Quantitative Photoacoustic Tomography Research Articles

Photoacoustic Quantification of Tissue Oxygenation Using Conditional Invertible Neural Networks.

Intelligent systems in interventional healthcare depend on the reliable perception of the environment. In this context, photoacoustic tomography (PAT) has emerged as a non-invasive, functional imaging modality with great clinical potential. Current research focuses on converting the high-dimensional, not human-interpretable spectral data into the underlying functional information, specifically the blood oxygenation. One of the largely unexplored issues stalling clinical advances is the fact that the quantification problem is ambiguous, i.e. that radically different tissue parameter configurations could lead to almost identical photoacoustic spectra. In the present work, we tackle this problem with conditional Invertible Neural Networks (cINNs). Going beyond traditional point estimates, our network is used to compute an approximation of the conditional posterior density of tissue parameters given the photoacoustic spectrum. To this end, an automatic mode detection algorithm extracts the plausible solution from the sample-based posterior. According to a comprehensive validation study based on both synthetic and real images, our approach is well-suited for exploring ambiguity in quantitative PAT.

A high contrast and resolution reconstruction algorithm in quantitative photoacoustic tomography

A framework for reconstruction of optical diffusion and absorption coefficients in quantitative photoacoustic tomography is presented. This framework is based on a Tikhonov-type functional with a regularization term promoting sparsity of the absorption coefficient and a prior involving a Kubelka–Munk absorption–diffusion relation that allows to obtain superior reconstructions. The reconstruction problem is formulated as the minimization of this functional subject to the differential constraint given by a photon-propagation model. The solution of this problem is obtained by a fast and robust sequential quadratic hamiltonian algorithm based on the Pontryagin maximum principle. Results of several numerical experiments demonstrate that the proposed computational strategy is able to obtain reconstructions of the optical coefficients with high contrast and resolution for a wide variety of objects.

Extractor-attention-predictor network for quantitative photoacoustic tomography

Quantitative photoacoustic tomography (qPAT) holds great potential in estimating chromophore concentrations, whereas the involved optical inverse problem, aiming to recover absorption coefficient distributions from photoacoustic images, remains challenging. To address this problem, we propose an extractor-attention-predictor network architecture (EAPNet), which employs a contracting–expanding structure to capture contextual information alongside a multilayer perceptron to enhance nonlinear modeling capability. A spatial attention module is introduced to facilitate the utilization of important information. We also use a balanced loss function to prevent network parameter updates from being biased towards specific regions. Our method obtains satisfactory quantitative metrics in simulated and real-world validations. Moreover, it demonstrates superior robustness to target properties and yields reliable results for targets with small size, deep location, or relatively low absorption intensity, indicating its broader applicability. The EAPNet, compared to the conventional UNet, exhibits improved efficiency, which significantly enhances performance while maintaining similar network size and computational complexity.

Single-stage approach for estimating optical parameters in spectral quantitative photoacoustictomography.

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.

A Bayesian approach for consistent reconstruction of inclusions

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of the corresponding posterior distributions in a small measurement noise limit. The methodology is general; it works for priors arising from any Hölder continuous transformation of Gaussian random fields and is applicable to a range of inverse problems. The level set and star-shaped prior distributions are examples of push-forward priors under Hölder continuous transformations that take advantage of the structure of inclusion detection problems. We show that the corresponding posterior mean converges to the ground truth in a proper probabilistic sense. Numerical tests on a two-dimensional quantitative photoacoustic tomography problem showcase the approach. The results highlight the convergence properties of the posterior distributions and the ability of the methodology to detect inclusions with sufficiently regular boundaries.

Quantitative Photoacoustic Tomography Using Iteratively Refined Wavefield Reconstruction Inversion: A Simulation Study.

