Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance

Abstract

Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A two-dimensional (2-D) radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimization scheme is then used to recover 2-D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography

“…We refrain from making definite judgments about the performance in relation to other reconstruction methods due to differences in the simulations. However, compared to the previous [17,32,36] reconstructions obtained using the RTE or Monte Carlo as the forward model, those presented here do seem to show a promising quality in general.…”

“…This approach necessitates solving the radiance in several points in space and angular directions which causes challenges to storing the angular solution and having good enough sampling to allow an acceptable level of noise. The approach has been utilized in QPAT in estimating either absorption or scattering while keeping the other one as a known constant [4,17].…”

Three-dimensional quantitative photoacoustic tomography using an adjoint radiance Monte Carlo model and gradient descent

“…To satisfy Eq. (12), a radiance MC algorithm (RMC) 19,31 is used. To obtain the radiance ϕðrÞ, the directional information of the photon traversing a voxel at positionr is stored by depositing the photon weight into the relevant spherical harmonics coefficients ψ lm ðrÞ.…”

“…Gradient-based methods have the potential to overcome these limitations. They have been implemented using the adjoint formalism, [17][18][19] which is applied using a finite element model of the diffusion approximation (DA) to the inversion of measured 3-D phantom images. 20 While the DA is valid in the diffusive regime and can be implemented efficiently, 21,22 highresolution PAT can cover depths in the ballistic and quasiballistic regimes, where the DA may not be valid.…”

“…23 Methods that aim to solve the radiative transfer equation (RTE) directly are computationally expensive and have only been demonstrated in twodimensional (2-D) images so far. [24][25][26][27] Monte Carlo (MC) models have recently gained attention [28][29][30][31] due to their highly parallelized architecture and advances in graphics-processing units and have already been applied to 2-D QPAT inversions 19 and in initial studies with limited parameter space in 3-D. 16,32 In this paper, a method for inverting multiwavelength 3-D images based on an adjoint formulation of a radiance MC model is demonstrated in silico. The challenges that are addressed in this work are (1) the optimization of the objective function using inherently noisy gradients, (2) accounting for the effect of the concentration-dependent Grüneisen parameter, and (3) the representation of the radiance in terms of spherical harmonics.…”