Biaxial driving can more efficiently convert electrical power to forward acoustic power in piezoelectric materials, and the interaction between the orthogonal electric fields can produce a combination of extensional and shear deformations as a function of the phase difference between them to allow dynamic steering of the beam with a single-element. In this study, we demonstrate for the first time the application of a single-element biaxially driven ring transducer in vivo for blood–brain barrier opening in mice, and compare it to that achieved with a conventional single-element highly focused (F# = 0.7) spherical transducer operating at a similar frequency. Transcranial focused ultrasound (0.45 MPa, 10 ms pulse length, 1 Hz repetition frequency, 30 s duration) was applied bilaterally to mice with a 40 μl/kg bolus of DefinityTM microbubbles, employing either a single-element biaxial ring (1.482 MHz, 10 mm inner diameter, 13.75 mm outer diameter) or spherical (1.5 MHz, 35 mm diameter, F# = 0.7; RK50, FUS Instruments) transducer on each side. Follow-up MRI scans (T1 pre- and post- 0.2 mmol/kg Gd injection, T2) were acquired to assess blood–brain barrier opening volume and potential damage. Compared to blood–brain barrier opening achieved with a conventional single-element spherical focused transducer, the opening volume achieved with a single-element biaxial ring transducer was 35% smaller (p = 0.002) with a device of a ring diameter of 40% the aperture size. Axial refocusing was further demonstrated with the single-element biaxial ring transducer, yielding a 1.63 mm deeper, five-fold larger opening volume (p = 0.048) relative to its small-focus mode. The biaxial ring transducer achieved a more localized opening compared to the spherical focused transducer under the same parameters, and further enabled dynamic axial refocusing with a single-element transducer with a smaller fabrication footprint.

Biomedical ultrasound is commonly produced by applying an oscillating electric field to a set of electrodes attached to faces perpendicular to the poling axis (propagation or P-electrodes) of a piezoceramic transducer. The ultrasound waves are generated by the mechanical deformation of the piezoceramic under the effect of the inverse piezoelectric effect. A different ultrasound generation by the piezoceramic can be obtained by applying 'biaxial' driving (Cole et al 2014, Pichardo et al 2015, Delgado et al 2021). This approach involves two sets of electrodes to produce two orthogonal electric fields: the first set attaches to faces perpendicular to the poling axis (P-electrodes), and the second set attaches to faces parallel or lateral to the poling axis (lateral or L-electrodes). Both have the same driving frequency. The interaction between the orthogonal electric fields produces a combination of extensional and shear deformations as a function of the phase difference between them, translating into the ability to dynamically steer the beam in prismatic-shaped piezoceramics (Delgado et al 2021) (figure 1(A)). The intensity of the lateral electric field further helps to control steering levels, where a steering angle of up to 30° has been demonstrated in prismatic-shaped transducers (Delgado et al 2021). This differs from traditional steering, accomplished with phased arrays by applying delays to elements based on time-of-flight to modify where the beam will converge (Hynynen and Jones 2016). A recent study demonstrated that biaxial driving is especially well-suited for a ring-shaped transducer configuration, given its axisymmetric configuration (Delgado et al 2023). It was observed that for a lead zirconate titanate (PZT) transducer with an inner diameter of 9.75 mm and a width of 2.0 mm, the biaxial driving produced controllable focusing with the ring transducer at its fundamental resonant frequency (482 kHz), as well as at its 3rd (1.362 MHz) and 5th (2.62 MHz) harmonics. In the case of ring-shaped transducers, the focus could be steered along the propagation axis (referred to in the present work as 'axial refocusing'). By adjusting the phase difference and power between P- and L-electrodes, the focal spot size could be reduced significantly; from 31.6 mm2 when using only P-electrodes to 3.4 mm2 when using biaxial driving at 482 kHz (Delgado et al 2023). The focal spot position can also be controlled (to the detriment of focal spot size) by applying different sets of power and phase between the electrodes (figure 1(B)). In essence, different phases produce a shift of the acoustic energy from being concentrated close to the transducer surface to moving farther away from it, while higher power supplied to the L-electrodes relative to the P-electrodes can reduce the focal area at the cost of reducing focal distance (figure 1(C)) (Delgado et al 2023). This ring-type biaxial transducer presents opportunities for addressing steering and efficiency issues with a smaller footprint for a new generation of fully steerable phased arrays. The dimensions of biaxial transducers achieved to date make them particularly suitable as single elements for small animal studies, or for assembly into an array format for clinical applications (Pichardo et al 2015, Delgado et al 2017, 2021, 2023).

