A viscoelastic model for the prediction of transcranial ultrasound propagation: application for the estimation of shear acoustic properties in the human skull

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.

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.

Influence of Plastination on Ultrasound Transmission Through the Human Skull

Development, optimization and validation of transcranial ultrasound methods require the use of fresh human or animal skulls. However, to avoid fresh skull degradation over time, fixation methods are required for conservation, such as formaldehyde buffer solution. This method allows for conservation of the skull properties over a relatively long period, but requires specific conditioning (de-gassing) and storage conditions, such that its practical use is limited. Plastination appears to be a unique solution for the preservation and transportation of body parts without constraints. However, the influence of this conservation process has yet to be characterized with respect to ultrasound transmission to verify that the acoustic and mechanical properties of the skulls are not altered by the plastination process. The objective of the study described here was to quantify the effect of plastination on ultrasound transmission through the temporal and parietal areas of the human skull between 200 kHz and 2 MHz. To achieve this, transmission measurements were performed on three different skulls and four areas before and after plastination. It was found that the plastination process results in a transmission loss of 5 dB. Moreover, results indicate that the plastination process does not induce any phase shift in the transmitted signal, validating the proper use of plastinated skulls for in vitro measurements and development of new transcranial ultrasound methods.

Effect of skull porosity on ultrasound transmission and wave mode conversion at large incidence angles

BACKGROUND

Transcranial ultrasound imaging and therapy depend on the efficient transmission of acoustic energy through the skull. Multiple previous studies have concluded that a large incidence angle should be avoided during transcranial-focused ultrasound therapy to ensure transmission through the skull. Alternatively, some other studies have shown that longitudinal-to-shear wave mode conversion might improve transmission through the skull when the incidence angle is increased above the critical angle (i.e., 25° to 30°).

PURPOSE

The effect of skull porosity on the transmission of ultrasound through the skull at varying incidence angles was investigated for the first time to elucidate why transmission through the skull at large angles of incidence is decreased in some cases but improved in other cases.

METHODS

Transcranial ultrasound transmission at varying incidence angles (0°-50°) was investigated in phantoms and ex vivo skull samples with varying bone porosity (0% to 28.54% ± 3.36%) using both numerical and experimental methods. First, the elastic acoustic wave transmission through the skull was simulated using micro-computed tomography data of ex vivo skull samples. The trans-skull pressure was compared between skull segments having three levels of porosity, that is, low porosity (2.65% ± 0.03%), medium porosity (13.41% ± 0.12%), and high porosity (26.9%). Next, transmission through two 3D-printed resin skull phantoms (compact vs. porous phantoms) was experimentally measured to test the effect of porous microstructure alone on ultrasound transmission through flat plates. Finally, the effect of skull porosity on ultrasound transmission was investigated experimentally by comparing transmission through two ex vivo human skull segments having similar thicknesses but different porosities (13.78% ± 2.05% vs. 28.54% ± 3.36%).

RESULTS

Numerical simulations indicated that an increase in transmission pressure occurs at large incidence angles for skull segments having low porosities but not for those with high porosity. In experimental studies, a similar phenomenon was observed. Specifically, for the low porosity skull sample (13.78% ± 2.05%), the normalized pressure was 0.25 when the incidence angle increased to 35°. However, for the high porosity sample (28.54% ± 3.36%), the pressure was no more than 0.1 at large incidence angles.

CONCLUSIONS

These results indicate that the skull porosity has an evident effect on the transmission of ultrasound at large incidence angles. The wave mode conversion at large, oblique incidence angles could enhance the transmission of ultrasound through parts of the skull having lower porosity in the trabecular layer. However, for transcranial ultrasound therapy in the presence of highly porous trabecular bone, transmission at a normal incidence angle is preferable relative to oblique incidence angles due to the higher transmission efficiency.

Optimizing transcranial ultrasound delivery at large incident angles by leveraging cranial leaky guided wave dispersion

We investigate the role of leaky guided waves in transcranial ultrasound transmission in temporal and parietal bones at large incidence angles. Our numerical and experimental results show that the dispersion characteristics of the fundamental leaky guided wave mode with longitudinal polarization can be leveraged to estimate the critical angle above which efficient shear mode conversion takes place, and below which major transmission drops can be expected. Simulations that employ a numerical propagator matrix and a Semi-Analytical approach establish the transcranial dispersion characteristics and transmission coefficients at different incident angles. Experimental transmission tests conducted at 500 kHz and radiation tests performed in the 200-800 kHz range confirm the numerical findings in terms of transmitted peak pressure and frequency-radiation angle spectra, based on which the connection between critical angles, dispersion and transmission is demonstrated. Our results support the identification of transcranial ultrasound strategies that leverage shear mode conversion, which is less sensitive to phase aberrations compared to normal incidence ultrasound. These findings can also enable higher transmission rates in cranial bones with low porosity by leveraging dispersion information extracted through signal processing, without requiring measurement of geometric and mechanical properties of the cranial bone.

