# Ultra-short time-echo based ray tracing for transcranial focused ultrasound aberration correction in human calvaria

Thomas Manuel, Thomas Bancel, Thomas Tiennot, Mélanie Didier, Mathieu Santin, Maxime Daniel, David Attali, Mickael Tanter, Stéphane Lehéricy,

Nadya Pyatigorskaya, et al.

► To cite this version:

Thomas Manuel, Thomas Bancel, Thomas Tiennot, Mélanie Didier, Mathieu Santin, et al. Ultra-short time-echo based ray tracing for transcranial focused ultrasound aberration correction in human calvaria. Physics in Medicine and Biology, In press, 10.1088/1361-6560/ad4f44. http://onlinelibrary.wiley.com/doi/abs/10.1088/1361-6560/ad4f44

HAL Id: hal-04776297

https://hal.science/hal-04776297v1

Submitted on 11 Nov 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Ultra-short time-echo based ray tracing for transcranial focused
ultrasound aberration correction in human calvaria

Thomas J. Manuel¹*, Thomas Bancel¹*, Thomas Tiennot¹, Mélanie Didier², Mathieu Santin², Maxime Daniel¹,
David Attali¹,³, Mickael Tanter¹, Stéphane Lehéricy², Nadya Pyatigorskaya², Jean-François Aubry¹.

*These authors contributed equally

¹Physics for Medicine Paris, Inserm U1273, ESPCI Paris, CNRS UMR8361, PSL University, Paris, France

²Centre de Neuro-imagerie de Recherche (CENIR), Inserm U 1127, CNRS UMR 7225, Sorbonne Université, UPMC Univ Paris 06, UMR S 1127, Institut du Cerveau et de la Moelle (ICM), F-75013, Paris, France

³GHU-Paris Psychiatrie et Neurosciences, Hôpital Sainte Anne, Université Paris Cité, 75014 Paris, France

Abstract

**Objective.** Magnetic resonance guided transcranial focused ultrasound holds great promises for treating neurological disorders. This technique relies on skull aberration correction which requires computed tomography (CT) scans of the skull of the patients. Recently, ultra-short time-echo (UTE) magnetic resonance (MR) sequences have unleashed the MRI potential to reveal internal bone structures. In this study, we measure the efficacy of transcranial aberration correction using UTE images.

*Approach.* We compare the efficacy of transcranial aberration correction using UTE scans to CT based correction on four skulls and two targets using a clinical device (Exablate Neuro, Insightec, Israel). We also evaluate the performance of a custom ray tracing algorithm using both UTE and CT estimates of acoustic properties and compare these against the performance of the manufacturer's proprietary aberration correction software.

**Main results.** UTE estimated skull maps in Hounsfield units (HU) had a mean absolute error of 242 ± 20 HU (n=4). The UTE skull maps were sufficiently accurate to improve pressure at the target (no correction: 0.44 ± 0.10, UTE correction: 0.79 ± 0.05, manufacturer CT: 0.80 ± 0.05), pressure confinement ratios (no correction: 0.45 ± 0.10, UTE correction: 0.80 ± 0.05, manufacturer CT: 0.81 ± 0.05), and targeting error (no correction: 1.06 ± 0.42 mm, UTE correction 0.30 ± 0.23 mm, manufacturer CT: 0.32 ± 0.22) (n=8 for all values). When using CT, our ray tracing algorithm performed slightly better than UTE based correction with pressure at the target (UTE: 0.79 ± 0.05, CT: 0.84 ± 0.04), pressure confinement ratios (UTE: 0.80 ± 0.05, CT: 0.84 ± 0.04), and targeting error (UTE: 0.30 ± 0.23 mm, CT: 0.17 ± 0.15).

**Significance.** These 3D transcranial measurements suggest that UTE sequences could replace CT scans in the case of MR guided focused ultrasound with minimal reduction in performance which will avoid ionizing radiation exposure to the patients and reduce procedure time and cost.
Introduction

Transcranial magnetic resonance (MR) guided focused ultrasound (MRgFUS) is an incisionless surgical technique currently used in clinics for the treatment of Essential Tremor (ET) (Mohammed, Patra, and Nanda 2018; Agrawal et al. 2021), Parkinson's diseases (Martínez-Fernández et al. 2018; Ko et al. 2023), epilepsy (Abe et al. 2020) and glioblastoma (Bunevicius, McDannold, and Golby 2020; Grasso et al. 2023). In these applications, ultrasound is transmitted through the intact skull to either locally heat tissue (ablation) or increase blood-brain barrier permeability through interactions with systemically administered microbubbles. The ExAblate 4000 system (InSightec, Haifa, Israel), which represents the state of the art, accomplishes precise acoustic focusing in the brain by predicting and correcting for skull induced distortions using a proprietary ray tracing algorithm, the performance of which has been independently benchmarked by several groups (Leung et al. 2021; Bancel et al. 2021; Jin et al. 2020). In these procedures, computed tomography (CT) is used for two purposes: 1) to inform patient screening based on skull density ratio (SDR) and skull volume (Chang et al. 2016; Jung et al. 2019); 2) to derive patient-specific maps of skull acoustic properties (Aubry et al. 2003) which enable precise acoustic focusing via ray tracing.

MRgFUS procedures would benefit in patient safety, procedure time, and cost by eliminating CT from the surgery procedure. Due to radiation dose, an estimated 1 in 4300 women who underwent a routine head CT scan at age 20 years will develop cancer from that CT scan (Smith-Bindman et al. 2009). Furthermore, acquiring CT adds additional costs and extra time in the clinic. Despite these drawbacks, CT scans are the standard for skull imaging because of the excellent bone tissue contrast offered by high attenuation of x-rays in bone. To remove the need for CT in MRgFUS procedures, an alternative imaging modality must demonstrate comparable patient screening and aberration correction performance.

MRI bone imaging sequences have recently been shown to perform similarly to CT for patient screening. Cabellero-Insaurriaga et al. demonstrated patient screening and treatment efficiency in 16 patients using zero echo time (ZTE) MRI, showing good agreement between SDR, skull thickness, and angle of incidence for transducer rays (Cabellero-Insaurriaga et al. 2019). Guo et al. show good correlation between SDR measured by ultra-short time echo (UTE) MRI compared with CT in 15 patients and were able to predict thermal outcomes of procedures using UTE derived acoustic maps (Guo et al. 2019). Furthermore, Miscouridou et al. demonstrated similar outcomes in transcranial pressure simulations using ZTE compared to CT (Miscouridou et al. 2022) which could provide added features to patient screening in the future.