Figure 1. Biaxial driving technique. (A) In a prismatic transducer, driving both the P- and L-electrodes steers the beam laterally. (B) In a ring transducer, driving both electrodes steers the focal spot position in the propagation direction. (C) In both approaches, the power and phase (ϕ) difference between the sinusoidal waveforms applied to the electrodes helps control steering levels.

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One application undergoing rapid development is the microbubble-mediated focused ultrasound-induced increase in blood–brain barrier permeability (Hynynen et al 2001, McMahon et al 2019, Meng et al 2019). Specialized vasculature of the blood–brain barrier prevents passage of over 98% of small-molecule drugs (Pardridge 2005) and nearly all large molecule drugs, significantly limiting the efficacy of drugs for the treatment of a variety of central nervous system diseases and disorders. Rather than re-engineering drugs for increased central nervous system penetration, focused ultrasound with intravenous microbubbles presents a minimally invasive approach to temporarily increase local blood–brain barrier permeability (McDannold et al 2012, O'Reilly et al 2017) while avoiding tissue and neuronal damage (Hynynen et al 2001). This new window of opportunity for drug delivery emerged into the clinic in 2015 and has since expanded with 16 trials worldwide (clinicaltrials.gov identifiers: NCT02253212, NCT04063514, NCT03616860, NCT04804709, NCT03322813, NCT04528680, NCT04417088, NCT04440358, NCT04446416, NCT02986932, NCT03739905, NCT04118764, NCT03119961, NCT03321487, NCT04370665, NCT03714243) (Carpentier et al 2016, Lipsman et al 2017, Abrahao et al 2019, Idbaih et al 2019, Mainprize et al 2019, Meng et al 2021).

In this study, we demonstrate the first in vivo application of a biaxial driving transducer for microbubble-mediated focused ultrasound-induced transient blood–brain barrier permeabilization in mice. We further compare blood–brain barrier permeability achieved with the single-element biaxial driving ring transducer (1.482 MHz, 13.75 mm outer diameter) to a more conventional single-element spherical focused transducer (1.5 MHz, 35 mm aperture diameter, F# = 0.7), and find more localized delivery is achievable with the biaxial transducer. Finally, we demonstrate axial refocusing capabilities of the single-element biaxial transducer in vivo.

2.1. Transducer fabrication and characterization

PZT composite was cut to a ring with an outer diameter of 13.75 mm, inner diameter of 10 mm, and height of 2.95 mm. The ring was secured on a 3D-printed resin cylindrical casing (28 mm diameter, 24 mm height; form 3, Formlabs) with epoxy (Epotek 301, Epotek Technologies), with a 1 mm shim stock and cork bed covering the base of the ring and air below as backing material. Two pairs of electrodes were placed following the propagation (P) and lateral (L) modes, respectively; with P-electrodes attached to the top and bottom faces of the ring perpendicular to the poling axis, and L-electrodes attached to the outer and inner walls of the ring lateral to the poling axis (figure 2). A vector network analyzer (ZVL3, Rohde and Schwarz) was used to determine the resonance frequency of the transducer (1.482 MHz). Both electrode sets were then matched to 50 Ω at the propagation resonance frequency.

Figure 2. Biaxial ring transducer driving. (A) Top view of the single-element ring biaxial driving transducer with dimensions, and blue and cyan lines indicating electrode pair placement. (B) Cross-sectional view of the biaxial ring transducer with electrode pairs. (C) Connection of lateral (L) electrodes, driving the inner and outer faces of the ring. (D) Connection of propagation (P) electrodes, driving the top and bottom faces of the ring. (E) Photograph of the biaxial ring transducer in its resin casing and cabling.