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 Comparative Feasibility Study for Transcranial Extracorporeal Shock Wave Therapy

The potential beneficial regenerative and stimulatory extracorporeal shock wave therapy (ESWT) applications to the central nervous system have garnered interest in recent years. Treatment zones for these indications are acoustically shielded by bones, which heavily impact generated sound fields. We present the results of high-resolution tissue-realistic simulations, comparing the viability of different ESWT applicators in their use for transcranial applications. The performances of electrohydraulic, electromagnetic, and piezoelectric transducers for key reflector geometries are compared. Based on density information obtained from CT imaging of the head, we utilized the non-linear wave propagation toolset Matlab k-Wave to obtain spatial therapeutic sound field geometries and waveforms. In order to understand the reliability of results on the appropriate modeling of the skull, three different bone attenuation models were compared. We find that all currently clinically ESWT applicator technologies show significant retention of peak pressures and energies past the bone barrier. Electromagnetic transducers maintain a significantly higher energy flux density compared to other technologies while low focusing strength piezoelectric applicators have the weakest transmissions. Attenuation estimates provide insights into sound field degradation and energy losses, indicating that effective transcranial therapies can readily be attained with current applicators. Furthermore, the presented approach will allow for future targeted in silico development and the design of applicators and therapy plans to ultimately improve therapeutic outcomes.

Establishing density-dependent longitudinal sound speed in the vertebral lamina

Focused ultrasound treatments of the spinal cord may be facilitated using a phased array transducer and beamforming to correct spine-induced focal aberrations. Simulations can non-invasively calculate aberration corrections using x-ray computed tomography (CT) data that are correlated to density (ρ) and longitudinal sound speed (c_L). We aimed to optimize vertebral lamina-specific c_L(ρ) functions at a physiological temperature (37 °C) to maximize time domain simulation accuracy. Odd-numbered ex vivo human thoracic vertebrae were imaged with a clinical CT-scanner (0.511 × 0.511 × 0.5 mm), then sonicated with a transducer (514 kHz) focused on the canal via the vertebral lamina. Vertebra-induced signal time shifts were extracted from pressure waveforms recorded within the canals. Measurements were repeated 5× per vertebra, with 2.5 mm vertical vertebra shifts between measurements. Linear functions relating c_L with CT-derived density were optimized. The optimized function was c_L(ρ)=0.35(ρ-ρ_w)+ c_L,w m/s, where w denotes water, giving the tested laminae a mean bulk density of 1600 ± 30 kg/m³ and a mean bulk c_L of 1670 ± 60 m/s. The optimized lamina c_L(ρ) function was accurate to λ/16 when implemented in a multi-layered ray acoustics model. This modelling accuracy will improve trans-spine ultrasound beamforming.

Acoustic properties across the human skull

Transcranial ultrasound is emerging as a noninvasive tool for targeted treatments of brain disorders. Transcranial ultrasound has been used for remotely mediated surgeries, transient opening of the blood-brain barrier, local drug delivery, and neuromodulation. However, all applications have been limited by the severe attenuation and phase distortion of ultrasound by the skull. Here, we characterized the dependence of the aberrations on specific anatomical segments of the skull. In particular, we measured ultrasound propagation properties throughout the perimeter of intact human skulls at 500 kHz. We found that the parietal bone provides substantially higher transmission (average pressure transmission 31 ± 7%) and smaller phase distortion (242 ± 44 degrees) than frontal (13 ± 2%, 425 ± 47 degrees) and occipital bone regions (16 ± 4%, 416 ± 35 degrees). In addition, we found that across skull regions, transmission strongly anti-correlated (R=-0.79) and phase distortion correlated (R=0.85) with skull thickness. This information guides the design, positioning, and skull correction functionality of next-generation devices for effective, safe, and reproducible transcranial focused ultrasound therapies.

