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We present an open-source differentiable acoustic simulator, j-Wave, which can solve time-varying and time-harmonic acoustic problems. It supports automatic differentiation, which is a program transformation technique that has many applications, especially in machine learning and scientific computing. j-Wave is composed of modular components that can be easily customized and reused. At the same time, it is compatible with some of the most popular machine learning libraries, such as JAX and TensorFlow. The accuracy of the simulation results for known configurations is evaluated against the widely used k-Wave toolbox and a cohort of acoustic simulation software. j-Wave is available from https://github.com/ucl-bug/jwave.

In this article, it is shown experimentally that a planar laser-generated ultrasound source with a hard reflective backing will generate higher acoustic pressures than a comparable source with an acoustically matched backing when the stress confinement condition is not met. Furthermore, while the source with an acoustically matched backing will have a broader bandwidth when the laser pulse is short enough to ensure stress confinement, the bandwidths of both source types will converge as the laser pulse duration increases beyond stress confinement. The explanation of the results is supported by numerical simulations.

Polyvinyl chloride plastisol (PVCP) has been increasingly used as a phantom material for photoacoustic and ultrasound imaging. As one of the most useful polymeric materials for industrial applications, its mechanical properties and behavior are well-known. Although the acoustic and optical properties of several formulations have previously been investigated, it is still unknown how these are affected by varying the fabrication method. Here, an improved and straightforward fabrication method is presented, and the effect of curing temperature and curing time on the PVCP acoustic and optical properties, as well as their stability over time, is investigated. The speed of sound and attenuation were determined over a frequency range from 2 to 15 MHz, while the optical attenuation spectra of samples were measured over a wavelength range from 500 to 2200 nm. The results indicate that the optimum properties are achieved at curing temperatures between 160 °C and 180 °C, while the required curing time decreases with increasing temperature. The properties of the fabricated phantoms were highly repeatable, meaning that the phantoms are not sensitive to the manufacturing conditions provided that the curing temperature and time are within the range of complete gelation-fusion (samples are optically clear) and below the limit of thermal degradation (indicated by the yellowish appearance of the sample). The samples' long-term stability was assessed over 16 weeks, and no significant change was observed in the measured acoustic and optical properties.

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations., Comment: 6 pages, 1 figure

Fast imaging methods are needed to promote widespread clinical adoption of Ultrasound Tomography (UST), and more widely available UST hardware could support the experimental validation of new measurement configurations. In this work, an open-source 256-element transducer ring array was developed (morganjroberts.github.io/open-UST) and manufactured using rapid prototyping, for only {\pounds}2k. Novel manufacturing techniques were used, resulting in a 1.17$^{\circ}$ mean beam axis skew angle, a 104 $\mu$m mean element position error, and a $\pm$13.6 $\mu$m deviation in matching layer thickness. The nominal acoustic performance was measured using hydrophone scans and watershot data, and the 61.2 dB SNR, 55.4$^{\circ}$ opening angle, 16.3 mm beamwidth and 54% transmit-receive bandwidth (-12 dB), were found to be similar to existing systems, and compatible with full waveform inversion reconstruction methods. The inter-element variation in acoustic performance was typically, Comment: 16 pages, 12 figures

Over the past decade, the range of applications in biomedical ultrasound exploiting 3D printing has rapidly expanded. For wavefront shaping specifically, 3D printing has enabled a diverse range of new, low-cost approaches for controlling acoustic fields. These methods rely on accurate knowledge of the bulk acoustic properties of the materials; however, to date, robust knowledge of these parameters is lacking for many materials that are commonly used. In this work, the acoustic properties of eight 3D-printed photopolymer materials were characterised over a frequency range from 1 to 3.5 MHz. The properties measured were the frequency-dependent phase velocity and attenuation, group velocity, signal velocity, and mass density. The materials were fabricated using two separate techniques [PolyJet and stereolithograph (SLA)], and included Agilus30, FLXA9960, FLXA9995, Formlabs Clear, RGDA8625, RGDA8630, VeroClear, and VeroWhite. The range of measured density values across all eight materials was 1120–1180 kg [Formula: see text] m−3, while the sound speed values were between 2020 to 2630 m [Formula: see text] s−1, and attenuation values typically in the range 3–9 dB [Formula: see text] [Formula: see text] cm−1.

Researchers in the Ultrasound Tomography community face a high barrier to entry, due to the high cost and lead times associated with custom transducer arrays. For this work, 16-element linear array transducer modules have been developed for an open-source, low-cost, ring array with low interelement variation. A module prototype was characterised using a hydrophone to measure the pressure field from each element, and the transmit frequency response. The measured average elevation and lateral plane skews were 0.41° and 2.07°, the elevation beamwidth was 8.1 mm ± 0.23 mm, and after normalisation the standard deviation in transmit amplitude spectrum between elements was 8%, averaged across all frequencies. The low interelement variation in these parameters suggests that an ideal transducer model could be used to represent the elements during image reconstruction, which could be based on measurements from only a subset of elements, simplifying preliminary UST work for end users.

