Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography

Abstract

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.

Efficient inversion strategies for estimating optical properties with Monte Carlo radiative transport models

“…30; alternative optimization strategies such as back-tracking line-search, or primal dual methods; 50 the use of preconditioning and/or second-order optimization methods; 51 and an in-depth comparison of these nonlinear adaptive models to the alternative approaches such as PMC. 27 In summary, we have successfully demonstrated a means by which stochastic forward models, not directly amenable to standard variational methods for optimization, can be employed efficiently in nonlinear image reconstruction. We expect this concept to lead to many new directions of research in optical image reconstruction.…”

“… 30 ; alternative optimization strategies such as back-tracking line-search, or primal dual methods; 50 the use of preconditioning and/or second-order optimization methods; 51 and an in-depth comparison of these nonlinear adaptive models to the alternative approaches such as PMC. 27 …”

“…11,25,26 However, for the full nonlinear problem, although PMC can be used for calculation of the problem Jacobian, this has to be recomputed at each iteration of, for example, a Gauss-Newton optimization scheme. 27 In this study, if we are to accept a level of variance and imperfection in our forward/adjoint models, this of course raises the question of how much variance is acceptable in order for SGD to be successful? Furthermore, what measure of the variance is the best indicator in terms of efficiency/performance for common Monte Carlo solvers?…”

“…In addition, an ultrasound source is incident on the medium, where the focus ηðrÞ is scanned through the sample. 44,45 Assuming for simplicity an ideal (delta function) ultrasound focus, the data of interest in this case are found to be of the form 46 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 2 7 ; 1 1 6 ; 4 3 9 bðrÞ ¼ ηðrÞΦ q ðrÞΦ m ðrÞ; (27) where Φ q is the fluence resulting from the optical source Q q , and Φ m is the resulting fluence from a virtual source Q m which is reciprocal to the detector J m . 46 From this point, we proceed in similar fashion as in Sec.…”

“… 11 , 25 , 26 However, for the full nonlinear problem, although PMC can be used for calculation of the problem Jacobian, this has to be recomputed at each iteration of, for example, a Gauss–Newton optimization scheme. 27 …”