Multitarget Transcranial Ultrasound Therapy in Small Animals Based on Phase-Only Acoustic Holographic Lens

Transcranial ultrasound therapy has become a noninvasive method for treating neurological and psychiatric disorders, and studies have further demonstrated that multitarget transcranial ultrasound therapy is a better solution. At present, multitarget transcranial ultrasound therapy in small animals can only be achieved by the multitransducer or phased array. However, multiple transducers may cause spatial interference, and the phased array system is complicated, expensive, and especially unsuitable for small animals. This study is the first to design and fabricate a miniature acoustic holography lens for multitarget transcranial ultrasound therapy in rats. The acoustic holographic lens, working at a frequency of 1.0 MHz, with a size of 10.08 mm ×10.08 mm and a pixel resolution of 0.72 mm, was designed, optimized, and fabricated. The dual-focus transcranial ultrasound generated based on the lens was measured; the full-width at half-maximum (FWHM) of the focal spots in the y -direction was 2.15 and 2.27 mm and in the z -direction was 2.3 and 2.36 mm. The focal length was 5.4 mm, and the distance between the two focuses was 5.6 mm, close to the desired values of 5.4 and 6.0 mm. Finally, the multiple-target blood-brain barrier opening in rats' bilateral secondary visual cortex (mediolateral area, V2ML) was demonstrated using the transcranial ultrasound therapy system based on the lens. These results demonstrate the good performance of the multitarget transcranial ultrasound therapy system for small animals, including high spatial resolution, small size, and low cost.

Simulation study on the effects of cancellous bone structure in the skull on ultrasonic wave propagation

The transcranial Doppler method (TCD) enables the measurement of cerebral blood flow velocity and detection of emboli by applying an ultrasound probe to the temporal bone window, or the orbital or greater occipital foramina. TCD is widely used for evaluation of cerebral vasospasm after subarachnoid hemorrhage, early detection of patients with arterial stenosis, and the assessment of brain death. However, measurements often become difficult in older women. Among various factors contributing to this problem, we focused on the effect of the diploe in the skull bone on the penetration of ultrasound into the brain. In particular, the effect of the cancellous bone structure in the diploe was investigated. Using a 2D digital bone model, wave propagation through the skull bone was investigated using the finite-difference time-domain (FDTD) method. We fabricated digital bone models with similar structure but different BV/TV (bone volume/total volume) values in the diploe. At a BV/TV of approximately 50–60% (similar to that of older women), the minimum ultrasound amplitude was observed as a result of scattering and multiple reflections in the cancellous diploe. These results suggest that structural changes such as osteoporosis may be one factor hampering TCD measurements.

Effect of Skull Porous Trabecular Structure on Transcranial Ultrasound Imaging in the Presence of Elastic Wave Mode Conversion at Varying Incidence Angle

With the advancement of aberration correction techniques, transcranial ultrasound imaging has exhibited great potential in applications such as imaging neurological function and guiding therapeutic ultrasound. However, the feasibility of transcranial imaging varies among individuals because of the differences in skull acoustic properties. To better understand the fundamental mechanisms underlying the variation in imaging performance, the effect of the structure of the porous trabecular bone on transcranial imaging performance (i.e., target localization errors and resolution) was investigated for the first time through the use of elastic wave simulations and experiments. Simulation studies using high-resolution computed tomography data from ex vivo skull samples revealed that imaging at large incidence angles reduced the target localization error for skulls having low porosity; however, as skull porosity increased, large angles of incidence resulted in degradation of resolution and increased target localization errors. Experimental results indicate that imaging at normal incidence introduced a localization error of 1.85 ± 0.10 mm, while imaging at a large incidence angle (40°) resulted in an increased localization error of 6.54 ± 1.33 mm and caused a single point target to no longer appear as a single, coherent target in the resulting image, which is consistent with simulation results. This first investigation of the effects of skull microstructure on transcranial ultrasound imaging indicates that imaging performance is highly dependent on the porosity of the skull, particularly at non-normal angles of incidence.

