
==== Front
101465726
35618
Brain Stimul
Brain Stimul
Brain stimulation
1935-861X
1876-4754

39094682
10.1016/j.brs.2024.07.019
nihpa2018136
Article
Model-based navigation of transcranial focused ultrasound neuromodulation in humans: Application to targeting the amygdala and thalamus
Daneshzand Mohammad ab1
Guerin Bastien ab*1
Kotlarz Parker ab
Chou Tina bc
Dougherty Darin D. bc
Edlow Brian L. abd
Nummenmaa Aapo ab
a Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
b Harvard Medical School, Boston, MA, USA
c Department of Psychiatry, Massachusetts General Hospital, Charlestown, MA, USA
d Center for Neurotechnology and Neurorecovery, Department of Neurology, Massachusetts General Hospital, Boston, MA, USA
1 Co-first authors.

* Corresponding author. Athinoula A. Martinos Center for Biomedical Imaging, Dept. of Radiology, Harvard Medical School, Massachusetts General Hospital, 149 13th Street, Charlestown, MA, 02129, USA., bguerin@mgh.harvard.edu (B. Guerin).
22 8 2024
Jul-Aug 2024
31 7 2024
02 9 2024
17 4 958969
https://creativecommons.org/licenses/by/4.0/ This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Background:

Transcranial focused ultrasound (tFUS) neuromodulation has shown promise in animals but is challenging to translate to humans because of the thicker skull that heavily scatters ultrasound waves.

Objective:

We develop and disseminate a model-based navigation (MBN) tool for acoustic dose delivery in the presence of skull aberrations that is easy to use by non-specialists.

Methods:

We pre-compute acoustic beams for thousands of virtual transducer locations on the scalp of the subject under study. We use the hybrid angular spectrum solver mSOUND, which runs in ~4 s per solve per CPU yielding pre-computation times under 1 h for scalp meshes with up to 4000 faces and a parallelization factor of 5. We combine this pre-computed set of beam solutions with optical tracking, thus allowing real-time display of the tFUS beam as the operator freely navigates the transducer around the subject’ scalp. We assess the impact of MBN versus line-of-sight targeting (LOST) positioning in simulations of 13 subjects.

Results:

Our navigation tool has a display refresh rate of ~10 Hz. In our simulations, MBN increased the acoustic dose in the thalamus and amygdala by 8–67 % compared to LOST and avoided complete target misses that affected 10–20 % of LOST cases. MBN also yielded a lower variability of the deposited dose across subjects than LOST.

Conclusions:

MBN may yield greater and more consistent (less variable) ultrasound dose deposition than transducer placement with line-of-sight targeting, and thus could become a helpful tool to improve the efficacy of tFUS neuromodulation.

Transcranial focused ultrasound (tFUS)
Low intensity focused ultrasound pulsation (LIFUP)
Neuronavigation
Acoustic modeling
Hybrid angular spectrum
Neuromodulation
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pmc1. Introduction

Transcranial focused ultrasound (tFUS) is an emerging non-invasive neuromodulation approach that allows engagement of deep brain targets with millimeter accuracy [1–5]. The ability of tFUS to reach deep structures makes it highly complementary to transcranial magnetic stimulation (TMS), which can only achieve direct stimulation in the cortex [6]. This is desirable because subcortical nodes of the motor [7], limbic [8,9], and arousal networks [7,10,11] are implicated in the pathogenesis of movement disorders [12,13], psychiatric disorders [14,15], and disorders of consciousness [16,17], respectively. TFUS has been shown to be efficacious in animals [18–26], but human translation has been slow because of the thicker human skull that increases acoustic absorption and scatters acoustic beams. These skull-related effects decrease the acoustic dose in the target region and make it challenging to deliver it to the correct location [27–31]. Although skull effects are recognized as an important consideration in human tFUS [27,29,30,32–34], the majority of human studies using a single focused transducer employ the line-of-sight targeting (LOST) approach for placement. In LOST, the transducer is placed so that the center of the target region, for example the amygdala or the thalamus, lies on the centerline of the device as shown in Fig. S3. LOST placement is challenging and usually requires MRI guidance, which is usually feasible using fiducials markers embedded in the transducer housing. In this approach, the center of the target region is located at a tissue depth corresponding to the focal distance of the transducer in water, which can be achieved using impedance matching pads with appropriate thickness [35,36]. A downside of LOST is that it assumes ideal water propagation and ignores beam scattering and absorption by the skull.

There are several simulation approaches capable of modeling the effects of the skull in tFUS, including spectral and pseudospectral approaches [37–41], finite difference time domain (FDTD) [33,42–45], hybrid angular spectrum (HAS) [32,46–52], finite element modeling [53] and boundary element modeling [54,55], however most of those tools are not easy to use by non-specialists. Some investigators perform a limited number of simulations per subject, often using k-wave [37,38], however setting and solving the subject-specific model requires hours of work, which is feasible for dose verification (one retrospective simulation per subject) but not dose delivery planning (which requires many simulations). K-plan [56] and Sim4Life [57] are commercial software with graphical user interfaces that make it easier to solve the acoustic propagation problem in a subject-specific manner, but those use k-wave and FDTD, respectively, and therefore also suffer from long simulation times that limit their usefulness for dose delivery planning.

In addition to those tools, some investigators have proposed fast simulation strategies for improved dose delivery planning in human tFUS. Yoon et al. [42] proposed a fast FDTD approach whereby the domain is discretized using an adaptive mesh and solved in parallel using a graphical processing unit (GPU), yielding computation times of ~30 s per solve. Shin et al. [58] proposed a super-resolution convolutional neural network combined with a fast low-resolution FDTD solve. Although the investigators report computation times of ~4 s in single-transducer benchmarks, it is not clear how fast this approach can be in practice. Indeed, there is a limit to how low-resolution the initial FDTD solve can be as this technique requires ~10 sample points per wavelength for stability, which represents a minimal resolution of 0.75 mm at 200 kHz and 0.3 mm at 500 kHz. Choi et al. [59] also proposed a neural network for rapid ultrasound beam prediction, but they evaluated the method at 250 kHz where beam aberrations and attenuation by the skull are moderate and easy to model. Importantly, the deep learning models of Shin et al. and Choi et al. are not general and need to be re-trained for new subjects, which takes days. Park et al. proposed a 3D-cGAN neural network for real-time tFUS neuronavigation and showed encouraging results in term of speed and accuracy [60]. However, they used a limited number training inputs (3720), which raises questions about the generalizability of this method to all subjects, transducers and targets. Another method consists in computing the average reflection coefficient of ultrasound waves entering the skull using a 3-layer model of the head and Snell laws [61]. This method provides a more accurate estimate of the ultrasound beam path than LOST, but is based on approximations and was only validated for shallow cortical targets that are easier to reach than the deep sub-cortical nuclei that are the focus of the present study. Another approximate method by the same group consists in performing a time-reversed acoustic simulation from the target region and then placing the transducer at the location corresponding the maximum of a ‘score function’ [62]. A limitation of the methods mentioned in this paragraph is that they are not distributed in an open source manner, which makes them difficult to compare and evaluate objectively.

