Computationally Efficient Transcranial Ultrasonic Focusing: Taking Advantage of the High Correlation Length of the Human Skull

Focal volume reduction in transcranial focused ultrasound using spherical wave expansions

Transcranial focused ultrasound (tFUS) has been gaining increased attention as a non-invasive modality for treating brain diseases. However, accurately focusing on brain structures remains a challenge as the ultrasound is severely distorted by the presence of the skull. In this article, we propose a promising distortion correction method based on spherical wave expansions. It is demonstrated that the focal gain is directly related to the zero-order spherical harmonic coefficient, and suppressing higher-order coefficients significantly reduces the focal volume. Simulation results show that this method can correct distortion and effectively balance focal gain and volume, achieving a smaller focal spot with lower grating lobes compared to the commonly used time reversal technique. We also verified the capability of shifting the focal position in real time without additional simulations. This work provides an effective approach for tFUS treatments, offering enhanced precision and reduced focal volume.

Transducer module apodization to reduce bone heating during focused ultrasound uterine fibroid ablation with phased arrays: A numerical study

BACKGROUND

During magnetic resonance-guided focused ultrasound (MRgFUS) surgery for uterine fibroids, ablation of fibrous tissues in proximity to the hips and spine is challenging due to heating within the bone that can cause patients to experience pain and potentially damage nerves. This far-field bone heating limits the volume of fibroid tissue that is treatable via MRgFUS.

PURPOSE

To investigate transducer module apodization for improving the ratio of focal-to-bone heating (Δ T ratio $\Delta T_{\mathrm{ratio}}$ ) when targeting fibroid tissue close to the hips and spine, to enable MRgFUS treatments closer to the bone.

METHODS

Acoustic and thermal simulations were performed using 3D magnetic resonance imaging (MRI)-derived anatomies of ten patients who underwent MRgFUS ablation for uterine fibroids using a low-frequency (0.5 MHz $0.5 \ \text{MHz}$ ) 6144-element flat fully-populated modular phased array system (Arrayus Technologies Inc., Burlington, Canada) at our institution as part of a larger clinical trial (NCT03323905). Transducer modules (64 elements $64 \ \text{elements}$ per module) whose beams intersected with no-pass zones delineated within the field were identified, their output power levels were reduced by varying blocking percentage levels, and the resulting temperature field distributions were evaluated across multiple sonications near the hip and spine bones in each patient. Acoustic and thermal simulations took approximately20 min $20 \ \text{min}$ (7 min $7 \ \text{min}$ ) and1 min $1 \ \text{min}$ (30 s $30 \ \text{s}$ ) to run for a single near-spine (near-hip) target, respectively.

RESULTS

For all simulated sonications, transducer module blocking improvedΔ T ratio $\Delta T_{\mathrm{ratio}}$ compared to the no blocking case. In just over half of sonications, full module blocking maximizedΔ T ratio $\Delta T_{\mathrm{ratio}}$ (increase of 82% ± $\pm$ 38% in 50% of hip targets and 49% ± $\pm$ 30% in 62% of spine targets vs. no blocking; mean ± SD), at the cost of more diffuse focusing (focal heating volumes increased by 13% ± 13% for hip targets and 39% ± 27% for spine targets) and thus requiring elevated total (hip: 6% ± 17%, spine: 37% ± 17%) and peak module-wise (hip: 65% ± 36%, spine: 101% ± 56%) acoustic power levels to achieve equivalent focal heating as the no blocking control case. In the remaining sonications, partial module blocking provided further improvements in bothΔ T ratio $\Delta T_{\mathrm{ratio}}$ (increased by 29% ± 25% in the hip and 15% ± 12% in the spine) and focal heating volume (decrease of 20% ± 10% in the hip and 34% ± 17% in the spine) relative to the full blocking case. The optimal blocking percentage value was dependent on the specific patient geometry and target location of interest. Although not all individual target locations saw the benefit, element-wise phase aberration corrections improved the averageΔ T ratio $\Delta T_{\mathrm{ratio}}$ compared to the no correction case (increase of 52% ± 47% in the hip, 35% ± 24% in the spine) and impacted the optimal blocking percentage value. Transducer module blocking enabled ablative treatments to be carried out closer to both hip and spine without overheating or damaging the bone (no blocking:42 ± 1 mm $42\pm 1 \ \text{mm}$ /17 ± 2 mm $17 \pm 2 \ \text{mm}$ , full blocking:38 ± 1 mm $38\pm 1 \ \text{mm}$ /8 ± 1 mm $8\pm 1 \ \text{mm}$ , optimal partial blocking:36 ± 1 mm $36\pm 1 \ \text{mm}$ /7 ± 1 mm $7\pm 1 \ \text{mm}$ for hip/spine).

