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

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.

Deep learning acceleration of iterative model-based light fluence correction for photoacoustic tomography

Photoacoustic tomography (PAT) is a promising imaging technique that can visualize the distribution of chromophores within biological tissue. However, the accuracy of PAT imaging is compromised by light fluence (LF), which hinders the quantification of light absorbers. Currently, model-based iterative methods are used for LF correction, but they require extensive computational resources due to repeated LF estimation based on differential light transport models. To improve LF correction efficiency, we propose to use Fourier neural operator (FNO), a neural network specially designed for estimating partial differential equations, to learn the forward projection of light transport in PAT. Trained using paired finite-element-based LF simulation data, our FNO model replaces the traditional computational heavy LF estimator during iterative correction, such that the correction procedure is considerably accelerated. Simulation and experimental results demonstrate that our method achieves comparable LF correction quality to traditional iterative methods while reducing the correction time by over 30 times.

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, andin vivostudies. 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.

Pixel-wise reconstruction of tissue absorption coefficients in photoacoustic tomography using a non-segmentation iterative method

In Photoacoustic Tomography (PAT), the acquired image represents a light energy deposition map of the imaging object. For quantitative imaging, the PAT image is converted into an absorption coefficient (μ a ) map by dividing the light fluence (LF). Previous methods usually assume a uniform tissueμ a distribution, and consequently degrade the LF correction results. Here, we propose a simple method to reconstruct the pixel-wiseμ a map. Our method is based on a non-segmentation-based iterative algorithm, which alternately optimizes the LF distribution and theμ a map. Using simulation data, as well as phantom and animal data, we implemented our algorithm and compared it to segmentation-based correction methods. The results show that our method can obtain accurate estimation of the LF distribution and therefore improve the image quality and feature visibility of theμ a map. Our method may facilitate efficient calculation of the concentration distributions of endogenous and exogenous agents in vivo.

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 Photoacoustic Reconstruction of the Optical Properties of Intervertebral Discs Using a Gradient Descent Scheme

The intervertebral discs (IVD) are among the essential organs of the human body, ensuring the mobility of the spine. These organs possess a high proportion of water. However, as the discs age, this content decreases, which can potentially lead to various diseases called degenerative disc diseases. This water content is therefore an important indicator of the well-being of the disc. In this paper, we propose photoacoustic imaging as a means of probing a disc and quantitatively recovering its molecular composition, which should allow concluding on its state. An adjoint-assisted gradient descent scheme is implemented to recover the optical absorption coefficient in the disc, from which, if spectroscopic measurements are performed, the molecular composition can be deduced. The algorithm was tested on synthetic measurements. A realistic numerical phantom was built from magnetic resonance imaging of an actual IVD of a pig. A simplified experiment, with a single laser source, was performed. Results show the feasibility of using photoacoustics imaging to probe IVDs. The influences of exact and approximate formulations of the gradient are studied. The impact of noise on the reconstructions is also evaluated.

In-silico investigation towards the non-invasive optical detection of blood lactate

This paper uses Monte Carlo simulations to investigate the interaction of short-wave infrared (SWIR) light with vascular tissue as a step toward the development of a non-invasive optical sensor for measuring blood lactate in humans. The primary focus of this work was to determine the optimal source-detector separation, penetration depth of light at SWIR wavelengths in tissue, and the optimal light power required for reliable detection of lactate. The investigation also focused on determining the non-linear variations in absorbance of lactate at a few select SWIR wavelengths. SWIR photons only penetrated 1.3 mm and did not travel beyond the hypodermal fat layer. The maximum output power was only 2.51% of the input power, demonstrating the need for a highly sensitive detection system. Simulations optimized a source-detector separation of 1 mm at 1684 nm for accurate measurement of lactate in blood.

Nonlinear iterative perturbation scheme with simplified spherical harmonics (SP3 ) light propagation model for quantitative photoacoustic tomography

When using quantitative photoacoustic tomography (q-PAT) reconstruction to recover the optical absorption coefficients of tissue, the commonly used diffusion equation has several limitations in the case of the objects that have small geometries and high-absorption or low-scattering areas. Furthermore, the conventional perturbation reconstruction strategy is unsatisfactory when the target tissue containing large heterogeneous features. We herein present a modified q-PAT implementation that employs the higher-order photon migration model achieving the tradeoff between mathematical rigidity and computational efficiency. Besides, a nonlinear iterative method is proposed to obtain the perturbations of optical absorption considering the updating of the sensitivity matrix in calculating the fluence perturbations. Consequently, the distribution of tissue optical properties can be recovered in a robust way even if the targets with high absorption are included. The proposed approach has been validated by simulation, phantom and in vivo experiments, exhibiting promising performances in image fidelity and quantitative feasibility for practical applications.

Tunable blood oxygenation in the vascular anatomy of a semi-anthropomorphic photoacoustic breast phantom

SIGNIFICANCE

Recovering accurate oxygenation estimations in the breast with quantitative photoacoustic tomography (QPAT) is not straightforward. Accurate light fluence models are required, but the unknown ground truth of the breast makes it difficult to validate them. Phantoms are often used for the validation, but most reported phantoms have a simple architecture. Fluence models developed in these simplistic objects are not accurate for application on the complex tissues of the breast.

AIM

We present a sophisticated breast phantom platform for photoacoustic (PA) and ultrasound (US) imaging in general, and specifically for QPAT. The breast phantom is semi-anthropomorphic in distribution of optical and acoustic properties and contains wall-less channels with blood.

