open-UST: An Open-Source Ultrasound Tomography Transducer Array System

Fast imaging methods are needed to promote 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 £2k. Novel manufacturing techniques were used, resulting in a 1.17° mean beam axis skew angle, a [Formula: see text] mean element position error, and a [Formula: see text] deviation in matching layer thickness. The nominal acoustic performance was measured using hydrophone scans and watershot data, and the 61.2 dB signal-to-noise ratio (SNR), 55.4° opening angle, 10.2 mm beamwidth, and 54% transmit-receive bandwidth (-12 dB) were found to be similar to existing systems and compatible with state-of-the-art full-waveform-inversion image reconstruction methods. The interelement variation in acoustic performance was typically < 10% without using normalization, meaning that the elements can be modeled identically during image reconstruction, removing the need for individual source definitions based on hydrophone measurements. Finally, data from a phantom experiment were successfully reconstructed. These results demonstrate that the open-UST system is accessible for users and is suitable for UST imaging research.

A learned Born series for highly-scattering media

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.

The effect of source backing materials and excitation pulse durations on laser-generated ultrasound waveforms

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.

The IPASC data format: A consensus data format for photoacoustic imaging

Photoacoustic imaging (PAI) is an emerging modality that has shown promise for improving patient management in a range of applications. Unfortunately, the current lack of uniformity in PAI data formats compromises inter-user data exchange and comparison, which impedes: technological progress; effective research collaboration; and efforts to deliver multi-centre clinical trials. To overcome this challenge, the International Photoacoustic Standardisation Consortium (IPASC) has established a data format with a defined consensus metadata structure and developed an open-source software application programming interface (API) to enable conversion from proprietary file formats into the IPASC format. The format is based on Hierarchical Data Format 5 (HDF5) and designed to store photoacoustic raw time series data. Internal quality control mechanisms are included to ensure completeness and consistency of the converted data. By unifying the variety of proprietary data and metadata definitions into a consensus format, IPASC hopes to facilitate the exchange and comparison of PAI data.

Measurement of the ultrasound attenuation and dispersion in 3D-printed photopolymer materials from 1 to 3.5 MHz

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  · m^-3, while the sound speed values were between 2020 to 2630 m  · s^-1, and attenuation values typically in the range 3-9 dB  ·  MHz^-1· cm^-1.

Modelling laser ultrasound waveforms: The effect of varying pulse duration and material properties

Optical generation of ultrasound using nanosecond duration laser pulses has generated great interest both in industrial and biomedical applications. The availability of portable laser devices using semiconductor technology and optical fibres, as well as numerous source material types based on nanocomposites, has proliferated the applications of laser ultrasound. The nanocomposites can be deposited on the tip of optical fibres as well as planar hard and soft backing materials using various fabrication techniques, making devices suitable for a variety of applications. The ability to choose the acoustic material properties and the laser pulse duration gives considerable control over the ultrasound output. Here, an analytical time-domain solution is derived for the acoustic pressure waveform generated by a planar optical ultrasound source consisting of an optically absorbing layer on a backing. It is shown that by varying the optical attenuation coefficient, the thickness of the absorbing layer, the acoustic properties of the materials, and the laser pulse duration, a wide variety of pulse shapes and trains can be generated. It is shown that a source with a reflecting backing can generate pulses with higher amplitude than a source with an acoustically-matched backing in the same circumstances when stress-confinement has not been satisfied.

100 MHz bandwidth planar laser-generated ultrasound source for hydrophone calibration

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.

Nonlinear ultrasound simulation in an axisymmetric coordinate system using a k-space pseudospectral method

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.

The Effect of Curing Temperature and Time on the Acoustic and Optical Properties of PVCP

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.

Analysis of the Directivity of Glass-Etalon Fabry-Pérot Ultrasound Sensors

Planar glass-etalon Fabry-Pérot (FP) optical ultrasound sensors offer an alternative to piezoelectric sensors for the measurements of high-intensity focused ultrasound (HIFU) fields and other metrological applications. In this work, a model of the frequency-dependent directional response of the FP sensor was developed using the global matrix method, treating the sensor as a multilayered elastic structure. The model was validated against the experimentally measured directional response of an air-backed cover-slip FP sensor with well-known material properties. In addition, the model was compared with the measurements of an all-hard-dielectric sensor suitable for HIFU measurements. The model was then used to calculate modal dispersion curves for both glass-etalon sensors, allowing the features of the directional response to be linked to specific wave phenomena. The features in the directivity of the air-backed cover-slip sensor are due to guided Lamb waves. Symmetric Lamb modes give rise to regions of high sensitivity, whereas anti-symmetric modes cause regions of low sensitivity. For the all-hard-dielectric sensor, two features correspond to the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity close to the shear critical angle is associated with a leaky-Rayleigh wave, which has a frequency-dependent phase speed. At higher frequencies, this feature is counteracted by a region of low sensitivity, which occurs when there is no difference in the vertical displacement of the mirrors forming the FP cavity. The model may be used to improve and optimize the design of FP sensors or could be used to assist with the accurate deconvolution of the directional response from array measurements in metrological and imaging applications.

Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods

Accurately representing acoustic source distributions is an important part of ultrasound simulation. This is challenging for grid-based collocation methods when such distributions do not coincide with the grid points, for instance when the source is a curved, two-dimensional surface embedded in a three-dimensional domain. Typically, grid points close to the source surface are defined as source points, but this can result in "staircasing" and substantial errors in the resulting acoustic fields. This paper describes a technique for accurately representing arbitrary source distributions within Fourier collocation methods. The method works by applying a discrete, band-limiting convolution operator to the continuous source distribution, after which source grid weights can be generated. This allows arbitrarily shaped sources, for example, focused bowls and circular pistons, to be defined on the grid without staircasing errors. The technique is examined through simulations of a range of ultrasound sources, and comparisons with analytical solutions show excellent accuracy and convergence rates. Extensions of the technique are also discussed, including application to initial value problems, distributed sensors, and moving sources.

Equivalent-Source Acoustic Holography for Projecting Measured Ultrasound Fields Through Complex Media

Holographic projections of experimental ultrasound measurements generally use the angular spectrum method or Rayleigh integral, where the measured data are imposed as a Dirichlet boundary condition. In contrast, full-wave models, which can account for more complex wave behavior, often use interior mass or velocity sources to introduce acoustic energy into the simulation. Here, a method to generate an equivalent interior source that reproduces the measurement data is proposed based on gradient-based optimization. The equivalent-source can then be used with full-wave models (for example, the open-source k-Wave toolbox) to compute holographic projections through complex media including nonlinearity and heterogeneous material properties. Numerical and experimental results using both time-domain and continuous-wave sources are used to demonstrate the accuracy of the approach.

Three dimensional photoacoustic tomography in Bayesian framework

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., maximum a posteriori estimate and posterior covariance. These are computed iteratively in a matrix-free form using a biconjugate gradient stabilized method utilizing the adjoint of the acoustic forward operator. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution in realistic measurement geometries and that the reliability of these estimates can be assessed.

Laser generated ultrasound sources using carbon-polymer nanocomposites for high frequency metrology

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.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion

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.

Accurate simulation of transcranial ultrasound propagation for ultrasonic neuromodulation and stimulation

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.

Direct Estimation of Optical Parameters From Photoacoustic Time Series in Quantitative Photoacoustic Tomography

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.

Characterisation of a phantom for multiwavelength quantitative photoacoustic imaging

Quantitative photoacoustic imaging (qPAI) has the potential to provide high- resolution in vivo images of chromophore concentration, which may be indicative of tissue function and pathology. Many strategies have been proposed recently for extracting quantitative information, but many have not been experimentally verified. Experimental phantom-based validation studies can be used to test the robustness and accuracy of such algorithms in order to ensure reliable in vivo application is possible. The phantoms used in such studies must have well-characterised optical and acoustic properties similar to tissue, and be versatile and stable. Polyvinyl chloride plastisol (PVCP) has been suggested as a phantom for quality control and system evaluation. By characterising its multiwavelength optical properties, broadband acoustic properties and thermoelastic behaviour, this paper examines its potential as a phantom for qPAI studies too. PVCP's acoustic properties were assessed for various formulations, as well as its intrinsic optical absorption, and scattering with added TiO2, over a range of wavelengths from 400-2000 nm. To change the absorption coefficient, pigment-based chromophores that are stable during the phantom fabrication process, were used. These yielded unique spectra analogous to tissue chromophores and linear with concentration. At the high peak powers typically used in photoacoustic imaging, nonlinear optical absorption was observed. The Grüneisen parameter was measured to be [Formula: see text]  =  1.01  ±  0.05, larger than typically found in tissue, though useful for increased PA signal. Single and multiwavelength 3D PA imaging of various fabricated PVCP phantoms were demonstrated.

Control of broadband optically generated ultrasound pulses using binary amplitude holograms

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.

Quantitative photoacoustic tomography using illuminations from a single direction

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This optical parameter estimation problem is ill-posed and needs to be approached within the framework of inverse problems. It has been shown that, in general, estimating the spatial distribution of more than one optical parameter is a nonunique problem unless more than one illumination pattern is used. Generally, this is overcome by illuminating the target from various directions. However, in some cases, for example when thick samples are investigated, illuminating the target from different directions may not be possible. In this work, the use of spatially modulated illumination patterns at one side of the target is investigated with simulations. The results show that the spatially modulated illumination patterns from a single direction could be used to provide multiple illuminations for quantitative photoacoustic tomography. Furthermore, the results show that the approach can be used to distinguish absorption and scattering inclusions located near the surface of the target. However, when compared to a full multidirection illumination setup, the approach cannot be used to image as deep inside tissues.