The limited view of a planar detector array results in artefacts in the reconstructed images. To address this, iterative image reconstruction methods have been proposed. However, there remains a need for a rigorous assessment of their performance in terms of artefact reduction, small structure detection, spatial resolution and robustness to noise. Additionally, an understanding of the impact of regularisation parameters on image fidelity and SNR as a function of the target geometry and instrument noise is required. The aim of this study is to explore these factors and advance the practical application of iterative reconstruction methods for in vivo images acquired using a planar detection geometry.

A new approach to photoacoustic tomography is presented in which a number of spatially overlapping photoacoustic time series measurements are aligned and registered to extend the effective imaging aperture. This approach not only improves the lateral resolution and imaging depth in tissues but also enables imaging of targets that are much larger than the physical size of the detector array.

An efficient and accurate image reconstruction algorithm for ultrasound tomography (UST) is described and demonstrated, which can recover accurate sound speed distribution from acoustic time series measurements made in soft tissue. The approach is based on a second-order iterative minimisation of the difference between the measurements and a model based on a ray-approximation to the heterogeneous Green's function. It overcomes the computational burden of full-wave solvers while avoiding the drawbacks of time-of-flight methods. Through the use of a second-order iterative minimisation scheme, applied stepwise from low to high frequencies, the effects of scattering are incorporated into the inversion.

Ultrasound tomography (UST) scanners allow quantitative images of the human breast’s acoustic properties to be derived with potential applications in screening, diagnosis and therapy planning. Time domain full waveform inversion (TD-FWI) is a promising UST image formation technique that fits the parameter fields of a wave physics model by gradient-based optimization. For high resolution 3D UST, it holds three key challenges: firstly, its central building block, the computation of the gradient for a single US measurement, has a restrictively large memory footprint. Secondly, this building block needs to be computed for each of the 103–104 measurements, resulting in a massive parallel computation usually performed on large computational clusters for days. Lastly, the structure of the underlying optimization problem may result in slow progression of the solver and convergence to a local minimum. In this work, we design and evaluate a comprehensive computational strategy to overcome these challenges: firstly, we exploit a gradient computation based on time reversal that dramatically reduces the memory footprint at the expense of one additional wave simulation per source. Secondly, we break the dependence on the number of measurements by using source encoding (SE) to compute stochastic gradient estimates. Also we describe a more accurate, TD-specific SE technique with a finer variance control and use a state-of-the-art stochastic LBFGS method. Lastly, we design an efficient TD multi-grid scheme together with preconditioning to speed up the convergence while avoiding local minima. All components are evaluated in extensive numerical proof-of-concept studies simulating a bowl-shaped 3D UST breast scanner prototype. Finally, we demonstrate that their combination allows us to obtain an accurate 442 × 442 × 222 voxel image with a resolution of 0.5 mm using Matlab on a single GPU within 24 h.

Ultrasound tomography (UST) has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional UST, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. This has led to renewed attention on UST image reconstruction algorithms. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray UST in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and two robust, accurate, and efficient derivative-free ray-linking algorithms are formulated and demonstrated and compared with a Jacobian-based benchmark approach. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight (TOF) picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.

Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. We derive a one-to-one map between wavefront directions in image and data spaces in PAT which suggests near equivalence between the recovery of the initial pressure and PAT data from compressed/subsampled measurements when assuming sparsity in Curvelet frame. As the latter is computationally more tractable, investigation to which extent this equivalence holds conducted in this paper is of immediate practical significance. To this end we formulate and compare DR, a two step approach based on the recovery of the complete volume of the photoacoustic data from the subsampled data followed by the acoustic inversion, and p0R, a one step approach where the photoacoustic image (the initial pressure, p0) is directly recovered from the subsampled data. Effective representation of the photoacoustic data requires basis defined on the range of the photoacoustic forward operator. To this end we propose a novel wedge-restriction of Curvelet transform which enables us to construct such basis. Both recovery problems are formulated in a variational framework. As the Curvelet frame is heavily overdetermined, we use reweighted l1 norm penalties to enhance the sparsity of the solution. The data reconstruction problem DR is a standard compressed sensing recovery problem, which we solve using an ADMMtype algorithm, SALSA. Subsequently, the initial pressure is recovered using time reversal as implemented in the k-Wave Toolbox. The p0 reconstruction problem, p0R, aims to recover the photoacoustic image directly via FISTA, or ADMM when in addition including a non-negativity constraint. We compare and discuss the relative merits of the two approaches and illustrate them on 2D simulated and 3D real data in a fair and rigorous manner., 06 August 2021 (Accepted Version)

