Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods

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.

Enabling strain imaging in realistic Eulerian ultrasound simulation methods

Cardiovascular strain imaging is continually improving due to ongoing advances in ultrasound acquisition and data processing techniques. The phantoms used for validation of new methods are often burdensome to make and lack flexibility to vary mechanical and acoustic properties. Simulations of US imaging provide an alternative with the required flexibility and ground truth strain data. However, the current Lagrangian US strain imaging models cannot simulate heterogeneous speed of sound distributions and higher-order scattering, which limits the realism of the simulations. More realistic Eulerian modelling techniques exist but have so far not been used for strain imaging. In this research, a novel sampling scheme was developed based on a band-limited interpolation of the medium, which enables accurate strain simulation in Eulerian methods. The scheme was validated in k-Wave using various numerical phantoms and by a comparison with Field II. The method allows for simulations with a large range in strain values and was accurate with errors smaller than -60 dB. Furthermore, an excellent agreement with the Fourier theory of US scattering was found. The ability to perform simulations with heterogeneous speed of sound distributions was demonstrated using a pulsating artery model. The developed sampling scheme contributes to more realistic strain imaging simulations, in which the effect of heterogenous acoustic properties can be taken into account.

A Forward Model Incorporating Elevation-Focused Transducer Properties for 3-D Full-Waveform Inversion in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging medical imaging modality that holds great promise for improving human health. Full-waveform inversion (FWI)-based image reconstruction methods account for the relevant wave physics to produce high spatial resolution images of the acoustic properties of the breast tissues. A practical USCT design employs a circular ring-array comprised of elevation-focused ultrasonic transducers, and volumetric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the 3-D volume is reconstructed by stacking together 2-D images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3-D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3-D image reconstruction when elevation-focused transducers are employed, a numerical description of the focusing properties of the transducers should be included in the forward model. To address this, a 3-D computational model of an elevation-focused transducer is developed to enable 3-D FWI-based reconstruction methods to be deployed in ring-array-based USCT. The focusing is achieved by applying a spatially varying temporal delay to the ultrasound pulse (emitter mode) and recorded signal (receiver mode). The proposed numerical transducer model is quantitatively validated and employed in computer simulation studies that demonstrate its use in image reconstruction for ring-array USCT.

A head template for computational dose modelling for transcranial focused ultrasound stimulation

Transcranial focused Ultrasound Stimulation (TUS) at low intensities is emerging as a novel non-invasive brain stimulation method with higher spatial resolution than established transcranial stimulation methods and the ability to selectively stimulate also deep brain areas. Accurate control of the focus position and strength of the TUS acoustic waves is important to enable a beneficial use of the high spatial resolution and to ensure safety. As the human skull causes strong attenuation and distortion of the waves, simulations of the transmitted waves are needed to accurately determine the TUS dose distribution inside the cranial cavity. The simulations require information of the skull morphology and its acoustic properties. Ideally, they are informed by computed tomography (CT) images of the individual head. However, suited individual imaging data is often not readily available. For this reason, we here introduce and validate a head template that can be used to estimate the average effects of the skull on the TUS acoustic wave in the population. The template was created from CT images of the heads of 29 individuals of different ages (between 20-50 years), gender and ethnicity using an iterative non-linear co-registration procedure. For validation, we compared acoustic and thermal simulations based on the template to the average of the simulation results of all 29 individual datasets. Acoustic simulations were performed for a model of a focused transducer driven at 500 kHz, placed at 24 standardized positions by means of the EEG 10-10 system. Additional simulations at 250 kHz and 750 kHz at 16 of the positions were used for further confirmation. The amount of ultrasound-induced heating at 500 kHz was estimated for the same 16 transducer positions. Our results show that the template represents the median of the acoustic pressure and temperature maps from the individuals reasonably well in most cases. This underpins the usefulness of the template for the planning and optimization of TUS interventions in studies of healthy young adults. Our results further indicate that the amount of variability between the individual simulation results depends on the position. Specifically, the simulated ultrasound-induced heating inside the skull exhibited strong interindividual variability for three posterior positions close to the midline, caused by a high variability of the local skull shape and composition. This should be taken into account when interpreting simulation results based on the template.