In this work, we propose a model-based navigation (MBN) approach whereby we pre-compute tFUS beam solutions corresponding to thousands of virtual transducers placed around the scalp of the subject under study. We embed this precomputation approach in a neuronavigation GUI connected to an optical tracking camera, thus allowing real-time visualization of the tFUS beam with a refresh rate of ~10 Hz as the operator freely moves the transducer around the subject’s scalp. Authors have proposed optical tracking approaches for tFUS navigation in the past [63,64], however MBN accounts for bone absorption and scattering in individualized skull models using a validated propagation code. In the current implementation, the pre-computation steps run in ~30 min per subject for a scalp mesh with ~4000 faces and a CPU parallelization factor of 10. If parallelization is not possible, pre-computation time increases to ~1 h for a scalp mesh with ~1000 faces, which still allows acquisition of MRI scans (required for navigation and beam computation) and tFUS sonication in a single study visit. Such rapid pre-computation times are possible thanks to the HAS code mSOUND which solves the generalized Westervelt equation in nonuniform acoustic media in ~4 s per transducer position at 650 kHz on a single CPU (Matlab implementation, 169×169×347 computational grid with resolution λ5=0.46mm), and has been validated by comparison with other approaches [51,52,65]. We provide open-source, user-friendly graphical user interfaces implemented as Matlab apps for the pre-computation and navigation steps in an effort to promote model-based acoustic dose modeling in tFUS human studies (https://github.com/bastpg).

2. Methods

Our model-based navigation (MBN) approach consists of two steps: Pre-computation (Fig. 1) and navigation (Fig. 2). Those steps have dedicated graphical user interfaces (GUI) that are easy to use by non-specialists.

2.1. Pre-processing

The first step is to load a head mask, bone porosity map and a segmentation index map of the subject’s head into the pre-computation GUI. The segmentation index map can be computed from a T1-weighted MRI input using Freesurfer [66] or SAMSEG [67] (the so-called ‘aseg’ map), which allows targeting of the L/R accumbens area, amygdala, caudate, hippocampus, pallidum, putamen, thalamus and ventral diencephalon. The porosity map can be estimated by scaling a CT or pseudo-CT volume of the subject, the latter can be computed using a number of methods including atlas-based [68–72], zero echo-time MRI [73–76] or deep learning [77–81]. In this work, we scale Hounsfield units (HU) to acoustic parameters following Aubry et al. [82]: ϕ=1−HU1000

x=ϕxbrain+1−ϕxbone

where ϕ is the bone porosity clipped to [0; 1] and x is a generic acoustic variable standing for the density (ρ), speed-of-sound (c) or acoustic attenuation (α). We use bone and brain acoustic properties from the IT’IS material database [83]: ρbrain,ρbone=1046,1908Kgm3, cbrain,cbone=1546,3514ms and αbrain,αbone=6.8,54.6Npm×Mhz. The head mask is obtained by simple thresholding of the CT (or pseudo-CT) volume. See additional information in supplementary material.

2.2. Pre-computation of acoustic beams

In the pre-computation GUI, the head mask is meshed into a model of the subject’s scalp using functions from the iso2mesh toolbox [84,85]. Each face of the scalp mesh represents a virtual transducer location, while the face’ normal represents the transducer normal at that position. The user can refine or coarsen the mesh as needed and exclude faces corresponding to unlikely positions of the transducer, e.g. below the eyes and ears. The total number of faces in the scalp mesh corresponds to the total number of virtual transducer locations solved for, and therefore controls the tradeoff between resolution of the scalp map and computation time. As shown in Figs. S1 and S2, we have found that using 1000 to 4000 virtual transducers (i.e., number of mesh faces) yields reasonable tradeoffs between resolution and computation time.

Next, the operator enters the details of the ultrasound transducer simulated (frequency, aperture diameter, focal distance and distance to scalp, see Fig. 1) into the pre-computation GUI and launches the pre-computation of beam solutions for all virtual transducers in parallel using mSOUND [52,86]. At present, our implementation is limited to virtual transducers located at a fixed distance to the subject’ scalp, which, in practice, corresponds to the thickness of the impedance matching gel pad. Moving the transducer away from the head, i.e. using a thicker impedance matching gel pad, requires solving the entire set of virtual transducer positions anew. We solve beam solutions in a limited computational domain of size 1.3d in the transverse direction, where d is the transducer aperture diameter, and 2f in the longitudinal or z direction, where f is the transducer focal distance in water. We found that this was adequate to fully characterize the scattered beam while minimizing computational time (see section 2.5 and Fig. S10). All simulations in this work were performed for the BrainSonix family of transducers (BrainSonix Corp, CA, USA) with focal distances F = 55 mm, 65 mm and 80 mm, 650 kHz operating frequency and 61 mm aperture diameter. See additional information in supplementary material.

2.3. Navigation

We developed a visualization GUI shown in Fig. 2 that allows the operator to explore the space of 3D acoustic beam solutions generated in the pre-computation step. The navigation GUI shows the distribution of the dose defined as the sum of the acoustic intensity in the target nucleus for all virtual transducers on the scalp mesh, a metric that we call ‘scalp map’ (one value of the dose per face of the mesh). Scalp maps are helpful to quickly visualize the distribution of the dose across virtual transducer positions. A scalp maps is specific to a subject, transducer and target nucleus; and its peak intensity indicates the transducer position yielding maximum dose deposition for the target nucleus, subject under study. Scalp maps do not provide information about the dose in regions outside the target nucleus however. To address this, we also display the acoustic dose in all nuclei for the selected transducer position, which is helpful to find transducer positions achieving a good balance between maximization of the dose in the target nucleus while minimizating it in other nuclei. For example, a tFUS study attempting to achieve high acoustic dose in the thalamus while minimizing the dose in surrounding nuclei may disfavor lateral beams associated with placement of the transducer on the temporal window, a situation visible in Fig. 9 and S7. In other words, the best transducer position may not always correspond to the maximum of the scalp map, a determination that is best made by the operator. Instead of plotting the raw scalp map, which can have a jagged appearance and yields unstable predictions of the optimal transducer position as a function of scalp mesh resolution, we use a smoothed version that stabilizes the navigation process (Figs. S1 and S2).