To eliminate the need for CT entirely, MRI bone imaging must also be effective at correcting for skull induced distortions during procedures. To this end, sequences like UTE and ZTE need to be tested for deriving patient specific maps of skull acoustic properties, and evaluated for their ability to improve transcranial focus quality using ray tracing or similar methods. Miller et al. provided the first example of this by demonstrating matched heating performance between corrections made by Insightec's ray tracing when using UTE and CT derived skull maps (Miller et al. 2015). These results were measured in three skulls using the 2D MR thermometry sequences which come with the Insightec system. Leung et al. also demonstrated potential for success in this regard in a study which used a combination of UTEs made from different echo times dubbed "MRsimCT" and saw similar performance with Insightec's ray tracing when using UTE compared to CT in three skulls measured by 3D hydrophone scans (Leung et al. 2022).

In this study, we use single-echo UTE scans from four human skulls to generate acoustic maps and compare these against CT. We apply these maps for aberration correction at two targets per skull (n=8)
using a custom ray tracing algorithm. We quantify the performance of this algorithm when using UTE and CT and also compare this to Insightec's algorithm using 3D hydrophone measurements. All cases perform similarly and offer significant improvements in pressure at the target, pressure confinement to the target, and targeting error compared to no correction. This work demonstrates that a custom UTE-based ray tracing approach challenges the current state of the art CT-based proprietary algorithm used in clinical MRgFUS procedures.

## Methods

### Skull preparation and image acquisition

Four dry human skulls (N=4) were used for this study. They were provided by the Institut d'Anatomie (UFR Biomédicale des Saints-Pères, Université Paris Descartes, Paris, France). The study was approved by the ethics committee of the Centre du Don des Corps, Université Paris Descartes, Paris. Donors gave informed consent before death (Chauvet et al. 2013). Two image modalities were acquired for each skull. Computed tomography (CT) scans were performed on a Sensation Cardiac 64 (Siemens, Germany) with a reconstruction kernel H70h (Marsac et al. 2017). The voltage was 80 kV and the resolution 0.45 x 0.45 mm² in the axial plane and a 0.4 mm slice thickness in the inferior-superior direction.

MRI scans were performed with a 32-channel head coil in a 3T Prisma Fit system (Siemens, Germany). A 3D-printed tank fitting the head coil dimensions was filled with degassed water and held the skulls in a head-first supine position. Brain mimicking gels were molded and placed inside each skull in attempt to better match in vivo imaging conditions. We followed a standard protocol, IEC 60601-2-37 (International Electrotechnical Commission 2015) for ultrasound phantom creation to make agar-based gels that exhibit soft-tissue acoustic properties (sound speed 1540 m/s, density 1050 kg/m³, attenuation coefficient of 0.4 dB cm⁻¹ MHz⁻¹). Before the scans, the skulls were degassed for at least 12 hours at a 2mbar vacuum pressure to replace the gas trapped inside the bone with water. UTE-PETRA sequences (Grodzki, Jakob, and Heismann 2012) were acquired on each skull with the following image parameters: echo-time: 0.07ms, repetition time: 5ms, flip angle: 3° and radial views: 150.000. The slice thickness was 0.5 mm with a 0.5 x 0.5 mm² resolution in the axial plane, for a total number of voxels of 448 x 448 x 448. Image acquisition time was 12 min. The sequence was repeated four times on each skull and averaged to increase the signal to noise ratio (SNR). An illustration of the setup and the resulting raw images is visible on Figure 1 for skull #1.
<figure><img src="image_2.png" /><figcaption>Figure 1: A) Raw UTE data of skull #1. B) The same raw UTE images, but displayed in MATLAB with colormap and contrast selected to emphasize image components and bias field. The 3D-printed recipient is visible in the axial plane (red dashed line). The brain mimicking gel positioned in the place of the brain is indicated on the coronal plane. The holder maintaining the skull in the vertical position is visible on the sagittal plane.</figcaption></figure>

## Acoustic pressure measurements

Acoustic experiments were conducted with an Exablate Neuro 4000 clinical system (Insightec, Tirat Carmel, Israël) installed at the Institut du Cerveau et de la Moëlle Épinière (ICM), located at la Pitié Salpêtrière hospital, Paris. The clinical system is an MR-guided High Intensity Focused Ultrasound (HIFU) system, which has been approved in Europe for thalamotomy (Lipsman et al. 2013; Martínez-Fernández et al. 2018; Jeanmonod et al. 2012; Magara et al. 2014; Mañez-Miró et al. 2019; Bretsztajn and Gedroyc 2018; Elias et al. 2016; 2013). This device is a hemi-spherical transducer with a diameter D=300mm and is composed of 1024 piezo-electric elements operated at a central frequency f₀=650 kHz. During clinical treatment, the transducer is used in a vertical position (transducer axis parallel to the ground) and the patient lies on the MR bed with the transducer around its head. In all experiments described in this article, the transducer was used in a horizontal position (transducer axis perpendicular to the ground) which enabled to fill the transducer with water and to position the skulls inside (Figure 2A).

The four skulls were immersed in water prior to each experiment and degassed for at least 12 hours at a 2mbar reduced pressure. Each skull was mounted on a stereotactic frame and positioned inside the transducer thanks to a 3D-printed positioning system described in (Maimbourg et al. 2018; 2020). The positioning system was then removed, and the skull attached to the stereotactic frame was placed inside the transducer previously filled with water (Figure 2A).

Two targets were defined for each skull. The first target was located along the midline of each skull. The second target was located 17.5 mm away from the first target in the patient's left position (Figure 2B). Moving along the left/right axis was motivated by the target used in the treatment of essential tremor (Elias et al. 2013), and 17.5mm was the maximum distance reachable in order to avoid contact between the screws holding the skulls and the transducer. The stereotactic frame holding the skull was translated so that the target always corresponded to the geometrical center of the transducer.
<figure><img src="image_3.png" /><figcaption>Figure 2: A) Skull positioned inside the transducer after removing the positioning system. The hydrophone holder is shown as well as the coordinate system of the 3D hydrophone scans. B) Axial CT scan for skull #4 showing the two different targets used in each skull: the first target (purple dot) is along the midline and the second target (red dot) is shifted 17.5 mm away from the midline.</figcaption></figure>

The transfer matrix relating the emission surface of the transducer and a set of control points around the geometric focus was acquired during a previous work (Bancel et al. 2021) with a needle hydrophone (HNA-0400, ONDA, Sunnyvale, CA, USA, tip dimension: 400µm) mounted on a motorized 3D positioner (UE41UP, Newport, Irvine, CA, USA) (Figure 2A).

The acoustic focus of the transducer was first determined in water (without the skull) by finding the position of the maximum pressure field with all the elements of the transducer emitting a spherical wave. Once each skull was positioned in front of the transducer, a transfer matrix was acquired around the acoustic focus: an ellipsoid volume (small semi-axis: 1 mm, large semi-axis: 1.1 mm) was first acquired with a spatial resolution of 0.2 x 0.2 x 0.3 mm, followed by a second ellipsoid volume (small semi-axis: 3 mm, large semi-axis: 4.8 mm) with a larger spatial resolution (0.5 mm x 0.5 mm x 0.8 mm). Each scan contained a total of 1345 points.

