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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.

The pseudospectral time domain (PSTD) method is popular as a wave equation solver, one of its advantages being that it permits the use of coarse grids, as long as the spatial sampling is greater than two points-per-wavelength. The k-space PSTD method improves on this by incorporating an additional factor to remove the numerical dispersion which arises from the discretisation of the time derivatives. However, the effect of the temporal discretisation of time-varying sources has not previously been considered, although it can lead to substantial errors in the predicted field unless the timestep is sufficiently small to ensure the highest frequency is sampled at many points-per-period. Here, a correction factor is derived which eliminates this source of error, resulting in a k-space PSTD method that retains the spatial sampling advantage of conventional PSTD schemes but is also accurate as long as the temporal sampling is greater than two points-per-period and the CFL number is < 1.

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.

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

© 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.

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.

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 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.

The generation of complex diffraction limited acoustic fields from a simple planar transducer is possible using cheap 3-D printable kinoforms. This approach is extremely promising for several areas of physical acoustics. However, one drawback is that the acoustic field generated from a given kinoform is fixed, limiting flexibility. In this work, multi-frequency acoustic kinoforms are investigated as a means to circumvent that limitation. These are kinoforms designed to generate different distributions of pressure at a target depth when driven at particular design frequencies. An optimisation approach based on direct search for the design of these structures from a set of input frequencies and target distributions is briefly described. The effect of different parameters of the kinoform on the performance are then established. These include the maximum thickness, frequency spacing and target depth. It is found that the maximum thickness has to be limited to avoid significant aberrations, the frequency spacing should be maximised within the usable bandwidth of the transducer, and the optimal thickness is influenced by the choice of target depth. The thin phase approximation is also shown to be increasingly inaccurate for increasing element thicknesses.

Non-invasive, focal neurostimulation with ultrasound is a potentially powerful neuroscientific tool that requires effective transcranial focusing of ultrasound to develop. Time-reversal (TR) focusing using numerical simulations of transcranial ultrasound propagation can correct for the effect of the skull, but relies on accurate simulations. Here, focusing requirements for ultrasonic neurostimulation are established through a review of previously employed ultrasonic parameters, and consideration of deep brain targets. The specific limitations of finite-difference time domain (FDTD) and k-space corrected pseudospectral time domain (PSTD) schemes are tested numerically to establish the spatial points per wavelength and temporal points per period needed to achieve the desired accuracy while minimizing the computational burden. These criteria are confirmed through convergence testing of a fully simulated TR protocol using a virtual skull. The k-space PSTD scheme performed as well as, or better than, the widely used FDTD scheme across all individual error tests and in the convergence of large scale models, recommending it for use in simulated TR. Staircasing was shown to be the most serious source of error. Convergence testing indicated that higher sampling is required to achieve fine control of the pressure amplitude at the target than is needed for accurate spatial targeting. Neinvazivní neurostimulace pomocí ultrazvuku je nové technika s širokým uplatněním při výzkumu mozku. Tato práce vyšetřuje možnosti cíleného zaměření svazku ultrazvukových vln a korekce aberací způsobné průchodem skrze lebku

To unlock the full capability of photoacoustic tomography as a quantitative, high resolution, molecular imaging modality, the problem of quantitative photoacoustic tomography must be solved. The aim in this is to extract clinically relevant functional information from photoacoustic images by finding the concentrations of the chromophores in the tissue. This is a challenging task due to the effect of the unknown but spatially and spectrally varying light fluence within the tissue. Many inversion schemes that include a model of the fluence have been proposed, but these have yet to make an impact in pre-clinical or clinical imaging. In this study, the statistical independence of the chromophore's distributions is proposed as a means of improving the robustness and hence the usefulness of the model-based inversion methods. This was achieved by minimising the mutual information between the estimated chromophore distributions in addition to the least squares data error within a gradient-based optimisation scheme. By applying the proposed inversion scheme to simulated multiwavelength photoacoustic images, it was shown that more accurate estimates for the concentrations of independent chromophores could be obtained in the presence of errors in the model parameters.

