Effects of pulse repetition frequency on bubble cloud characteristics and ablation in single-cycle histotripsy

Objective. Histotripsy is a cavitation-based ultrasound ablation method in development for multiple clinical applications. This work investigates the effects of pulse repetition frequency (PRF) on bubble cloud characteristics and ablative capabilities for histotripsy using single-cycle pulsing methods. Approach. Bubble clouds produced by a 500 kHz histotripsy system at PRFs from 0.1 to 1000 Hz were visualized using high-speed optical imaging in 1% agarose tissue phantoms at peak negative pressures, p-, of 2–36 MPa. Main results. Results showed a decrease in the cavitation cloud threshold with increasing PRF, ranging from 26.7 ± 0.5 MPa at 0.1 Hz to 15.0 ± 1.9 MPa at 1000 Hz. Bubble cloud analysis showed cavitation clouds generated at low PRFs (0.1–1 Hz) were characterized by consistently dense bubble clouds (41.7 ± 2.8 bubbles mm−2 at 0.1 Hz), that closely matched regions of the focus above the histotripsy intrinsic threshold. Bubble clouds formed at higher PRFs measured lower cloud densities (23.1 ± 4.0 bubbles mm−2 at 1000 Hz), with the lowest density measured for 10 Hz (8.8 ± 4.1 bubbles mm−2). Furthermore, higher PRFs showed increased pulse-to-pulse correlation, characteristic of cavitation memory effects; however, bubble clouds still filled the entire volume of the focus due to their initial density and enhanced bubble expansion from the restimulation of residual nuclei at the higher PRFs. Histotripsy ablation assessed through lesion analysis in red blood cell (RBC) phantoms showed higher PRFs generated lesions with lower adherence to the initial focal region compared to low PRF ablations; however, no trend of decreasing ablation efficiency with PRF was observed, with similar efficiencies observed for all the PRFs tested in this study. Significance. Notably, this result is different than what has previously been shown for shock-scattering histotripsy, which has shown decreased ablation efficiencies at higher PRFs. Overall, this study demonstrates the essential effects of PRF on single-cycle histotripsy procedures that should be considered to help guide future histotripsy pulsing strategies.


Introduction
Histotripsy is a non-thermal focused ultrasound ablation method that utilizes the precise control of acoustic cavitation to mechanically disintegrate soft tissue (Bader et al 2019, Xu et al 2021).Tissue destruction in histotripsy is caused by very large strains applied at high strain rates by expanding and collapsing cavitation bubbles (Vlaisavljevich et al 2016a, Mancia et al 2017).For single-cycle histotripsy treatments, the region in which these cavitation bubbles can occur is tightly controlled by manipulating the sound field using focused ultrasound with multiple prior studies showing that cavitation is limited to regions where the peak negative pressure, p-, exceeds the histotripsy intrinsic threshold of ∼25-28 MPa (Lin et al 2014, Vlaisavljevich et al 2015a, Xu et al 2021).By precisely controlling the region in which the pressure exceeds the cavitation threshold, a millimeter-scaled three-dimensional volume can be subjected to histotripsy-induced damage (Lin et al 2014, Edsall et al 2021).Furthermore, by translating the focal region either electronically (Lundt et al 2018) or by robotically maneuvering the transducer array (Vlaisavljevich et al 2013, Lundt et al 2017, Smolock et al 2018), histotripsy systems can be used to create larger volumetric lesions.Histotripsy is currently being developed for multiple applications in clinical and pre-clinical stages (Xu et al 2021, Vidal-Jove et al 2022).