The water was degassed and cooled before putting the skull in place. Water circulation was stopped before inserting the skull to avoid contamination of the clinical device. The elements of the transducer were successively triggered in transmit for each point in space $l \in [1,1345]$, and insonated for 500µs at the same electrical power (0.5W per element). The signal received at the hydrophone was recorded and its amplitude ($h_{li}$) and phase ($\varphi_{li}$) at 650 kHz were extracted for each element $i \in [1,1024]$ of the transducer. The harmonic transfer matrix at 650 kHz was thus recorded for each skull: $H_{li}(\omega) = h_{li} \cdot e^{j \cdot \varphi_{li}}$ where ($\omega$) denotes the single frequency for which the matrix is recorded (hence “harmonic”).

For each skull and target, we used the transfer matrix to compute the pressure field obtained by any set of emission signals $E(\omega) = [a_i e^{j \cdot \varphi_i}]$ ($i$ being one element of the transducer). The pressure value at position $j$ in the scanned volume is given by equation 1.
$$P(\omega) = H(\omega) \cdot E(\omega) = \sum_{i \in [1 \ 1024]} h_{j,i}(\omega) a_i e^{j \cdot \varphi_i} \quad (\text{eq. 1})$$

During the transfer matrix acquisition, the hydrophone correction at the target ($\varphi_{hydro}$) was acquired. It corresponds to the ideal correction and is equal to the phase shift of each element measured with the hydrophone located at the center of the transducer.

### Custom ray tracing algorithm

A custom ray tracing algorithm was developed to compute a phase distribution for an arbitrary distribution of elements across a transducer aperture to focus transcranially to an arbitrary target. Key differences between this algorithm and prior described approaches (Jin et al. 2020) is that multiple rays are used per element, and that a combination of partially refracted rays and straight rays are used. We withhold exact implementation details of our algorithm.

### Correction performance assessment

The performance with no correction (uniform phase applied to all elements), phases from UTE based ray tracing, phases from CT based ray tracing, and phases from Insightec's proprietary algorithm were each evaluated for four skulls at two targets per skull. No amplitude correction was used for ray tracing or hydrophone correction. Targeting error was defined as the Cartesian distance between the voxel with the highest pressure and the coordinate of the intended target. The discrete precision of this measurement was 0.2 x 0.2 x 0.3 mm. Pressure at target was defined as the pressure at the target coordinate with the test phases divided by the pressure at the target coordinate with hydrophone-based phases. We measured the -3 dB focus extent in water to be an 1.0 x 1.0 x 1.8 mm ellipsoid. Pressure confinement was calculated as the ratio between the sum of pressure within this ellipsoid for measurements using the test phases compared to the sum of pressure within this ellipsoid using the hydrophone phases. This metric was derived to give a sense of how well pressure is confined to the target area and was selected because it is more sensitive to aberration distortion than measuring the volume of the focus using a threshold.

### CT Image processing

A coarse CT skull mask was computed using a Hounsfield unit (HU) threshold of 500. The skull mask was refined by additional morphologic operations (first connected component selection, image closing and image filling). Details about the full processing of the skull mask extraction can be found in (Bancel et al. 2021). Speed of sound was linearly extrapolated from HU by setting the maximum bone speed of sound to 3000 m.s⁻¹ (Marsac et al. 2017).

### Skull mask extraction from UTE images

A flow chart as well as step by step images for this UTE skull mask extraction are provided in supplementary materials to accompany the brief description in this section. Skull mask extraction from UTE was challenging due to large intensity variations across the images which can be seen in Figure 1. A temporary image was created in MATLAB R2021a by applying a median filter (3 voxel kernel) followed by a 3D Gaussian filter (20 voxel standard deviation) to capture course noise and bias from the image. This temporary image was subtracted from the original image to produce a corrected image. The average intensity of the corrected image was then adjusted to match the average intensity of the initial image to reverse any histogram shift. An additional 3D Gaussian filter (2 voxel standard deviation) was then applied to remove high frequency variation. Next, k-means segmentation was used to label voxels
corresponding to skull. From this segmentation, the largest connected component (skull) was extracted using MATLAB's binary image connected components functions "bwconncomp" and "bwareaopen".

This final connected component was close to a functioning skull mask, but in a few cases failed to include sinuses filled with gel, or erroneously included low intensity portions of the skull holder. To correct these features, images were imported into 3D Slicer 5.2.2 (Fedorov et al. 2012), and the segmentation editor was used to fill holes (automatic) and remove signal from the holder (manual). Next, Slicer's implementation of the N4ITK bias correction algorithm was applied with default settings to remove additional bias (Tustison et al. 2010). In our case, it was important to perform bias correction after masking the skull and to use this mask as an input for the N4ITK option "Mask Image".

A final "smart erosion" step was applied to remove bright voxels around the edge of the skull mask. With UTE, outer table skull voxels constituting the edge of the skull will have dark intensities. This "smart erosion" step was taken to remove bright voxels which remained on the edge of the mask, representing signals from the gel which held the skull. This was implemented iteratively in MATLAB using the "edge3" function to find the edges of the skull, the "imdilate" function to dilate this edge mask, and a threshold to remove bright voxels within the mask, three times. The resulting mask was taken to be the final mask of the UTE images and used to mask the previously bias corrected images to produce the final UTE skull images which correspond only to skull tissue. The result of masking for a representative image is displayed in figure 3, panel A juxtaposed with its CT pair.

## Mapping UTE intensity to HU

The UTE skull images were first roughly registered to their corresponding CT manually using 3D Slicer linear transforms. Both the CT and UTE were resampled to have matching field of views and voxels of 0.38 mm isotropic voxels. The UTE images were then roughly scaled to Hounsfield units (HU) using the linear conversion $-3[I_{UTE}] + 2000$ where $I_{UTE}$ is the voxel intensity in the UTE image. This initial imprecise conversion served the purpose of scaling the datasets to similar intensity range to improve automatic registration. A linear registration transform was then computed using Slicer's implementation of the BRAINSFit registration algorithm (H. Johnson, Harris, and Williams 2007). The registered UTE was then interpolated using a "nearest neighbors" approximation such that the CT and UTE images had voxels with identical coordinate systems.

Now that the UTE is registered to the CT and masked to include only skull, there is a spatial one-to-one mapping between UTE voxels and CT voxels which can be used to find the linear fit between UTE and CT voxels. The data was combined for all four skulls and used to implement a single fit. From each skull, only voxels which were in both the CT based mask and UTE based mask were included. An additional exclusion was applied to high error voxels, computed as voxels with greater than 350 HU with the linear conversion $-3[I_{UTE}] + 2000$ applied. This exclusion was included to aide a better fit, but was not included in the calculation of errors within the skull mask (all skull mask voxels are included to compute HU errors).