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Acoustic pressure characterization of the biaxial and spherical focused transducers was performed with a 0.2 mm diameter needle hydrophone (NH0200, Precision Acoustics, incertitude 15%) mounted on a robotic 3D positioner system (UMS3 scanning tank, Precision Acoustics) in a tank filled with deionized, degassed water. Scans in the XY plane (laterally) were acquired from −2 to 2 mm (where 0 = transducer center) in both axes with 0.25 mm steps. Scans in the XZ plane (axially) were acquired from −1 to 1 mm laterally and from 2 to 11 mm (biaxial driving transducer) or from 20.75 to 29.75 mm (spherical focused transducer) axially with 0.25 mm steps.

For the single-element biaxial ring transducer, power was applied to the P- and L-electrodes in either a 1:1 or 1:1.5 ratio, respectively, as measured with a power meter at phase 0°. Measured applied voltages were then kept constant for all phase shifts. The biaxial transducer was driven with a 1.482 MHz sine wave with 10 cycle pulses at 100 Hz applied to both electrodes, with a 1:1 or 1:1.5 power ratio at the P- and L-electrodes, respectively. Acoustic pressure maps were obtained for a range of phase shifts from 0° to 315° in 45° increments (with additional measurements at 150° and 165°) to assess focal point and area shifts. Pressure calibration was then conducted with a 1:1.5 P- to L-electrode power ratio at a 270° phase shift for 'small-focus' mode use, and with a 1:1 P- to L-electrode power ratio at a 165° phase shift for the maximum focal distance and area shift (for maximal focal adjustments in 'large-focus' mode). The single-element spherical focused transducer (FUS Instruments) was made of PZT material to be focused with F# = 0.7, a diameter of 35 mm, operating at 1.5 MHz. This transducer was characterized with application of a 1.5 MHz sine wave with 10 cycle pulses at 100 Hz. For in vivo experimentation, both the single-element spherical transducer and single-element biaxial ring transducers were compatible and integrated with a stereotactic navigation unit used for small-animal experimentation (RK50, FUS Instruments).

2.2. Animal preparation

All procedures involving animals were carried out under an approved protocol in accordance with the guidelines and regulations of the University of Calgary's Animal Care Committee. C57Bl/6 mice (n = 8, age 9–10 weeks, 25.3 ± 3.3 g, Charles River Laboratories) were anesthetized and maintained at surgical depth with isoflurane (5% induction, 2% maintenance) using oxygen as the carrier gas. Tail veins were cannulated using a 27 G catheter. The scalp of the animal was then shaved, and remaining hair was removed with depilatory cream to avoid air bubbles and ensure coupling. Mice were then positioned prone on a heating pad to maintain a core body temperature of 37 °C as monitored and controlled by a rectal thermistor (RightTemp® Jr. Homeothermic Control Module, Kent Scientific Corp.) and placed under the transducer of the small-animal stereotactic navigation unit (RK50, FUS Instruments). Mice were then aligned and fixed in place with a bite bar and ear bars (figure 3). Lidocaine analgesic was then applied to the scalp and allowed to absorb for 5 min, at which point a scalpel was used to make an incision in the skin on the scalp along the midline. Lambda and bregma on the skull were then identified and utilized as reference points in the stereotactic navigation unit. A deionized, degassed water chamber with a polyimide membrane was then coupled to the skull with ultrasound gel from below, and the transducer was immersed from above into the water for treatment.

Figure 3. Brain atlas-guided focused ultrasound setup. (A) Top view schematic of animal setup in the RK50 atlas-based focused ultrasound system, utilizing (B) a single-element spherical transducer or (C) a single-element biaxial ring transducer. (D) Side view of animal setup demonstrating placement of transducers. (E) Screenshots from the atlas-based software showing the target selected in the atlas (above) and MR-based (Allen Mouse MRI dataset) orthogonal views (below) of the selected target, indicated by the cyan ellipses.