Reconstruction-classification method for quantitative photoacoustic tomography

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 two and three dimensions, and delivers superior image quality with respect to traditional reconstruction-only approaches.

Modeling power law absorption and dispersion in viscoelastic solids using a split-field and the fractional Laplacian

The absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law. It is now well established that this type of loss behavior can be modeled using fractional derivatives. However, previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives. These operators are non-local in time, which makes them difficult to compute in a memory efficient manner. Here, a fractional Kelvin-Voigt model is derived based on the fractional Laplacian. This is obtained by splitting the particle velocity into compressional and shear components using a dyadic wavenumber tensor. This allows the temporal fractional derivatives in the Kelvin-Voigt model to be replaced with spatial fractional derivatives using a lossless dispersion relation with the appropriate compressional or shear wave speed. The model is discretized using the Fourier collocation spectral method, which allows the fractional operators to be efficiently computed. The field splitting also allows the use of a k-space corrected finite difference scheme for time integration to minimize numerical dispersion. The absorption and dispersion behavior of the fractional Laplacian model is analyzed for both high and low loss materials. The accuracy and utility of the model is then demonstrated through several numerical experiments, including the transmission of focused ultrasound waves through the skull.

Bayesian Image Reconstruction in Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating chromophore concentrations inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This is a hybrid imaging problem in which the solution of one inverse problem acts as the data for another ill-posed inverse problem. In the optical reconstruction of quantitative photoacoustic tomography, the data is obtained as a solution of an acoustic inverse initial value problem. Thus, both the data and the noise are affected by the method applied to solve the acoustic inverse problem. In this paper, the noise of optical data is modelled as Gaussian distributed with mean and covariance approximated by solving several acoustic inverse initial value problems using acoustic noise samples as data. Furthermore, Bayesian approximation error modelling is applied to compensate for the modelling errors in the optical data caused by the acoustic solver. The results show that modelling of the noise statistics and the approximation errors can improve the optical reconstructions.

A first-order k-space model for elastic wave propagation in heterogeneous media

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

Time domain simulation of harmonic ultrasound images and beam patterns in 3D using the k-space pseudospectral method

A k-space pseudospectral model is developed for the fast full-wave simulation of nonlinear ultrasound propagation through heterogeneous media. The model uses a novel equation of state to account for nonlinearity in addition to power law absorption. The spectral calculation of the spatial gradients enables a significant reduction in the number of required grid nodes compared to finite difference methods. The model is parallelized using a graphical processing unit (GPU) which allows the simulation of individual ultrasound scan lines using a 256 x 256 x 128 voxel grid in less than five minutes. Several numerical examples are given, including the simulation of harmonic ultrasound images and beam patterns using a linear phased array transducer.

A k-space Green's function solution for acoustic initial value problems in homogeneous media with power law absorption

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.

Measurement of the ultrasound attenuation and dispersion in whole human blood and its components from 0-70 MHz

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.

Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian

The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.

k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields

A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.

Photoacoustic tomography with a single detector in a reverberant cavity

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.

Estimating chromophore distributions from multiwavelength photoacoustic images

Biomedical photoacoustic tomography (PAT) can provide qualitative images of biomedical soft tissue with high spatial resolution. However, whether it is possible to give accurate quantitative estimates of the spatially varying concentrations of the sources of photoacoustic contrast-endogenous or exogenous chromophores-remains an open question. Even if the chromophores' absorption spectra are known, the problem is nonlinear and ill-posed. We describe a framework for obtaining such quantitative estimates. When the optical scattering distribution is known, adjoint and gradient-based optimization techniques can be used to recover the concentration distributions of the individual chromophores that contribute to the overall tissue absorption. When the scattering distribution is unknown, prior knowledge of the wavelength dependence of the scattering is shown to be sufficient to overcome the absorption-scattering nonuniqueness and allow both distributions of chromophore concentrations and scattering to be recovered from multiwavelength photoacoustic images.

k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics

Biomedical applications of photoacoustics, in particular photoacoustic tomography, require efficient models of photoacoustic propagation that can incorporate realistic properties of soft tissue, such as acoustic inhomogeneities both for purposes of simulation and for use in model-based image reconstruction methods. k-space methods are well suited to modeling high-frequency acoustics applications as they require fewer mesh points per wavelength than conventional finite element and finite difference models, and larger time steps can be taken without a loss of stability or accuracy. They are also straightforward to encode numerically, making them appealing as a general tool. The rationale behind k-space methods and the k-space approach to the numerical modeling of photoacoustic waves in fluids are covered in this paper. Three existing k-space models are applied to photoacoustics and demonstrated with examples: an exact model for homogeneous media, a second-order model that can take into account heterogeneous media, and a first-order model that can incorporate absorbing boundary conditions.