## Results

### Mapping UTE to CT
The best fit from UTE to CT voxel intensities using voxels within the union of UTE and CT skull masks was -2.55 [$I_{UTE}$] + 1772 where $I_{UTE}$ is the voxel intensity in the UTE image. CT intensities are in units of Hounsfield units (HU). This linear relationship was applied to the UTE images to generate UTE based images representing estimates of HU. Following the rescaling of UTE intensities to HU, the mean absolute error (MAE) for all voxels within the skull mask of the four images was 242 ± 20 HU (Figure 3, Panel C). The root mean squared error (RMSE) was 360 ± 24 HU. UTE based HU maps were used to generate a 2D histogram (Figure 3, Panel B).

<figure><img src="image_4.png" /><figcaption>Figure 3. A) Comparison between masked and bias corrected UTE and CT data for a representative axial slice. B) 2D histogram comparing UTE inferred HU to CT for each of the four skulls. Histogram colormaps indicate the number of voxels in each intensity bin. C) Mean absolute error (MAE), root mean squared error (RMSE), and bias error between UTE inferred HU and computed tomography (CT) within the skull mask for four cadaver skulls. HU: Hounsfield units</figcaption></figure>

## Speed of sound mapping

The UTE based HU images were used to estimate skull tissue speed of sound on a voxel wise basis. Figure 4 shows 3 orthogonal image slices comparing the speed of sound maps generated by UTE based HU images compared to CT images.
<figure><img src="image_5.png" /><figcaption>Figure 4. Comparison of speed of sound maps (meters per second: m/s) computing using ultra-short time-echo (UTE) and computed tomography (CT) images for the four skulls used in this study. Corresponding mean absolute errors (MAE) are displayed in the center.</figcaption></figure>

## Ray tracing performance

Figure 5 displays pressure recovery, pressure confinement, and targeting errors measured for four skulls and two targets using four different phase correction conditions. Pressures at the target were 0.44 ± 0.10, 0.79 ± 0.05, 0.84 ± 0.04, and 0.80 ± 0.05 for no correction, ray tracing with UTE, ray tracing with CT, and Insightec's proprietary algorithm respectively. The pressure confinement ratios were 0.45 ± 0.09, 0.80 ± 0.05, 0.81 ± .04, and 0.81 ± .05 for no correction, ray tracing with UTE, ray tracing with CT, and Insightec's proprietary algorithm respectively. The targeting error was 1.06 ± 0.42 mm, 0.30 ± 0.23 mm, 0.17 ± 0.15 mm, and 0.32 ± 0.22 mm for no correction, ray tracing with UTE, ray tracing with CT, and Insightec's proprietary algorithm respectively.
<figure><img src="image_6.png" /><figcaption>Figure 5. Measured ray tracing performance in four skulls at two targets quantified using pressure at target, pressure confinement, and targeting error. We tested no correction, UTE based ray tracing, CT based ray tracing, and the proprietary Insightec CT algorithm for each target/skull combination. Averages (n=8) are shown on the right for each metric. Pressure at target is the ratio of the pressure at the target to the pressure at the target obtained with hydrophone correction. Pressure confinement is the ratio of the sum of pressures within the ideal focus size (~3dB) achieved with test phases compared to that achieved with hydrophone based phases. Targeting error is the cartesian distance between the target and the focus maximum.</figcaption></figure>

Measurements of 3D pressure maps were obtained for each skull/target combination (n=8) using h-matrix propagation. Figure 6 displays three planes of the 3D pressure maps for each of the five phase correction conditions tested. We chose to display data points with the highest UTE based pressure recovery (skull 1 target 2, 0.85) and lowest UTE based pressure recovery (skull 2 target 2, 0.71) to represent the range of performance observed. Qualitatively, performance differences between UTE based ray tracing, CT based ray tracing, and Insightec's algorithm are minimal and show clear improvements over no correction. The mean absolute error (MAE) in UTE based HU images was not well correlated with any of the focusing performance metrics.
<figure><img src="image_7.png" /><figcaption>Figure 6. Measured 3D pressure maps for the skull/dataset pairs with highest (0.85, top group) and lowest (0.71, bottom group) pressure at target with UTE based ray tracing. The columns represent different phase correction scenarios (Left to right: No correction, UTE based ray tracing correction, CT based ray tracing correction, Insightec's proprietary algorithm, Hydrophone based correction. White cross hairs show the target location. Color map and scale are constant across the image and correspond to the color bar and axis scales presented. Press: pressure.</figcaption></figure>

Figures 5 and 6 compared UTE and CT ray tracing based on performance metrics. We also compared UTE and CT ray tracing by extracting the most important features calculated by ray tracing using the two imaging modalities. Figure 7 shows the average speed of sounds within the skull for rays, the average thickness of skull through which the rays traveled, and the average incidence angle on the outer skull surface computed using UTE and CT. The averages across skull target pairs are: speed of sound (m/s) 2369 ± 89 (CT), 2386 ± 135 (UTE), p=0.511; thickness (mm) 6.34 ± 0.74 (CT), 6.60 ± 0.71 (UTE), p=.002; incidence angle (degrees) 11.4 ± 2.72 (CT), 11.5 ± 2.81 (UTE), p=0.376. All t-test are 2-tailed, paired student's t-test. Only thickness estimates showed a significant difference, but the magnitude of the difference (0.26 mm) was smaller than the UTE image voxel size (0.50 x 0.50 x 0.50 mm) and the CT voxel size (0.45 x 0.45 x 0.40 mm). Skull 2, which performed the worst across all metrics, has the highest speed of sound estimate, but we are unable to conclude if the two observations are definitively related.
<figure><img src="image_8.png" /><figcaption>Figure 7. Comparison of extracted features from the ray tracing algorithm using CT and UTE. The speed of sound and the thicknesses shown here are the average experienced along rays for the given skull/target pair.</figcaption></figure>

We compared the performance of our custom approach and Insightec's algorithm to a previously published "straight ray" approach (Table 1) (Lu et al. 2022). When using both CT and UTE, straight rays outperformed the no correction group for all metrics, but underperformed compared to our custom algorithm. The performance of straight rays was worse when using UTE, with pressure ratios at the target of 0.63 ± 0.18 compared to 0.75 ± 0.04 when using CT. Further analysis revealed that the drop in performance occurred mostly in the second, off center target group (target 1: 0.77 ± 0.05, target 2: 0.49 ± 0.14). Our custom algorithm achieved similar results for both targets using UTE (target 1: 0.80 ± 0.03, target 2: 0.78 ± 0.07).