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.

Full-Waveform Inversion for Breast Ultrasound Tomography Using Line-Shape Modeled Elements

OBJECTIVE

The objective of the work described here was to incorporate the spatial shapes of the transducer elements into the framework of the full-waveform inversion.

METHODS

An element is treated as its cross-section in the 2-D imaging plane, that is, a line segment. The elements are not simply modeled as a set of point sources on their surface to avoid staircasing artifacts. By use of the Fourier collocation method, an element is spatially represented as the discrete convolution between its spatial distribution and a band-limited delta function. The excitation pulses on the emitters and recorded signals on the receivers are then weighted based on the discrete convolution results. Digital and physical experiments are implemented to validate the method.

DISCUSSION

It is meaningful to model the shapes of the elements if their spatial sizes are similar to or larger than the acoustic wavelengths. It should, however, be noted that because this article focuses on 2-D imaging, the inter-plane effects are not considered.

CONCLUSION

The approach helps reduce the root mean square errors and increase the structural similarity of the reconstructed images. It also helps to improve the stability of convergence and to accelerate the convergence speed.

Ultrasound computed tomography based on full waveform inversion with source directivity calibration

Ultrasound computed tomography based on full waveform inversion has the potential to provide high-resolution images of human tissues in a quantitative manner. A successful ultrasound computed tomography system requires the decent knowledge of acquisition array, including the spatial position and the directivity of each transducer, to meet the high-level demand of clinical applications. The conventional full waveform inversion algorithm assumes a point source with the omni-directional emission. Such assumption does not hold when the directivity of emitting transducer is not negligible. For a practical implementation, an efficient and accurate self-checking evaluation of directivity is crucial prior to the reconstruction of images. We propose to measure the directivity of each emitting transducer using the full-matrix captured data obtained with a water-immersed and target-free experiment. We introduce the weighted virtual point-source array to act as the proxy of emitting transducer during the numerical simulation. The weights of different points in the virtual array can be calculated from the observed data using the gradient-based local optimization method. Although the full waveform imaging method relies on the finite-difference solver of wave equation, such directivity estimation benefits from the introduction of analytical solver. The trick significantly reduces the numerical cost, enabling an automatic directivity self-check at boot. We verify the feasibility, efficiency, and accuracy of the virtual array method through simulated and experimental tests. For the experimental test, we also illustrate that full waveform inversion with directivity calibration can reduce the artifacts introduced by the conventional point source assumption, improving the quality of reconstructed images..

A numerical investigation of passive acoustic mapping for monitoring bubble-mediated focused ultrasound treatment of the spinal cord

Focused ultrasound (FUS) combined with intravenous microbubbles (MBs) has been shown to increase drug delivery to the spinal cord in animal models. Eventual clinical translation of such a technique in the sensitive spinal cord requires robust treatment monitoring to ensure efficacy, localization, safety, and provide key intraprocedural feedback. Here, the use of passive acoustic mapping (PAM) of MB emissions with a spine-specific detector array in the context of transvertebral FUS sonications is investigated in silico. Using computed tomography-derived human vertebral geometry, transvertebral detection of MBs is evaluated over varying source locations with and without phase and amplitude corrections (PACs). The impact of prefocal cavitation is studied by simulating concurrent cavitation events in the canal and pre-laminar region. Spatially sensitive application of phase and amplitude is used to balance signal strengths emanating from different axial depths in combination with multiple dynamic ranges to elicit multisource viewing. Collectively, the results of this study encourage the use of PAM in transvertebral FUS applications with PACs to not only localize sources originating in the spinal canal but also multiple sources of innate amplitude mismatches when corrective methods are applied.