Planar Fabry-Perot (FP) ultrasound sensor arrays have been used to produce in-vivo photoacoustic images of high quality due to their broad detection bandwidth, small element size, and dense spatial sampling. However like all planar arrays, FP sensors suffer from the limited view problem. Here, a multi-angle FP sensor system is described that mitigates the partial view effects of a planar FP sensor while retaining its detection advantages. The possibility of improving data acquisition speed through the use of sub-sampling techniques is also explored. The capabilities of the system are demonstrated with 3D images of pre-clinical targets

The planar Fabry Perot (FP) photoacoustic scanner provides exquisite high resolution 3D images of soft tissue structures for sub-cm penetration depths. However, as the FP sensor is optically addressed by sequentially scanning an interrogation laser beam over its surface, the acquisition speed is low. To address this, a novel scanner architecture employing 8 interrogation beams and an optimised sub-sampling framework have been developed that increase the data acquisition speed significantly. With a 200Hz repetition rate excitation laser, full 3D images can be obtained within 10 seconds. Further increases in imaging speed with only minor decreases in image quality can be obtained by applying sub-sampling techniques with rates as low as 12.5%. This paper shows 3D images reconstructed from sub-sampled data for an ex vivo dataset, and results from a dynamic phantom imaging experiment.

Quantitative photoacoustic tomography seeks to estimate the optical parameters of a target given photoacoustic measurements as a data. Conventionally the problem is split into two steps: 1) the acoustical inverse problem of estimating the acoustic initial pressure distribution from the acoustical time series data; 2) the optical inverse problem of estimating the optical absorption and scattering from the initial pressure distributions. In this work, an approach for estimating the optical absorption and scattering directly from the acoustical time series is investigated with simulations. The work combines a homogeneous acoustical forward model, based on the Green's function solution of the wave equation, and a finite element method based diffusion approximation model of light propagation into a single forward model. This model maps the optical parameters of interest into a time domain signal. The model is used with a Bayesian approach to ill-posed inverse problems to form estimates of the posterior distributions for the parameters of interest. In addition to being able to provide point estimates of the parameters of interest, i.e. reconstruct the absorption and scattering distributions, the approach can be used to derive information on the uncertainty associated with the estimates.

Photoacoustic tomography can, in principle, provide quantitatively accurate, high-resolution, images of chromophore distributions in 3D in vivo. However, achieving this goal requires not only dealing with the optical fluence-related spatial and spectral distortion but also having access to high quality, calibrated, measurements and using image reconstruction algorithms free from inaccurate assumptions. Furthermore, accurate knowledge of experimental parameters, such as the positions of the ultrasound detectors and the illumination pattern, is necessary for the reconstruction step. A meticulous and rigorous experimental phantom study was conducted to show that highly-resolved 3D estimation of chromophore distributions can be achieved: a crucial step towards in vivo implementation. The phantom consisted of four 580 μm diameter tubes with different ratios of copper sulphate and nickel sulphate as hemoglobin analogues, submersed in a background medium of intralipid and india ink. The optical absorption, scattering, photostability, and Gruneisen parameter were characterised for all components independently. A V-shaped imaging scanner enabled 3D imaging with the high resolution, high sensitivity, and wide bandwidth characteristic of Fabry-Perot ultrasound sensors, but without the limited-view disadvantage of single-plane scanners. The optical beam profile and position were determined experimentally. Nine wavelengths between 750 and 1110 nm were used. The images of the chromophore concentrations were obtained using a model-based, two-step, procedure, that did not require image segmentation. First, the acoustic reconstruction was solved with an iterative time-reversal algorithm to obtain images of the initial acoustic pressure at each of the nine wavelengths for an 18×17×13 mm3 volume with 50μm voxels. Then, 3D high resolution estimates of the chromophore concentrations were obtained by using a diffusion model of light transport in an iterative nonlinear optimisation scheme. Among the lessons to be drawn from this study, one is fundamental: in order to obtain accurate estimates of chromophores (or their ratios) it is not only necessary to model the light fluence accurately, but it is just as crucial to obtain accurate estimates of the initial acoustic pressure distributions, and to account for variations in the thermoelastic efficiency (Gruneisen parameter).