A full-wave model for nonlinear ultrasound propagation through a heterogeneous and absorbing medium in an axisymmetric coordinate system is developed. The model equations are solved using a nonstandard or k-space pseudospectral time domain method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method, and spatial gradients in the radial direction are calculated using discrete trigonometric transforms. Time integration is performed using a k-space corrected finite difference scheme. This scheme is exact for plane waves propagating linearly in the axial direction in a homogeneous and lossless medium and significantly reduces numerical dispersion in the more general case. The implementation of the model is described, and performance benchmarks are given for a range of grid sizes. The model is validated by comparison with several analytical solutions. This includes one-dimensional absorption and nonlinearity, the pressure field generated by plane-piston and bowl transducers, and the scattering of a plane wave by a sphere. The general utility of the model is then demonstrated by simulating nonlinear transcranial ultrasound using a simplified head model.

Significance: Two-dimensional (2-D) fully convolutional neural networks have been shown capable of producing maps of sO2 from 2-D simulated images of simple tissue models. However, their potential to produce accurate estimates in vivo is uncertain as they are limited by the 2-D nature of the training data when the problem is inherently three-dimensional (3-D), and they have not been tested with realistic images. Aim: To demonstrate the capability of deep neural networks to process whole 3-D images and output 3-D maps of vascular sO2 from realistic tissue models/images. Approach: Two separate fully convolutional neural networks were trained to produce 3-D maps of vascular blood oxygen saturation and vessel positions from multiwavelength simulated images of tissue models. Results: The mean of the absolute difference between the true mean vessel sO2 and the network output for 40 examples was 4.4% and the standard deviation was 4.5%. Conclusions: 3-D fully convolutional networks were shown capable of producing accurate sO2 maps using the full extent of spatial information contained within 3-D images generated under conditions mimicking real imaging scenarios. We demonstrate that networks can cope with some of the confounding effects present in real images such as limited-view artifacts and have the potential to produce accurate estimates in vivo.

Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in particular has many computational advantages. However, the use of a discrete Fourier basis is also inherently restricted to solving problems with periodic boundary conditions. Here, a family of spectral collocation methods based on the use of a sine or cosine basis is described. These retain the computational advantages of the Fourier collocation method but instead allow homogeneous Dirichlet (sound-soft) and Neumann (sound-hard) boundary conditions to be imposed. The basis function weights are computed numerically using the discrete sine and cosine transforms, which can be implemented using O(N log N) operations analogous to the fast Fourier transform. Practical details of how to implement spectral methods using discrete sine and cosine transforms are provided. The technique is then illustrated through the solution of the wave equation in a rectangular domain subject to different combinations of boundary conditions. The extension to boundaries with arbitrary real reflection coefficients or boundaries that are non-reflecting is also demonstrated using the weighted summation of the solutions with Dirichlet and Neumann boundary conditions., 21 pages, 10 figures

A 3D high resolution scanner has been developed specifically for clinical use. The novel scanner architecture employing multiple interrogation beams can acquire a 3D image in less than 1 second. An initial technical validation study has been undertaken in human volunteers to determine repeatability, reproducibility and patient acceptability. Thereafter, a first-in-man clinical study aimed at assessing diagnostic accuracy in patients with inflammatory diseases has been completed.

High-frequency calibration of hydrophones is becoming increasingly important, both for clinical and scientific applications of ultrasound, and user safety. At present, the calibrations available routinely to the user community extend to 60 MHz. However, hydrophones that can measure beyond this are available, and ultrasonic fields often contain energy at higher frequencies, e.g., generated through nonlinear propagation of high-amplitude ultrasound used for therapeutic applications, and the increasing use of higher frequencies in imaging. Therefore, there is a need for calibrations up to at least 100 MHz, to allow ultrasonic fields to be accurately characterized, and the risk of harmful bioeffects to be properly assessed. Currently, sets of focused piezoelectric transducers are used to meet the pressure amplitude and bandwidth requirements of Primary Standard calibration facilities. However, when the frequency is high enough such that the size of the ultrasound focus becomes less than the hydrophone element’s diameter, the uncertainty due to spatial averaging becomes significant, and can be as high as 20% at 100 MHz. As an alternate to piezoelectric transducers, a laser-generated ultrasound calibration source was designed, fabricated, and characterized. The source consists of an optically absorbing carbon-polymer nanocomposite excited by a large-diameter 1064 nm laser pulse of 2.6 ns duration. Peak pressure amplitudes of several Mega-Pascal were readily achievable, and the signal contained measurable frequency components up to 100 MHz. The variation in the pressure amplitudes was less than 2% from its mean over a three-hour test period. The ultrasound beam was sufficiently broad that the uncertainties due to spatial averaging were negligible.