The ultimate goal of photoacoustic tomography is to accurately map the absorption coefficient throughout the imaged tissue. Most studies either assume that acoustic properties of biological tissues such as speed of sound (SOS) and acoustic attenuation are homogeneous or fluence is uniform throughout the entire tissue. These assumptions reduce the accuracy of estimations of derived absorption coefficients (DeACs). Our quantitative photoacoustic tomography (qPAT) method estimates DeACs using iteratively refined wavefield reconstruction inversion (IR-WRI) which incorporates the alternating direction method of multipliers to solve the cycle skipping challenge associated with full wave inversion algorithms. Our method compensates for SOS inhomogeneity, fluence decay, and acoustic attenuation. We evaluate the performance of our method on a neonatal head digital phantom.

Quantitative photoacoustic tomography: modeling and inverse problems.

Quantitative photoacoustic tomography (QPAT) exploits the photoacoustic effect with the aim of estimating images of clinically relevant quantities related to the tissue's optical absorption. The technique has two aspects: an acoustic part, where the initial acoustic pressure distribution is estimated from measured photoacoustic time-series, and an optical part, where the distributions of the optical parameters are estimated from the initial pressure. Our study is focused on the optical part. In particular, computational modeling of light propagation (forward problem) and numerical solution methodologies of the image reconstruction (inverse problem) are discussed. The commonly used mathematical models of how light and sound propagate in biological tissue are reviewed. A short overview of how the acoustic inverse problem is usually treated is given. The optical inverse problem and methods for its solution are reviewed. In addition, some limitations of real-life measurements and their effect on the inverse problems are discussed. An overview of QPAT with a focus on the optical part was given. Computational modeling and inverse problems of QPAT were addressed, and some key challenges were discussed. Furthermore, the developments for tackling these problems were reviewed. Although modeling of light transport is well-understood and there is a well-developed framework of inverse mathematics for approaching the inverse problem of QPAT, there are still challenges in taking these methodologies to practice. Modeling and inverse problems of QPAT together were discussed. The scope was limited to the optical part, and the acoustic aspects were discussed only to the extent that they relate to the optical aspect.

Wavelength-dependent error minimization for quantitative spectroscopic photoacoustic tomography with a ring-array system

PurposePhotoacoustic tomography (PAT) is a non-invasive and high-resolution imaging technique that can provide functional and molecular information from the optical properties of pathological tissues, such as cancer. Spectroscopic PAT (sPAT) is capable of supplying information such as oxygen saturation (sO2), which is an important biological indicator for diseases such as cancer. However, the wavelength dependent nature of sPAT makes it challenging to provide accurate quantitative measurements of tissue oxygenation beyond shallow depths. We have previously reported the utility of combined ultrasound tomography and PAT to achieve optical and acoustic compensated PAT images at a single wavelength and for enhanced PAT images at larger depths. In this work we further explore the utility of the optical and acoustic compensation PAT algorithm to minimize the wavelength dependency in sPAT by showcasing improvements in spectral unmixing. Materials and MethodsTwo optically and acoustically characterized heterogenous phantoms were manufactured to test the ability of the system and developed algorithm to minimize the wavelength-dependence driven error in sPAT spectral unmixing. The PA inclusions within each phantom were composed of a mixture of two sulfate dyes, copper sulfate (CuSO4) and nickel sulfate (NiSO4), with known optical spectra. Improvements between uncompensated and optically and acoustically compensated PAT (OAcPAT) were quantified as the relative percent error between the measured results and the ground truth. ResultsThe results of our phantom studies demonstrate that OAcPAT can significantly improve the accuracy of sPAT measurements in a heterogenous medium and especially at larger inclusions depths which can reach to up to 12% improvement in measurement errors. This significant improvement can play a vital role in reliability of future in-vivo biomarker quantifications. ConclusionsUtilizing UST for model-based optical and acoustic compensation of PAT images was proposed by our group previously. In this work, we further demonstrated the efficacy of the developed algorithm in sPAT by minimizing the error caused by the tissue’s optical heterogeneity on improving spectral unmixing, which is a major limiting factor in reliability of sPAT measurements. Such synergistic combination of UST and PAT provides a window of opportunity to achieve bias-free quantitative sPAT measurements, which plays an important role in future pre-clinical and clinical utility of PAT.