Navigation is done either manually, by clicking on a virtual transducer position on the salp map, or automatically by connecting the navigation computer to an optical tracking camera, as shown in Fig. 3. In this work, we use a Polaris Spectra optical tracking camera (Northern Digital Inc, Waterloo, Canada). Both Localite (Localite GmbH, Bonn, Germany) and Brainsight (Rogue Reserach, Cambridge, USA) navigation systems are supported by the navigation GUI. Tracking is performed by mounting a reference tracker on the subject’s head and a coil tracker on the transducer, which allows measuring their relative position and orientation with 2 mm and 1° accuracy. See additional information in supplementary material.

2.4. Comparison with line-of-sight targeting (LOST)

We compared dose depositions achieved with MBN and LOST in 13 subjects. We also compared MBN to an approach whereby scalp maps are computed assuming acoustic propagation in uniform water (we call this approach ‘Water’). Additional information in supplementary material.

2.5. Comparison of mSOUND with finite difference time domain

See supplementary material.

3. Results

Figs. 4 and 5 show distributions of the acoustic dose in the left/right amygdala and thalamus of 13 subjects using transducer placement optimization with LOST and MBN, respectively, for BrainSonix transducers with focal distances F = 55 mm, 65 mm and 80 mm. Fig. 4 indicates that LOST best reaches the amygdala using the short F = 55 mm focal distance, while the thalamus is best reached using the longer F = 80 mm focal distance. This is not the case with MBN, where the longer F = 80 mm focal distance is optimal (in average for all subjects) both for the amygdala and the thalamus. Another finding is that the distribution of the dose was less variable across subjects with MBN than with LOST: For example, the dose variation was 4.8:1 when targeting the left amygdala with LOST and 2.5:1 when targeting the left thalamus (F=80 mm), whereas it was 3.4:1 and 1.5:1 with MBN, respectively (these represent 34 % and 50 % reductions of the dose variability when using MBN compared to LOST).

The distributions of LOST, ‘Water’ and MBN doses in the left/right amygdala and thalamus of the 13 subjects are compared in Fig. 6. In average, MBN increased the acoustic dose by 8–67 % compared to LOST, yielding statistically significant differences in all simulated scenarios except when targeting the right amygdala with the F = 55 mm and F = 65 mm transducers. The ‘Water’ dose distribution sits roughly between MBN and LOST, which is intuitive since ‘Water’ considers all possible transducer positions and is more general than LOST, but does not model skull effects.

Figs. 7 and 8 show MBN scalp maps associated with the right thalamus and amygdala and the F = 80 mm transducer in 6 of the 13 subjects (scalp maps for the left thalamus and amygdala are shown in Figs. S5 and S6). Those maps vary significantly between subjects, especially for the thalamus target where the optimal MBN location is sometimes on the temporal window (Fig. 7, subjects 3, 4, 5 and 8), a location used in many LOST studies, and sometimes in more superior locations (Fig. 7, subjects 11 and 13). Optimal MBN locations for the amygdala target were more consistent across subjects because this nucleus is shallower and less central than the thalamus (i.e., closer to the temporal lobe), thus always yielding optimal positions on the ipsilateral temporal window.

Figs. 9 and 10 show MBN and LOST beams targeting the right amygdala and right thalamus overlaid on T1 MRI images for 6 of the 13 subjects (left thalamus and left amygdala beams are shown in Figs. S7 and S8). Those indicate that LOST, when properly implemented, generally does a good job at targeting the thalamus and amygdala, with only a few complete misses (subjects 3 and 11 in Fig. 10, subjects 11 and 13 in Fig. S8). MBN avoids those complete misses and further increases the dose in all scenarios.

4. Discussion

4.1. Model-based navigation for transcranial focused ultrasound

We propose a modeling-based navigation (MBN) approach for optimal placement of transcranial focused ultrasound (tFUS) transducers that accounts for skull-induced beam aberration and scattering. The approach combines pre-calculatation of acoustic beams at thousands of virtual locations with optical tracking of the transducer’s position and orientation in 3D space, thus enabling real-time visualization of the tFUS beam as the operator freely moves the transducer on the subject’s scalp. We provide acoustic dose deposition metrics to aid navigation, including ‘scalp maps’ representing the distribution of the acoustic dose in the target nucleus for all virtual transducer locations. Scalp maps are specific to a target nucleus, subject and transducer and allow quick determination of transducer locations yielding high dose deposition in the region of interest. A major goal of this work is to facilitate the deployment of state-of-the-art tFUS modeling in human studies, which we believe is critical for successful translation of tFUS into humans. For this reason, we provide Matlab GUIs that are easy to use by non-specialists without a computational background which we distribute in an open-source manner (https://github.com/bastpg).

4.2. Comparison of MBN with LOST

We simulated tFUS scenarios targeting the amygdala and the thalamus in 13 subjects. Those simulations indicate that MBN improves tFUS targeting by 8–67 % compared to line-of-sight targeting (LOST) and avoids complete target misses that otherwise affect 10–20 % of LOST cases. We also found that variation of the dose across subjects was smaller with MBN than with LOST. Specifically, the LOST dose varied 4.8-, 3.9-, 2.5- and 2.1-fold across subjects when targeting the left amygdala, right amygdala, left thalamus and right thalamus, respectively, with the F = 80 mm transducer. In contrast, the MBN dose variation across subjects was 3.4-, 3.1-, 1.5- and 1.7-fold for those targets. Large variations of the acoustic dose are caused by variations of the skull porosity and geometry across subjects that are accentuated by inconsistent transducer positioning when using LOST. Greater and more uniform dose delivery across subjects using MBN is desirable as this may lead to greater efficacy and reduced variability of clinical outcomes.