CONCLUSION

The proposed transducer apodization scheme shows promise for improving MRgFUS treatments of uterine fibroids, and may ultimately increase the effective treatment envelope of MRgFUS surgery in the body by enabling tissue ablation closer to bony structures.

A novel transcranial MR Guided focused ultrasound method based on the ultrashort echo time skull acoustic model and phase retrieval techniques

Transcranial ultrasound stimulation (TUS) has been clinically applied as a neuromodulation tool. Particularly, the phase array ultrasound can be applied in TUS to non-invasively focus on the cortex or deep brain. However, the vital phase distortion of the ultrasound induced by the skull limits its clinical application. In the current study, we aimed to develop a hybrid method that combines the ultrashort echo time (UTE) magnetic resonance imaging (MRI) sequences with the prDeep technique to achieve focusing ventral intermediate thalamic nucleus (VIM). The time-reversal (TR) approach of the UTE numerical acoustic model of the skull combined with the prDeep algorithm was used to reduce the number of iterations. The skull acoustic model simulation therapy process was establish to valid this method's prediction and focus performance, and the classical TR method were considered as the gold standard (GS). Our approach could restore 75% of the GS intensity in 25 iteration steps, with a superior the noise immunity. Our findings demonstrate that the phase aberration caused by the skull can be estimated using phase retrieval techniques to achieve a fast and accurate transcranial focus. The method has excellent adaptability and anti-noise capacity for satisfying complex and changeable scenarios.

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.

A rapid element pressure field simulation method for transcranial phase correction in focused ultrasound therapy

Transcranial focused ultrasound ablation has emerged as a promising technique for treating neurological disorders. The clinical system exclusively employed the ray tracing method to compute phase aberrations induced by the human skull, taking into account computational time constraints. However, this method compromises slightly on accuracy compared to simulation-based methods. This study evaluates a fast simulation method that simulates the time-harmonic pressure field within the region of interest for effective phase correction. Experimental validation was carried out using a 512-element, 670 kHz hemispherical transducer for fourex vivoskulls. The ray tracing method achieved a restoration ratio of 64.81% ± 4.33% of acoustic intensity normalized to hydrophone measurements. In comparison, the rapid simulation method demonstrated improved results with a restoration ratio of 73.10% ± 7.46%, albeit slightly lower than the full-wave simulation which achieved a restoration ratio of 75.87% ± 5.40%. The rapid simulation methods exhibited computational times that were less than five minutes for parallel computation with 8 threads. The incident angle was calculated, and a maximum difference of 6.8 degrees was found when the fixed position of the skull was changed. Meanwhile, the restoration ratio of acoustic intensity was validated to be above 70% for different target positions away from the geometrical focus of the transducer. The favorable balance between time consumption and correction accuracy makes this method valuable for clinical treatment applications.

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.

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.

Transcranial ultrasound simulations: A review

Transcranial ultrasound is more and more used for therapy and imaging of the brain. However, the skull is a highly attenuating and aberrating medium, with different structures and acoustic properties among samples and even within a sample. Thus, case-specific simulations are needed to perform transcranial focused ultrasound interventions safely. In this article, we provide a review of the different methods used to model the skull and to simulate ultrasound propagation through it.

Comparison between MR and CT imaging used to correct for skull-induced phase aberrations during transcranial focused ultrasound

Transcranial focused ultrasound with the InSightec Exablate system uses thermal ablation for the treatment of movement and mood disorders and blood brain barrier disruption for tumor therapy. The system uses computed tomography (CT) images to calculate phase corrections that account for aberrations caused by the human skull. This work investigates whether magnetic resonance (MR) images can be used as an alternative to CT images to calculate phase corrections. Phase corrections were calculated using the gold standard hydrophone method and the standard of care InSightec ray tracing method. MR binary image mask, MR-simulated-CT (MRsimCT), and CT images of three ex vivo human skulls were supplied as inputs to the InSightec ray tracing method. The degassed ex vivo human skulls were sonicated with a 670 kHz hemispherical phased array transducer (InSightec Exablate 4000). 3D raster scans of the beam profiles were acquired using a hydrophone mounted on a 3-axis positioner system. Focal spots were evaluated using six metrics: pressure at the target, peak pressure, intensity at the target, peak intensity, positioning error, and focal spot volume. Targets at the geometric focus and 5 mm lateral to the geometric focus were investigated. There was no statistical difference between any of the metrics at either target using either MRsimCT or CT for phase aberration correction. As opposed to the MRsimCT, the use of CT images for aberration correction requires registration to the treatment day MR images; CT misregistration within a range of ± 2 degrees of rotation error along three dimensions was shown to reduce focal spot intensity by up to 9.4%. MRsimCT images used for phase aberration correction for the skull produce similar results as CT-based correction, while avoiding both CT to MR registration errors and unnecessary patient exposure to ionizing radiation.