APPROACH

3D printing approaches are used to develop the solid 3D breast phantom from custom polyvinyl chloride plastisol formulations and additives for replicating the tissue optical and acoustic properties. A flow circuit was developed to flush the channels with bovine blood with a controlled oxygen saturation level. To showcase the phantom's functionality, PA measurements were performed on the phantom with two oxygenation levels. Image reconstructions with and without fluence compensation from Monte Carlo simulations were analyzed for the accuracy of oxygen saturation estimations.

RESULTS

We present design aspects of the phantom, demonstrate how it is developed, and present its breast-like appearance in PA and US imaging. The oxygen saturations were estimated in two regions of interest with and without using the fluence models. The fluence compensation positively influenced the SO2 estimations in all cases and confirmed that highly accurate fluence models are required to minimize estimation errors.

CONCLUSIONS

This phantom allows studies to be performed in PA in carefully controlled laboratory settings to validate approaches to recover both qualitative and quantitative features sought after in in-vivo studies. We believe that testing with phantoms of this complexity can streamline the transition of new PA technologies from the laboratory to studies in the clinic.

Perturbation Monte Carlo Method for Quantitative Photoacoustic Tomography

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.

Evaluation of Fluence Correction Algorithms in Multispectral Photoacoustic Imaging

Multispectral photoacoustic imaging (MPAI) is a promising emerging diagnostic technology, but fluence artifacts can degrade device performance. Our goal was to develop well-validated phantom-based test methods for evaluating and comparing MPAI fluence correction algorithms, including a heuristic diffusion approximation, Monte Carlo simulations, and an algorithm we developed based on novel application of the diffusion dipole model (DDM). Phantoms simulated a range of breast-mimicking optical properties and contained channels filled with chromophore solutions (ink, hemoglobin, or copper sulfate) or connected to a previously developed blood flow circuit providing tunable oxygen saturation (SO₂). The DDM algorithm achieved similar spectral recovery and SO₂ measurement accuracy to Monte Carlo-based corrections with lower computational cost, potentially providing an accurate, real-time correction approach. Algorithms were sensitive to optical property uncertainty, but error was minimized by matching phantom albedo. The developed test methods may provide a foundation for standardized assessment of MPAI fluence correction algorithm performance.

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

SIGNIFICANCE

Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop an approach to reduce this bottleneck, which has significant implications for quantitative tomographic imaging in a variety of medical and industrial applications.

AIM

Our aim is to enable computationally efficient image reconstruction in (hybrid) diffuse optical modalities using stochastic forward models.

APPROACH

Using Monte Carlo, we compute a fully stochastic gradient of an objective function for a given imaging problem. Leveraging techniques from the machine learning community, we then adaptively control the accuracy of this gradient throughout the iterative inversion scheme to substantially reduce computational resources at each step.

RESULTS

For example problems of quantitative photoacoustic tomography and ultrasound-modulated optical tomography, we demonstrate that solutions are attainable using a total computational expense that is comparable to (or less than) that which is required for a single high-accuracy forward run of the same Monte Carlo model.

CONCLUSIONS

This approach demonstrates significant computational savings when approaching the full nonlinear inverse problem of optical property estimation using stochastic methods.

Improving vascular imaging with co-planar mutually guided photoacoustic and diffuse optical tomography: a simulation study

Diffuse optical tomography (DOT) and photoacoustic tomography (PAT) are functional imaging modalities that provide absorption coefficient maps of the tissue. Spatial resolution of DOT is relatively low due to light scattering characteristics of the tissue. On the other hand, although PAT can resolve regions of different absorptions with a high spatial resolution, measuring the absolute value of optical absorptions using PAT is challenging due to unknown light fluence distribution in the tissue. Development of image guidance techniques using a priori information of imaging target structure has been shown to increase the accuracy of DOT. PAT is one such method that can be used as a complementary modality to serve as a guide for DOT image reconstruction. On the other hand, estimated fluence map provided by DOT can be used to quantitatively correct PAT images. In this study we introduce a mutually-guided imaging system for fast and simultaneous optical and photoacoustic measurements of tissue absorption map, where DOT is guided by the PAT image and vice versa. Using the obtained absorption map of the tissue, we then estimate the tissue scattering map. We conducted this study using a series of simulations on digital phantoms and demonstrated the effectiveness of the proposed method.

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.

Quantitative PA tomography of high resolution 3-D images: Experimental validation in a tissue phantom

Quantitative photoacoustic tomography aims to recover the spatial distribution of absolute chromophore concentrations and their ratios from deep tissue, high-resolution images. In this study, a model-based inversion scheme based on a Monte-Carlo light transport model is experimentally validated on 3-D multispectral images of a tissue phantom acquired using an all-optical scanner with a planar detection geometry. A calibrated absorber allowed scaling of the measured data during the inversion, while an acoustic correction method was employed to compensate the effects of limited view detection. Chromophore- and fluence-dependent step sizes and Adam optimization were implemented to achieve rapid convergence. High resolution 3-D maps of absolute concentrations and their ratios were recovered with high accuracy. Potential applications of this method include quantitative functional and molecular photoacoustic tomography of deep tissue in preclinical and clinical studies.

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

Quantitative photoacoustic tomography aims to recover maps of the local concentrations of tissue chromophores from multispectral images. While model-based inversion schemes are promising approaches, major challenges to their practical implementation include the unknown fluence distribution and the scale of the inverse problem. We describe an inversion scheme based on a radiance Monte Carlo model and an adjoint-assisted gradient optimization that incorporates fluence-dependent step sizes and adaptive moment estimation. The inversion is shown to recover absolute chromophore concentrations, blood oxygen saturation, and the Grüneisen parameter from in silico three-dimensional phantom images for different radiance approximations. The scattering coefficient is assumed to be homogeneous and known a priori.

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.

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.