The Optical Inverse Problem in Quantitative Photoacoustic Tomography: A Review

Photoacoustic tomography is a fast-growing biomedical imaging modality that combines rich optical contrast with a high acoustic resolution, at depths in tissues. Building upon the foundation of this technique, novel quantitative photoacoustic tomography fully leverages its advantages while further delivering improved quantification capabilities to produce high-accuracy concentration estimates, which has attracted substantial research interest in recent years. The kernel challenge associated with quantitative photoacoustic tomography is an optical inverse problem aiming to recover the absorption coefficient distribution from the conventional photoacoustic image. Although the crucial importance of the optical inversion has been widely acknowledged, achieving it has remained a persistent challenge due to the inherent non-linearity and non-uniqueness. In the past decade, numerous methods were proposed and have made noticeable progress in addressing this concern. Nevertheless, a review has been conspicuously absent for a long time. Aiming to bridge this gap, the present study comprehensively investigates the recent research in this field, and methods identified with significant value are introduced in this paper. Moreover, all included methods are systematically classified based on their underlying principles. Finally, we summarize each category and highlight its remaining challenges and potential future research directions.

Quantitative photoacoustic tomography with light fluence compensation based on radiance Monte Carlo model

Objective. Photoacoustic tomography (PAT) is a rapidly evolving imaging modality that provides images with high contrast and spatial resolution showing the optical properties of biological tissues. The photoacoustic pressure is proportional to the product of the optical absorption coefficient and the local light fluence. The essential challenge in reconstructing quantitative images representing spatially varying absorption coefficients is the unknown light fluence. In addition, optical attenuation induces spatial variations in the light fluence, and the heterogeneity of the fluence determines the limits of reconstruction quality and depth. Approach. In this work, a reconstruction enhancement scheme is proposed to compensate for the variation in the light fluence in the absorption coefficient recovery. The inverse problem of the radiance Monte Carlo model describing light transport through the tissue is solved by using an alternating optimization strategy. In the iteration, the absorption coefficients and photon weights are alternately updated. Main results. The method provides highly accurate quantitative images of absorption coefficients in simulations, phantoms, and in vivo studies. The results show that the method has great potential for improving the accuracy of absorption coefficient recovery compared to conventional reconstruction methods that ignore light fluence variations. Comparison with state-of-the-art fluence compensation methods shows significant improvements in root mean square error, normalized mean square absolute distance, and structural similarity metrics. Significance. This method achieves high precision quantitative imaging by compensating for nonuniform light fluence without increasing the complexity and operation of the imaging system.

Ultrasound-enhanced Unet model for quantitative photoacoustic tomography of ovarian lesions

Quantitative photoacoustic tomography (QPAT) is a valuable tool in characterizing ovarian lesions for accurate diagnosis. However, accurately reconstructing a lesion’s optical absorption distributions from photoacoustic signals measured with multiple wavelengths is challenging because it involves an ill-posed inverse problem with three unknowns: the Grüneisen parameter (Γ), the absorption distribution, and the optical fluence (ϕ). Here, we propose a novel ultrasound-enhanced Unet model (US-Unet) that reconstructs optical absorption distribution from PAT data. A pre-trained ResNet-18 extracts the US features typically identified as morphologies of suspicious ovarian lesions, and a Unet is implemented to reconstruct optical absorption coefficient maps, using the initial pressure and US features extracted by ResNet-18. To test this US-Unet model, we calculated the blood oxygenation saturation values and total hemoglobin concentrations from 655 regions of interest (ROIs) (421 benign, 200 malignant, and 34 borderline ROIs) obtained from clinical images of 35 patients with ovarian/adnexal lesions. A logistic regression model was used to compute the ROC, the area under the ROC curve (AUC) was 0.94, and the accuracy was 0.89. To the best of our knowledge, this is the first study to reconstruct quantitative PAT with PA signals and US-based structural features.