Parapoxvirus infections in New Zealand farmed red deer (Cervus elaphus)

Outbreaks of infection due to a parapoxvirus were reported on eight New Zealand deer farms. Scabby lesions were seen variably on the muzzle, lips, face, ears and neck of red deer (Cervus elaphus) with morbidity rates reaching 100%. On three farms multifocal lesions were also present on the velvet. Deaths were reported on two properties where the lesions were extensive and secondary bacterial infections had occurred. On one of these farms multifactorial disease was suspected. Poxvirus particles were seen by negative contrast electron microscopy in scab material from all eight properties. Morphologically the deer virus resembled a parapoxvirus, but restriction endonuclease analysis showed its DNA fragment patterns were distinct from those of orf (contagious ecthyma) virus.

Fast calculation of pulsed photoacoustic fields in fluids using k-space methods

Two related numerical models that calculate the time-dependent pressure field radiated by an arbitrary photoacoustic source in a fluid, such as that generated by the absorption of a short laser pulse, are presented. Frequency-wavenumber (k-space) implementations have been used to produce fast and accurate predictions. Model I calculates the field everywhere at any instant of time, and is useful for visualizing the three-dimensional evolution of the wave field. Model II calculates pressure time series for points on a straight line or plane and is therefore useful for simulating array measurements. By mapping the vertical wavenumber spectrum directly to frequency, this model can calculate time series up to 50 times faster than current numerical models of photoacoustic propagation. As the propagating and evanescent parts of the field are calculated separately, model II can be used to calculate far- and near-field radiation patterns. Also, it can readily be adapted to calculate the velocity potential and thus particle velocity and acoustic intensity vectors. Both models exploit the efficiency of the fast Fourier transform, and can include the frequency-dependent directional response of an acoustic detector straightforwardly. The models were verified by comparison with a known analytic solution and a slower, but well-understood, numerical model.

The Rayleigh-like collapse of a conical bubble

Key to the dynamics of the type of bubble collapse which is associated with such phenomena as sonoluminescence and the emission of strong rebound pressures into the liquid is the role of the liquid inertia. Following the initial formulation of the collapse of an empty spherical cavity, such collapses have been termed "Rayleigh-like." Today this type of cavitation is termed "inertial," reflecting the dominant role of the liquid inertia in the early stages of the collapse. While the inertia in models of spherical bubble collapses depends primarily on the liquid, experimental control of the liquid inertia has not readily been achievable without changing the liquid density and, consequently, changing other liquid properties. In this paper, novel experimental apparatus is described whereby the inertia at the early stages of the collapse of a conical bubble can easily be controlled. The collapse is capable of producing luminescence. The similarity between the collapses of spherical and conical bubbles is investigated analytically, and compared with experimental measurements of the gas pressures generated by the collapse, the bubble wall speeds, and the collapse times.

Serology of aNeosporaabortion outbreak on a dairy farm in New Zealand: A case study

AIM

To describe the kinetics of serological titres after an abortion outbreak in April-May 1995 due to Neospora caninum affected 17 dairy cows in a herd of 320.

METHODS

Thirty-five cows, that had either aborted, carried mummified calves, were not pregnant or calved normally were: bled several times at regular intervals and the sera tested for Neospora antibodies in the indirect fluorescence antibody test (IFAT).

RESULTS

Maximal IFAT titres of up to 1:4000 occurred within 6 weeks of the abortion outbreak, decreased over the next 2 months to < or = 1:200 and remained at this level until the next scheduled bleed a further 2 months later. A rise in titres was subsequently observed in the cows that had aborted or were not pregnant (at the time of the abortions) or had carried mummified foetuses. Seroconversion was also observed in some of the control cows, which had, up until then, remained seronegative. A dog and cat in contact with the cows in the herd investigated were, however, negative in the IFAT.

CONCLUSIONS

Maximal serological titres in Neospora abortions are observed within weeks of the abortion event and then quickly return to very low levels. Subsequently, a recrudescence of titres can be observed in infected cows during the next pregnancy, without it being associated with repeat abortions.

Magnesium supplementation of lactating ewes and lamb growth

Ewes rearing twin lambs on a restricted ration of irrigated pasture were either supplemented daily with 12.5 mg magnesium chloride or not. Serum magnesium levels measured 24 hours after the previous day's dose did not differ between treatments. They averaged 0.74 mmol/l during the period of supplementation with 36% of values below 0.7 mmol/l, the lower limit of the "normal" range. Milk consumption by and liveweight gains of lambs were not increased by magnesium supplementation indicating that ewe magnesium levels below 0.7 mmol/l serum did not limit production in this instance.