Clinical development of histotripsy has motivated many prior studies of the cavitation dynamics involved in the ablation process, particularly for pulsing methods applied at low pulse repetition frequencies (PRFs) (Maxwell et al 2013, Vlaisavljevich et al 2015b, Lundt et al 2017).Using high-speed photography, the mechanism behind histotripsy cavitation dynamics has been explored in optically clear tissue-mimicking environments, such as gelatin or agarose tissue phantoms (Maxwell et al 2010, Vlaisavljevich et al 2016a, Edsall et al 2021).Early studies applying multi-cycle pulses to tissue-mimicking gel phantoms showed that the dense histotripsy cavitation clouds were produced from backscattering of the positive pressure wave scattering from an initial cavitation bubble generated at the focus of the transducer (Maxwell et al 2011b).Building on these findings as well as improvements in histotripsy transducer technology (Kim et al 2014), subsequent studies developed single-cycle intrinsic threshold pulsing strategies in which cavitation bubble clouds are nucleated directly from the incident negative pressure phase of the pulse, allowing for more precise and consistent histotripsy treatments (Maxwell et al 2013, Lin et al 2014).More recent studies have characterized the effects of other properties on intrinsic threshold histotripsy bubble cloud behavior including temperature (Vlaisavljevich et al 2016b), transducer f-number (Vlaisavljevich et al 2017) and center frequency (Edsall et al 2021), with results showing that histotripsy ablation consistently occurs only in the regions exposed to the cavitation bubbles.Furthermore, these studies demonstrate that the ablation efficiency (number of pulses required to ablate a targeted region of the tissue), is dependent upon the density of the bubbles within the cloud and the expansion of the bubbles.These studies provide an understanding of the physics underlying the nucleation and dynamics involved with histotripsy and have been essential to the ongoing development of histotripsy for specific clinical applications.However, the reliance on pulsing at low PRFs has been a critical limitation of these studies since low PRF pulsing provides a controlled condition for studying histotripsy but does not replicate the pulsing conditions that are practical for clinical use.
Translation of histotripsy into a clinical ablation method often requires rapid volumetric ablation to apply the therapy within a reasonable treatment time.Although multiple strategies have been investigated to increase the rate of volumetric ablation in histotripsy, such as the use of electronic focal steering methods (Lundt et al 2017, Lundt et al 2018), the most straightforward approach to reducing treatment time is to increase the therapy PRF.The effects of PRF on shock-scattering histotripsy have been explored and provide evidence that higher PRF treatments are faster, but less precise, less controllable, and less efficient than lower PRF treatments (Wang et al 2012).Specifically, decreases in the cavitation threshold and significant increases in off-target cavitation were observed in higher PRFs (Shi et al 2018).Furthermore, a seminal paper by Wang et al demonstrated that, as PRF increased, the spatial correlation of nucleation events increased for subsequent pulses (Wang et al 2012).This effect, termed 'the cavitation memory effect', is defined as the re-stimulation of residual cavitation nuclei left behind after the antecedent pulse.Because of increased memory effects, higher PRF treatments have been consistently shown to require significantly more pulses to ablate the focal area in shock-scattering histotripsy (Wang et al 2012, Duryea et al 2015, Shi et al 2018).Prior works investigating single-cycle histotripsy for volumetric tissue ablation have suggested there will be similar memory effects and trends in ablation efficiency (Lundt et al 2017, Lundt et al 2018).However, the effects of PRF on single-cycle histotripsy have not been well explored in controlled studies.
Here, we systematically characterize the bubble cloud characteristics and ablation for single-cycle histotripsy across a broad range of PRFs.The effects of PRF were quantified using high-speed optical imaging of bubble clouds generated from single-cycle 500 kHz histotripsy pulses applied to agarose tissue phantoms.Three aspects of histotripsy cavitation were assessed to better quantify the effects of PRF on single-cycle histotripsy.First, a series of tests were performed to determine the effect PRF has on the histotripsy cavitation cloud threshold.Second, a series of experiments were performed to determine the changes in the reiterative bubble cloud dynamics.These experiments characterized multiple features of the histotripsy cavitation clouds including bubble cloud area, bubble cloud density, bubble size, and pulse-to-pulse spatial correlation of bubbles.In a third set of experiments, the effects of PRF on ablation precision and efficiency were assessed inside tissue-mimicking phantoms containing a layer of red blood cells (RBCs).Based on prior work, we hypothesized that increasing PRF would lead to increased cavitation memory effects, reduced bubble cloud density, decreased ablation precision, and decreased ablation efficiency.