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Focused ultrasound was applied using a small-animal stereotactic navigation system (RK50, FUS Instruments) that utilizes the Allen Mouse Brain Atlas co-registered with the identified lambda and bregma points as well as the focus of the transducer: in this study, either the single-element focused spherical transducer or the single-element biaxial ring transducer was employed. When the focused spherical transducer was utilized, the RK50 system's power amplifier (RK50, FUS Instruments) was used. When the biaxial ring transducer was employed, each electrode was driven with a 43 dB RF power amplifier (UltraX-20, E&I Ltd) after being attenuated by 20 dB. The hippocampal formation (field CA1, stratum lacunosum-moleculare) was targeted bilaterally, with the single-element focused spherical transducer on one side and the single-element biaxial ring transducer contralaterally (n = 8 mice). The offset from the brain was adjusted to account for the different focal depths of each transducer such that the same region was targeted. Treatments were applied with one transducer at a time in a randomized order upon microbubble injection and were staggered by 15 min to ensure clearance of the prior injectate.

For treatment, DefinityTM microbubbles were activated in a VialMix for 45 s at room temperature and allowed to passively cool for 15 min Prior to each treatment, the vial of microbubbles was gently resuspended and allowed to decant for 2 min prior to extracting 50 μl with an 18 G blunt needle. Microbubbles were then diluted in saline for intravenous injection at a dosage of 40 μl kg−1 in a 50 μl bolus, followed by a 100 μl saline flush through the catheter. Upon completion of the saline flush (∼10 s post microbubble injection), focused ultrasound was delivered at the center frequency of the transducer (1.5 MHz for the spherical transducer, 1.482 MHz for the biaxial transducer) in 10 ms pulses with a pulse repetition frequency of 1 Hz for 30 s, at a fixed pressure of 0.45 MPa (free-field hydrophone measurement). The biaxial transducer was utilized with a 1:1.5 power ratio applied to the P- and L-electrodes, respectively, with a 270° phase shift.

2.4. Axial refocusing

For a subset of mice (n = 3), only the biaxial ring transducer was utilized to demonstrate its dynamic axial refocusing capabilities. Here, the same injection regimen was applied: microbubbles were injected intravenously at a dosage of 40 μl/kg in a 50 μl bolus, followed by a 100 μl saline flush through the catheter. Upon completion of the saline flush (∼10 s post microbubble injection), focused ultrasound was delivered at 1.482 MHz in 10 ms pulses with a pulse repetition frequency of 1 Hz for 30 s, at a fixed pressure of 0.45 MPa (free-field hydrophone measurement). The cortex (primary somatosensory area, layer 6a) was targeted bilaterally, using the stereotactic navigation system (utilizing the Allen Mouse Brain Atlas co-registered with the identified lambda and bregma points) to place the transducer above the target in the same coordinates on each side. The biaxial transducer was operated in its small-focus mode (1:1.5 power ratio applied to the P- and L-electrodes, respectively, with a 270° phase shift) on one side, and with a shift in power and phase contralaterally: to demonstrate the largest focal area and depth increase, a large-focus mode was tested with a 1:1 power ratio applied to the P- and L-electrodes respectively, with a 165° phase shift. To achieve 0.45 MPa in small-focus mode, the voltages applied to the P- and L-electrodes were 0.715 and 1.044 Vpp, respectively, prior to a power gain of 23 dB. To achieve 0.45 MPa in large-focus mode, the voltages applied prior to the power gain to the P- and L-electrodes were 4.095 and 4.88 Vpp, respectively.

2.5. Magnetic resonance (MR) imaging

A series of MR images were acquired following sonication to assess treatment efficacy and safety. Following focused ultrasound treatments, mice were removed from the small-animal stereotactic navigation ultrasound system and transferred to a small-animal MR-compatible cradle with an air heater system (SA Instruments), and isoflurane anesthesia was maintained. Animals were positioned prone on the cradle with the head fixed with a bite bar and ear bars, and small-animal MR-compatible monitoring system (Model 1025, SA Instruments) respiratory sensor and rectal thermistor were placed. The cradle was then transferred to a 9.4 T MRI (BioSpec, Bruker). Pre- and post-contrast (0.2 mmol/kg Gadolinium, Bayer Inc.) T1-weighted MR images (3D FLASH sequence, 25 ms repetition time, 3.2 ms echo time, 15° flip angle, 1.44 × 1.44 × 0.96 cm3 FOV, 0.1 × 0.1 × 0.1 mm3 voxel size) were acquired to assess blood–brain barrier integrity. T2-weighted MR imaging (RARE sequence, 24 ms repetition time, 4000 ms echo time, 1.92 × 1.92 cm2 FOV, 0.5 mm slice thickness, 0.075 × 0.075 × 0.5 mm3 voxel size) was then acquired to identify potential edema and hemorrhage.