Computation of ultrasound propagation in a population of nonlinearly oscillating microbubbles including multiple scattering

In contrast-enhanced echography, the simulation of nonlinear propagation of ultrasound through a population of oscillating microbubbles imposes a computational challenge. Also, the numerical complexity increases because each scatterer has individual properties. To address these problems, the Iterative Nonlinear Contrast Source (INCS) method has been extended to include a large population of nonlinearly responding microbubbles. The original INCS method solves the Westervelt equation in a four-dimensional spatiotemporal domain by generating increasingly accurate field corrections to iteratively update the acoustic pressure. The field corrections are computed by the convolution of a nonlinear contrast source with the Green's function of the linear background medium. Because the convolution integral allows a coarse discretization, INCS can efficiently deal with large-scale problems. To include a population of microbubbles, these are considered as individual contrast point sources with their own nonlinear response. The field corrections are computed as before, but now, in each iteration, the temporal signature of each contrast point source is computed by solving the bubble's Marmottant equation. Physically, each iteration adds an order of multiple scattering. Here, the performance of the extended INCS method and the significance of multiple scattering is demonstrated through various results from different configurations.

Image reconstruction algorithm for laser-induced ultrasonic imaging: The single sensor scanning synthetic aperture focusing technique

This paper aims to implement a laser-induced ultrasound imaging reconstruction method based on the delay-and-sum beamforming through the synthetic aperture focusing technique (SAFT) for a circular scanning, performed with a tomograph that had one acoustic sensor and a system that rotates the sample around a fixed axis. The proposed method, called the Single-sensor Scanning Synthetic Aperture Focusing Technique, considers the size of the sensor and the detection procedure inside the SAFT's algebra. This image reconstruction method was evaluated numerically, using the Green function for the laser-induced ultrasound wave equation to generate a forward problem, and experimentally, using a solid object of polylactic acid, and a Sprague-Dawley rat heart located in a tissue-mimicking phantom. The resulting images were compared to those obtained from the time reversal and the conventional delay-and-sum reconstruction algorithms. The presented method removes the sidelobe artifacts and the comet tail sign, which produces a more distinguishable target on the image. In addition, the proposed method has a faster performance and lower computational load. The implementation of this method in photoacoustic microscopy techniques for image reconstruction is discussed.

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.

Modeling toolchain for realistic simulation of photoacoustic data acquisition

SIGNIFICANCE

Physics-based simulations of photoacoustic (PA) signals are used to validate new methods, to characterize PA setups and to generate training datasets for machine learning. However, a thoroughly validated PA simulation toolchain that can simulate realistic images is still lacking.

AIM

A quantitative toolchain was developed to model PA image acquisition in complex tissues, by simulating both the optical fluence and the acoustic wave propagation.

APPROACH

Sampling techniques were developed to decrease artifacts in acoustic simulations. The performance of the simulations was analyzed by measuring the point spread function (PSF) and using a rotatable three-channel phantom, filled with cholesterol, a human carotid plaque sample, and porcine blood. Ex vivo human plaque samples were simulated to validate the methods in more complex tissues.

RESULTS

The sampling techniques could enhance the quality of the simulated PA images effectively. The resolution and intensity of the PSF in the turbid medium matched the experimental data well. Overall, the appearance, signal-to-noise ratio and speckle of the images could be simulated accurately.

CONCLUSIONS

A PA toolchain was developed and validated, and the results indicate a great potential of PA simulations in more complex and heterogeneous media.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

A Spatial Multitarget Ultrasound Neuromodulation System Using High-Powered 2-D Array Transducer

Transcranial focused ultrasound (tFUS) is increasingly used in experimental neuroscience due to its neuromodulatory effectiveness in animal studies. However, achieving multitarget tFUS in small animals is typically limited by transducer size, energy transfer efficiency, and brain volume. The objective of this work was to construct an ultrasound system for multitarget neuromodulation in small animals. First, a miniaturized high-powered 2-D array transducer was developed. The phase delay of each array element was calculated based on the multifocal time-reversal method, generating multiple foci simultaneously in a 3-D field. The effects of the axial focal length, interfocus spacing (lateral distance between the two focal centers), and the number of foci on the focal properties of the pressure field were examined through numerical simulations. In-vitro ultrasonic measurements and transcranial simulations on a rat skull were conducted. The minimum interfocus spacing separating two -6-dB foci and the peak full-width at half-maximum were positively correlated with axial focal length; the relative relationship between the interfocus spacing and pressure field properties was similar for each axial focal length. The maximum acoustic pressure and spatial average intensity at focus in deionized water were 2.21 MPa and 133 W/cm², respectively. The simulated and experimental results were compared, demonstrating agreement in both peak position and focus shape. The ultrasound system can provide a neuroscientific platform for evaluating the feasibility of multitarget ultrasound stimulation treatment protocols, thus improving the understanding of functional neuroanatomy.