Experimental setup and histotripsy transducer calibration
Histotripsy treatments were performed inside 1% agarose gel phantoms (Type VII-A, Sigma Aldrich Corporation, St. Louis, MO, USA) using a custom 32-element, 500 kHz histotripsy transducer with a geometric focus of 75 mm, transverse and elevational aperture sizes of 128 mm and 112 mm, respectively, and f-numbers of 0.61 (transverse) and 0.71 (elevational).Figure 1(a) illustrates the experimental setup in which the histotripsy transducer was driven by a custom high-voltage pulser designed for single cycle therapy pulses, controlled by a field-programmable gate array (FPGA) board (Altera DE0-Nano Terasic Technology, Dover, DE, USA) connected to a desktop computer with MATLAB 2017a (The MathWorks, Natick, MA, USA).The transducer was mounted to a fixed rod attached to a custom 3D positioning system that steered agarose gel phantoms into the focus of the transducer (figure 1(b)).
The −6 dB focal dimensions of the 500 kHz transducer were measured by a rod hydrophone (HNR-500, Onda Corp, Sunnyvale, CA, USA) to be 7.0 × 2.0 × 2.0 mm.The acoustic waveforms produced by the therapeutic transducer at the focus were measured in a free field using a custom fiber optic probe hydrophone (FOPH) (Parsons et al 2006).Figure 2(a) shows an example histotripsy pulse produced by the 500 kHz transducer with a single large negative pressure phase characteristic of intrinsic threshold histotripsy.Additionally, figure 2(b) shows a two-dimensional grid scan of the sound field taken in the focal plane.2.2.High-speed imaging setup Cavitation was visualized using high-speed optical imaging inside optically clear agarose gel phantoms with two different imaging systems.A high-speed camera (miniAX100, Photron USA, San Diego, CA) operated with a 100 mm lens at 1:1 (Mulvus 100 mm f/2M ZF.2 Macro Lens, Zeiss, Jena, Germany) and a 48 mm extension tube was used for cavitation thresholding imaging.The image resolution was 1024 × 1024 with a pixel size of 15 μm/pixel.In a second set of experiments, a faster high-speed camera (Nova S12 monochrome, Photron USA, San Diego, CA) with an 85 mm lens at 3:1 (Mitakon Zhongyi Creator 85 mm f/2.8 1-5x Super Macro Lens) was used to assess bubble cloud characteristics and ablation inside clear agarose gel phantoms.The image resolution was set to 512 × 1024 with a pixel size of 8.5 μm/pixel.Both setups used the same high-intensity light array (GS Vitec Multi-LED QT Light, MultiLED G8 controller, 320 W power supply, Soden-Salmünster, Germany).Cameras were mounted to a scissor jack fixed to the observation table at a set distance from the water tank for repeatable setups (figure 1(b)).