2.6. Data analysis

In Python (3.9), Dicomifier (Lamy Revision c8b3caf1, https://github.com/lamyj/dicomifier) was used to convert Bruker MRI data to NIfTI files for further analysis. Pre- and post- contrast enhanced T1-weighted images were co-registered using the ITKElastix toolbox, and the pre-contrast images were subtracted from the post-contrast enhanced images. To evaluate the effect of contrast enhancement, a standardization map was then obtained by dividing the subtracted images by the pre-contrast-enhanced images (Lee 2019). Standardized datasets were then further analyzed in 3D Slicer (5.2.1, slicer.org, (Fedorov et al 2012)) by segmenting the perfused region (indicating blood–brain barrier opening) with level tracing, slice-by-slice. A semi-automated approach was used, where naturally perfused regions (e.g. ventricles) and edges (where motion could cause artefacts) were manually avoided. The volume of blood–brain barrier opening was then computed from the number of perfused voxels multiplied by the volume of a single voxel. Measured opening volumes were compared for statistical significance with t-tests. The depth of focal blood–brain barrier opening was determined from the centroid of the segmented blood–brain barrier opening volume. Blood–brain barrier opening segmentation masks were then overlayed with the co-registered T2-weighted images and assessed for hyperintensities indicative of edema.

3.1. Transducer characterization

Figure 4 shows the normalized acoustic pressure field of the single-element biaxial ring transducer when applying power to only the P-electrode, or when applying a 1:1 or 1:1.5 power ratio to the P- and L-electrodes, respectively, and sweeping through phase shifts. The single-element biaxial ring was found to have a beam of (−6 dB) dimensions 0.74 mm (lateral) by 5.70 mm (axial), with a maximum cross-sectional area of 3.25 mm2 at a focal point of 7.35 mm axially from the transducer when driven in its small-focus mode (1:1.5 power ratio applied to the P- and L-electrodes, respectively, with a 270° phase shift (figure 5(A)). When utilized in its large-focus mode (1:1 power ratio applied to the P- and L-electrodes, respectively, with a 165° phase shift) to demonstrate the largest focal area and depth, the beam was found to have dimensions (−6 dB) of 1.01 mm (lateral) by 11.42 mm (axial), with a maximum cross-sectional area of 8.47 mm2 at a focal point of 10.8 mm axially from the transducer (figure 5(B)).

Figure 4. Biaxial ring transducer characterization. (A) Normalized pressure maps displaying contours (up to −28 dB) of the biaxial ring transducer pressure focus (axial) when operating with the P-electrode only, or with differing phase shifts with a 1:1.5 power ratio (top) or a 1:1 power ratio (bottom) applied to the P- and L- electrodes, respectively. A cross-sectional view sketch of the biaxial ring transducer is included to clarify origin and direction of the beam, where Z = 0 is the surface of the transducer. (B) Axial distance of the focus when operating with a 1:1.5 or 1:1 power ratio on the P- and L- electrodes as a function of phase. (C) Maximum cross-sectional beam focal area (−6 dB) when operating with a 1:1.5 or 1:1 power ratio on the P- and L- electrodes as a function of phase.

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Figure 5. Comparison of transducer beam profiles for study parameters. (A) Axial (top) and orthogonal (at the focus centroid; bottom) pressure maps displaying power contours (up to −28 dB) of the biaxial ring transducer operating with a 1:1.5 power ratio on the P- and L- electrodes respectively, with a 270° phase shift for its small-focus mode used in this study. (B) Axial (top) and orthogonal (at the focus centroid; bottom) pressure maps of the biaxial ring transducer operating with a 1:1 power ratio on the electrodes, with a 165° phase shift for the maximum focal distance and area shifts (large-focus mode). (C) Axial (top) and orthogonal (at the focus centroid; bottom) pressure maps of the single-element focused spherical transducer used for comparison in this study. Note that Z = 0 is the surface of the transducer.

