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

ITRUSST consensus on standardised reporting for transcranial ultrasound stimulation

As transcranial ultrasound stimulation (TUS) advances as a precise, non-invasive neuromodulatory method, there is a need for consistent reporting standards to enable comparison and reproducibility across studies. To this end, the International Transcranial Ultrasonic Stimulation Safety and Standards Consortium (ITRUSST) formed a subcommittee of experts across several domains to review and suggest standardised reporting parameters for low intensity TUS, resulting in the guide presented here. The scope of the guide is limited to reporting the ultrasound aspects of a study. The guide and supplementary material provide a simple checklist covering the reporting of: (1) the transducer and drive system, (2) the drive system settings, (3) the free field acoustic parameters, (4) the pulse timing parameters, (5) in situ estimates of exposure parameters in the brain, and (6) intensity parameters. Detailed explanations for each of the parameters, including discussions on assumptions, measurements, and calculations, are also provided.

New semi-analytical method for fast transcranial ultrasonic field simulation

Objective.To optimize and ensure the safety of ultrasound brain therapy, personalized transcranial ultrasound simulations are very useful. They allow to predict the pressure field, depending on the patient skull and probe position. Most transcranial ultrasound simulations are based on numerical methods which have a long computation time and a high memory usage. The goal of this study is to develop a new semi-analytical field computation method that combines realism and computation speed.Approach.Instead of the classic ray tracing, the ultrasonic paths are computed by time of flight minimization. Then the pressure field is computed using the pencil method. This method requires a smooth and homogeneous skull model. The simulation algorithm, so-called SplineBeam, was numerically validated, by comparison with existing solvers, and experimentally validated by comparison with hydrophone measured pressure fields through anex vivohuman skull.Main results.SplineBeam simulated pressure fields were close to the experimentally measured ones, with a focus position difference of the order of the positioning error and a maximum pressure difference lower than 6.02%. In addition, for those configurations, SplineBeam computation time was lower than another simulation software, k-Wave's, by two orders of magnitude, thanks to its capacity to compute the field only at the focal spot.Significance.These results show the potential of this new method to compute fast and realistic transcranial pressure fields. The combination of this two assets makes it a promising tool for real time transcranial pressure field prediction during ultrasound brain therapy interventions.

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.

ITRUSST Consensus on Standardised Reporting for Transcranial Ultrasound Stimulation

As transcranial ultrasound stimulation (TUS) advances as a precise, non-invasive neuromodulatory method, there is a need for consistent reporting standards to enable comparison and reproducibility across studies. To this end, the International Transcranial Ultrasonic Stimulation Safety and Standards Consortium (ITRUSST) formed a subcommittee of experts across several domains to review and suggest standardised reporting parameters for low intensity TUS, resulting in the guide presented here. The scope of the guide is limited to reporting the ultrasound aspects of a study. The guide and supplementary material provide a simple checklist covering the reporting of: (1) the transducer and drive system, (2) the drive system settings, (3) the free field acoustic parameters, (4) the pulse timing parameters, (5) in situ estimates of exposure parameters in the brain, and (6) intensity parameters. Detailed explanations for each of the parameters, including discussions on assumptions, measurements, and calculations, are also provided.

An efficient method for transcranial ultrasound focus correction based on the coupling of boundary integrals and finite elements

Transcranial focused ultrasound is a novel technique for the noninvasive treatment of brain diseases. The success of the treatment greatly depends on achieving precise and efficient intraoperative focus. However, compensating for aberrated ultrasound waves caused by the skull through numerical simulation-based phase corrections is a challenging task due to the significant computational burden involved in solving the acoustic wave equation. In this article, we propose a promising strategy using the coupling of the boundary integral equation method (BIEM) and the finite element method (FEM) to overcome the above limitation. Specifically, we adopt the BIEM to obtain the Robin-to-Dirichlet maps on the boundaries of the skull and then couple the maps to the FEM matrices via a dual interpolation technique, resulting in a computational domain including only the skull. Three simulation experiments were conducted to evaluate the effectiveness of the proposed method, including a convergence test and two skull-induced aberration corrections in 2D and 3D ultrasound. The results show that the method's convergence is guaranteed as the element size decreases, leading to a decrease in pressure error. The computation times for simulating a 500 kHz ultrasound field on a regular desktop computer were found to be 0.47 ± 0.01 s in the 2D case and 43.72 ± 1.49 s in the 3D case, provided that lower-upper decomposition (approximately 13 s in 2D and 2.5 h in 3D) was implemented in advance. We also demonstrated that more accurate transcranial focusing can be achieved by phase correction compared to the noncorrected results (with errors of 1.02 mm vs. 6.45 mm in 2D and 0.28 mm vs. 3.07 mm in 3D). The proposed strategy is valuable for enabling online ultrasound simulations during treatment, facilitating real-time adjustments and interventions.