Cavitation threshold analysis
The effect PRF has on the cavitation threshold for single-cycle histotripsy was tested using a previously defined method (Maxwell et al 2010, Vlaisavljevich et al 2016a, Edsall et al 2021).In summary, 100 pulses were delivered to 1% agarose gel phantoms (n = 3) at varying peak negative pressures (0-35 MPa, +2 MPa intervals) for a wide range of PRFs (0.1, 1, 10, 100, and 1000 Hz).Using the Photron miniAX100 camera setup, single image capture was triggered by the FPGA controller board 10 μs after pulse arrival for every histotripsy pulse to allow for complete bubble nucleation throughout the entire focal zone (Vlaisavljevich et al 2015a, Edsall et al 2021).Following a previously outlined analysis, image thresholding was used to identify regions of cavitation formation in each image (Maxwell et al 2010, Vlaisavljevich et al 2016a, Edsall et al 2021).For each PRF, the probability that cavitation will be observed during a single pulse was modeled using a sigmoidal function with respect to peak negative pressure (Maxwell et al 2011b, Vlaisavljevich et al 2017, Edsall et The cavitation threshold for each PRF (p t_0.1Hz , p t_1Hz , p t_10Hz , p t_100Hz , and p t_1000Hz ) was defined as the pressure at which the probability that cavitation will be observed in 50% of pulses.The transition variable, σ, is set to give the difference in pressure where the probability changes from approximately 15% to 85%.Additionally, p − min , was defined as the minimum pressure at which the probability of observing cavitation was greater than zero.Curve fits and plots were generated in MATLAB.Student's t-tests were performed using Excel (Microsoft 365, Excel, Microsoft Corporation, Redmond, Washington, USA) to determine significance (α = 0.05) between p t , σ, and p − min .A subsequent Wald-Wolfowitz runs test for randomness (Gibbons and Chakraborti 2011) was performed for all samples and PRFs in MATLAB to determine if cavitation events were isolated observations or if there was a pulse-to-pulse dependence in the observation of cavitation events.Since these tests were focused on samples that had observable cavitation only on a portion of pulses, this analysis was not conducted for cases in which cavitation occurred, or did not occur, on nearly every pulse.As such, samples with <5% of pulses with observable cavitation and samples with observable cavitation in >95% of pulses were eliminated from the analysis

Bubble cloud characteristics analysis
In a second set of experiments, the effects PRF has on bubble cloud characteristics for single-cycle histotripsy were investigated.For each PRF (0.1, 1, 10, 100, and 1000 Hz), 100 pulses were delivered to 1% agarose gel phantoms (n = 6) at a p-of 35 MPa.Using the Photron Nova S12 high-speed camera, single image capture was triggered by the FPGA controller board at 6.5 and 52 μs after pulse arrival to visualize the bubble clouds immediately after the full cloud was nucleated as well as a corresponding image of the cloud after significant bubble expansion had occurred.Images were converted to binary and analyzed using an algorithm, written in MATLAB, for bubble cloud characteristics (Edsall et al 2021) and pulse-to-pulse spatial correlation of pixels (Shi et al 2018) (figure 3).For every image, individual bubble centroids, bubble radii, total binarized cloud area, and cloud density (bubbles/mm 2 ) were quantified.It is important to note that the bubble cloud characteristics analysis had difficulty distinguishing bubbles in cases of densely packed clouds with expanding bubbles overlapping each other.Due to this effect, in dense bubble clouds, overlapping bubbles could have been grouped leading to a potential underestimation of the cloud density and an overestimate in the mean bubble diameter.This effect is demonstrated in the high PRF cases in figure 3.In addition to characterizing the bubble cloud for each pulse, a Pearson correlation coefficient of positive pixels was generated between subsequent pulses, using a priorly specified method (Shi et al 2018), to determine the effects PRF has on the degree of memory effect in treatments.Each characteristic described above was plotted as a function of pulse number for each PRF using MATLAB.The statistical analysis for bubble cloud characteristics was performed in Excel, where Student's t-tests were used to determine significance (α = 0.05).

RBC ablation analysis
In a final set of experiments, high-speed imaging was used to visualize the effects PRF has on ablation for singlecycle histotripsy.For each PRF (0.1, 1, 10, 100, 1000 Hz), 500 pulses were delivered to a thin layer of red blood cells (RBCs) encapsulated in 1% agarose gel phantoms (n = 4) at 35 MPa.Using the Photron Nova S12 camera setup, single image capture was triggered by the FPGA controller board at 6.5, 52, and 900 μs after pulse arrival to visualize full cloud formation, corresponding expansion, and the resulting lesion for every histotripsy pulse.Lesion images were binarized and image thresholding was used to determine the total lesion area.Ablation efficiency for each test was calculated by normalizing the lesion area at each pulse by the area of the bubble cloud from pulse #1, which is assumed to be the central cross-sectional plane of the focus.The statistical analysis for ablation efficiency was performed in Excel, where Student's t-tests were used to determine significance (α = 0.05).The total ablated area and ablation efficiency were plotted for each PRF as a function of pulse number using MATLAB.