High intensity transcranial focused ultrasound is an FDA approved treatment for essential tremor, while low-intensity applications such as neurostimulation and opening the blood brain barrier are under active research. Simulations of transcranial ultrasound propagation are used both for focusing through the skull, and predicting intracranial fields. Maps of the skull acoustic properties are necessary for accurate simulations, and can be derived from medical images using a variety of methods. The skull maps range from segmented, homogeneous models, to fully heterogeneous models derived from medical image intensity. In the present work, the impact of uncertainties in the skull properties is examined using a model of transcranial propagation from a single element focused transducer. The impact of changes in bone layer geometry and the sound speed, density, and acoustic absorption values is quantified through a numerical sensitivity analysis. Sound speed is shown to be the most influential acoustic property, and must be defined with less than 4% error to obtain acceptable accuracy in simulated focus pressure, position, and volume. Changes in the skull thickness of as little as 0.1 mm can cause an error in peak intracranial pressure of greater than 5%, while smoothing with a 1 [Formula: see text] kernel to imitate the effect of obtaining skull maps from low resolution images causes an increase of over 50% in peak pressure. The numerical results are confirmed experimentally through comparison with sonications made through 3D printed and resin cast skull bone phantoms.

A class of nonstandard pseudospectral time domain (PSTD) schemes for solving time-dependent hyperbolic and parabolic partial differential equations (PDEs) is introduced. These schemes use the Fourier collocation spectral method to compute spatial gradients and a nonstandard finite difference scheme to integrate forwards in time. The modified denominator function that makes the finite difference time scheme exact is transformed into the spatial frequency domain or k-space using the dispersion relation for the governing PDE. This allows the correction factor to be applied in the spatial frequency domain as part of the spatial gradient calculation. The derived schemes can be formulated to be unconditionally stable, and apply to PDEs in any space dimension. Examples of the resulting nonstandard PSTD schemes for several PDEs are given, including the wave equation, diffusion equation, and convection-diffusion equation., Comment: Update to section 4 (application to PDEs with non-constant coefficients)

Ultrasound is typically measured using phase-sensitive piezoelectric sensors. Interest in phase-insensitive sensors has grown recently, with proposed applications in ultrasound attenuation tomography of the breast. The advantage of phase-insensitive imaging is that it does not suffer from degradation of image quality due to phase-aberration and narrow directional response. 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 incoming ultrasound wave. The negative divergence of the time-averaged acoustic intensity is used as a heat source in the thermal simulation for the time-evolution of 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 uses 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. A physical model for the directionality of the sensor response is then proposed.

The number of ultrasound detectors required to produce photoacoustic tomography images can be reduced significantly by fully enclosing the imaging target in an acoustically reverberant cavity and exploiting the multiple reflections. This is demonstrated experimentally.

Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when model solutions include localised steep gradients. In this paper, one-dimensional mesh density functions are presented which are based on a spatially localised measure of the bandwidth of the approximated model solution. In considering bandwidth, these mesh density functions are well-justified for spectral methods, but are not strictly tied to the error properties of any particular spatial interpolant, and are hence widely applicable. The bandwidth mesh density functions are illustrated in two ways. First, by applying them to Chebyshev polynomial approximation of two test functions, and second, through use in periodic spectral and finite-difference moving mesh methods applied to a number of model problems in acoustics. These problems include a heterogeneous advection equation, the viscous Burgers’ equation, and the Korteweg-de Vries equation. Simulation results demonstrate solution convergence rates that are up to an order of magnitude faster using the bandwidth mesh density functions than uniform meshes, and around three times faster than those using the arclength mesh density function.

