Experiments and simulations demonstrating the rapid ultrasonic rewarming of frozen tissue cryovials.

The development of methods to safely rewarm large cryopreserved biological samples remains a barrier to the widespread adoption of cryopreservation. Here, experiments and simulations were performed to demonstrate that ultrasound can increase rewarming rates relative to thermal conduction alone. An ultrasonic rewarming setup based on a custom 444 kHz tubular piezoelectric transducer was designed, characterized, and tested with 2 ml cryovials filled with frozen ground beef. Rewarming rates were characterized in the -20 °C to 5 °C range. Thermal conduction-based rewarming was compared to thermal conduction plus ultrasonic rewarming, demonstrating a tenfold increase in rewarming rate when ultrasound was applied. The maximum recorded rewarming rate with ultrasound was 57° C/min, approximately 2.5 times faster than with thermal conduction alone. Coupled acoustic and thermal simulations were developed and showed good agreement with the heating rates demonstrated experimentally and were also used to demonstrate spatial heating distributions with small (<3° C) temperature differentials throughout the sample when the sample was below 0° C. The experiments and simulations demonstrate the potential for ultrasonic cryovial rewarming with a possible application to large volume rewarming, as faster rewarming rates may improve the viability of cryopreserved tissues and reduce the time needed for cells to regain normal function.

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 and measurement of laser-generated focused ultrasound: Can interventional transducers achieve therapeutic effects?

Laser-generated focused ultrasound (LGFU) transducers used for ultrasound therapy commonly have large diameters (6-15 mm), but smaller lateral dimensions (<4 mm) are required for interventional applications. To address the question of whether miniaturized LGFU transducers could generate sufficient pressure at the focus to enable therapeutic effects, a modelling and measurement study is performed. Measurements are carried out for both linear and nonlinear propagation for various illumination schemes and compared with the model. The model comprises several innovations. First, the model allows for radially varying acoustic input distributions on the surface of the LGFU transducer, which arise from the excitation light impinging on the curved transducer surfaces. This realistic representation of the source prevents the overestimation of the achievable pressures (shown here to be as high as 1.8 times). Second, an alternative inverse Gaussian illumination paradigm is proposed to achieve higher pressures; a 35% increase is observed in the measurements. Simulations show that LGFU transducers as small as 3.5 mm could generate sufficient peak negative pressures at the focus to exceed the cavitation threshold in water and blood. Transducers of this scale could be integrated with interventional devices, thereby opening new opportunities for therapeutic applications from inside the body.

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.

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.

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.

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.

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.

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.

Safety Review of Therapeutic Ultrasound for Spinal Cord Neuromodulation and Blood-Spinal Cord Barrier Opening.

New focused ultrasound spinal cord applications have emerged, particularly those improving therapeutic agent delivery to the spinal cord via blood-spinal cord barrier opening and the neuromodulation of spinal cord tracts. One hurdle in the development of these applications is safety. It may be possible to use safety trends from seminal and subsequent works in focused ultrasound to guide the development of safety guidelines for spinal cord applications. We collated data from decades of pre-clinical studies and illustrate a clear relationship between damage, time-averaged spatial peak intensity and exposure duration. This relationship suggests a thermal mechanism underlies ultrasound-induced spinal cord damage. We developed minimum and mean thresholds for damage from these pre-clinical studies. When these thresholds were plotted against the parameters used in recent pre-clinical ultrasonic spinal cord neuromodulation studies, the majority of the neuromodulation studies were near or above the minimum threshold. This suggests that a thermal neuromodulatory effect may exist for ultrasonic spinal cord neuromodulation, and that the thermal dose must be carefully controlled to avoid damage to the spinal cord. By contrast, the intensity-exposure duration threshold had no predictive value when applied to blood-spinal cord barrier opening studies that employed injected contrast agents. Most blood-spinal cord barrier opening studies observed slight to severe damage, except for small animal studies that employed an active feedback control method to limit pressures based on measured bubble oscillation behavior. The development of new focused ultrasound spinal cord applications perhaps reflects the recent success in the development of focused ultrasound brain applications, and recent work has begun on the translation of these technologies from brain to spinal cord. However, a great deal of work remains to be done, particularly with respect to developing and accepting safety standards for these applications.

Strategies and safety simulations for ultrasonic cervical spinal cord neuromodulation.

Objective. Focused ultrasound spinal cord neuromodulation has been demonstrated in small animals. However, most of the tested neuromodulatory exposures are similar in intensity and exposure duration to the reported small animal threshold for possible spinal cord damage. All efforts must be made to minimize the risk and assure the safety of potential human studies, while maximizing potential treatment efficacy. This requires an understanding of ultrasound propagation and heat deposition within the human spine.Approach. Combined acoustic and thermal modelling was used to assess the pressure and heat distributions produced by a 500 kHz source focused to the C5/C6 level via two approaches (a) the posterior acoustic window between vertebral posterior arches, and (b) the lateral intervertebral foramen from which the C6 spinal nerve exits. Pulse trains of fifty 0.1 s pulses (pulse repetition frequency: 0.33 Hz, free-field spatial peak pulse-averaged intensity: 10 W cm-2) were simulated for four subjects and for ±10 mm translational and ±10∘rotational source positioning errors.Main results.Target pressures ranged between 20%-70% of free-field spatial peak pressures with the posterior approach, and 20%-100% with the lateral approach. When the posterior source was optimally positioned, peak spine heating values were below 1 ∘C, but source mispositioning resulted in bone heating up to 4 ∘C. Heating with the lateral approach did not exceed 2 ∘C within the mispositioning range. There were substantial inter-subject differences in target pressures and peak heating values. Target pressure varied three to four-fold between subjects, depending on approach, while peak heating varied approximately two-fold between subjects. This results in a nearly ten-fold range between subjects in the target pressure achieved per degree of maximum heating.Significance. This study highlights the utility of trans-spine ultrasound simulation software and need for precise source-anatomy positioning to assure the subject-specific safety and efficacy of focused ultrasound spinal cord therapies.