Effects of PRF on the cavitation threshold
In the first set of experiments determining the effects PRF has on the cavitation threshold, results showed that the minimum pressure required to generate histotripsy bubble clouds decreased for higher PRFs. Figure 4 shows example images of cavitation generated in agarose phantoms after the 100th pulse for each PRF at pressures ranging from 18 to 32 MPa.For 0.1-10 Hz, isolated cavitation events were detected in <5% of pulses at pressure levels of ∼20-22 MPa, with these sub-threshold cavitation events only lasting for a single pulse or a few pulses without forming a larger cavitation cloud on subsequent pulses.The results of the sigmoidal function for the cavitation threshold, p t , for each PRF along with associated σ and p - min values for each condition are given in table 1.There were no observable trends in the minimum pressure in which cavitation was observed across PRFs.The fitted curves for 0.1 Hz samples (figure 5(a)) showed characteristic intrinsic threshold curves where p t_0.1Hz and σ 0.1Hz equaled 26.7 ± 0.5 MPa and 2.9 ± 0.80 MPa, respectively.As the PRF was increased to 1 Hz and 10 Hz (figure 5(b/c)), results showed no significant difference between p t_1Hz (26.2 ± 1.3 MPa) and p t_10Hz (26.0 ± 1.8 MPa) with p t_0.1Hz (p = 0.52 and p = 0.56, respectively).At the highest PRFs tested in this study (figure 5(d/e)), results showed that cavitation events were more often observed at significantly lower pressures for 100 and 1000 Hz in comparison with 0.1 Hz, yielding a cavitation threshold of p t_100Hz = 21.5 ± 1.3 MPa and p t_1000Hz = 15.0 ± 1.6 MPa, respectively (p < 0.05).There was an observed increase in σ 1Hz (4.2 ± 0.79 MPa), σ 10Hz (3.6 ± 1.60 MPa), σ 100Hz (3.9 ± 2.9 MPa), and σ 1000Hz (5.1 ± 2.24 MPa) in comparison with σ 0.1Hz (2.9 ± 0.8 MPa), but these differences were not significant due to large deviations between samples in the higher PRFs.It is worth noting that the cavitation threshold seemed to converge to the p − min as the PRF increased to 1000 Hz.Specifically, from table 1, p t and p - min showed a significant difference at PRFs of 0.1-100 Hz (p < 0.05); however, the difference between p t and p − min was not significant at 1000 Hz (p = 0.28).As a result of the decrease in cavitation threshold at higher PRFs, it was observed that a dense bubble cloud formed after multiple pulses at pressures as low as 20 MPa for the 1000 Hz condition and as low as 24 MPa at 100 Hz (figure 4).For these higher PRFs, whenever cavitation events were observed on an initial pulse, cavitation persisted for the duration of the 100-pulse exposure with a larger bubble cloud being formed over multiple pulses before reaching a final bubble cloud size.This is further evident by the results from the run test for randomness showing dependence between observable cavitation events at pressures >14 MPa for 1000 Hz (p = 0.004) and >24 MPa for 100 Hz (p = 0.001).This result was not observed for the lower PRFs (0.1-10 Hz), whereupon cavitation at these lower pressure levels did not persist across subsequent pulses.These cases show examples of histotripsy bubble clouds being formed at sub-intrinsic threshold pressures for high PRFs using single-cycle pulses.In this process with successive pulses, new cavitation events formed adjacent to the previously generated bubbles, and upon the delivery of multiple pulses, a full histotripsy cloud was formed at these sub-intrinsic threshold pressures (figure 4).