We found that scalp maps varied greatly across subjects and target nuclei, which shows that tFUS dose delivery planning should be done in a study- and subject-specific manner. We studied two brain targets in this work: The amygdala, which is small and lateral, and the thalamus, which is larger and located centrally in the brain. Thalamus scalp maps displayed broad transducer placement regions associated with high dose deposition, indicating that there is some latitude in the exact placement of the transducer and that targeting is relatively robust to unavoidable navigation errors. In contrast, amygdala scalp maps were sparse with narrow regions associated with high dose deposition, making precise positioning and navigation more critical in this case. See additional discussion on MBN vs. ‘Water’ in supplementary material (Fig. 11).

4.3. Quantitative dose calibration

In addition to dose delivery planning, MBN provides dose metrics that could be helpful to explain the variability of clinical and neuroimaging (fMRI, EEG etc.) outcome measures [87–92]. In this work we report the uncalibrated acoustic dose intensity in arbitrary units for the commercial BrainSonix transducers [93]. System-specific calibration to absolute units (W/m2) requires mapping the transducer beam in water using a hydrophone, a step that needs to be performed by the operator. Absolute calibration of dose metrics in W/m2 is essential for assessment of thermal and mechanical effects but not so much for dose delivery planning (i.e. Where should the transducer be placed?) since such a calibration factor applies to all transducer positions and all subjects in the same way.

Subject-specific computation of the thermal safety index could be achieved by adding a thermal solver to our suite of tools, for example the open-source Pennes bioheat solver in k-wave. Thermal simulations are slow, therefore this step may only be performed for the final, optimal transducer location. The mechanical index on the other hand, i.e. the ratio of peak negative pressure (in MPa) to the square root of the frequency (in MHz), is trivial to compute and could easily be displayed as an additional map provided that the operator supplies the acoustic intensity calibration factor. Subject-specific calculations of thermal and mechanical indices allow assessing safety in individual subjects, which could possibly lead to less constraining, but still safe, acoustic intensity limits in human studies.

4.4. Definition of target nuclei

MBN requires an ‘aseg’ segmentation map of sub-cortical nuclei from Freesurfer [66] (~2 h per subject) or SAMSEG [67] (~13 min with a parallelization factor of 10) which supports targeting of the L/R accumbens area, amygdala, caudate, hippocampus, pallidum, putamen, thalamus and ventral diencephalon. In the future, it could be valuable to include sub-segmentation atlases of the thalamus [94], amygdala [95], brainstem [96] and hippocampus [97] in MBN since the resolution of tFUS may permit targeting sub-regions of those nuclei. Another idea could be to add white matter fiber atlases derived from subject-specific [98–100] or population average diffusion MRI data [101] into MBN, which may eventually be of interest as white matter targets have been shown to be effective for the treatment of psychiatric disorders using deep brain stimulation [102–107].

4.5. Computational times and requirements

Computing power and memory requirements are moderate for MBN as modern personal computers and laptops often come standard with 4–8 CPU cores and 4 GB of RAM or more, which is enough to run MBN in the most basic configuration (1 h pre-computation, 1000 virtual transducers, 1 CPU). Of course, the more CPU cores, the better (computation time decreases to 30 min for 4000 virtual transducers using 10 CPUs). Such short pre-computation times are feasible thanks to the speed of mSOUND, which runs in ~4 s per virtual transducer, and allow conducting the MRI examination and tFUS sonication portions of a study in a single visit. By comparison, k-wave and GPU-accelerated FDTD run in ~15 min and ~2 min, respectively, which would yield days of pre-computation for the entire set of virtual transducers even when distributing the calculation on multiple cores. To minimize computation time, we run mSOUND in a reduced computational domain of size 1.3d in the transverse direction and 2f in the longitudinal direction, where d and f are the aperture diameter and the focal distance of the transducer, respectively. Such computational domain size prohibits modeling of internal reflections and standing wave effects; however Fig. S10 shows that this does not significantly impact the accuracy of hotspot position and shape predictions at 650 kHz. See additional discussion in supplementary material.

4.6. Smoothing of scalp maps

See supplementary material.

4.7. Validation of MBN predictions

This work was an simulation study that needs to be validated by comparison with experimental data. The mSOUND solver is a validated tool [51,52,65] and the largest source of error in our predictions likely originates from inaccurate estimation of acoustic properties from CT or pseudo-CT data. This is a difficult and active area of research, and our tool reflects the state-of-knowledge in the field. For example, CT scans at clinical resolutions do not allow characterization of the geometry of pores in cortical bone, an information that is needed for accurate modeling of ultrasound scattering through the skull. Using additional metrics such a T2-weighted MRI or ultrasound transmission measurements may help improve modeling accuracy, however such considerations are beyond the scope of this work [29]. As the field progresses, we will update our tool so that it reflects the state-of-the-art. A reassuring fact is that acoustic absorption, which is difficult to estimate accurately, mainly affects absolute dose quantification [108] whereas the speed-of-sound, which is easier to estimate from Hounsfield units, is the main determinant of hotspot position and shape [31]. Therefore, MBN predictions of optimal transducer locations are likely reasonably accurate, but quantitative dose predictions across subjects should be interpreted with caution. See additional discussion in supplementary material.

Supplementary Material

1

Acknowledgements

We thank Dr. Yun Jing for help with mSOUND and Dr. Kyungho Yoon for providing us with the Sound Wave Rider FDTD code. We thank Dr. David Izquierdo and Dr. Ciprian Catana for sharing the CT/MRI dataset of 13 patients used in those simulations. This work was funded by awards from the Massachusetts General Hospital Allison McCance Center for Brain Health, Tiny Blue Dot Foundation, NIH Director’s Office (DP2HD101400) and the Massachusetts General Hospital Chen Institute.

Fig. 1. Pre-calculation GUI. Panel 1: The operator loads and visualizes the head mask, bone porosity and segmentation index map of deep nuclei structures (‘aseg’ map from FreeSurfer/SAMSEG). Toggling between those maps is useful to check for possible alignment errors. Panel 2: A mesh of the scalp is generated and visualized. The operator can adapt the number of faces in the mesh by changing the average triangle edge length and removing faces that do not correspond to valid transducer positions (e.g. below the ears). Faces’ normal are displayed to verify their proper orientation. Panel 3: Details of the transducer modeled. Panel 4: As the computation proceeds, mSOUND computes beam solutions corresponding to the transducer positions/faces of the scalp mesh in parallel. A typical pre-calculation time is 30 min for 4000 mesh faces with a parallel factor 10.