<table><thead><tr><th></th><th>Custom algorithm</th><th>Insightec</th><th>Straight rays</th><th>No correction</th></tr></thead><tbody><tr><td rowspan="3">CT</td><td>Press. at targ ratio</td><td>0.84 ± 0.04</td><td>0.80 ± 0.05</td><td>0.75 ± 0.04</td><td>0.44 ± 0.10</td></tr><tr><td>Press. confinement ratio</td><td>0.81 ± 0.04</td><td>0.81 ± 0.05</td><td>0.76 ± 0.04</td><td>0.45 ± 0.09</td></tr><tr><td>Targetting error [mm]</td><td>0.17 ± 0.15</td><td>0.32 ± 0.22</td><td>0.26 ± 0.14</td><td>1.06 ± 0.42</td></tr><tr><td rowspan="3">UTE</td><td>Press. at targ ratio</td><td>0.79 ± 0.05</td><td>-</td><td>0.63 ± 0.18</td><td>0.44 ± 0.10</td></tr><tr><td>Press. confinement ratio</td><td>0.80 ± 0.05</td><td>-</td><td>0.64 ± 0.18</td><td>0.45 ± 0.09</td></tr><tr><td>Targetting error [mm]</td><td>0.30 ± 0.22</td><td>-</td><td>0.55 ± 0.74</td><td>1.06 ± 0.42</td></tr></tbody></table>
Discussion

Replacing CT with MRI bone imaging sequences could eliminate patient radiation dose, lower cost and reduce duration in MRgFUS procedures. To this end, this study investigated the suitability of UTE for skull aberration correction. We acquired UTE scans of four subjects along with complimentary CT scans and used the Exablate Neuro 4000 clinical system to test transcranial focusing. Hydrophone measurements coupled with transfer matrix propagation were used to sample 3D transcranial pressure fields. We observed good agreement between Hounsfield unit estimation (MAE = 242 ± 20 HU) generated by UTE compared with CT and minimal difference in pressure at the target, pressure confinement to the target, and targeting error when using UTE derived maps for ray tracing both with our ray tracing algorithm and with Insightec's algorithm at eight targets.

Our results align well with the two measurement-based studies previously demonstrating transcranial
aberration correction using UTE. In Miller et al., a binary skull map generated from UTE based
segmentation was sufficient to produce peak temperature rise and focus sharpness in a 2D MR-
thermometry plane of matched quality to that achieved using CT with the Insightec system (Miller et
2015). Leung et al. found that a UTE based image derived from two UTEs with echo times of 50 and
2510 µs was able to perform as well as CT based correction with the Insightec system (Leung et al. 2022).
This multi-echo UTE was designed to improve contrast in bone by matching the relaxation-rate of two
tissue groups and combining these with a subtraction (E. M. Johnson et al. 2017). Our study used a UTE
sequence with an echo time of 70 µs (averaged 4 times) and a custom ray tracing algorithm. Our
performance with UTE was similar to Insightec's algorithm using CT: pressure recovery at the target
(0.79 ±0.05 vs. 0.80 ±0.05, p=0.35), pressure confinement (0.80 ±0.05 vs. 0.81 ±0.05, p=0.32), and
targeting accuracy (0.30 ±0.22 mm vs. 0.32 ±0.22 mm, p=0.76) using a two-sided student's t-test for p-
values. However, our ray tracing algorithm achieved slightly better performance using CT than UTE
(Figure 5 and table 1). It is possible that the performance of our UTE scans would benefit from using
multiple echo times.

MRI generates CT-like images of bone tissue using UTE, ZTE, or machine learning approaches which synthesize CT images using more complicated mappings. UTE and ZTE both exploit the very short T2 relaxation time of cortical bone and exhibit only minor tradeoffs in factors like scan time, contrast flexibility, sensitivity to gradient imperfections (Chong, Lee, and Sim 2021). The contrasts offered by UTE and ZTE have been linked to acoustic attenuation which enables more complicated models than was implemented in this work (Webb et al. 2021).

Machine learning approaches for CT generation using MRI shows great potential and has been
investigated by several groups with a focus on MRgFUS procedures. Liu and Sigona et al. used a
conditional generative adversarial network (cGAN) trained by T1-weighted MRI of 86 subjects to
generate synthetic CT images. They observed highly correlated SDR and skull thickness measures with
the synthetic CT and evaluated their performance in k-Wave (Treeby and Cox 2010) for time reversal
using phases computed by Kranion (Sammartino et al. 2019). A similar study from Koh et al. trained a
cGAN with T1-weighted MRI of 15 subjects and found no significant difference between SDR and skull
thickness measures and good agreement between acoustic simulations (Koh et al. 2022). Miscouridou et al. compared ultrasound simulations using ZTE with two convolutional neural network U-Net architectures (Miscouridou et al. 2022). One U-Net was trained on T1-weighted images (171 patients) and the other on ZTE (90 patients). The U-Net trained with ZTE performed the best for acoustic simulations. Mean absolute error was 192 ±28 HU for Liu and Sigona et al., 280 ±24 HU for Koh et al., 222 ±78 HU for Miscouridou et al. (U-Net with ZTE), and 242 ±20 HU for our UTE. MAE was not correlated with any of the performance metrics in our data, which suggest physical acoustic measurements may be necessary to evaluate the true benefit of these approaches.

A gap remains between the performance of ray tracing based phase correction and hydrophone based phase correction using both CT and UTE, but the missing phenomenon to be modeled is not clear. It is natural to suppose that the phases produced by ray tracing algorithms could be improved by incorporating acoustic phenomena such as diffraction, multiple reflections, and absorption. Supporting this hypothesis, Xu et. al. recently tested three simulation techniques using CT incorporating these features that achieved greater intensity recovery in 4 skulls compared to straight ray tracing (Xu, Wu, and Shen 2023). However, they did not have access to a more involved ray tracing algorithm such as the Insightec algorithm or the one used in this paper which would likely perform better than simple straight rays. Conversely, Bancel et al. measured the performance of phases derived from k-Wave simulations (Treeby and Cox 2010) which incorporated these phenomena and did not observe much improvement in pressure recovery compared to Insightec's ray tracing (Bancel et al. 2021). In fact, for two of the three HU to acoustic property conversion models tested, the recovered pressure decreased using k-Wave compared to Insightec's ray tracing. The third conversion model tested improved pressure recovery using k-Wave simulations (by 2% at one target and 1% at the other target). Shear waves are known to occur in the skull with high incidence angles but were not modeled in that study (White, Clement, and Hynynen 2006). It is possible to model shear waves in the skull using ray tracing which may improve accuracy for high incidence angle rays. A recent simulation analysis on ray-tracing sensitivity to skull properties explores several of these topics in depth (Drainville et al. 2023).