Shedding light on ultrasound in action: Optical and optoacoustic monitoring of ultrasound brain interventions

Monitoring brain responses to ultrasonic interventions is becoming an important pillar of a growing number of applications employing acoustic waves to actuate and cure the brain. Optical interrogation of living tissues provides a unique means for retrieving functional and molecular information related to brain activity and disease-specific biomarkers. The hybrid optoacoustic imaging methods have further enabled deep-tissue imaging with optical contrast at high spatial and temporal resolution. The marriage between light and sound thus brings together the highly complementary advantages of both modalities toward high precision interrogation, stimulation, and therapy of the brain with strong impact in the fields of ultrasound neuromodulation, gene and drug delivery, or noninvasive treatments of neurological and neurodegenerative disorders. In this review, we elaborate on current advances in optical and optoacoustic monitoring of ultrasound interventions. We describe the main principles and mechanisms underlying each method before diving into the corresponding biomedical applications. We identify areas of improvement as well as promising approaches with clinical translation potential.

Investigating pulse-echo sound speed estimation in breast ultrasound with deep learning

Ultrasound is an adjunct tool to mammography that can quickly and safely aid physicians in diagnosing breast abnormalities. Clinical ultrasound often assumes a constant sound speed to form diagnostic B-mode images. However, the components of breast tissue, such as glandular tissue, fat, and lesions, differ in sound speed. Given a constant sound speed assumption, these differences can degrade the quality of reconstructed images via phase aberration. Sound speed images can be a powerful tool for improving image quality and identifying diseases if properly estimated. To this end, we propose a supervised deep-learning approach for sound speed estimation from analytic ultrasound signals. We develop a large-scale simulated ultrasound dataset that generates representative breast tissue samples by modeling breast gland, skin, and lesions with varying echogenicity and sound speed. We adopt a fully convolutional neural network architecture trained on a simulated dataset to produce an estimated sound speed map. The simulated tissue is interrogated with a plane wave transmit sequence, and the complex-value reconstructed images are used as input for the convolutional network. The network is trained on the sound speed distribution map of the simulated data, and the trained model can estimate sound speed given reconstructed pulse-echo signals. We further incorporate thermal noise augmentation during training to enhance model robustness to artifacts found in real ultrasound data. To highlight the ability of our model to provide accurate sound speed estimations, we evaluate it on simulated, phantom, and in-vivo breast ultrasound data.

Evaluation of acoustic-thermal simulations of in vivo magnetic resonance guided focused ultrasound ablative therapy

PURPOSE

To evaluate numerical simulations of focused ultrasound (FUS) with a rabbit model, comparing simulated heating characteristics with magnetic resonance temperature imaging (MRTI) data collected during in vivo treatment.

METHODS

A rabbit model was treated with FUS sonications in the biceps femoris with 3D MRTI collected. Acoustic and thermal properties of the rabbit muscle were determined experimentally. Numerical models of the rabbits were created, and tissue-type-specific properties were assigned. FUS simulations were performed using both the hybrid angular spectrum (HAS) method and k-Wave. Simulated power deposition patterns were converted to temperature maps using a Pennes' bioheat equation-based thermal solver. Agreement of pressure between the simulation techniques and temperature between the simulation and experimental heating was evaluated. Contributions of scattering and absorption attenuation were considered.

RESULTS

Simulated peak pressures derived using the HAS method exceeded the simulated peak pressures from k-Wave by 1.6 ± 2.7%. The location and FWHM of the peak pressure calculated from HAS and k-Wave showed good agreement. When muscle acoustic absorption value in the simulations was adjusted to approximately 54% of the measured attenuation, the average root-mean-squared error between simulated and experimental spatial-average temperature profiles was 0.046 ± 0.019 °C/W. Mean distance between simulated and experimental COTMs was 3.25 ± 1.37 mm. Transverse FWHMs of simulated sonications were smaller than in in vivo sonications. Longitudinal FWHMs were similar.

CONCLUSIONS

Presented results demonstrate agreement between HAS and k-Wave simulations and that FUS simulations can accurately predict focal position and heating for in vivo applications in soft tissue.