Fig. 2. Navigation GUI. The operator loads the results of the pre-calculation, selects the target brain nucleus and can save the various display panels as Matlab figures. The current implementation of the tool uses the so-called ‘aseg’ map generated by Freesurfer and SAMSEG, which supports selection of the L/R accumbens area, amygdala, caudate, hippocampus, pallidum, putamen, thalamus and ventral diencephalon. The ‘Navigate’ panel allows exploring the set of beam solutions by clicking on faces of the scalp map or connecting the tool to a Localite or Brainsight optical tracking camera. There are two main displays on the right-hand side: The top panel is a bar graph of the dose in all the sub-cortical nuclei and the lower panel is the smoothed scalp map with a 3D display of the beam at the current transducer location.

Fig. 3. Real-time model-based tFUS navigation with optical tracking. The optical camera tracks both the subject and the transducer and streams this information into the navigation GUI, which allows real-time visualization of the tFUS beam as the operator freely moves the transducer on the subject’ scalp.

Fig. 4. Dose deposited with line-of-sight targeting (LOST) in the left amygdala (A), right amygdala (B), left thalamus (C) and right thalamus (D) in 13 subjects using transducers with focal distances F = 55 mm, 65 mm and 80 mm. The ‘average’ bars show the average and standard deviation of deposited dose values across subjects. The min:max values indicate the range of deposited dose values across subjects for each focal distance (for example, min:max = 10:1 indicates that there is a 10-fold variation of the dose across subjects).

Fig. 5. Dose deposited with model-based navigation (MBN) in the left amygdala (A), right amygdala (B), left thalamus (C) and right thalamus (D) in 13 subjects using transducers with focal distances F = 55 mm, 65 mm and 80 mm. The ‘average’ bars show the average and standard deviation of deposited dose values across subjects. The min:max values indicate the range of deposited dose values across subjects for each focal distance (for example, min:max = 10:1 indicates that there is a 10-fold variation of the dose across subjects).

Fig. 6. Violin plots showing the distribution, mean and standard deviation of the acoustic dose in the left amygdala (A), right amygdala (B), left thalamus (C) and right thalamus (D) when using line-of-sight targeting (LOST), water simulation (Water) and model-based navigation (MBN) for transducers with focal distances F = 55 mm, F = 65 mm and F = 80 mm. Brackets indicate statistically significant increases of the deposited dose with MBN compared to LOST (two-sided t-test, p = 0.05).

Fig. 7. Model-based navigation (MBN) scalp maps targeting the right thalamus with the F = 80 mm transducer. The value next to each map indicates the peak dose deposition in the target at the optimal MBN transducer position. Colormaps are scaled to that value. Optimal MBN transducer locations are shown in black, LOST locations in white.

Fig. 8. Model-based navigation (MBN) scalp maps targeting the right amygdala with the F = 80 mm transducer. The value next to each map indicates the peak dose deposition in the target at the optimal MBN transducer position. Colormaps are scaled to that value. Optimal MBN transducer locations are shown in black, LOST locations in white.

Fig. 9. TFUS beams targeting the right thalamus, overlaid on T1-images for 6 of the 13 subjects in this study. The first and second rows show beam solutions associated with line-of-sight targeting (LOST) and model-based navigation (MBN), respectively. The transducer is shown in dark blue (the transducer centerline ends in a small dot indicating the water focal distance, which is F = 80 mm both for LOST and MBN since this is the optimal configuration for this target as shown in Figs. 4 and 5). The outline of the target nuclei is in green. The cyan numbers indicate the dose deposited in the target region in arbitrary units.

Fig. 10. TFUS beams targeting the right amygdala, overlaid on T1-images for 6 of the 13 subjects in this study. The first and second rows show beam solutions associated with line-of-sight targeting (LOST) and model-based navigation (MBN), respectively. The transducer is shown in dark blue (the transducer centerline ends in a small dot indicating the water focal depth, which is F = 55 mm both for LOST and F = 80 mm for MBN since these are the optimal configurations for this target as shown in Figs. 4 and 5). The outline of the target nuclei is in green. The cyan numbers indicate the dose deposited in the target region in arbitrary units.

Fig. 11. Scalp maps of the dose in the right thalamus for 6 of the 13 test subjects, obtained with modeling of the skull (model-based navigation, MBN) and without modeling of the skull (water simulation, ‘Water’). In the ‘Water’ approach, the ideal beam profile of the transducer in water is overlapped onto the geometry of the head of the subject for all virtual transducer positions. Therefore, ‘Water’ can be viewed as a generalization of LOST. The transducer modeled has a focal distance F = 80 mm. Optimal transducer locations corresponding to the peak of those maps are shown in black.

CRediT authorship contribution statement

Mohammad Daneshzand: Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Conceptualization. Bastien Guerin: Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Parker Kotlarz: Writing – review & editing, Software. Tina Chou: Writing – review & editing. Darin D. Dougherty: Writing – review & editing, Funding acquisition. Brian L. Edlow: Writing – review & editing, Funding acquisition. Aapo Nummenmaa: Writing – review & editing, Supervision, Methodology, Conceptualization.

Declaration of Competing interest

none.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.brs.2024.07.019.
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References