The small number of skulls (four) limits the confidence which can be drawn from these encouraging results. Prior studies have demonstrated a large variation in acoustic properties across individual skulls which highlights the need to include as many skulls as possible in any transcranial ultrasound investigation (Vyas et al. 2016; McDannold, White, and Cosgrove 2019). However, access to cadaver skulls for hydrophone measurements presents a challenge, and is likely why comparable works have only used three skulls (Miller et al. 2015; Leung et al. 2022). It is likely that the addition of more skulls, using images taken of full human heads, or using different MR scanners will yield a different optimal fit for UTE to HU conversion. The dried skulls were soaked in degassed water to better match in vivo conditions where the porous space in the skulls is filled with fluid, and the mapping between UTE and HU could be different *in vivo* where bone marrow and other fluids which are not pure water saturate the porous spaces in the skull. Nevertheless, the results here suggest that the contrast of UTE in skull bone may be sufficient to find a mapping which enables effective aberration correction using ray tracing informed by UTE.

## Conclusion

In this work, we demonstrate that UTE is able to generate acoustic maps and enable aberration correction for MRgFUS procedures in a dataset containing 4 human calvaria with two targets each. 3D pressure recovery, targeting error, and pressure confinement were all comparable between ray tracing with UTE and CT derived acoustic maps and significantly improved compared to no correction. We also validate the performance of our custom ray tracing algorithm compared to a proprietary algorithm using both CT and
UTE. These results suggest that CT can be eliminated from MRgFUS workflows saving time and exposure to radiation for patients.

Acknowledgements

This work was supported by the Bettencourt Schueller Foundation (Ultrabrain project) and the "Agence Nationale de la Recherche" with the reference ANR-21-CE18-0021-02. The work performed in this publication was performed with the support of the Inserm Technology Research Accelerator (Inserm ART) in Biomedical Ultrasound, Paris, France and the Focused Ultrasound Foundation Center of Excellence in Paris. The acquisition of the transfer matrices was achieved in collaboration and with the financial support of Insightec Ltd, to which we are grateful.
Bibliography

Abe, Keiichi, Toshio Yamaguchi, Hiroki Hori, Masatake Sumi, Shiro Horisawa, Takaomi Taira, and Tomokatsu Hori. 2020. "Magnetic Resonance-Guided Focused Ultrasound for Mesial Temporal Lobe Epilepsy: A Case Report." *BMC Neurology* 20 (1): 160. https://doi.org/10.1186/s12883-020-01744-x.

Agrawal, Mohit, Kanwaljeet Garg, Raghu Samala, Roopa Rajan, Vikas Naik, and Manmohan Singh. 2021. "Outcome and Complications of MR Guided Focused Ultrasound for Essential Tremor: A Systematic Review and Meta-Analysis." *Frontiers in Neurology* 12 (May): 654711. https://doi.org/10.3389/fneur.2021.654711.

Aubry, J.-F., M. Tanter, M. Pernot, J.-L. Thomas, and M. Fink. 2003. "Experimental Demonstration of Noninvasive Transskull Adaptive Focusing Based on Prior Computed Tomography Scans." *The Journal of the Acoustical Society of America* 113 (1): 84–93. https://doi.org/10.1121/1.1529663.

Bancel, Thomas, Alexandre Houdouin, Philippe Annic, Itay Rachmilevitch, Yeruham Shapira, Mickael Tanter, and Jean-François Aubry. 2021. "Comparison Between Ray-Tracing and Full-Wave Simulation for Transcranial Ultrasound Focusing on a Clinical System Using the Transfer Matrix Formalism." *IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control* 68 (7): 2554–65. https://doi.org/10.1109/TUFFC.2021.3063055.

Bretsztajn, Laure, and Wladyslaw Gedroyc. 2018. "Brain-Focussed Ultrasound: What's the 'FUS' All about? A Review of Current and Emerging Neurological Applications." *The British Journal of Radiology*, March, 20170481. https://doi.org/10.1259/bjr.20170481.

Bunevicius, Adomas, Nathan Judson McDannold, and Alexandra J Golby. 2020. "Focused Ultrasound Strategies for Brain Tumor Therapy." *Operative Neurosurgery* 19 (1): 9–18. https://doi.org/10.1093/ons/opz374.

Caballero-Insaurriaga, Jaime, Rafael Rodríguez-Rojas, Raúl Martínez-Fernández, Marta Del-Alamo, Laura Díaz-Jiménez, María Ávila, María Martínez-Rodrigo, Pablo García-Polo, and José A. Pineda-Pardo. 2019. "Zero TE MRI Applications to Transcranial MR-Guided Focused Ultrasound: Patient Screening and Treatment Efficiency Estimation." *Journal of Magnetic Resonance Imaging* 50 (5): 1583–92. https://doi.org/10.1002/jmri.26746.

Chang, Won Seok, Hyun Ho Jung, Eyal Zadicario, Itay Rachmilevitch, Tal Tlusty, Shuki Vitek, and Jin Woo Chang. 2016. "Factors Associated with Successful Magnetic Resonance-Guided Focused Ultrasound Treatment: Efficiency of Acoustic Energy Delivery through the Skull." *Journal of Neurosurgery* 124 (2): 411–16. https://doi.org/10.3171/2015.3.JNS142592.

Chauvet, Dorian, Laurent Marsac, Mathieu Pernot, Anne-Laure Boch, Rémy Guillevin, Najat Salameh, Line Souris, et al. 2013. "Targeting Accuracy of Transcranial Magnetic Resonance-Guided High-Intensity Focused Ultrasound Brain Therapy: A Fresh Cadaver Model." *Journal of Neurosurgery* 118 (5): 1046–52. https://doi.org/10.3171/2013.1.JNS12559.

Chong, Le Roy, Kathy Lee, and Fang Yang Sim. 2021. "3D MRI with CT-like Bone Contrast – An Overview of Current Approaches and Practical Clinical Implementation." *European Journal of Radiology* 143 (October): 109915. https://doi.org/10.1016/j.ejrad.2021.109915.

Drainville, Robert Andrew, Sylvain Chatillon, David Moore, John Snell, Frederic Padilla, and Cyril Lafon. 2023. "A Simulation Study on the Sensitivity of Transcranial Ray-Tracing Ultrasound Modeling to Skull Properties." *The Journal of the Acoustical Society of America* 154 (2): 1211–25. https://doi.org/10.1121/10.0020761.
Elias, W. Jeffrey, Diane Huss, Tiffini Voss, Johanna Loomba, Mohamad Khaled, Eyal Zadicario, Robert C. Frysinger, et al. 2013. "A Pilot Study of Focused Ultrasound Thalamotomy for Essential Tremor." *New England Journal of Medicine* 369 (7): 640–48. https://doi.org/10.1056/NEJMoa1300962.

