Quantitative photoacoustic tomography by stochastic search: direct recovery of the optical absorption field

Single-stage approach for estimating optical parameters in spectral quantitative photoacoustic tomography

In quantitative photoacoustic tomography, the optical parameters of a target, most importantly the concentrations of chromophores such as deoxygenated and oxygenated hemoglobin, are estimated from photoacoustic data measured on the boundary of the target. In this work, a numerical approximation of a forward model for spectral quantitative photoacoustic tomography is constructed by utilizing the diffusion approximation for light propagation, the acoustic wave equation for ultrasound propagation, and spectral models of optical absorption and scattering to describe the wavelength dependence of the optical parameters. The related inverse problem is approached in the framework of Bayesian inverse problems. Concentrations of four chromophores (deoxygenated and oxygenated hemoglobin, water, and lipid), two scattering parameters (reference scattering and scattering power), and the Grüneisen parameter are estimated in a single-stage from photoacoustic data. The methodology is evaluated using numerical simulations in different full-view and limited-view imaging settings. The results show that, utilizing spectral data and models, the spectral optical parameters and the Grüneisen parameter can be simultaneously estimated. Furthermore, the approach can also be utilized in limited-view imaging situations.

One-step fluorescence photoacoustic tomography with the optical radiative transfer model

We present adjoint-based Jacobian as well as gradient evaluations and corresponding reconstruction schemes to solve the fully nonlinear, optical radiative transfer modeled one-step fluorescence photoacoustic tomographic (FPAT) problem, which aims to reconstruct the map of absorption coefficient of the exogenous fluorophore from boundary photoacoustic data. The radiative transport equation (RTE) and frequency-domain photoacoustic equation have been employed to model light and photoacoustic wave propagation, respectively. Levenberg-Marquardt and Broyden-Fletcher-Goldfarb-Shanno reconstruction schemes have been used corresponding to the evaluated Jacobians and gradients, respectively. Numerical reconstructions obtained from the two schemes have been validated for scattering-dominant as well as nonscattering-dominant media in 2D. To the best of our knowledge, these are the first one-step FPAT reconstruction results in literature based on the optical RTE model.

Gradient-based one-step fluorescence photoacoustic tomography

We propose a gradient-based scheme to solve the fluorescence photoacoustic tomographic (FPAT) problem in a fully nonlinear one-step setting, which aims to reconstruct the map of the absorption coefficient of an exogenous fluorophore from boundary photoacoustic pressure data. Adjoint-based gradient evaluation is presented for the FPAT problem in a frequency-domain photoacoustic equation setting. Numerical validations of the resulting Broyden-Fletcher-Goldfarb-Shanno (BFGS) reconstruction scheme are carried out in two dimensions for full- as well as limited-data test cases, and the results are compared with existing Jacobian-based one-step FPAT reconstructions. The reasonably comparable results of the one-step gradient- and Jacobian-based FPAT reconstruction schemes, coupled with the significant computational savings of the former, potentially set up the one-step gradient-based schemes as an advantageous method of choice for FPAT reconstructions. Further reconstruction studies carried out using quantitative photoacoustic tomography (QPAT)-based chromophore reconstructions as inputs to the FPAT inversions show a robustness of fluorophore absorption coefficient reconstructions to the QPAT-obtained inputs.

Comparative study of one-step and two-step quantitative fluorescence photoacoustic tomography

Fluorescence optical tomography (FOT) is a well-known imaging technique, where fluorescent biological markers are injected to tag targeted tissues (tumors, proteins), and the absorption coefficient of fluorophore is reconstructed to provide contrast-enhanced images. Conventional FOT is known to have lack of stability to noise and shallow imaging depth due to strong optical scattering in biological tissue. Photoacoustic tomography (PAT) has been previously proposed to combine with FOT to resolve this issue. We propose a fully nonlinear one-step reconstruction in a diffuse-approximation modeled fluorescence photoacoustic tomographic (FPAT) setting, where the absorption coefficient of exogenous fluorophore is recovered directly from the photoacoustic data. Computational validations in two dimensions in single- and dual-grid reconstruction settings using full as well as partial data have been provided in support of the proposed algorithm. One-step schemes are particularly useful with respect to dual representations of field (optical and pressure) variables and optical parameters, especially in limited-data settings, which effectively help in constraining the optimization search space. We have compared the results of one- and two-step FPAT schemes and concluded that the one-step reconstructions are superior as compared with the corresponding two-step reconstructions. To the best of our knowledge, these are the first comparisons of one-step and two-step reconstructions in FPAT.

Recent progress in photoacoustic molecular imaging

By acoustically detecting the optical absorption contrast, photoacoustic (PA) tomography (PAT) has broken the penetration limits of traditional high-resolution optical imaging. Through spectroscopic analysis of the target's optical absorption, PAT can identify a wealth of endogenous and exogenous molecules and thus is inherently capable of molecular imaging with high sensitivity. PAT's molecular sensitivity is uniquely accompanied by non-ionizing radiation, high spatial resolution, and deep penetration in biological tissues, which other optical imaging modalities cannot achieve yet. In this concise review, we summarize the most recent technological advancements in PA molecular imaging and highlight the novel molecular probes specifically made for PAT in deep tissues. We conclude with a brief discussion of the opportunities for future advancements.

Uncertainties in the 2004 Sumatra-Andaman source through nonlinear stochastic inversion of tsunami waves

Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems.

Quantitative photoacoustic tomography augmented with surface light measurements

Quantitative photoacoustic tomography is an imaging modality in which distributions of optical parameters inside tissue are estimated from photoacoustic images. This optical parameter estimation is an ill-posed problem and it needs to be approached in the framework of inverse problems. In this work, utilising surface light measurements in quantitative photoacoustic tomography is studied. Estimation of absorption and scattering is formulated as a minimisation problem utilising both internal quantitative photoacoustic data and surface light data. The image reconstruction problem is studied with two-dimensional numerical simulations in various imaging situations using the diffusion approximation as the model for light propagation. The results show that quantitative photoacoustic tomography augmented with surface light data can improve both absorption and scattering estimates when compared to the conventional quantitative photoacoustic tomography.