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The single-element focused spherical transducer (1.5 MHz, 35 mm element diameter, F# 0.7; FUS Instruments) was found to have a beam of (−6 dB) dimensions 0.98 mm (lateral) by 5.46 mm (axial), with a maximum cross-sectional area of 4.15 mm2 at a focal point of 25.5 mm axially from the transducer (figure 5(C)). Focal spot metrics of the biaxial transducer driven in small- and large-focus modes, as well as the focused spherical transducer are summarized in table 1.

Table 1. Focal spot metrics of the biaxial transducer (1.482 MHz, 13.75 mm outer diameter, 10 mm inner diameter, 2.95 mm thickness) in small- (7.35 mm focal depth) and large- (10.8 mm focal depth) focus modes, and of the focused spherical transducer (1.5 MHz, 35 mm diameter, F-number 0.7, 25.5 mm focal depth). The axial cross-sectional area, lateral and axial dimensions, and calculated ellipsoid volume metrics are provided.

TransducerMetric−1 dB−2 dB−3 dB−6 dB−7 dB−8 dB−9 dBBiaxial (small focus)Area (mm2)0.310.921.483.253.824.324.87 Width (mm)0.220.410.520.740.810.840.89 Length (mm)2.213.003.715.706.046.617.08 Volume (mm3)0.050.260.521.622.092.442.91Biaxial (large focus)Area (mm2)1.272.554.058.479.5210.5711.45 Width (mm)0.420.580.741.011.111.201.29 Length (mm)4.075.727.1011.4211.7011.9212.17 Volume (mm3)0.381.012.026.127.589.0310.59SphericalArea (mm2)0.631.391.994.154.785.556.84 Width (mm)0.390.590.650.981.031.101.12 Length (mm)2.173.093.945.465.986.488.28 Volume (mm3)0.180.560.882.723.294.115.463.2. Blood–brain barrier opening

MR images indicate treatment efficacy and safety (figure 6). Successful increase in blood–brain barrier permeability was determined by leakage of gadolinium in contrast-enhanced T1-weighted images. With the single-element spherical transducer, the average blood–brain barrier opening volume was 3.78 ± 0.84 mm3, while a statistically significant 35% smaller (p = 0.002) opening of 2.46 ± 0.62 mm3 was achieved with the single-element biaxial ring transducer. As an indication of safety, there was little or no evidence of edema in T2-weighted images (with 1 mouse exhibiting minor edema in the cortex).

Figure 6. Blood–brain barrier opening transducer comparison. (A) T1-weighted pre-contrast orthogonal images with the spherical focused transducer treatment on the left and biaxial driving transducer treatment on the right. (B) Post-contrast T1-weighted images depicting blood–brain barrier opening. (C) Subtracted and standardized T1-weighted skull-stripped images depicting blood–brain barrier opening. (D) Contoured blood–brain barrier opening regions overlayed on the standardized images (sample slice displayed). (E) T2-weighted image to assess for possible edema following ultrasound treatments. (F) Box and whisker plot comparing blood–brain barrier opening volume achieved with the single-element focused spherical transducer and the single-element biaxial ring transducer. ** = p < 0.01.

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A comparison of blood–brain barrier opening when applying biaxial driving in its small-focus mode in the present study, with a 1:1.5 power ratio applied to the P- and L-electrodes respectively with a 270° phase shift, compared to steering for its largest focal area and depth (with a 1:1 power ratio applied to the P- and L-electrodes respectively, with a 165° phase shift) can be found in figure 7. The small-focus biaxial driving resulted in an average blood–brain barrier opening volume of 2.06 ± 0.67 mm3, while the large-focus mode resulted in a five-times larger (p = 0.048) opening of 10.54 ± 3.45 mm3 with an average depth of focal opening 1.63 mm deeper. With both small and large focus mode driving of the biaxial ring transducer, no evidence of edema was found in T2-weighted images.