Biomedical photoacoustic tomography, which can provide high resolution 3D soft tissue images based on the optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is becoming possible. The need for rapid image formation and the practical restrictions on data acquisition that arise from the constraints of a clinical workflow are presenting new image reconstruction challenges. There are many classical approaches to image reconstruction, but ameliorating the effects of incomplete or imperfect data through the incorporation of accurate priors is challenging and leads to slow algorithms. Recently, the application of Deep Learning, or deep neural networks, to this problem has received a great deal of attention. This paper reviews the literature on learned image reconstruction, summarising the current trends, and explains how these new approaches fit within, and to some extent have arisen from, a framework that encompasses classical reconstruction methods. In particular, it shows how these new techniques can be understood from a Bayesian perspective, providing useful insights. The paper also provides a concise tutorial demonstration of three prototypical approaches to learned image reconstruction. The code and data sets for these demonstrations are available to researchers. It is anticipated that it is in in vivo applications - where data may be sparse, fast imaging critical and priors difficult to construct by hand - that Deep Learning will have the most impact. With this in mind, the paper concludes with some indications of possible future research directions.

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull., 23 pages, 13 figures

Ultrasound computed tomography (USCT) is a non-invasive imaging technique that provides information about the acoustic properties of soft tissues in the body, such as the speed of sound (SS) and acoustic attenuation (AA). Knowledge of these properties can improve the discrimination between benign and malignant masses, especially in breast cancer studies. Full wave inversion (FWI) methods for image reconstruction in USCT provide the best image quality compared to more approximate methods. Using FWI, the SS is usually recovered in the time domain, and the AA is usually recovered in the frequency domain. Nevertheless, as both properties can be obtained from the same data, it is desirable to have a common framework to reconstruct both distributions. In this work, an algorithm is proposed to reconstruct both the SS and AA distributions using a time domain FWI methodology based on the fractional Laplacian wave equation, an adjoint field formulation, and a gradient-descent method. The optimization code employs a Compute Unified Device Architecture version of the software k-Wave, which provides high computational efficiency. The performance of the method was evaluated using simulated noisy data from numerical breast phantoms. Errors were less than 0.5% in the recovered SS and 10% in the AA.

The Fabry-Perot (FP) ultrasound sensor can detect ultrasound over a broadband frequency range (tens of MHz) with small element sizes (tens of microns). The FP sensor is an optical interferometer where an incident acoustic wave modulates the optical path length via two mechanisms. The first is from a change in the optical-cavity thickness and the second is from a strain-induced change in refractive index. One way to investigate the transduction mechanisms is to examine the sensor’s frequency-dependent directional response. Previously, the strain-optic effect was neglected when modeling the directional response, however, some experimental studies have shown it to be significant in some circumstances. In this paper, the contributions of the two mechanisms are investigated for a planar air-backed glass-etalon Fabry-Perot sensor. The sensor was modeled as a multilayered elastic structure, and the strain and displacement fields were calculated using the partial wave method. For an optically isotropic, homogeneous and non-absorbing spacer material the strain-optic effect is only dependent on two coefficients, p 11 and p 12 . The modeled directivity was similar when including or excluding the strain-optic coefficients and had good agreement with directional response measurements made on an air-backed glass-etalon sensor. The directional response is dominated by the normal strain in the sensor except at the compressional critical angle where the transverse strain is larger than normal strain. Understanding how the strain-optic mechanism affects the directional response can help improve future sensor design. For example, exploiting materials with large strain-optic coefficients could increase the sensitivity of Fabry-Perot sensors.

Knowledge of the temperature dependence of the material properties of tissue-mimicking materials is useful or essential for many applications. This includes photoacoustic thermometry where the temperature dependence of the Gruneisen parameter of tissues leads to changes in the recorded photoacoustic signal amplitude with temperature. Here, a setup is described that can measure the temperature dependence of the speed of sound and photoacoustic conversion efficiency (µ a Γ) of tissue-mimicking materials. Agar-based phantoms, copolymer-in-oil, gel wax, PVCP, silicone and water were characterised in the newly developed setup for temperatures between 22°C and 50°C. This information provides a valuable resource for material characterisation and future development of tissue-mimicking materials.

Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with boundary conditions imposed at each interface. While these methods are well-known, coding the required matrix formation, inversion, and analysis for general multi-layered systems is non-trivial and time-consuming. Here, a new open-source toolbox called ElasticMatrix is described which solves the problem of acoustic and elastic wave propagation in multi-layered media for isotropic and transverse-isotropic materials where the wave propagation occurs in a material plane of symmetry. The toolbox is implemented in MATLAB using an object oriented programming framework and is designed to be easy to use and extend. Methods are provided for calculating and plotting dispersion curves, displacement and stress fields, reflection and transmission coefficients, and slowness profiles.

k-Wave is an open-source MATLAB toolbox designed for the time-domain simulation of propagating acoustic waves in 1D, 2D, or 3D. The first release was in 2009, and focused on the simulation of photoacoustic initial value problems and the reconstruction of photoacoustic images from simulated or experimental data. In the ten years since, there have been eight major releases, extending both the functionality and the computational performance of the toolbox. There are now more than 10,000 registered users worldwide, and the toolbox has become the defacto standard for simulation studies in photoacoustic imaging. The development team responsible for k-Wave has also grown, with expertise now spanning physics, mathematics, inverse problems, numerical methods, software engineering, and high-performance computing. In this presentation, the major theoretical, algorithmic, and computational developments of k-Wave will be described, along with the underlying design inputs and decisions that led to these developments. A roadmap for the future development of k-Wave will also be presented. This includes new transducer classes, stair-case free sources, native support for multiple GPUs, adaptive grid refinement using moving mesh methods, gradient-based iterative photoacoustic image reconstruction, performance and accuracy improvements for the elastic wave models, and automatic job-submission to run k-Wave simulations remotely using HPC-as-a-service.

Photoacoustic imaging instruments based on the Fabry Perot ultrasound sensing concept have been used extensively for the preclinical assessment of mouse models and shown to provide high fidelity images to sub-cm depths. In a new development, a 3D high resolution scanner based on the same technology has now been specifically engineered into a format comprising a mobile platform and a convenient hand-held imaging probe for clinical use. A number of key engineering developments designed to advance the clinical translation of the technology have been implemented. The system now employs a novel 32-channel optical scanning architecture and a 1kHz PRF excitation laser providing an order-of-magnitude faster acquisition than previous pre-clinical embodiments. 3D images can now be acquired within 1 second, and video rate 2D synthetic aperture imaging is achievable. Image acquisition speed can be further accelerated by employing sub-sampling techniques based on total variation and deep learning image reconstruction, e.g. 3D images can be obtained at the rate of 4Hz with a typical 25% sub-sampling factor. To further aid clinical utility, the scanner allows rapid switching between the two imaging modes. This enables the ROI to be searched for and located in real-time using the 2D video rate mode prior to 3D image acquisition. Additional recent technical developments include bias wavelength tracking for temperature compensation, synthetic 1.5D array based receive beam forming for out-of-plane signal rejection, fast image reconstruction and visualisation and the implementation of an intuitive user-friendly interface. To confirm clinical applicability, proof-of-concept studies both in healthy volunteers and patients have been conducted using the system. Following ethical and local regulatory approval, consenting patients were recruited from a single tertiary care hospital. Participants had previously been diagnosed with peripheral vascular disease (PVD), head and neck malignant tumours (including nodal deposits), inflammatory arthritis, or were under active clinical investigation for these conditions. We obtained mutliwavelength 3D images of the superficial vasculature in critically-ischaemic and normally perfused regions in patients with PVD. In both cases, the photoacoustic images were compared to clinical B-mode and Doppler ultrasound scans. The results show that the scanner is able to visualise the spatial-temporal changes in human microvasculature and thus may be able to identify regions of ischaemia otherwise undetectable using existing modalities. Images of small joint arthopathies, and malignant lymph nodes were also obtained, and compared with contemporaneous high resolution ultrasound. Patients found the use of the scanner highly acceptable, both in degree of comfort and the duration of the scan procedure. This exploratory phase clinical study represents an initial step towards establishing the clinical utility of photoacoustic imaging in a range of clinical conditions.