Elias, W. Jeffrey, Nir Lipsman, William G. Ondo, Pejman Ghanouni, Young G. Kim, Wonhee Lee, Michael Schwartz, et al. 2016. "A Randomized Trial of Focused Ultrasound Thalamotomy for Essential Tremor." *New England Journal of Medicine* 375 (8): 730–39. https://doi.org/10.1056/NEJMoa1600159.

Fedorov, Andriy, Reinhard Beichel, Jayashree Kalpathy-Cramer, Julien Finet, Jean-Christophe Fillion-Robin, Sonia Pujol, Christian Bauer, et al. 2012. "3D Slicer as an Image Computing Platform for the Quantitative Imaging Network." *Magnetic Resonance Imaging*, Quantitative Imaging in Cancer, 30 (9): 1323–41. https://doi.org/10.1016/j.mri.2012.05.001.

Grasso, Giovanni, Fabio Torregrossa, Manfredi Noto, Eleonora Bruno, Paola Feraco, Felice Buscemi, Tommaso Vincenzo Bartolotta, and Cesare Gagliardo. 2023. "MR-Guided Focused Ultrasound–Induced Blood-Brain Barrier Opening for Brain Metastasis: A Review." *Neurosurgical Focus* 55 (2): E11. https://doi.org/10.3171/2023.5.FOCUS23227.

Grodzki, David M., Peter M. Jakob, and Bjoern Heismann. 2012. "Ultrashort Echo Time Imaging Using Pointwise Encoding Time Reduction with Radial Acquisition (PETRA)." *Magnetic Resonance in Medicine* 67 (2): 510–18. https://doi.org/10.1002/mrm.23017.

Guo, Sijia, Jiachen Zhuo, Guang Li, Dheeraj Gandhi, Mor Dayan, Paul Fishman, Howard Eisenberg, Elias R. Melhem, and Rao P. Gullapalli. 2019. "Feasibility of Ultrashort Echo Time Images Using Full-Wave Acoustic and Thermal Modeling for Transcranial MRI-Guided Focused Ultrasound (tcMRgFUS) Planning." *Physics in Medicine & Biology* 64 (9): 095008. https://doi.org/10.1088/1361-6560/ab12f7.

International Electrotechnical Commission. 2015. "IEC 60601-2-33 Medical Electrical Equipment-Part 2-33: Particular Requirements for the Basic Safety and Essential Performance of Magnetic Resonance Equipment for Medical Diagnosis." *Int Electrotech Comm.*

Jeanmonod, Daniel, Beat Werner, Anne Morel, Lars Michels, Eyal Zadicario, Gilat Schiff, and Ernst Martin. 2012. "Transcranial Magnetic Resonance Imaging–Guided Focused Ultrasound: Noninvasive Central Lateral Thalamotomy for Chronic Neuropathic Pain." *Neurosurgical Focus* 32 (1): E1. https://doi.org/10.3171/2011.10.FOCUS11248.

Jin, Changzhu, David Moore, John Snell, and Dong-Guk Paeng. 2020. "An Open-Source Phase Correction Toolkit for Transcranial Focused Ultrasound." *BMC Biomedical Engineering* 2 (1): 9. https://doi.org/10.1186/s42490-020-00043-3.

Johnson, Ethan M., Urvi Vyas, Pejman Ghanouni, Kim Butts Pauly, and John M. Pauly. 2017. "Improved Cortical Bone Specificity in UTE MR Imaging." *Magnetic Resonance in Medicine* 77 (2): 684–95. https://doi.org/10.1002/mrm.26160.

Johnson, Hans, Gregory Harris, and Kent Williams. 2007. "BRAINSFIT: Mutual Information Registrations of Whole-Brain 3D Images, Using the Insight Toolkit," October. https://doi.org/10.54294/hmb052.

Jung, Na Young, Itay Rachmilevitch, Ohad Sibiger, Talia Amar, Eyal Zadicario, and Jin Woo Chang. 2019. "Factors Related to Successful Energy Transmission of Focused Ultrasound through a Skull : A Study in Human Cadavers and Its Comparison with Clinical Experiences." *Journal of Korean Neurosurgical Society* 62 (6): 712–22. https://doi.org/10.3340/jkns.2018.0226.

Ko, Tzu-Hsiang, Yu-Hsuan Lee, Lung Chan, Kevin Wen-Kai Tsai, Chien-Tai Hong, and Wei-Lun Lo. 2023. "Magnetic Resonance–Guided Focused Ultrasound Surgery for Parkinson’s Disease: A Mini-Review and Comparison between Deep Brain Stimulation." *Parkinsonism & Related Disorders* 111 (June): 105431. https://doi.org/10.1016/j.parkreldis.2023.105431.
Koh, Heekyung, Tae Young Park, Yong An Chung, Jong-Hwan Lee, and Hyungmin Kim. 2022. "Acoustic Simulation for Transcranial Focused Ultrasound Using GAN-Based Synthetic CT." *IEEE Journal of Biomedical and Health Informatics* 26 (1): 161–71. https://doi.org/10.1109/JBHI.2021.3103387.

Leung, Steven A., David Moore, Yekaterina Gilbo, John Snell, Taylor D. Webb, Craig H. Meyer, G. Wilson Miller, Pejman Ghanouni, and Kim Butts Pauly. 2022. "Comparison between MR and CT Imaging Used to Correct for Skull-Induced Phase Aberrations during Transcranial Focused Ultrasound." *Scientific Reports* 12 (1): 13407. https://doi.org/10.1038/s41598-022-17319-4.

Leung, Steven A., David Moore, Taylor D. Webb, John Snell, Pejman Ghanouni, and Kim Butts Pauly. 2021. "Transcranial Focused Ultrasound Phase Correction Using the Hybrid Angular Spectrum Method." *Scientific Reports* 11 (1): 6532. https://doi.org/10.1038/s41598-021-85535-5.

Lipsman, Nir, Michael L Schwartz, Yuexi Huang, Liesly Lee, Tejas Sankar, Martin Chapman, Kullervo Hynynen, and Andres M Lozano. 2013. "MR-Guided Focused Ultrasound Thalamotomy for Essential Tremor: A Proof-of-Concept Study." *The Lancet Neurology* 12 (5): 462–68. https://doi.org/10.1016/S1474-4422(13)70048-6.

Lu, Ning, Timothy L. Hall, Jonathan R. Sukovich, Sang Won Choi, John Snell, Nathan McDannold, and Zhen Xu. 2022. "Two-Step Aberration Correction: Application to Transcranial Histotripsy." *Physics in Medicine and Biology* 67 (12): 10.1088/1361-6560/ac72ed. https://doi.org/10.1088/1361-6560/ac72ed.