Photoacoustic image synthesis with generative adversarial networks

Photoacoustic tomography (PAT) has the potential to recover morphological and functional tissue properties with high spatial resolution. However, previous attempts to solve the optical inverse problem with supervised machine learning were hampered by the absence of labeled reference data. While this bottleneck has been tackled by simulating training data, the domain gap between real and simulated images remains an unsolved challenge. We propose a novel approach to PAT image synthesis that involves subdividing the challenge of generating plausible simulations into two disjoint problems: (1) Probabilistic generation of realistic tissue morphology, and (2) pixel-wise assignment of corresponding optical and acoustic properties. The former is achieved with Generative Adversarial Networks (GANs) trained on semantically annotated medical imaging data. According to a validation study on a downstream task our approach yields more realistic synthetic images than the traditional model-based approach and could therefore become a fundamental step for deep learning-based quantitative PAT (qPAT).

Modeling photoacoustic pressure generation in colloidal suspensions at different volume fractions based on a multi-scale approach

Further development of quantitative photoacoustic tomography requires understanding the photoacoustic pressure generation by modeling the generation process. This study modeled the initial photoacoustic pressure in colloidal suspensions, used as tissue phantoms, at different volume fractions on a multi-scale approach. We modeled the thermodynamic and light scattering properties on a microscopic scale with/without treating the hard-sphere interaction between colloidal particles. Meanwhile, we did the light energy density on a macroscopic scale. We showed that the hard-sphere interaction significantly influences the initial pressure and related quantities at a high volume fraction except for the thermodynamic properties. We also showed the initial pressure at the absorber inside the medium logarithmically decreases with increasing the volume fractions. This result is mainly due to the decay of the light energy density with light scattering. Our numerical results suggest that modeling light scattering and propagation is crucial over modeling thermal expansion.

Stability for quantitative photoacoustic tomography revisited

This paper deals with the issue of stability in determining the absorption and the diffusion coefficients in quantitative photoacoustic imaging. We establish a global conditional Hölder stability inequality from the knowledge of two internal data obtained from optical waves, generated by two point sources in a region where the optical coefficients are known.

Adaptive stochastic Gauss-Newton method with optical Monte Carlo for quantitative photoacoustic tomography.

.Significance: The image reconstruction problem in quantitative photoacoustic tomography (QPAT) is an ill-posed inverse problem. Monte Carlo method for light transport can be utilized in solving this image reconstruction problem.Aim: The aim was to develop an adaptive image reconstruction method where the number of photon packets in Monte Carlo simulation is varied to achieve a sufficient accuracy with reduced computational burden.Approach: The image reconstruction problem was formulated as a minimization problem. An adaptive stochastic Gauss–Newton (A-SGN) method combined with Monte Carlo method for light transport was developed. In the algorithm, the number of photon packets used on Gauss–Newton (GN) iteration was varied utilizing a so-called norm test.Results: The approach was evaluated with numerical simulations. With the proposed approach, the number of photon packets needed for solving the inverse problem was significantly smaller than in a conventional approach where the number of photon packets was fixed for each GN iteration.Conclusions: The A-SGN method with a norm test can be utilized in QPAT to provide accurate and computationally efficient solutions.

Quantitative endoscopic photoacoustic tomography using a convolutional neural network.