Review of the Low-Temperature Acoustic Properties of Water, Aqueous Solutions, Lipids, and Soft Biological Tissues.

Existing data on the acoustic properties of low-temperature biological materials is limited and widely dispersed across fields. This makes it difficult to employ this information in the development of ultrasound applications in the medical field, such as cryosurgery and rewarming of cryopreserved tissues. In this review, the low-temperature acoustic properties of biological materials, and the measurement methods used to acquire them were collected from a range of scientific fields. The measurements were reviewed from the acoustic setup to thermal methodologies for samples preparation, temperature monitoring, and system insulation. The collected data contain the longitudinal and shear velocity, and attenuation coefficient of biological soft tissues and biologically relevant substances-water, aqueous solutions, and lipids-in the temperature range down to -50 °C and in the frequency range from 108 kHz to 25 MHz. The multiple reflection method (MRM) was found to be the preferred method for low-temperature samples, with a buffer rod inserted between the transducer and sample to avoid direct contact. Longitudinal velocity changes are observed through the phase transition zone, which is sharp in pure water, and occurs more slowly and at lower temperatures with added solutes. Lipids show longer transition zones with smaller sound velocity changes; with the longitudinal velocity changes observed during phase transition in tissues lying between these two extremes. More general conclusions on the shear velocity and attenuation coefficient at low-temperatures are restricted by the limited data. This review enhance knowledge guiding for further development of ultrasound applications in low-temperature biomedical fields, and may help to increase the precision and standardization of low-temperature acoustic property measurements.

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.

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.

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.

On-the-Fly Calculation of Time-Averaged Acoustic Intensity in Time-Domain Ultrasound Simulations Using a k-Space Pseudospectral Method.

This article presents a method to calculate the average acoustic intensity during ultrasound simulation using a new approach that exploits compression of intermediate results. One of the applications of high-intensity focused ultrasound (HIFU) simulations is the calculation of the thermal dose, which indicates the amount of tissue destroyed using a state-of-the-art k-space pseudospectral method. The thermal simulation is preceded by the calculation of the average intensity within the acoustic simulation. Due to the time staggering between the particle velocity and the acoustic pressure used in such simulations, the average intensity calculation is typically executed offline after the acoustic simulation consuming both disk space and time (the data can spread over terabytes). Our new approach calculates the average intensity during the acoustic simulation using the output coefficients of a new compression method which enables resolving the time staggering on-the-fly with huge disk space savings. To reduce RAM requirements, the article also presents a new 40-bit method for encoding compression complex coefficients. Experimental numerical simulations with the proposed method have shown that disk space requirements are up to 99% lower. The simulation speed was not significantly affected by the approach and the compression error did not affect the prediction accuracy of the thermal dose. From the standpoint of supercomputers, the new approach is significantly more economical. Saving computing resources increases the chances of real use of acoustic simulations in practice. The method can be applied to signals of a similar character, e.g., for electromagnetic radio waves.

Classical and Learned MR to Pseudo-CT Mappings for Accurate Transcranial Ultrasound Simulation.

Model-based treatment planning for transcranial ultrasound therapy typically involves mapping the acoustic properties of the skull from an X-ray computed tomography (CT) image of the head. Here, three methods for generating pseudo-CT (pCT) images from magnetic resonance (MR) images were compared as an alternative to CT. A convolutional neural network (U-Net) was trained on paired MR-CT images to generate pCT T images from either T1-weighted or zero-echo time (ZTE) MR images (denoted tCT and zCT, respectively). A direct mapping from ZTE to pCT was also implemented (denoted cCT). When comparing the pCT and ground-truth CT images for the test set, the mean absolute error was 133, 83, and 145 Hounsfield units (HU) across the whole head, and 398, 222, and 336 HU within the skull for the tCT, zCT, and cCT images, respectively. Ultrasound simulations were also performed using the generated pCT images and compared to simulations based on CT. An annular array transducer was used targeting the visual or motor cortex. The mean differences in the simulated focal pressure, focal position, and focal volume were 9.9%, 1.5 mm, and 15.1% for simulations based on the tCT images; 5.7%, 0.6 mm, and 5.7% for the zCT; and 6.7%, 0.9 mm, and 12.1% for the cCT. The improved results for images mapped from ZTE highlight the advantage of using imaging sequences, which improves the contrast of the skull bone. Overall, these results demonstrate that acoustic simulations based on MR images can give comparable accuracy to those based on CT.

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 temperature-dependent output of lead zirconate titanate transducers.

The effect of temperature and electrical drive conditions on the output of lead zirconate titanate (PZT) transducers is of particular interest in ultrasound metrology and medical ultrasound applications. In this work, the temperature-dependent output of two single-element PZT transducers was measured between 22 °C and 46 °C. Two independent measurement methods were used, namely radiation force balance measurements and laser vibrometry. When driven at constant voltage using a 50 Ω matched signal generator and amplifier using continuous wave (CW) or quasi-CW excitation, the output of the two transducers increased on average by 0.6 % per degree, largely due to an increase in transducer efficiency with temperature. The two measurement methods showed close agreement. Similar trends were observed when using single cycle excitation with the same signal chain. However, when driven using a pulser (which is not electrically matched), the two transducers exhibited different behaviour depending on their electrical impedance. Accounting for the temperature-dependent output of PZT transducers could have implications for many areas of ultrasound metrology, for example, in therapeutic ultrasound where a coupling fluid at an increased or decreased temperature is often used.