Transcranial Ultrasonic Focusing by a Phased Array Based on Micro-CT Images

In this paper, we utilize micro-computed tomography (micro-CT) to obtain micro-CT images with a resolution of 60 μm and establish a micro-CT model based on the k-wave toolbox, which can visualize the microstructures in trabecular bone, including pores and bone layers. The transcranial ultrasound phased array focusing field characteristics in the micro-CT model are investigated. The ultrasonic waves are multiply scattered in skull and time delays calculations from the transducer to the focusing point are difficult. For this reason, we adopt the pulse compression method and the linear frequency modulation Barker code to compute the time delay and implement phased array focusing in the micro-CT model. It is shown by the simulation results that ultrasonic loss is mainly caused by scattering from the microstructures of the trabecular bone. The ratio of main and side lobes of the cross-correlation calculation is improved by 5.53 dB using the pulse compression method. The focusing quality and the calculation accuracy of time delay are improved. Meanwhile, the beamwidth at the focal point and the sound pressure amplitude decrease with the increase in the signal frequency. Focusing at different depths indicates that the beamwidth broadens with the increase in the focusing depth, and beam deflection focusing maintains good consistency in the focusing effect at a distance of 9 mm from the focal point. This indicates that the phased-array method has good focusing results and focus tunability in deep cranial brain. In addition, the sound pressure at the focal point can be increased by 8.2% through amplitude regulation, thereby enhancing focusing efficiency. The preliminary experiment verification is conducted with an ex vivo skull. It is shown by the experimental results that the phased array focusing method using pulse compression to calculate the time delay can significantly improve the sound field focusing effect and is a very effective transcranial ultrasound focusing method.

Real-Time Acoustic Simulation Framework for tFUS: A Feasibility Study Using Navigation System

Transcranial focused ultrasound (tFUS), in which acoustic energy is focused on a small region in the brain through the skull, is a non-invasive therapeutic method with high spatial resolution and depth penetration. Image-guided navigation has been widely utilized to visualize the location of acoustic focus in the cranial cavity. However, this system is often inaccurate because of the significant aberrations caused by the skull. Therefore, acoustic simulations using a numerical solver have been widely adopted to compensate for this inaccuracy. Although the simulation can predict the intracranial acoustic pressure field, real-time application during tFUS treatment is almost impossible due to the high computational cost. In this study, we propose a neural network-based real-time acoustic simulation framework and test its feasibility by implementing a simulation-guided navigation (SGN) system. Real-time acoustic simulation is performed using a 3D conditional generative adversarial network (3D-cGAN) model featuring residual blocks and multiple loss functions. This network was trained by the conventional numerical acoustic simulation program (i.e., k-Wave). The SGN system is then implemented by integrating real-time acoustic simulation with a conventional image-guided navigation system. The proposed system can provide simulation results with a frame rate of 5 Hz (i.e., about 0.2 s), including all processing times. In numerical validation (3D-cGAN vs. k-Wave), the average peak intracranial pressure error was 6.8 ± 5.5%, and the average acoustic focus position error was 5.3 ± 7.7 mm. In experimental validation using a skull phantom (3D-cGAN vs. actual measurement), the average peak intracranial pressure error was 4.5%, and the average acoustic focus position error was 6.6 mm. These results demonstrate that the SGN system can predict the intracranial acoustic field according to transducer placement in real-time.

High-throughput ultrasound neuromodulation in awake and freely behaving rats

Transcranial ultrasound neuromodulation is a promising potential therapeutic tool for the noninvasive treatment of neuropsychiatric disorders. However, the expansive parameter space and difficulties in controlling for peripheral auditory effects make it challenging to identify ultrasound sequences and brain targets that may provide therapeutic efficacy. Careful preclinical investigations in clinically relevant behavioral models are critically needed to identify suitable brain targets and acoustic parameters. However, there is a lack of ultrasound devices allowing for multi-target experimental investigations in awake and unrestrained rodents. We developed a miniaturized 64-element ultrasound array that enables neurointerventional investigations with within-trial active control targets in freely behaving rats. We first characterized the acoustic field with measurements in free water and with transcranial propagation. We then confirmed in vivo that the array can target multiple brain regions via electronic steering, and verified that wearing the device does not cause significant impairments to animal motility. Finally, we demonstrated the performance of our system in a high-throughput neuromodulation experiment, where we found that ultrasound stimulation of the rat central medial thalamus, but not an active control target, promotes arousal and increases locomotor activity.