[1] Paulus W . Transcranial brain stimulation: potential and limitations. eNeuroforum 2014;5 :29–36.
[2] Bystritsky A , A review of low-intensity focused ultrasound pulsation. Brain Stimul 2011;4 :125–36. 10.1016/j.brs.2011.03.007. Preprint at. 21777872
[3] Tyler WJ , Remote excitation of neuronal circuits using low-intensity, low-frequency ultrasound. PLoS One 2008;3.
[4] Gavrilov LR , The effect of focused ultrasound on the skin and deep nerve structures of man and animal. Prog Brain Res 1976;43 :279–92.1257484
[5] Fry WJ . Intense ultrasound in investigations of the central nervous system. In: Advances in biological and medical physics, vol. 6 . Elsevier; 1959. p. 281–348.
[6] Tremblay S , Clinical utility and prospective of TMS–EEG. Clin Neurophysiol 2019;130 :802–44.30772238
[7] Singh K , Functional connectome of arousal and motor brainstem nuclei in living humans by 7 Tesla resting-state fMRI. Neuroimage 2022;249 :118865.35031472
[8] Morgane PJ , Galler JR , Mokler DJ . A review of systems and networks of the limbic forebrain/limbic midbrain. Prog Neurobiol 2005;75 :143–60.15784304
[9] Venkatraman A , Edlow BL , Immordino-Yang MH . The brainstem in emotion: a review. Front Neuroanat 2017;11 :15.28337130
[10] Cauzzo S , Functional connectome of brainstem nuclei involved in autonomic, limbic, pain and sensory processing in living humans from 7 Tesla resting state fMRI. Neuroimage 2022;250 :118925.35074504
[11] Edlow BL , Neuroanatomic connectivity of the human ascending arousal system critical to consciousness and its disorders. J Neuropathol Exp Neurol 2012;71 :531–46.22592840
[12] Horn A , Deep brain stimulation induced normalization of the human functional connectome in Parkinson’s disease. Brain 2019;142 :3129–43.31412106
[13] Benussi A , Long term clinical and neurophysiological effects of cerebellar transcranial direct current stimulation in patients with neurodegenerative ataxia. Brain Stimul 2017;10 :242–50.27838276
[14] Siddiqi SH , Brain stimulation and brain lesions converge on common causal circuits in neuropsychiatric disease. Nat Hum Behav 2021;5 :1707–16.34239076
[15] Widge AS , Treating refractory mental illness with closed-loop brain stimulation: progress towards a patient-specific transdiagnostic approach. Exp Neurol 2017;287 :461–72.27485972
[16] Schiff ND , Behavioural improvements with thalamic stimulation after severe traumatic brain injury. Nature 2007;448 :600–3.17671503
[17] Monti MM , Schnakers C , Korb AS , Bystritsky A , Vespa PM . Non-invasive ultrasonic thalamic stimulation in disorders of consciousness after severe brain injury: a first-in-man report. Brain Stimul 2016;9 :940–1.27567470
[18] Yoo SS , Focused ultrasound modulates region-specific brain activity. Neuroimage 2011;56 :1267–75.21354315
[19] Tufail Y , Transcranial Pulsed ultrasound stimulates intact brain circuits. Neuron 2010;66 :681–94.20547127
[20] Ye PP , Brown JR , Pauly KB . Frequency dependence of ultrasound neurostimulation in the mouse brain. Ultrasound Med Biol 2016;42 :1512–30.27090861
[21] King RL , Brown JR , Newsome WT , Pauly KB . Effective parameters for ultrasound-induced in vivo neurostimulation. Ultrasound Med Biol 2013;39 :312–31.23219040
[22] Kamimura HAS , Focused ultrasound neuromodulation of cortical and subcortical brain structures using 1.9 MHz. Med Phys 2016;43 :5730–5.27782686
[23] King RL , Brown JR , Pauly KB . Localization of ultrasound-induced in vivo neurostimulation in the mouse model. Ultrasound Med Biol 2014;40 :1512–22.24642220
[24] Dallapiazza RF , Noninvasive neuromodulation and thalamic mapping with low-intensity focused ultrasound. J Neurosurg 2017;128 :875–84.28430035
[25] Deffieux T , Low-intensity focused ultrasound modulates monkey visuomotor behavior. Curr Biol 2013;23 :2430–3.24239121
[26] Folloni D , Manipulation of subcortical and deep cortical activity in the primate brain using transcranial focused ultrasound stimulation. Neuron 2019; 101 :1109–16.30765166
[27] Leung SA , Comparison between MR and CT imaging used to correct for skull-induced phase aberrations during transcranial focused ultrasound. Sci Rep 2022;12 .
[28] Hynynen K , Sun J . Trans-skull ultrasound therapy: the feasibility of using image-derived skull thickness information to correct the phase distortion. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46 :752–5.18238476
[29] Webb TD , Improving transcranial acoustic targeting: the limits of CT based velocity estimates and the role of MR. IEEE Trans Ultrason Ferroelectr Freq Control 2022. 10.1109/TUFFC.2022.3192224.
[30] Webb TD , Acoustic attenuation: multifrequency measurement and relationship to CT and MR imaging. IEEE Trans Ultrason Ferroelectr Freq Control 2021;68 :1532–45.33226938
[31] Leung SA , Webb TD , Bitton RR , Ghanouni P , Butts Pauly K . A rapid beam simulation framework for transcranial focused ultrasound. Sci Rep 2019;9 .
[32] Leung SA , Transcranial focused ultrasound phase correction using the hybrid angular spectrum method. Sci Rep 2021;11 :6532.33753771
[33] Baron C , Aubry J-F , Tanter M , Meairs S , Fink M . Simulation of intracranial acoustic fields in clinical trials of sonothrombolysis. Ultrasound Med Biol 2009; 35 :1148–58.19394756
[34] Darmani G , Non-invasive transcranial ultrasound stimulation for neuromodulation. Clin Neurophysiol 2022;135 :51–73.35033772
[35] Sarica C , Human Studies of Transcranial Ultrasound neuromodulation: a systematic review of effectiveness and safety. Brain Stimul 2022;15 :737–46. 10.1016/j.brs.2022.05.002. Preprint at. 35533835
[36] Summers PM , Hanlon CA . BrainRuler-a free, open-access tool for calculating scalp to cortex distance. Brain Stimul: Basic, Translational, and Clinical Research in Neuromodulation 2017;10 :1009–10.
[37] Wang K , Teoh E , Jaros J , Treeby BE . Modelling nonlinear ultrasound propagation in absorbing media using the k-Wave toolbox: experimental validation. In: 2012 IEEE international ultrasonics symposium. IEEE; 2012. p. 523–6.
[38] Treeby BE , Cox BT . k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields. J Biomed Opt 2010;15 :21314.
[39] Martin E , Jaros J , Treeby BE . Experimental validation of k-wave: nonlinear wave propagation in layered, absorbing fluid media. IEEE Trans Ultrason Ferroelectr Freq Control 2019;67 :81–91.31535990