Boosting transducer matrix sensitivity for 3D large field ultrasound localization microscopy using a multi-lens diffracting layer: a simulation study

Mapping blood microflows of the whole brain is crucial for early diagnosis of cerebral diseases. Ultrasound localization microscopy (ULM) was recently applied to map and quantify blood microflows in 2D in the brain of adult patients down to the micron scale. Whole brain 3D clinical ULM remains challenging due to the transcranial energy loss which significantly reduces the imaging sensitivity. Large aperture probes with a large surface can increase both resolution and sensitivity. However, a large active surface implies thousands of acoustic elements, with limited clinical translation. In this study, we investigate via simulations a new high-sensitive 3D imaging approach based on large diverging elements, combined with an adapted beamforming with corrected delay laws, to increase sensitivity. First, pressure fields from single elements with different sizes and shapes were simulated. High directivity was measured for curved element while maintaining high transmit pressure. Matrix arrays of 256 elements with a dimension of 10 × 10 cm with small (λ/2), large (4λ), and curved elements (4λ) were compared through point spread functions analysis. A large synthetic microvessel phantom filled with 100 microbubbles per frame was imaged using the matrix arrays in a transcranial configuration. 93% of the bubbles were detected with the proposed approach demonstrating that the multi-lens diffracting layer has a strong potential to enable 3D ULM over a large field of view through the bones.

Towards controlled drug delivery in brain tumors with microbubble-enhanced focused ultrasound

Brain tumors are particularly challenging malignancies, due to their location in a structurally and functionally distinct part of the human body - the central nervous system (CNS). The CNS is separated and protected by a unique system of brain and blood vessel cells which together prevent most bloodborne therapeutics from entering the brain tumor microenvironment (TME). Recently, great strides have been made through microbubble (MB) ultrasound contrast agents in conjunction with ultrasound energy to locally increase the permeability of brain vessels and modulate the brain TME. As we elaborate in this review, this physical method can effectively deliver a wide range of anticancer agents, including chemotherapeutics, antibodies, and nanoparticle drug conjugates across a range of preclinical brain tumors, including high grade glioma (glioblastoma), diffuse intrinsic pontine gliomas, and brain metastasis. Moreover, recent evidence suggests that this technology can promote the effective delivery of novel immunotherapeutic agents, including immune check-point inhibitors and chimeric antigen receptor T cells, among others. With early clinical studies demonstrating safety, and several Phase I/II trials testing the preclinical findings underway, this technology is making firm steps towards shaping the future treatments of primary and metastatic brain cancer. By elaborating on its key components, including ultrasound systems and MB technology, along with methods for closed-loop spatial and temporal control of MB activity, we highlight how this technology can be tuned to enable new, personalized treatment strategies for primary brain malignancies and brain metastases.

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.

Transcranial focused ultrasound phase correction using the hybrid angular spectrum method

The InSightec Exablate system is the standard of care used for transcranial focused ultrasound ablation treatments in the United States. The system calculates phase corrections that account for aberrations caused by the human skull. This work investigates whether skull aberration correction can be improved by comparing the standard of care InSightec ray tracing method with the hybrid angular spectrum (HAS) method and the gold standard hydrophone method. Three degassed ex vivo human skulls were sonicated with a 670 kHz hemispherical phased array transducer (InSightec Exablate 4000). Phase corrections were calculated using four different methods (straight ray tracing, InSightec ray tracing, HAS, and hydrophone) and were used to drive the transducer. 3D raster scans of the beam profiles were acquired using a hydrophone mounted on a 3-axis positioner system. Focal spots were evaluated using six metrics: pressure at the target, peak pressure, intensity at the target, peak intensity, positioning error, and focal spot volume. For three skulls, the InSightec ray tracing method achieved 52 ± 21% normalized target intensity (normalized to hydrophone), 76 ± 17% normalized peak intensity, and 0.72 ± 0.47 mm positioning error. The HAS method achieved 74 ± 9% normalized target intensity, 81 ± 9% normalized peak intensity, and 0.35 ± 0.09 mm positioning error. The InSightec-to-HAS improvement in focal spot targeting provides promise in improving treatment outcomes. These improvements to skull aberration correction are also highly relevant for the applications of focused ultrasound neuromodulation and blood brain barrier opening, which are currently being translated for human use.