Generating Patient-Specific Acoustic Simulations for Transcranial Focused Ultrasound Procedures Based on Optical Tracking Information

Optical tracking is a real-time transducer positioning method for transcranial focused ultrasound (tFUS) procedures, but the predicted focus from optical tracking typically does not incorporate subject-specific skull information. Acoustic simulations can estimate the pressure field when propagating through the cranium but rely on accurately replicating the positioning of the transducer and skull in a simulated space. Here, we develop and characterize the accuracy of a workflow that creates simulation grids based on optical tracking information in a neuronavigated phantom with and without transmission through an ex vivo skull cap. The software pipeline could replicate the geometry of the tFUS procedure within the limits of the optical tracking system (transcranial target registration error (TRE): 3.9 ± 0.7 mm). The simulated focus and the free-field focus predicted by optical tracking had low Euclidean distance errors of 0.5±0.1 and 1.2±0.4 mm for phantom and skull cap, respectively, and some skull-specific effects were captured by the simulation. However, the TRE of simulation informed by optical tracking was 4.6±0.2, which is as large or greater than the focal spot size used by many tFUS systems. By updating the position of the transducer using the original TRE offset, we reduced the simulated TRE to 1.1 ± 0.4 mm. Our study describes a software pipeline for treatment planning, evaluates its accuracy, and demonstrates an approach using MR-acoustic radiation force imaging as a method to improve dosimetry. Overall, our software pipeline helps estimate acoustic exposure, and our study highlights the need for image feedback to increase the accuracy of tFUS dosimetry.

Evaluation of synthetically generated computed tomography for use in transcranial focused ultrasound procedures

Purpose

Transcranial focused ultrasound (tFUS) is a therapeutic ultrasound method that focuses sound through the skull to a small region noninvasively and often under magnetic resonance imaging (MRI) guidance. CT imaging is used to estimate the acoustic properties that vary between individual skulls to enable effective focusing during tFUS procedures, exposing patients to potentially harmful radiation. A method to estimate acoustic parameters in the skull without the need for CT is desirable.

Approach

We synthesized CT images from routinely acquired T1-weighted MRI using a 3D patch-based conditional generative adversarial network and evaluated the performance of synthesized CT (sCT) images for treatment planning with tFUS. We compared the performance of sCT with real CT (rCT) images for tFUS planning using Kranion and simulations using the acoustic toolbox, k-Wave. Simulations were performed for 3 tFUS scenarios: (1) no aberration correction, (2) correction with phases calculated from Kranion, and (3) phase shifts calculated from time reversal.

Results

From Kranion, the skull density ratio, skull thickness, and number of active elements between rCT and sCT had Pearson's correlation coefficients of 0.94, 0.92, and 0.98, respectively. Among 20 targets, differences in simulated peak pressure between rCT and sCT were largest without phase correction (12.4 % ± 8.1 % ) and smallest with Kranion phases (7.3 % ± 6.0 % ). The distance between peak focal locations between rCT and sCT was < 1.3    mm for all simulation cases.

Conclusions

Real and synthetically generated skulls had comparable image similarity, skull measurements, and acoustic simulation metrics. Our work demonstrated similar results for 10 testing cases comparing MR-sCTs and rCTs for tFUS planning. Source code and a docker image with the trained model are available at https://github.com/han-liu/SynCT_TcMRgFUS.

A simulation study on the sensitivity of transcranial ray-tracing ultrasound modeling to skull properties

In transcranial focused ultrasound therapies, such as treating essential tremor via thermal ablation in the thalamus, acoustic energy is focused through the skull using a phased-array transducer. Ray tracing is a computationally efficient method that can correct skull-induced phase aberrations via per-element phase delay calculations using patient-specific computed tomography (CT) data. However, recent studies show that variations in CT-derived Hounsfield unit may account for only 50% of the speed of sound variability in human skull specimens, potentially limiting clinical transcranial ultrasound applications. Therefore, understanding the sensitivity of treatment planning methods to material parameter variations is essential. The present work uses a ray-tracing simulation model to explore how imprecision in model inputs, arising from clinically significant uncertainties in skull properties or considerations of acoustic phenomena, affects acoustic focusing quality through the skull. We propose and validate new methods to optimize ray-tracing skull simulations for clinical treatment planning, relevant for predicting intracranial target's thermal rise, using experimental data from ex-vivo human skulls.