Compared to piezoelectric based photoacoustic (PA) scanners, the planar Fabry-Perot (FP) scanner has several advantages. It can provide small element size with high sensitivity, a smooth broadband frequency response, and is transparent to excitation light. This enables the FP scanner to provide excellent high-resolution in vivo PA images of soft tissue to depths up to approximately 10 mm. However, unlike piezoelectric scanners, the FP scanner in its current form cannot provide a pulse-echo ultrasound (US) as well as a PA image, which is useful because of the additional tissue contrast it provides. To address this, a dual mode FP scanner-based system that, for the first time, can acquire co-registered 3D PA and US images has been developed. In order to provide an optical US generation capability, the FP ultrasound sensor was coated with a novel Gold-Nanoparticle-PDMS composite which was excited with nanosecond laser pulses to generate plane wave US pulses. By modifying the FP sensor in this way, it now acts as an US transmitter as well as a receiver. The coating is highly absorbing at the US generation wavelength (>95%) but transparent at the PA excitation wavelength, the latter to allow the system to also operate in PA imaging mode as before. The generated US pulses exhibited peak pressures in the MPa range, which is comparable to the output of conventional piezoelectric based medical US scanners. The pulses had a broad bandwidth (>40 MHz) and the emitted wavefront was planar to within λ/10 at 10 MHz. PA and pulse-echo US signals were mapped in turn by the FP scanner over centimetre scale areas with a step size of 100 μm and an element size of 64 μm. The -3dB bandwidth of the FP sensor was 30 MHz. Reconstruction methods using a k-space formulation recovered co-registered 3D PA and US images. The system’s lateral spatial resolution was evaluated by imaging a line target at depths up to 10 mm and ranged between 50 and 120 μm for both modes. Arbitrarily shaped 3D objects were imaged to demonstrate the volumetric US imaging capability of the scanner. Tissue mimicking phantoms, with impedance mismatches representative of soft tissues, and ex vivo tissue samples were imaged with the system as well as a conventional clinical US scanner for comparison. Finally, the system obtained promising high-resolution 3D dual mode PA-US images for a variety of phantoms with contrast based on both optical absorption and acoustic impedance. This novel all-optical system has the potential to add complementary morphological contrast to photoacoustic vascular images which could aid the clinical assessment of superficial tumours, lymph node disease and other conditions.

There are occasions, perhaps due to hardware constraints, or to speed-up data acquisition, when it is helpful to be able to reconstruct a photoacoustic image from an under-sampled or incomplete data set. Here, we will show how Deep Learning can be used to improve image reconstruction in such cases. Deep Learning is a type of machine learning in which a multi-layered neural network is trained from a set of examples to perform a task. Convolutional Neural Networks (CNNs), a type of deep neural network in which one or more layers perform convolutions, have seen spectacular success in recent years in tasks as diverse as image classification, language processing and game playing. In this work, a series of CNNs were trained to perform the steps of an iterative, gradient-based, image reconstruction algorithm from under-sampled data. This has two advantages: first, the iterative reconstruction is accelerated by learning more efficient updates for each iterate; second, the CNNs effectively learn a prior from the training data set, meaning that it is not necessary to make potentially unrealistic regularising assumptions about the image sparsity or smoothness, for instance. In addition, we show an example in which the CNNs learn to remove artifacts that arise when a slow but accurate acoustic model is replaced by a fast but approximate model. Reconstructions from simulated as well as in vivo data will be shown.

Photoacoustic breast imaging has been under development for more than a decade now, and is progressively moving towards the clinics to investigate its performance in tumor detection and diagnosis. Several system types have been built, all with their own characteristics and corresponding imaging performances. Different studies have observed variations in tumor appearances. Some works have seen peripheral blood vessels in the tumor region, while others showed mass-like appearances at the tumor site. These varying tumor presentations may be caused by the deviations in system characteristics, but can also be caused by anatomical differences of the tumors. While we can still learn a lot from in-vivo studies, accurate simulation studies are needed to understand the tumor appearances in full detail. We have developed a simulation toolbox to perform 3D full breast photoacoustic simulations. To investigate the tumor appearance, several tumor models are embedded inside a MRI-segmented digital breast phantom [Y. Lou et al (2017)], which is pendant in a hemispherical imaging tank filled with water. Illumination fibers and US detectors are placed on the surface of the imaging bowl. The toolbox easily allows to adjust laser and detector characteristics. Illumination of the breast is simulated with GPU-accelerated Monte Carlo simulations [Q. Fang et al. (2009)]. The subsequent acoustic signal generation and propagation is modeled with k-wave (GPU-accelerated, [B.E. Treeby et al. (2010)]). Finally, images are reconstructed to evaluate the tumor appearance.

The linear unmixing technique is an appealing method for estimating blood oxygen saturation (sO2) from multiwavelength photoacoustic tomography images, as estimates can be acquired with a straightforward matrix inversion. However, the technique can only rarely provide accurate estimates in vivo, as it requires that the light fluence at the voxels of interest is constant with wavelength. One way to extend the set of cases where accurate information related to sO2 can be acquired with the technique is by taking the difference in sO2 estimates between vessels. Assuming images are perfectly reconstructed, the intervascular difference in sO2 estimates is accurate if the error in the estimates due to the wavelength dependence of the fluence is identical for both. An in silico study was performed to uncover what kinds of conditions may give rise to accurate sO2 differences for a vessel pair. Basic criteria were formulated in simple tissue models consisting of a pair of vessels immersed in two-layer skin models. To assess whether these criteria might still be valid in more realistic imaging scenarios, the sO2 difference was estimated for vessels in more complex tissue models.