Multiperspective Bistatic Ultrasound Imaging and Elastography of the Ex Vivo Abdominal Aorta

Knowledge of aneurysm geometry and local mechanical wall parameters using ultrasound (US) can contribute to a better prediction of rupture risk in abdominal aortic aneurysms (AAAs). However, aortic strain imaging using conventional US is limited by the lateral lumen-wall contrast and resolution. In this study, ultrafast multiperspective bistatic (MP BS) imaging is used to improve aortic US, in which two curved array transducers receive simultaneously on each transmit event. The advantage of such bistatic US imaging on both image quality and strain estimations was investigated by comparing it to single-perspective monostatic (SP MS) and MP monostatic (MP MS) imaging, i.e., alternately transmitting and receiving with either transducer. Experimental strain imaging was performed in US simulations and in an experimental study on porcine aortas. Different compounding strategies were tested to retrieve the most useful information from each received US signal. Finally, apart from the conventional sector grid in curved array US imaging, a polar grid with respect to the vessel's local coordinate system is introduced. This new reconstruction method demonstrated improved displacement estimations in aortic US. The US simulations showed increased strain estimation accuracy using MP BS imaging bistatic imaging compared to MP MS imaging, with a decrease in the average relative error between 41% and 84% in vessel wall regions between transducers. In the experimental results, the mean image contrast-to-noise ratio was improved by up to 8 dB in the vessel wall regions between transducers. This resulted in an increased mean elastographic signal-to-noise ratio by about 15 dB in radial strain and 6 dB in circumferential strain.

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

A Spectral Method for Two-Dimensional Ocean Acoustic Propagation

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

Discrete Approximations of Acoustic Source Distributions

The modeling of source a distributions of finite spatial extent in ultrasound and medical imaging applications is a problem of longstanding interest. In time-domain methods, such as the finite-difference time-domain or pseudospectral approaches, one requirement is the representation of such distributions over a grid, normally Cartesian. Various artifacts, including staircasing errors, can arise. In this short contribution, the problem of the representation of distribution over a grid is framed as an optimization problem in the Fourier domain over a preselected set of grid points, thus maintaining control over computational cost and allowing the fine-tuning of the optimization to the wavenumber range of interest for a particular numerical method. Numerical results are presented in the important special case of the spherical cap or bowl source.

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.

Measurement and simulation of steered acoustic fields generated by a multielement array for therapeutic ultrasound

Modelling of fields generated by therapeutic ultrasound arrays can be prone to errors arising from differences from nominal transducer parameters, and variations in relative outputs of array elements when driven under different conditions, especially when simulating steered fields. Here, the effect of element size, element positions, relative source pressure variations, and electrical crosstalk on the accuracy of modelling pressure fields generated by a 555 kHz 32-element ultrasonic array were investigated. For this transducer, errors in pressure amplitude and focal position were respectively reduced from 20% to 4% and 3.3 mm to 1.5 mm using crosstalk prediction, and experimentally determined positions.

Modeling continuous source distributions in wave-based virtual acoustics

All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point-like sources at grid locations. Such a representation requires interpolation over the grid and leads to common staircasing effects, particularly under rotation or translation of the distribution. In this article, a different representation is shown, based on a spherical harmonic representation of a given distribution. The source itself is decoupled from any particular arrangement of grid points, and is compactly represented as a series of filter responses used to drive a canonical set of source terms, each activating a given spherical harmonic directivity pattern. Such filter responses are derived for a variety of commonly encountered distributions. Simulation results are presented, illustrating various features of such a representation, including convergence, behaviour under rotation, the extension to the time varying case, and differences in computational cost relative to standard grid-based source representations.

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.