize the Bayesian approximation error method to compensate for the modeling errors between the diffusion approximation and Monte Carlo model for light transport. The approach is studied with two-dimensional numerical simulations with varying optical parameters and noise levels. The results show that Bayesian approximation error method can be used to reduce the effects of the modeling errors in quantitative photoacoustic tomography in a wide range of optical parameters. [ABSTRACT FROM AUTHOR]