[40] Stanziola A , Arridge SR , Cox BT , Treeby BE . j-Wave: an open-source differentiable wave simulator. SoftwareX 2023;22 :101338.
[41] Afanasiev M , Modular and flexible spectral-element waveform modelling in two and three dimensions. Geophys J Int 2019;216 :1675–92.
[42] Yoon K , Lee W , Croce P , Cammalleri A , Yoo SS . Multi-resolution simulation of focused ultrasound propagation through ovine skull from a single-element transducer. Phys Med Biol 2018;63 .
[43] Deffieux T , Konofagou EE . Numerical study of a simple transcranial focused ultrasound system applied to blood-brain barrier opening. IEEE Trans Ultrason Ferroelectr Freq Control 2010;57 :2637–53.21156360
[44] Mueller JK , Ai L , Bansal P , Legon W . Numerical evaluation of the skull for human neuromodulation with transcranial focused ultrasound. J Neural Eng 2017;14 : 066012.28777075
[45] Robertson JLB , Cox BT , Jaros J , Treeby BE . Accurate simulation of transcranial ultrasound propagation for ultrasonic neuromodulation and stimulation. J Acoust Soc Am 2017;141 :1726–38.28372121
[46] Vyas U , Christensen D . Ultrasound beam propagation using the hybrid angular spectrum method. In: 2008 30th annual international conference of the IEEE engineering in medicine and biology society. IEEE; 2008. p. 2526–9.
[47] Johnson SL , Christensen DA , Dillon CR , Payne A . Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms. Int J Hyperther 2018;35 : 578–90.
[48] Vyas U , Christensen D . Ultrasound beam simulations in inhomogeneous tissue geometries using the hybrid angular spectrum method. IEEE Trans Ultrason Ferroelectr Freq Control 2012;59 :1093–100.22711405
[49] Almquist S , Parker D , Christensen D . Simulation of hemispherical transducers for transcranial HIFU treatments using the hybrid angular spectrum approach. J Ther Ultrasound 2015;3 :1–2.25635224
[50] Hansen M , Christensen D , Payne A . Experimental validation of acoustic and thermal modeling in heterogeneous phantoms using the hybrid angular spectrum method. Int J Hyperther 2021;38 :1617–26.
[51] Gu J , Jing Y . Numerical modeling of ultrasound propagation in weakly heterogeneous media using a mixed-domain method. IEEE Trans Ultrason Ferroelectr Freq Control 2018;65 :1258–67.29993378
[52] Gu J , Jing Y . A modified mixed domain method for modeling acoustic wave propagation in strongly heterogeneous media. J Acoust Soc Am 2020;147 : 4055–68.32611145
[53] Zhang S , Kang M , Xu Y , Li C , Dong F . Finite-element modeling of tissue responses to focused ultrasound with different intensities. IEEE Trans Instrum Meas 2021; 71 :1–10.
[54] Shen F , An efficient method for transcranial ultrasound focus correction based on the coupling of boundary integrals and finite elements. Ultrasonics 2024;137 :107181.37847943
[55] van’t Wout E , Gélat P , Betcke T , Arridge S . A fast boundary element method for the scattering analysis of high-intensity focused ultrasound. J Acoust Soc Am 2015;138 :2726–37.26627749
[56] Brainbox, C. U. K. k-Plan Ultrasound Planning. https://brainbox-neuro.com/products/k-plan.
[57] ZMT Zurich MedTech AG, Z. S. Sim4Life. https://zmt.swiss/sim4life/.
[58] Shin M , Peng Z , Kim H-J , Yoo S-S , Yoon K . Multivariable-incorporating super-resolution convolutional neural network for transcranial focused ultrasound simulation. 2023.
[59] Choi M , Jang M , Yoo SS , Noh G , Yoon K . Deep neural network for navigation of a single-element transducer during transcranial focused ultrasound therapy: proof of concept. IEEE J Biomed Health Inform 2022;26 :5653–64.35969551
[60] Park TY , Real-time acoustic simulation framework for tFUS: a feasibility study using navigation system. Neuroimage 2023;282 :120411.37844771
[61] Park TY , Pahk KJ , Kim H . Method to optimize the placement of a single-element transducer for transcranial focused ultrasound. Comput Methods Programs Biomed 2019;179 :104982.31443869
[62] Park TY , Differential evolution method to find optimal location of a single-element transducer for transcranial focused ultrasound therapy. Comput Methods Programs Biomed 2022;219 :106777.35397411
[63] Zettinig O , Toward real-time 3D ultrasound registration-based visual servoing for interventional navigation. In: 2016 IEEE international conference on robotics and automation (ICRA). IEEE; 2016. p. 945–50.
[64] Kim H , Chiu A , Park S , Yoo S . Image-guided navigation of single-element focused ultrasound transducer. Int J Imaging Syst Technol 2012;22 :177–84.25232203
[65] Aubry J-F , Benchmark problems for transcranial ultrasound simulation: intercomparison of compressional wave models. J Acoust Soc Am 2022;152 : 1003–19.36050189
[66] Fischl B . FreeSurfer. Neuroimage 2012;62 :774–81.22248573
[67] Puonti O , Iglesias JE , Van Leemput K . Fast and sequence-adaptive whole-brain segmentation using parametric Bayesian modeling. Neuroimage 2016;143 : 235–49.27612647
[68] Izquierdo-Garcia D , An SPM8-based approach for attenuation correction combining segmentation and nonrigid template formation: application to simultaneous PET/MR brain imaging. J Nucl Med 2014;55 :1825–30.25278515
[69] Burgos N , Attenuation correction synthesis for hybrid PET-MR scanners: application to brain studies. IEEE Trans Med Imaging 2014;33 :2332–41.25055381
[70] Wang T , MRI-based treatment planning for brain stereotactic radiosurgery: dosimetric validation of a learning-based pseudo-CT generation method. Med Dosim 2019;44 :199–204.30115539
[71] Arabi H , Koutsouvelis N , Rouzaud M , Miralbell R , Zaidi H . Atlas-guided generation of pseudo-CT images for MRI-only and hybrid PET–MRI-guided radiotherapy treatment planning. Phys Med Biol 2016;61 :6531.27524504
[72] Uh J , Merchant TE , Li Y , Li X , Hua C . MRI-based treatment planning with pseudo CT generated through atlas registration. Med Phys 2014;41 :051711.24784377
[73] Wiesinger F , Zero TE-based pseudo-CT image conversion in the head and its application in PET/MR attenuation correction and MR-guided radiation therapy planning. Magn Reson Med 2018;80 :1440–51.29457287
[74] Johnson EM , Vyas U , Ghanouni P , Pauly KB , Pauly JM . Improved cortical bone specificity in UTE MR Imaging. Magn Reson Med 2017;77 :684–95.26972442