Estimation of optical absorption and scattering of a target is an inverse problem associated with quantitative photoacoustic tomography. Conventionally, the problem is expressed as two folded. First, images of initial pressure distribution created by absorption of a light pulse are formed based on acoustic boundary measurements. Then, the optical properties are determined based on these photoacoustic images. The optical stage of the inverse problem can thus suffer from, for example, artefacts caused by the acoustic stage. These could be caused by imperfections in the acoustic measurement setting, of which an example is a limited view acoustic measurement geometry. In this work, the forward model of quantitative photoacoustic tomography is treated as a coupled acoustic and optical model and the inverse problem is solved by using a Bayesian approach. Spatial distribution of the optical properties of the imaged target are estimated directly from the photoacoustic time series in varying acoustic detection and optical illumination configurations. It is numerically demonstrated, that estimation of optical properties of the imaged target is feasible in limited view acoustic detection setting.

A new method for the creation of patterned, focused, optically generated acoustic fields using a single optical pulse is introduced. This utilises multi-layer ‘holograms’ composed of several spatially separate absorbing layers. Each layer is individually patterned so as to focus at a set of targeted points. To create the patterns, a ray-tracing model was implemented to calculate the impulse response of pixels within each absorbing layer to a set of targeted points. An optimisation approach was then used to find the optimal pattern for each layer to create a field evenly focused at each of the target points. The method was validated using both numerical simulations and acoustic field measurements. It was demonstrated that a 3×3 array of acoustic foci could be generated from a 3-layer hologram using a single laser pulse.

In this work, the use of binary amplitude holography is investigated as a mechanism to focus broadband acoustic pulses generated by high peak-power pulsed lasers. Two algorithms are described for the calculation of the binary holograms; one using ray-tracing, and one using an optimization based on direct binary search. It is shown using numerical simulations that when a binary amplitude hologram is excited by a train of laser pulses at its design frequency, the acoustic field can be focused at a pre-determined distribution of points, including single and multiple focal points, and line and square foci. The numerical results are validated by acoustic field measurements from binary amplitude holograms, excited by a high peak-power laser.

Acoustical attenuation (AA) maps in Ultrasound Computed Tomography (USCT) provide enhanced contrast between tissues compared to the speed of sound (SS), which is the most common property of tissue studied with this technique. Currently, the full wave inversion (FWI) methods used for their reconstruction are very different: the AA is mainly estimated using frequency domain algorithms, while the SS is more often recovered in the time domain. In this work we present a novel strategy to recover the attenuation maps through a straightforward and simplified procedure in the time domain. A gradient descent method was employed to optimize iteratively the attenuation distribution. The expression for the functional gradient of the norm of the global deviation between experimental and simulated data was obtained using an adjoint method. The optimization code, implemented in C++, employs a CUDA version of the k-Wave software to perform forward and backward wave propagation. Noisy simulated data was used to test the performance of the proposed method. The simplicity of the formulation of this new method may facilitate the reconstruction of AA and SS maps under a common framework in USCT.

Independent component analysis (ICA) is a blind source unmixing method that may be used under certain circumstances to decompose multi-wavelength photoacoustic (PA) images into separate components representing individual chromophores. It has the advantages of being fast, easy to implement and computationally inexpensive. This study uses simulated multi-wavelength PA images to investigate the conditions required for ICA to be an accurate unmixing method and compares its performance to linear inversion. An approximate fluence adjustment based on spatially homogeneous optical properties equal to that of the background region was applied to the PA images before unmixing with ICA or LI. ICA is shown to provide accurate separation of the chromophores in cases where the absorption coefficients are lower than certain thresholds, some of which are comparable to physiologically relevant values. However, the results also show that the performance of ICA abruptly deteriorates when the absorption is increased beyond these thresholds. In addition, the accuracy of ICA decreases in the presence of spatially inhomogeneous absorption in the background.