Comparison Between Ray-Tracing and Full-Wave Simulation for Transcranial Ultrasound Focusing on a Clinical System Using the Transfer Matrix Formalism

Only one high-intensity focused ultrasound device has been clinically approved for transcranial brain surgery at the time of writing. The device operates within 650 and 720 kHz and corrects the phase distortions induced by the skull of each patient using a multielement phased array. Phase correction is estimated adaptively using a proprietary algorithm based on computed-tomography (CT) images of the patient's skull. In this article, we assess the performance of the phase correction computed by the clinical device and compare it to: 1) the correction obtained with a previously validated full-wave simulation algorithm using an open-source pseudo-spectral toolbox and 2) a hydrophone-based correction performed invasively to measure the aberrations induced by the skull at 650 kHz. For the full-wave simulation, three different mappings between CT Hounsfield units and the longitudinal speed of sound inside the skull were tested. All methods are compared with the exact same setup due to transfer matrices acquired with the clinical system for N = 5 skulls and T = 2 different targets for each skull. We show that the clinical ray-tracing software and the full-wave simulation restore, respectively, 84% ± 5% and 86% ± 5% of the pressure obtained with hydrophone-based correction for targets located in central brain regions. On the second target (off-center), we also report that the performance of both algorithms degrades when the average incident angles of the acoustic beam at the skull surface increase. When incident angles are higher than 20°, the restored pressure drops below 75% of the pressure restored with hydrophone-based correction.

Multiple Linear Regression Estimation of Onset Time Delay for Experimental Transcranial Narrowband Ultrasound Signals

Focused ultrasound is an emerging medical technique for transcranial procedures and requires the precise modeling of ultrasound signal propagation through the skull. To verify models, the onset time delay (OTD) between two signals measured at the same spatial location, with and without the presence of a skull in the path of the signal, is compared between simulations and experiments. Current methods to automatically identify OTD use correlation-based algorithms. However, these techniques suffer from poor results caused by signal distortion and low signal-to-noise ratios in experimental signals. In this study, we compare the effectiveness of machine learning (multiple linear regression) to three correlation-based time-delay estimation techniques in estimating the OTD of a signal pair. A sample of 1643 signal pairs, with the center frequencies of either 270 or 836 kHz, had their delays manually identified as a benchmark. Density, thickness, incidence angle, frequency, and x and y offsets from the center were used as predictors. We find that, compared with manual identification, machine learning is 80.4% more accurate than cross correlation across all test signals and is noise-independent through all noise bins. The median of the errors was less than 0.3 periods was observed for signals with a frequency of 270 kHz and less than 1.1 periods for signals with a frequency of 836 kHz, with little estimate bias. Overall, linear multivariable regression is determined to provide the best estimate of the OTD of two signals.

Design of a Versatile Angle-Rotatable Skull-Shaped Conformal Transcranial Focused Ultrasound Transducer for Noninvasive Brain Therapy

Phase-controlled focused ultrasound transducers have opened up a new way to noninvasively treat brain diseases. However, due to the geometry and the heterogeneous medium of the human skull, the currently used hemispherical transducers cannot guarantee that the ultrasound emitted by the transducer penetrates the skull normally; consequently, the impact of the shear wave on the treatment area has to be considered. The usual approach is to turn off elements in the transducer with excessively large incident angles, but this approach reduces the efficiency of the transducer. This article presents the design of a novel transducer that can be rotated according to the different geometric shapes of the skull. The incident angles of the elements in the transducer are modified so that the effect of the shear wave on the treatment area can be ignored and the efficiency of the transducer is improved. The results of computed tomography (CT) model simulation of nine skulls verify the versatility and feasibility of the new transducer. We believe that this kind of rotatable transducer has clinical and engineering significance.

A Porcine Model of Transvertebral Ultrasound and Microbubble-Mediated Blood-Spinal Cord Barrier Opening

Blood-spinal cord barrier opening, using focused ultrasound and microbubbles, has the potential to improve drug delivery for the treatment of spinal cord pathologies. Delivering and detecting ultrasound through the spine is a challenge for clinical translation. We have previously developed short burst, phase keying exposures, which can be used in a dual-aperture configuration to address clinical scale targeting challenges. Here we demonstrate the use of these pulses for blood-spinal cord barrier opening, in vivo in pigs.

Methods: The spinal cords of Yorkshire pigs (n=8) were targeted through the vertebral laminae, in the lower thoracic to upper lumbar region using focused ultrasound (486 kHz) and microbubbles. Four animals were treated with a combination of pulsed sinusoidal exposures (1.0-4.0 MPa, non-derated) and pulsed short burst, phase keying exposures (1.0-2.0 MPa, non-derated). Four animals were treated using ramped short burst, phase keying exposures (1.8-2.1 MPa, non-derated). A 250 kHz narrowband receiver was used to detect acoustic emissions from microbubbles. Blood-spinal cord barrier opening was assessed by the extravasation of Evans blue dye. Histological analysis of the spinal cords was used to assess tissue damage and excised vertebral samples were used in benchtop experiments.