Endoscopic photoacoustic tomography (EPAT) is a catheter-based hybrid imaging modality capable of providing structural and functional information of biological luminal structures, such as coronary arterial vessels and the digestive tract. The recovery of the optical properties of the imaged tissue from acoustic measurements achieved by optical inversion is essential for implementing quantitative EPAT (qEPAT). In this paper, a convolutional neural network (CNN) based on deep gradient descent is developed for qEPAT. The network enables the reconstruction of images representing the spatially varying absorption coefficient in cross-sections of the tubular structures from limited measurement data. The forward operator reflecting the mapping from the absorption coefficient to the optical deposition due to pulsed irradiation is embedded into the network training. The network parameters are optimized layer by layer through the deep gradient descent mechanism using the numerically simulated data. The operation processes of the forward operator and its adjoint operator are separated from the network training. The trained network outputs an image representing the distribution of absorption coefficients by inputting an image that represents the optical deposition. The method has been tested with computer-generated phantoms mimicking coronary arterial vessels containing various tissue types. Results suggest that the structural similarity of the images reconstructed by our method is increased by about 10% in comparison with the non-learning method based on error minimization in the case of the same measuring view.

Automatic 3-D segmentation and volumetric light fluence correction for photoacoustic tomography based on optimal 3-D graph search.

Preclinical imaging with photoacoustic tomography (PAT) has attracted wide attention in recent years since it is capable of providing molecular contrast with deep imaging depth. The automatic extraction and segmentation of the animal in PAT images is crucial for improving image analysis efficiency and enabling advanced image post-processing, such as light fluence (LF) correction for quantitative PAT imaging. Previous automatic segmentation methods are mostly two-dimensional approaches, which failed to conserve the 3-D surface continuity because the image slices were processed separately. This discontinuity problem further hampers LF correction, which, ideally, should be carried out in 3-D due to spatially diffused illumination. Here, to solve these problems, we propose a volumetric auto-segmentation method for small animal PAT imaging based on the 3-D optimal graph search (3-D GS) algorithm. The 3-D GS algorithm takes into account the relation among image slices by constructing a 3-D node-weighted directed graph, and thus ensures surface continuity. In view of the characteristics of PAT images, we improve the original 3-D GS algorithm on graph construction, solution guidance and cost assignment, such that the accuracy and smoothness of the segmented animal surface were guaranteed. We tested the performance of the proposed method by conducting in vivo nude mice imaging experiments with a commercial preclinical cross-sectional PAT system. The results showed that our method successfully retained the continuous global surface structure of the whole 3-D animal body, as well as smooth local subcutaneous tumor boundaries at different development stages. Moreover, based on the 3-D segmentation result, we were able to simulate volumetric LF distribution of the entire animal body and obtained LF corrected PAT images with enhanced structural visibility and uniform image intensity.

Infinite-Dimensional Inverse Problems with Finite Measurements

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems satisfying Lipschitz stability we show that the same estimate holds even with a finite number of measurements. We also derive a globally convergent reconstruction algorithm based on the Landweber iteration. This theory applies to nonlinear ill-posed problems such as electrical impedance tomography, inverse scattering and quantitative photoacoustic tomography, under the assumption that the unknown belongs to a finite-dimensional subspace.

Hölder stability of quantitative photoacoustic tomography based on partial data

We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography. In practice, the internal information is only partially provided near the boundary due to the high attenuation property of the medium and the limitation of the equipment. Our main contribution is to prove a Hölder stability of the inverse problem in a subregion where the internal information is reliably provided based on the stability estimation of a Cauchy problem satisfied by the diffusion coefficient. The exponent of the Hölder stability converges to a positive constant independent of the subregion as the subregion contracts towards the boundary. Numerical experiments demonstrates that it is possible to locally reconstruct the diffusion and absorption coefficients for smooth and even discontinuous media.

Quantitative PAT with simplified P N approximation

The photoacoustic tomography (PAT) is a hybrid modality that combines the optics and acoustics to obtain high resolution and high contrast imaging of heterogeneous media. In this work, our objective is to study the inverse problem in the quantitative step of PAT which aims to reconstruct the optical coefficients of the governing radiative transport equation from the ultrasound measurements. In our analysis, we take the simplified P N approximation of the radiative transport equation as the physical model and then show the uniqueness and stability for this modified inverse problem. Numerical simulations based on synthetic data are presented to validate our analysis.