Ultrasound is typically measured using phase-sensitive piezoelectric sensors. Interest in phase-insensitive sensors has grown recently, with proposed applications including ultrasound attenuation tomography of the breast and acoustic power measurement. One advantage of phase-insensitive detectors, in contrast to conventional phase-sensitive detectors, is that they do not suffer from a narrow directional response at high frequencies due to phase cancellation. A numerical model of a phase-insensitive pyroelectric ultrasound sensor is presented. The model consists of three coupled components run in sequence: acoustic, thermal, and electrical. The acoustic simulation models the propagation and absorption of the incident ultrasound wave. The absorbed acoustic power density is used as a heat source in the thermal simulation of the time-evolution of the temperature in the sensor. Both the acoustic and thermal simulations are performed using the k-Wave MATLAB toolbox with an assumption that shear waves are not supported in the medium. The final component of the model is a pyroelectric circuit model which outputs the sensor response based on the temperature change in the sensor. The modelled pyroelectric sensor response and directional dependence are compared to empirical data.

Measurement and modelling of nonlinear ultrasound fields underpins many aspects of clinical ultrasound therapies from transducer design, to treatment planning and computational dosimetry, and quality assurance during the manufacture and use of devices. Measurement of high amplitude nonlinear ultrasound fields presents a significant challenge due to the extreme pressures, temperature rises, and mechanical effects that are generated. Additionally, understanding the properties of suitable sensors and their effect on the measurement is critical to ensure that accurate measurements are obtained. Modelling the propagation of ultrasound under these conditions is similarly challenging, as simulations can become large and computationally expensive when highly nonlinear fields are simulated over clinically relevant domains, and experimental validation becomes more difficult. Here we discuss our approach to overcoming these challenges to perform accurate measurement and modelling of high intensity therapeutic ultrasound fields using the open-source k-Wave toolbox, and devices based on Fabry-Perot interferometers developed for measurement of high acoustic pressures.

Acoustic holograms can be used to form complex distributions of pressure in 3D at MHz frequencies from simple inexpensive ultrasound sources. The generation of such fields is vital to a diverse range of applications in physical acoustics. However, at present, the application of acoustic holograms is severely hindered by the static nature of the resulting fields. In this work, it is shown that by intentionally reducing the diffraction efficiency of each hologram, it is possible to create stackable acoustic holograms that can be repositioned to reconfigure the combined acoustic field. An experimental test-case consisting of two holograms, each designed to generate a distinct distribution of acoustic foci, is used to demonstrate the feasibility of this approach. Field scans taken for four different positions of the two holograms confirm that the individual patterns for each hologram can be arbitrary translated relative to one another. This allows for the generation of a much greater range of fields from a single transducer than could be created using a single hologram.

The image reconstruction problem (or inverse problem) in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse. Recently, a Bayesian approach to photoacoustic image reconstruction with uncertainty quantification was proposed and studied with two dimensional numerical simulations. In this paper, the approach is extended to three spatial dimensions and, in addition to numerical simulations, experimental data are considered. The solution of the inverse problem is obtained by computing point estimates, i.e.

Light absorbing polymer nanocomposites have been widely investigated as a source of broadband and high amplitude ultrasound generated via pulsed laser excitation. Biomedical applications of such sources include both imaging and ablative therapies. Fabrication of light absorbing nanocomposite sources has mostly involved elaborate chemistry. Here, a nanocomposite composed of multi-walled carbon nanotubes mechanically dispersed in polydimethylsiloxane polymer is used. The nanocomposite film was backed on optically clear polydimethylsiloxane and laboratory grade glass slides. The two backed sources were investigated using two lasers whose full-width half maximum durations were 2.6 and 4.0 ns. It was found that the characteristics of the acoustic field generated from the nanocomposite source showed a significant dependence on the backing when the stress confinement criterion is not satisfied.

A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: images with good spatial resolution and contrast can be obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning systems if sparsity-constrained image reconstruction techniques such as total variation regularization are used. Now, we show how a further increase of image quality can be achieved for imaging dynamic processes in living tissue (4D PAT). The key idea is to exploit the additional temporal redundancy of the data by coupling the previously used spatial image reconstruction models with sparsity-constrained motion estimation models. While simulated data from a two-dimensional numerical phantom will be used to illustrate the main properties of this recently developed joint-image-reconstruction-and-motion-estimation framework, measured data from a dynamic experimental phantom will also be used to demonstrate their potential for challenging, large-scale, real-world, three-dimensional scenarios. The latter only becomes feasible if a carefully designed combination of tailored optimization schemes is employed, which we describe and examine in more detail.