Results: Ramped short burst, phase keying exposures successfully modified the blood-spinal cord barrier at 16/24 targeted locations, as assessed by the extravasation of Evans blue dye. At 4 of these locations, opening was confirmed with minimal adverse effects observed through histology. Transmission measurements through excised vertebrae indicated a mean transmission of (47.0 ± 7.0 %) to the target.

Conclusions: This study presents the first evidence of focused ultrasound-induced blood-spinal cord barrier opening in a large animal model, through the intact spine. This represents an important step towards clinical translation.

Numerical Evaluation of the Influence of Skull Heterogeneity on Transcranial Ultrasonic Focusing

In transcranial penetration, ultrasound undergoes refraction, diffraction, multi-reflection, and mode conversion. These factors lead to phase aberration and waveform distortion, which impede the realization of transcranial ultrasonic imaging and therapy. Ray tracing has been used to correct the phase aberration and is computationally more efficient than traditional full-wave simulation. However, when ray tracing has been used for transcranial investigation, it has generally been on the premise that the skull medium is homogeneous. To find suitable homogeneity that balances computational speed and accuracy, the present work investigates how the focus deviates after phase-aberration compensation with ray tracing using time-reversal theory. The waveforms are synthetized with ray tracing for phase aberration, by which the properties of the skull bone are simplified for refraction calculation as those of either (i) the cortical bone or (ii) the mean of the entire skull bone, and the focusing accuracy is evaluated for each hypothesis. The propagation of ultrasound for transcranial focusing is simulated with the elastic model using the k-space pseudospectral method. Unlike the fluid model, the elastic model does not omit shear waves in the skull bones, and the influence of that omission is investigated, with the fluid model resulting in a focal deflection of 0.5 mm. The focusing deviations are huge when the properties of the skull bone are idealized with ray tracing as those of the mean of the entire skull bone. The focusing accuracy improves when the properties of the skull bone are idealized as those of the cortical bone. The results reveal minimal deviation (8.6, 3.9, and 3.2% in the three Cartesian coordinates) in the focal region and suggest that transcranial focusing deflections are caused mostly by ultrasonic refraction on the surface of the skull bone. A heterogeneous skull bone causes wave bending but minimal focusing deflection. The proposed simplification of a homogeneous skull bone is more accurate for transcranial ultrasonic path estimation and offers promising applications in transcranial ultrasonic focusing and imaging.

Superposition method for modelling boundaries between media in viscoelastic finite difference time domain simulations

Finite-difference time domain (FDTD) techniques are widely used to model the propagation of viscoelastic waves through complex and heterogeneous structures. However, in the specific case of media mixing liquid and solid, attempts to model continuous media onto a Cartesian grid produces errors when the liquid-solid interface between different media do not align precisely with the Cartesian grid. The increase in spatial resolution required to eliminate this grid staircasing effect can be computationally prohibitive. Here, a modification to the Virieux staggered-grid FDTD scheme called the superposition method is presented. This method is intended to reduce this staircasing effect while keeping a manageable computational time. The method was validated by comparing low-spatial-resolution simulations against simulations with sufficiently high resolution to provide reasonably accurate results at any incident angle. The comparison of the root-mean-square of the stress amplitude maps showed that the amplitude of artifactual waves could be reduced by several orders of magnitude when compared to the Virieux staggered-grid FDTD method and that the superposition method helped to significantly reduce the staircasing effect in FDTD simulations.

Modeling ultrasound propagation through material of increasing geometrical complexity

Ultrasound is increasingly being recognized as a neuromodulatory and therapeutic tool, inducing a broad range of bio-effects in the tissue of experimental animals and humans. To achieve these effects in a predictable manner in the human brain, the thick cancellous skull presents a problem, causing attenuation. In order to overcome this challenge, as a first step, the acoustic properties of a set of simple bone-modeling resin samples that displayed an increasing geometrical complexity (increasing step sizes) were analyzed. Using two Non-Destructive Testing (NDT) transducers, we found that Wiener deconvolution predicted the Ultrasound Acoustic Response (UAR) and attenuation caused by the samples. However, whereas the UAR of samples with step sizes larger than the wavelength could be accurately estimated, the prediction was not accurate when the sample had a smaller step size. Furthermore, a Finite Element Analysis (FEA) performed in ANSYS determined that the scattering and refraction of sound waves was significantly higher in complex samples with smaller step sizes compared to simple samples with a larger step size. Together, this reveals an interaction of frequency and geometrical complexity in predicting the UAR and attenuation. These findings could in future be applied to poro-visco-elastic materials that better model the human skull.