Multivariable-incorporating super-resolution residual network for transcranial focused ultrasound simulation

BACKGROUND AND OBJECTIVE

Transcranial focused ultrasound (tFUS) has emerged as a new non-invasive brain stimulation (NIBS) modality, with its exquisite ability to reach deep brain areas at a high spatial resolution. Accurate placement of an acoustic focus to a target region of the brain is crucial during tFUS treatment; however, the distortion of acoustic wave propagation through the intact skull casts challenges. High-resolution numerical simulation allows for monitoring of the acoustic pressure field in the cranium but also demands extensive computational loads. In this study, we adopt a super-resolution residual network technique based on a deep convolution to enhance the prediction quality of the FUS acoustic pressure field in the targeted brain regions.

METHODS

The training dataset was acquired by numerical simulations performed at low-(1.0 mm) and high-resolutions (0.5mm) on three ex vivo human calvariae. Five different super-resolution (SR) network models were trained by using a multivariable dataset in 3D, which incorporated information on the acoustic pressure field, wave velocity, and localized skull computed tomography (CT) images.

RESULTS

The accuracy of 80.87±4.50% in predicting the focal volume with a substantial improvement of 86.91% in computational cost compared to the conventional high-resolution numerical simulation was achieved. The results suggest that the method can greatly reduce the simulation time without sacrificing accuracy and improve the accuracy further with the use of additional inputs.

CONCLUSIONS

In this research, we developed multivariable-incorporating SR neural networks for transcranial focused ultrasound simulation. Our super-resolution technique may contribute to promoting the safety and efficacy of tFUS-mediated NIBS by providing on-site feedback information on the intracranial pressure field to the operator.

Wave Equation Modeling via Physics-Informed Neural Networks: Models of Soft and Hard Constraints for Initial and Boundary Conditions

Therapeutic ultrasound waves are the main instruments used in many noninvasive clinical procedures. They are continuously transforming medical treatments through mechanical and thermal effects. To allow for effective and safe delivery of ultrasound waves, numerical modeling methods such as the Finite Difference Method (FDM) and the Finite Element Method (FEM) are used. However, modeling the acoustic wave equation can result in several computational complications. In this work, we study the accuracy of using Physics-Informed Neural Networks (PINNs) to solve the wave equation when applying different combinations of initial and boundary conditions (ICs and BCs) constraints. By exploiting the mesh-free nature of PINNs and their prediction speed, we specifically model the wave equation with a continuous time-dependent point source function. Four main models are designed and studied to monitor the effects of soft or hard constraints on the prediction accuracy and performance. The predicted solutions in all the models were compared to an FDM solution for prediction error estimation. The trials of this work reveal that the wave equation modeled by a PINN with soft IC and BC (soft-soft) constraints reflects the lowest prediction error among the four combinations of constraints.

Modeling frequency shifts of collective bubble resonances with the boundary element method

Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance. This work investigates the transition in resonance behavior using a modal analysis of a mass-spring system and a boundary element method. The computational complexity of the full-wave solver is significantly reduced to a linear dependence on the number of bubbles in a rectangular array. The simulated acoustic fields confirm the initial downshift in resonance frequency and the strong influence of collective resonances when the array has hundreds of bubbles covering more than half of the wavelength. These results are essential in understanding the low-frequency resonance characteristics of bubble ensembles, which have important applications in diverse fields such as underwater acoustics, quantum physics, and metamaterial design.

S.M.A.R.T. F.U.S: Surrogate Model of Attenuation and Refraction in Transcranial Focused Ultrasound

Low-intensity focused ultrasound (LIFU) is an increasingly applied method for achieving non-invasive brain stimulation. However, transmission of ultrasound through the human skull can substantially affect focal point characteristics of LIFU, including dramatic attenuation in intensity and refraction of focal point location. These effects depend on a high-dimensional parameter space, making these effects difficult to estimate from previous work. Instead, focal point properties of LIFU experiments are often estimated using numerical simulation of LIFU sonication through skull. However, this procedure presents many entry barriers to even computationally savvy investigators and often requires expensive computational hardware, impeding LIFU research. We present a novel MATLAB toolbox (data: doi:10.5068/D1QD60; Matlab Scripts: https://doi.org/10.5281/zenodo.5811122) for rapidly estimating beam properties of LIFU transmitted through bone. Users provide specific values for frequency of LIFU, bone thickness, angle at which LIFU is applied, depth of the LIFU focal point, and diameter of the transducer used and receive an estimation of the degree of refraction/attenuation expected for the given parameters.

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.

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.