Figure 7. Biaxial transducer beam steering. (A) T1-weighted pre-contrast orthogonal images with the biaxial driving transducer treatment operating in small-focus mode on the left, and in maximal steering large-focus mode on the right. (B) Post-contrast T1-weighted images depicting blood–brain barrier opening. (C) Subtracted and standardized T1-weighted skull-stripped images depicting blood–brain barrier opening. (D) Contoured blood–brain barrier opening regions overlayed on the standardized images (sample slice displayed). (E) T2-weighted image to assess for possible edema following ultrasound treatments. (F) Box and whisker plot comparing blood–brain barrier opening volume achieved with the single-element biaxial ring transducer in its small-focus mode and with maximal steering in large-focus mode. * = p < 0.05.

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This study demonstrated the first in vivo application of a biaxial driving transducer, for microbubble-mediated focused ultrasound-induced blood–brain barrier opening in mice. Blood–brain barrier opening achieved with a single-element biaxial driving ring transducer was found to be 35% smaller in volume than that achieved with a conventional single-element spherical focused transducer (figure 6(F)). We note that the single-element biaxial driving transducer was fabricated to have a similar center frequency and a casing of similar size as the spherical transducer to facilitate its mounting and use within the small-animal stereotactic navigation unit (RK50, FUS Instruments), but that other biaxial driving transducers have been characterized and tested in silico and in vitro to demonstrate feasibility and efficacy of the technique (Cole et al 2014, Pichardo et al 2015, Delgado et al 2017, 2021, 2023). Importantly, biaxial driving has also been found to reduce side lobes compared to conventional driving (Delgado et al 2023), and no significant side lobes were detected here (figure 5). It is further worth emphasizing that the biaxial transducer used here has an outer ring diameter of 40% of the aperture size of the highly focused (F# = 0.7) spherical transducer yet produced a smaller opening volume. If the spherical transducer were of the same diameter as the biaxial ring transducer with the same focal length, the focal spot would be twice as long, which is significant at the scale of the murine brain. As another comparison, it is useful to consider the biaxial transducer being operated with only the P-electrodes. This would effectively render it a standard ring transducer of identical dimensions. In this case, performance would be similar to the small-focus mode (with a slightly larger focal area and focal distance as in figure 4), albeit with a lower efficiency and without the ability to refocus axially. Single-element axial refocusing (a form of partial beam steering) was further demonstrated with the biaxial ring transducer, yielding up to a 1.63 mm deeper, five-fold larger opening volume relative to its small-focus mode (figure 7(F)). These opening volumes follow the benchtop-characterized beam sizes to approximately −7 dB (table 1). This notably corresponds to a lower pressure limit of ∼0.2 MPa, with similar pressure thresholds for blood–brain barrier opening being reported in the literature (Hynynen et al 2006, McDannold et al 2006, 2007, Baseri et al 2010).

There is a notably large parameter space that impacts blood–brain barrier opening, including the sonication parameters (frequency, pressure, pulse length, pulse repetition frequency, exposure duration) (McDannold et al 2008, Chopra et al 2010, Choi et al 2011), contrast agent (agent type, dose, and size distribution) (McDannold et al 2007, Choi et al 2010, Samiotaki et al 2012, McMahon and Hynynen 2017, Bing et al 2018), and anesthesia administration (Itani and Mattrey 2011, McDannold et al 2017). The approach is further complicated by inter- and intra-subject biological variability in skull transmission efficiency (Fry and Barger 1978, Pichardo et al 2011) and local target vasculature (density, diameter, flow rate) (Sassaroli and Hynynen 2005, McDannold et al 2012, Nhan et al 2013, Hosseinkhah et al 2015, Poon et al 2021, Katz et al 2023). In this study, the ultrasound parameters and microbubble dose were not varied, but were in range of previous blood–brain barrier opening preclinical studies (Baseri et al 2010, Bing et al 2018, Kovacs et al 2018, Meng et al 2019, Poon et al 2021). In addition, acoustic monitoring and control were not implemented. The geometry of the biaxial ring transducer is favorable for monitoring, allowing the central area for receiver placement. Acoustic feedback control based on microbubble activity is perhaps the most promising approach to 'dosing' blood–brain barrier opening, particularly given the aforementioned parameter variability that can affect its efficacy and safety profile (McMahon et al 2019, Meng et al 2019), and will be integrated into future studies.

The small footprint of biaxial transducers yet maintained ability for high efficiency and axial refocusing with a single element presents opportun