The characterization of ultrasound fields generated by diagnostic and therapeutic equipment is an essential requirement for performance validation and to demonstrate compliance against established safety limits. This requires hydrophones calibrated to a traceable standard. Currently, the upper calibration frequency range available to the user community is limited to 60 MHz. However, high frequencies are increasingly being used for both imaging and therapy necessitating calibration frequencies up to 100 MHz. The precise calibration of hydrophones requires a source of high amplitude, broadband, quasi-planar, and stable ultrasound fields. There are challenges to using conventional piezoelectric sources, and laser generated ultrasound sources offer a promising solution. In this study, various nanocomposites consisting of a bulk polymer matrix and multi-walled carbon nanotubes were fabricated and tested using pulsed laser of a few nanoseconds for their suitability as a source for high frequency calibration of hydrophones. The pressure amplitude and bandwidths were measured using a broadband hydrophone from 27 different nanocomposite sources. The effect of nonlinear propagation of high amplitude laser generated ultrasound on bandwidth and the effect of bandlimited sensitivity response on the deconvolved pressure waveform were numerically investigated. The stability of the nanocomposite sources under sustained laser pulse excitation was also examined.

© 2009 by Taylor & Francis Group, LLC. This chapter describes a general model-based inversion scheme for recovering the concentrations of tissue chromophores from multiwavelength photoacoustic images. A diffusion-based finite element (FE) forward model of light transport is used to generate images of absorbed optical energy at different wavelengths as a function of chromophore concentrations. By iteratively adjusting the latter until the model output matches the measured multiwavelength images, a set of quantitative concentration maps that reveal the abundance of each chromophore can be obtained. The technique can be used to quantify physiologically important endogenous chromophores such as oxy (HbO2) and deoxyhemoglobin (HHb), or exogenous chromophores such as those used in molecular imaging. The aim of this chapter is to describe the theory and practice of this approach and is divided into two parts. In the first, we describe a simplified implementation in which the concentrations of multiple chromophores are recovered from experimental measurements of multi-wavelength time-resolved photoacoustic signals detected at 122a single spatial point in a tissue-mimicking phantom. In the second, the progress that has been made towards developing the computational methods required to solve the general problem of recovering maps of chromophore concentrations from photoacoustic images is described. First, the problem is set in context by considering what a photoacoustic image represents, the physical parameters that can be obtained from it, and the underlying hypothesis and methodology of the inversion scheme.

Deep photoacoustic imaging of mammalian cells featuring genetically encoded contrast is reported.

Accurate characterization of ultrasound fields generated by diagnostic and therapeutic transducers is critical for patient safety. This requires hydrophones calibrated to a traceable standard and currently the upper calibration frequency range available to the user community is limited to a frequency of 40 MHz. However, the increasing use of high frequencies for both imaging and therapy necessitates calibrations to frequencies well beyond this range. For this to be possible, a source of high amplitude, broadband, quasi-planar and stable ultrasound fields is required. This is difficult to achieve using conventional piezoelectric sources, but laser generated ultrasound is a promising technique in this regard. In this study, various polymer-carbon nanotube nanocomposites (PNC) were fabricated and tested for their suitability for such an application by varying the polymer type, carbon nanotubes weight content in the polymer, and PNC thickness. A broadband hydrophone was used to measure the peak pressure and bandwidth of the laser generated ultrasound pulse. Peak-positive pressures of up to 8 MPa and −6dB bandwidths of up to 40 MHz were recorded. There is a nonlinear dependence of the peak pressure on the laser fluence and the bandwidth scales inversely proportionally to the peak pressure. The high-pressure plane waves generated from this preliminary investigation has demonstrated that laser generated ultrasound sources are a promising technique for high frequency calibration of hydrophones.

The k-Wave MATLAB toolbox is widely used to conduct medical ultrasound simulations. It uses a Fourier collocation method to numerically solve the governing model equations, and introduces sources by adding acoustic pressure at points on an orthogonal grid. This approach introduces two errors when sources don't exactly align with the grid. These are phase errors arising from shifting source points to nearby grid nodes, and amplitude errors arising from an angular dependence in the density of source points. These two errors are collectively referred to as ‘staircasing’. Staircasing errors can be overcome by considering the band-limited representation of sources that arises from the use of a Fourier collocation method. To do so, sources are discretised by convolving a band-limited point source with the desired source geometry. To validate this approach, a comparison is made with current k-Wave source algorithms and with the FOCUS ultrasound simulation code. The new sources are shown to eliminate staircasing errors.

The control of acoustic fields in 3-D is vital in many areas of physical acoustics. Recently, a new approach for the generation of complex diffraction limited acoustic fields in 3-D was introduced. This works by calculating a phase hologram designed to generate a desired acoustic field. The output of a simple planar transducer is then mapped onto this phase distribution using a 3-D printed kinoform attached to the transducer. One limitation of this approach is that the acoustic field generated by each kinoform is fixed. A way to overcome this is to adapt a technique from optical holography and encode several target distributions onto different frequencies. The field can then be changed by varying the driving frequency of the transducer. The goal of this work was to demonstrate this approach and to investigate the design of these kinoforms.