Development of custom RF coils for use in a small animal platform for magnetic resonance-guided focused ultrasound hyperthermia compatible with a clinical MRI scanner

Three different magnetic resonance imaging (MRI) coils were developed and assessed for use with an experimental platform designed to generate hyperthermia in mice using magnetic resonance-guided focused ultrasound (MRgFUS). An ergonomic animal treatment bed was integrated with MRI coils. Three different coil designs optimized for small targets were tested, and performance in targeting and conducting accurate temperature imaging was evaluated. Two transmit/receive surface coils of different diameters (4 and 7 cm) and a transmit-only/receive-only (TORO) coil were used. A software platform was developed to provide real-time targeting and temperature maps and to deliver controlled ultrasound exposure. MR thermometry was conducted on different targets, including fresh chicken breasts and mouse cadavers. Multiple experiments were performed in which tissues were targeted with high reproducibility. The TORO coil was the most resilient to temperature drift, resulting in an increase in the calculated temperature of 0.29 ± 0.12 °C, compared to 1.27 ± 0.13 °C and 0.47 ± 0.04 °C for the medium and small coils, respectively. Controlled closed-loop hyperthermia exposure was successfully performed with all three coils. Considering all assessments, the TORO coil exhibited the best overall performance for thermometry acquisition when accounting for stability, precision, temperature spread and resilience to temperature drift. B₁ maps of the three coils confirmed that the TORO coil exhibited the most homogeneous B₁ field, which explained the improved thermometry performance. The use of coils specifically designed for small targets within the proposed experimental platform allowed accurate thermometry during hyperthermia.

Simulating transvertebral ultrasound propagation with a multi-layered ray acoustics model

The simulation accuracy of transvertebral ultrasound propagation using a multi-layered ray acoustics model based on CT-derived vertebral geometry was investigated through comparison with experimental measurements of pressure fields in ex vivo human vertebral foramen. A spherically focused transducer (5 cm diameter, f-number 1.2, 514 kHz) was geometrically focused to the centre of individual thoracic vertebral foramen, through the posterior bony elements. Transducer propagation paths through the laminae and the spinous processes were tested. Simulation transducer-vertebra configurations were registered to experiment transducer-vertebra configurations, and simulation accuracy of the simulation model was evaluated for predicting maximum transmitted pressure to the canal, voxel pressure in the canal, and focal distortion. Accuracy in predicting maximum transmitted pressure was calculated by vertebra, and it is shown that simulation predicts maximum pressure with a greater degree of accuracy than a vertebra-specific insertion loss. Simulation error in voxel pressure was evaluated using root-mean-square error and cross-correlation, and found to be similar to the water-only case. Simulation accuracy in predicting focal distortion was evaluated by comparing experiment and simulation maximum pressure location and weighted  >50% focal volume location. Average simulation error across all measurements and simulations in maximum pressure location and weighted  >50% focal volume location were 2.3 mm and 1.5 mm, respectively. These errors are small relative to the dimensions of the transducer focus (4.9 mm full width half maximum), the spinal cord (10 mm diameter), and vertebral canal diameter (15-20 mm diameter). These results suggest that ray acoustics can be applied to simulating transvertebral ultrasound propagation.

A random phased-array for MR-guided transcranial ultrasound neuromodulation in non-human primates

Transcranial focused ultrasound (FUS) is a non-invasive technique for therapy and study of brain neural activation. Here we report on the design and characterization of a new MR-guided FUS transducer for neuromodulation in non-human primates at 650 kHz. The array is randomized with 128 elements 6.6 mm in diameter, radius of curvature 7.2 cm, opening diameter 10.3 cm (focal ratio 0.7), and 46% coverage. Simulations were used to optimize transducer geometry with respect to focus size, grating lobes, and directivity. Focus size and grating lobes during electronic steering were quantified using hydrophone measurements in water and a three-axis stage. A novel combination of optical tracking and acoustic mapping enabled measurement of the 3D pressure distribution in the cortical region of an ex vivo skull to within ~3.5 mm of the surface, and allowed accurate modelling of the experiment via non-homogeneous 3D acoustic simulations. The data demonstrates acoustic focusing beyond the skull bone, with the focus slightly broadened and shifted proximal to the skull. The fabricated design is capable of targeting regions within the S1 sensorimotor cortex of macaques.