The planar Fabry Perot (FP) photoacoustic scanner has been shown to provide exquisite high resolution 3D images of soft tissue structures in vivo to depths up to approximately 10mm. However a significant limitation of current embodiments of the concept is low image acquisition speed. To increase acquisition speed, a novel multi-beam scanner architecture has been developed. This enables a line of equally spaced 8 interrogation beams to be scanned simultaneously across the FP sensor and the photoacoustic signals detected in parallel. In addition, an excitation laser operating at 200Hz was used. The combination of parallelising the detection and the high pulse repetition frequency (PRF) of the excitation laser has enabled dramatic reductions in image acquisition time to be achieved. A 3D image can now be acquired in 10 seconds and 2D images at video rates are now possible. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Reconstructing images from measured time domain signals is an essential step in tomography-mode photoacoustic imaging. However, in practice, there are many complicating factors that make it difficult to obtain high-resolution images. These include incomplete or undersampled data, filtering effects, acoustic and optical attenuation, and uncertainties in the material parameters. Here, the processing and image reconstruction steps routinely used by the Photoacoustic Imaging Group at University College London are discussed. These include correction for acoustic and optical attenuation, spatial resampling, material parameter selection, image reconstruction, and log compression. The effect of each of these steps is demonstrated using a representative in vivo dataset. All of the algorithms discussed form part of the open-source k-Wave toolbox (available from http://www.k-wave.org).

The ability to accurately quantify chromophore concentration from photoacoustic images would have a major impact on pre-clinical and clinical imaging. Recent years have seen significant advances in the theoretical understanding of quantitative photoacoustic imaging and in the development of model-based inversion strategies that overcome issues such as non-uniqueness and non-linearity. Nevertheless, their full in vivo implementation has not successfully been achieved, partially because experimental uncertainties complicate the transition. In this study, a sensitivity analysis is performed to assess the impact on accuracy of having uncertainty in critical experimental parameters such as scattering, beam diameter, beam position and calibration factor. This study was performed using two virtual phantoms, at one illumination and four optical wavelengths. The model-based inversion was applied in 3 variants - one just inverting for chromophores and two others further inverting for either a scaling factor or the scatterer concentration. The performance of these model-based inversions is also compared to linear unmixing strategies - with and without fluence correction. The results show that experimental uncertainties in a priori fixed parameters - especially calibration factor and scatterer concentration - significantly affect accuracy of model-based inversions and therefore measures to ameliorate this uncertainty should be considered. Including a scaling parameter in the inversion appears to improve quantification estimates. Furthermore, even with realistic levels of experimental uncertainty in model-based input parameters, they outperform linear unmixing approaches. If parameter uncertainty is large and has significant impact on accuracy, the parameter can be included as an unknown in model-based schemes.

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

We propose a novel multispectral reconstruction-classification method for simultaneously recovering absorption and scattering coefficients from images of absorbed optical energy. In contrast with pre-existing chromophore reconstruction methods, this approach does not require prior knowledge of the characteristic spectra of the absorbers, which is not always available. Numerical experiments performed on anatomically realistic 3D phantoms show that this approach allows for improved recovery of both the optical absorption and scattering with respect to reconstruction-only methods, and accurate classification of chromophores of clinical interest.

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the optical parameters inside tissue from photoacoustic images. The method proceeds from photoacoustic tomography by taking the estimated initial pressure distributions as data and estimating the absolute values of the optical parameters. Therefore, both the data and the noise of the second (optical) inverse problem are affected by the method applied to solve the first (acoustic) inverse problem. In this work, the Bayesian approach for quantitative photoacoustic tomography is taken. Modelling of noise and errors and incorporating their statistics into the solution of the inverse problem are investigated.

Fabry-Perot (FP) sensors have been used to produce in-vivo photoacoustic images of exquisite quality. However, for simplicity of construction FP sensors are produced in a planar form. Planar sensors suffer from a limited detection aperture, due to their planarity. We present a novel sensor geometry that allowed a greater field of view by placing a second sensor orthogonal to the first. This captured data from the deeper lying regions of interest and mitigated the limited view.