Magara, Anouk, Robert Bühler, David Moser, Milek Kowalski, Payam Pourtehrani, and Daniel Jeanmonod. 2014. "First Experience with MR-Guided Focused Ultrasound in the Treatment of Parkinson's Disease." *Journal of Therapeutic Ultrasound* 2 (1): 11. https://doi.org/10.1186/2050-5736-2-11.

Maimbourg, Guillaume, Alexandre Houdouin, Thomas Deffieux, Mickael Tanter, and Jean-François Aubry. 2018. "3D-Printed Adaptive Acoustic Lens as a Disruptive Technology for Transcranial Ultrasound Therapy Using Single-Element Transducers." *Physics in Medicine & Biology* 63 (2): 025026. https://doi.org/10.1088/1361-6560/aaa037.

Maimbourg, Guillaume, Alexandre Houdouin, Thomas Deffieux, Mickael Tanter, and Jean-François Aubry. 2020. "Steering Capabilities of an Acoustic Lens for Transcranial Therapy: Numerical and Experimental Studies." *IEEE Transactions on Biomedical Engineering* 67 (1): 27–37. https://doi.org/10.1109/TBME.2019.2907556.

Máñez-Miró, Jorge U, Raúl Martínez-Fernández, Marta del Alamo, José A Pineda-Pardo, Beatriz Fernández-Rodríguez, Fernando Alonso-Frech, José Carlos Álvarez-Cermeño, and José A Obeso. 2019. "Focused Ultrasound Thalamotomy for Multiple Sclerosis-Associated Tremor." *Multiple Sclerosis Journal*, October, 135245851986159. https://doi.org/10.1177/1352458519861597.

Marsac, L., D. Chauvet, R. La Greca, A.-L. Boch, K. Chaumoitre, M. Tanter, and J.-F. Aubry. 2017. "Ex Vivo Optimisation of a Heterogeneous Speed of Sound Model of the Human Skull for Non-Invasive Transcranial Focused Ultrasound at 1 MHz." *International Journal of Hyperthermia* 33 (6): 635–45. https://doi.org/10.1080/02656736.2017.1295322.

Martínez-Fernández, Raul, Rafael Rodríguez-Rojas, Marta del Álamo, Frida Hernández-Fernández, José A Pineda-Pardo, Michele Dileone, Fernando Alonso-Frech, et al. 2018. "Focused Ultrasound Subthalamotomy in Patients with Asymmetric Parkinson's Disease: A Pilot Study." *The Lancet Neurology* 17 (1): 54–63. https://doi.org/10.1016/S1474-4422(17)30403-9.

McDannold, Nathan, P. Jason White, and Rees Cosgrove. 2019. "Elementwise Approach for Simulating Transcranial MRI-Guided Focused Ultrasound Thermal Ablation." *Physical Review Research* 1 (3): 033205. https://doi.org/10.1103/PhysRevResearch.1.033205.

Miller, G. Wilson, Matthew Eames, John Snell, and Jean-François Aubry. 2015. "Ultrashort Echo-Time MRI versus CT for Skull Aberration Correction in MR-Guided Transcranial Focused Ultrasound: In
Vitro Comparison on Human Calvaria." *Medical Physics* 42 (5): 2223-33.
https://doi.org/10.1118/1.4916656.

Miscouridou, Maria, José A. Pineda-Pardo, Charlotte J. Stagg, Bradley E. Treeby, and Antonio Stanziola. 2022. "Classical and Learned MR to Pseudo-CT Mappings for Accurate Transcranial Ultrasound Simulation." *IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control* 69 (10): 2896-2905. https://doi.org/10.1109/TUFFC.2022.3198522.

Mohammed, Nasser, Devi Patra, and Anil Nanda. 2018. "A Meta-Analysis of Outcomes and Complications of Magnetic Resonance-Guided Focused Ultrasound in the Treatment of Essential Tremor." *Neurosurgical Focus* 44 (2): E4. https://doi.org/10.3171/2017.11.FOCUS17628.

Sammartino, Francesco, Dylan W. Beam, John Snell, and Vibhor Krishna. 2019. "Kranion, an Open-Source Environment for Planning Transcranial Focused Ultrasound Surgery: Technical Note." *Journal of Neurosurgery* 132 (4): 1249-55. https://doi.org/10.3171/2018.11.JNS181995.

Smith-Bindman, Rebecca, Jafi Lipson, Ralph Marcus, Kwang Pyo Kim, Mahadevappa Mahesh, Robert Gould, Amy Berrington de Gonzalez, and Diana L. Miglioretti. 2009. "Radiation Dose Associated with Common Computed Tomography Examinations and the Associated Lifetime Attributable Risk of Cancer." *Archives of Internal Medicine* 169 (22): 2078-86.
https://doi.org/10.1001/archinternmed.2009.427.

Treeby, Bradley E., and Benjamin T. Cox. 2010. "K-Wave: MATLAB Toolbox for the Simulation and Reconstruction of Photoacoustic Wave Fields." *Journal of Biomedical Optics* 15 (2): 021314.
https://doi.org/10.1117/1.3360308.

Tustison, Nicholas J., Brian B. Avants, Philip A. Cook, Yuanjie Zheng, Alexander Egan, Paul A. Yushkevich, and James C. Gee. 2010. "N4ITK: Improved N3 Bias Correction." *IEEE Transactions on Medical Imaging* 29 (6): 1310-20. https://doi.org/10.1109/TMI.2010.2046908.

Vyas, Urvi, Pejman Ghanouni, Casey H. Halpern, Jeff Elias, and Kim Butts Pauly. 2016. "Predicting Variation in Subject Thermal Response during Transcranial Magnetic Resonance Guided Focused Ultrasound Surgery: Comparison in Seventeen Subject Datasets." *Medical Physics* 43 (9): 5170-80. https://doi.org/10.1118/1.4955436.

Webb, Taylor D., Steven A. Leung, Pejman Ghanouni, Jeremy J. Dahl, Norbert J. Pelc, and Kim Butts Pauly. 2021. "Acoustic Attenuation: Multifrequency Measurement and Relationship To CT and MR Imaging." *IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control* 68 (5): 1532-45. https://doi.org/10.1109/TUFFC.2020.3039743.

White, P. J., G. T. Clement, and K. Hynynen. 2006. "Longitudinal and Shear Mode Ultrasound Propagation in Human Skull Bone." *Ultrasound in Medicine & Biology* 32 (7): 1085-96.
https://doi.org/10.1016/j.ultrasmedbio.2006.03.015.

Xu, Peng, Nan Wu, and Guofeng Shen. 2023. "A Rapid Element Pressure Field Simulation Method for Transcranial Phase Correction in Focused Ultrasound Therapy." *Physics in Medicine & Biology* 68 (23): 235015. https://doi.org/10.1088/1361-6560/ad0a59.