[75] Miller GW , Eames M , Snell J , Aubry J . Ultrashort echo-time MRI versus CT for skull aberration correction in MR-guided transcranial focused ultrasound: in vitro comparison on human calvaria. Med Phys 2015;42 :2223–33.25979016
[76] Guo S , Feasibility of ultrashort echo time images using full-wave acoustic and thermal modeling for transcranial MRI-guided focused ultrasound (tcMRgFUS) planning. Phys Med Biol 2019;64 :095008.30909173
[77] Liu H , Evaluation of synthetically generated CT for use in transcranial focused ultrasound procedures. 2022. arXiv preprint arXiv:2210.14775.
[78] Miscouridou M , Pineda-Pardo JA , Stagg CJ , Treeby BE , Stanziola A . Classical and learned MR to pseudo-CT mappings for accurate transcranial ultrasound simulation. IEEE Trans Ultrason Ferroelectr Freq Control 2022;69 :2896–905.35984788
[79] Su P , Transcranial MR imaging–guided focused ultrasound interventions using deep learning synthesized CT. Am J Neuroradiol 2020;41 :1841–8.32883668
[80] Yaakub SN , Pseudo-CTs from T1-weighted MRI for planning of low-intensity transcranial focused ultrasound neuromodulation: an open-source tool. Brain Stimul: Basic, Translational, and Clinical Research in Neuromodulation 2023;16 : 75–8.
[81] Koh H , Park TY , Chung YA , Lee J-H , Kim H . Acoustic simulation for transcranial focused ultrasound using GAN-based synthetic CT. IEEE J Biomed Health Inform 2021;26 :161–71.
[82] Aubry J-F , Tanter M , Pernot M , Thomas J-L , Fink M . Experimental demonstration of noninvasive transskull adaptive focusing based on prior computed tomography scans. J Acoust Soc Am 2003;113 :84–93.12558249
[83] IT’IS Foundation. IT’IS Foundation Material Property Database. https://itis.swiss/virtual-population/tissue-properties/database/.
[84] Fang Q , Boas DA . Tetrahedral mesh generation from volumetric binary and grayscale images. Proceedings - 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009;2009 :1142–5. 10.1109/ISBI.2009.5193259.
[85] Tran AP , Yan S , Fang Q . Improving model-based functional near-infrared spectroscopy analysis using mesh-based anatomical and light-transport models. Neurophotonics 2020;7 :15008.
[86] Gu J , Jing Y mSOUND. An open source toolbox for modeling acoustic wave propagation in heterogeneous media. IEEE Trans Ultrason Ferroelectr Freq Control 2021;68 :1476–86.33444136
[87] Cain JA , Real time and delayed effects of subcortical low intensity focused ultrasound. Sci Rep 2021;11 :1–14.33414495
[88] Cain JA , Ultrasonic deep brain neuromodulation in acute disorders of consciousness: a proof-of-concept. Brain Sci 2022;12 :428.35447960
[89] Ai L , Bansal P , Mueller JK , Legon W . Effects of transcranial focused ultrasound on human primary motor cortex using 7T fMRI: a pilot study. BMC Neurosci 2018; 19 :1–10.29338692
[90] Legon W , Ai L , Bansal P , Mueller JK . Neuromodulation with single-element transcranial focused ultrasound in human thalamus. Hum Brain Mapp 2018;39 : 1995–2006.29380485
[91] Ai L , Mueller JK , Grant A , Eryaman Y , Legon W . Transcranial focused ultrasound for BOLD fMRI signal modulation in humans. In: 2016 38th annual international conference of the IEEE engineering in medicine and biology society (EMBC). IEEE; 2016. p. 1758–61.
[92] Legon W , Bansal P , Tyshynsky R , Ai L , Mueller JK . Transcranial focused ultrasound neuromodulation of the human primary motor cortex. Sci Rep 2018;8.29311689
[93] Schafer ME , Spivak NM , Korb AS , Bystritsky A . Design, development and operation of a low intensity focused ultrasound pulsation (LIFUP) system for clinical use. IEEE Trans Ultrason Ferroelectr Freq Control 2020:1–11. 10.1109/tuffc.2020.3006781.
[94] Iglesias JE , A probabilistic atlas of the human thalamic nuclei combining ex vivo MRI and histology. Neuroimage 2018;183 :314–26.30121337
[95] Saygin ZM , High-resolution magnetic resonance imaging reveals nuclei of the human amygdala: manual segmentation to automatic atlas. Neuroimage 2017;155 :370–82.28479476
[96] Iglesias JE , Bayesian segmentation of brainstem structures in MRI. Neuroimage 2015;113 :184–95.25776214
[97] Iglesias JE , A computational atlas of the hippocampal formation using ex vivo, ultra-high resolution MRI: application to adaptive segmentation of in vivo MRI. Neuroimage 2015;115 :117–37.25936807
[98] Clayden JD , Storkey AJ , Bastin ME . A probabilistic model-based approach to consistent white matter tract segmentation. IEEE Trans Med Imaging 2007;26 : 1555–61.18041270
[99] Wasserthal J , Neher P , Maier-Hein KH . TractSeg-Fast and accurate white matter tract segmentation. Neuroimage 2018;183 :239–53.30086412
[100] Kreilkamp BAK , Weber B , Richardson MP , Keller SS . Automated tractography in patients with temporal lobe epilepsy using TRActs Constrained by UnderLying Anatomy (TRACULA). Neuroimage Clin 2017;14 :67–76.28138428
[101] Neudorfer C , Lead-DBS v3. 0: mapping deep brain stimulation effects to local anatomy and global networks. Neuroimage 2023;119862.36610682
[102] Gutman DA , Holtzheimer PE , Behrens TEJ , Johansen-Berg H , Mayberg HS . A tractography analysis of two deep brain stimulation white matter targets for depression. Biol Psychiatry 2009;65 :276–82.19013554
[103] Johansen-Berg H , Anatomical connectivity of the subgenual cingulate region targeted with deep brain stimulation for treatment-resistant depression. Cerebr Cortex 2008;18 :1374–83.
[104] Lozano AM , Subcallosal cingulate gyrus deep brain stimulation for treatment-resistant depression. Biol Psychiatry 2008;64 :461–7.18639234
[105] Riva-Posse P , Defining critical white matter pathways mediating successful subcallosal cingulate deep brain stimulation for treatment-resistant depression. Biol Psychiatry 2014;76 :963–9.24832866
[106] Mayberg HS , Deep brain stimulation for treatment-resistant depression. Neuron 2005;45 :651–60.15748841
[107] Riva-Posse P , A connectomic approach for subcallosal cingulate deep brain stimulation surgery: prospective targeting in treatment-resistant depression. Mol Psychiatry 2017;23 :843–9.28397839
[108] Robertson J , Martin E , Cox B , Treeby BE . Sensitivity of simulated transcranial ultrasound fields to acoustic medium property maps. Phys Med Biol 2017;62 : 2559–80.28165334