An efficient Green’s function solution for acoustic initial value problems in homogeneous media with power law absorption is derived. The solution is based on the homogeneous wave equation for lossless media with two additional terms. These terms are dependent on the fractional Laplacian and separately account for power law absorption and dispersion. Given initial conditions for the pressure and its temporal derivative, the solution allows the pressure field for any time t>0 to be calculated in a single step using the Fourier transform and an exact k-space time propagator. For regularly spaced Cartesian grids, the former can be computed efficiently using the fast Fourier transform. Because no time stepping is required, the solution facilitates the efficient computation of the pressure field in one, two, or three dimensions without stability constraints. Several computational aspects of the solution are discussed, including the effect of using a truncated Fourier series to represent discrete initial conditions, the use of smoothing, and the properties of the encapsulated absorption and dispersion.

The ultrasound attenuation coefficient and dispersion from 0–70 MHz in whole human blood and its components (red blood cells and plasma) at 37°C is reported. The measurements are made using a fixed path substitution technique that exploits optical mechanisms for the generation and detection of ultrasound. This allows the measurements to cover a broad frequency range with a single source and receiver. The measured attenuation coefficient and dispersion in solutions of red blood cells and physiological saline for total haemoglobin concentrations of 10, 15 and 20 g/dL are presented. The attenuation coefficient and dispersion in whole human blood taken from four healthy volunteers by venipuncture is also reported. The power law dependence of the attenuation coefficient is shown to vary across the measured frequency range. This is due to the varying frequency dependence of the different mechanisms responsible for the attenuation. The attenuation coefficient measured at high frequencies is found to be significantly higher than that predicted by historical power law parameters. A review of the attenuation mechanisms in blood along with previously reported experimental measurements is given. Values for the sound speed and density in the tested samples are also presented. (E-mail: btreeby@mpb.ucl.ac.uk )

Several different reconstruction algorithms have been proposed for photoacoustic tomography, most of which presuppose that the acoustic properties of the medium are constant and homogeneous. In practice, there are often unknown spatial variations in the acoustic properties, and these algorithms give, at best, only approximate estimates of the true image. The question as to which approach is the most robust in these circumstances is therefore one of practical importance. Image reconstruction by "time reversal"-using a numerical propagation model with a time-varying boundary condition corresponding to the measured data in reversed temporal order-has been shown to be less restrictive in its assumptions than most, and therefore a good candidate for a general and practically useful algorithm. Here, it is shown that such reconstruction algorithms can "trap" time reversed scattered waves, leading to artifacts within the image region. Two ways to mitigate this effect are proposed.

The broadband ultrasonic characterization of biological fluids and tissues is important for the continued development and application of high-resolution ultrasound imaging modalities. Here, a photoacoustic technique for the transmission measurement of temperature-dependent ultrasonic attenuation and dispersion is described. The system uses a photoacoustic plane wave source constructed from a polymethylmethacrylate substrate with a thin optically absorbent layer. Broadband ultrasonic waves are generated by illuminating the absorbent layer with nanosecond pulses of laser light. The transmitted ultrasound waves are detected by a planar 7-microm high-finesse Fabry-Perot interferometer. Temperature-induced thickness changes in the Fabry-Perot interferometer are tracked to monitor the sample temperature and maintain the sensor sensitivity. The measured -6 dB bandwidth for the combined source and sensor is 1 to 35 MHz, with an attenuation corrected signal level at 100 MHz of -10 dB. The system is demonstrated through temperature-dependent ultrasound measurements in castor oil and olive oil. Power law attenuation parameters are extracted by fitting the experimental attenuation data to a frequency power law while simultaneously fitting the dispersion data to the corresponding Kramers-Krönig relation. The extracted parameters are compared with other calibration measurements previously reported in the literature.

In conventional biomedical photoacoustic tomography (PAT), ultrasonic pulses generated through the absorption of nanosecond pulses of near-infrared light are recorded over an array of detectors and used to recover an image of the initial acoustic pressure distribution within soft tissue. This image is related to the tissue optical coefficients and therefore carries information about the tissue physiology. For high resolution imaging, a large-area detector array with a high density of small, sensitive elements is required. Such arrays can be expensive, so reverberant-field PAT has been suggested as a means of obtaining PAT images using arrays with a smaller number of detectors. By recording the reflections from an acoustically reverberant cavity surrounding the sample, in addition to the primary acoustic pulse, sufficient information may be captured to allow an image to be reconstructed without the need for a large-area array. An initial study using two-dimensional simulations was performed to assess the feasibility of using a single detector for PAT. It is shown that reverberant-field data recorded at a single detector are sufficient to reconstruct the initial pressure distribution accurately, so long as the shape of the reverberant cavity makes it ray-chaotic. The practicalities of such an approach to photoacoustic imaging are discussed.

Biomedical photoacoustic tomography (PAT) is a soft-tissue imaging modality which combines the high spatial resolution of ultrasound (US) with the contrast and spectroscopic opportunities afforded by imaging optical absorption. Planar US arrays composed of piezoelectric or optical detector elements with small element sizes and fast acquisition times are readily available, making them an attractive option for imaging applications. An exact and efficient, FFT-based PAT reconstruction algorithm, that converts acoustic measurements recorded over a plane to a PAT image, is known. However, to capture sufficient data for an exact PAT reconstruction with a planar geometry requires an infinitely wide array. In practice it will be finite, resulting in a loss of resolution and introducing artefacts into the image. To overcome this limitation it is proposed that acoustic image sources, provided by enclosing the target in a reverberant cavity, are used to generate a periodically repeating sound field. Measurements of this periodic sound field can be used to reconstruct a PAT image exactly from measurements of reverberation made over a finite aperture. The existing FFT-based PAT reconstruction algorithm with only minor additional modifications can be used to generate the image in this case.

We propose a combined reconstruction-classification method for simultaneously recovering absorption and scattering in turbid media from images of absorbed optical energy. This method exploits knowledge that optical parameters are determined by a limited number of classes to iteratively improve their estimate. Numerical experiments show that the proposed approach allows for accurate recovery of absorption and scattering in 2 and 3 dimensions, and delivers superior image quality with respect to traditional reconstruction-only approaches., Comment: 10 pages, 7 figures

Photoacoustic imaging can provide high resolution images of tissue structure, pathology and function. As these images can be obtained at multiple wavelengths, quantitatively accurate, spatially resolved, estimates for chromophore concentration, for example, may be obtainable. Such a capability would find a wide range of clinical and pre-clinical applications. However, despite a growing body of theoretical papers on how this might be achieved, there is a noticeable lack of studies providing validated evidence that it can be achieved experimentally, either in vitro or in vivo. Well-defined, versatile and stable phantom materials are essential to assess the accuracy, robustness and applicability of multispectral Quantitative Photoacoustic Imaging (qPAI) algorithms in experimental scenarios. This study assesses the potential of polyvinyl chloride plastisol (PVCP) as a phantom material for qPAI, building on previous work that focussed on using PVCP for quality control. Parameters that might be controlled or tuned to assess the performance of qPAI algorithms were studied: broadband acoustic properties, multiwavelength optical properties with added absorbers and scatterers, and photoacoustic effciency. The optical and acoustic properties of PVCP can be tuned to be broadly representative of soft tissue. The Gruneisen parameter is larger than expected in tissue, which is an advantage as it increases the signal-to-noise ratio of the photoacoustic measurements. Interestingly, when the absorption was altered by adding absorbers, the absorption spectra measured using high peak power nanosecond-pulsed sources (typical in photoacoustics) were repeatably different from the ones measured using the low power source in the spectrophotometer, indicative of photochemical reactions taking place.

Photoacoustic images of exquisite quality have previously been obtained using planar Fabry-Perot ultrasound sensors, as they can synthesize detection arrays with small, highly sensitive, elements. However, their planarity prevents reconstruction of structures perpendicular to the sensor plane, which gives rise to limited-view artifacts. Here, a novel FP sensor array configuration is described that incorporates two orthogonal planar arrays in order to overcome this limitation. Three dimensional photoacoustic images of suitably structured phantoms, obtained using a time reversal reconstruction algorithm, are used to demonstrate the significant improvement in the reconstructed images.