Effects of PRF on bubble cloud characteristics
PRF effects on bubble cloud characteristics were quantified in a second set of experiments.Early time point images taken 6.5 μs after pulse arrival (figure 6) showed dense bubble clouds consistently formed after the first pulse for all PRF conditions.For 0.1 and 1 Hz PRFs, dense bubble cloud behavior with cavitation precisely adhering to the same elliptical geometry as the first pulse was observed consistently across all 100 pulses.For PRFs ³10 Hz, results showed different bubble cloud characteristics starting at pulse #2, with larger individual bubbles observed within less defined bubble clouds for subsequent pulses.The larger bubble size observed for these cases remained consistent across all subsequent pulses.Figure 7(a) shows the mean individual bubble diameters measured at this timepoint, with results showing pulses #2-100 had larger bubbles for 10, 100, and 1000 Hz PRFs compared to the bubble diameters measured at 0.1 and 1 Hz bubble clouds (and pulse #1 at higher PRF).
The average bubble size increased from 86.0 ± 2 μm and 83.0 ± 2 μm at 0.1 and 1 Hz, respectively, to 221 ± 27 μm, 162 ± 18 μm, and 146 ± 10 μm at 10, 100, and 1000 Hz (p < 0.05).Comparing the effects of PRF on bubble cloud area (figure 7(b)) showed an observable increase in bubble cloud area at 10-1000 Hz PRFs, which also coincided with a consistent and predictable prefocal shift occurring after pulse #2 for these PRFs.More specifically, high-speed imaging showed a half-ring, or rim, of bubbles generated by acoustic scattering formed consistently on pulse #2 for PRFs of 10-1000 Hz, which accounted for a pre-focal shift of the bubble cloud location (figure 6).Analysis of the cloud area showed consistent cloud area generation for 0.1 and 1 Hz (1.20 ± 0.04 mm 2 and 1.08 ± 0.03 mm 2 , respectively).As PRF increased, the total area increased (figure 7  Further differences in bubble cloud characteristics were quantified by analyzing changes in pulse-to-pulse spatial correlation ('cavitation memory effects') and bubble cloud density.The results from the correlation analysis, shown in figure 8(a), illustrate lower correlation coefficients for 0.1 and 1 Hz (0.38 ± 0.01 and 0.37 ± 0.01, respectively), a higher correlation coefficient for 10 Hz (0.50 ± 0.03), and a further increase in the pulse-topulse spatial correlation of bubbles for 100 and 1000 Hz (0.65 ± 0.03 and 0.72 ± 0.03, respectively).These results show a trend of increasing cavitation memory effect as a function of increasing PRF.The bubble number density measurements shown in figure 8(b) demonstrate that the highest bubble cloud densities were for the low PRF cases, with 41.7 ± 2.8 bubbles mm −2 and 45.3 ± 2.5 bubbles mm −2 for 0.1 Hz and 1 Hz, respectively.The lowest cloud density was observed at 10 Hz (8.8 ± 4.1 bubbles mm −2 ), with intermediate density clouds seen for 100 Hz (18.2 ± 5.4 bubbles mm −2 ) and 1000 Hz (23.1 ± 4.0 bubbles mm −2 ), respectively (p < 0.05).It was also noted that the cloud density increased as a function of pulse number at the higher PRFs, corresponding to the breakdown of the gel phantom.
In the late time point images, taken 52 μs after pulse arrival, larger cloud areas were observed for each PRF (figure 9).Expanded cloud images could not be quantified in the same manner as early time point images taken 6.5 μs after pulse arrival due to overlapping bubbles; however, changes in expanded bubble cloud characteristics could still be observed in the later time point images.Bubble clouds generated at 0.1 and 1 Hz PRF showed  consistent expansion patterns across all pulses with large bubbles concentrated in the front of the cloud and smaller bubbles remaining in the rear of the cloud.As more pulses were delivered, the bubbles in the rear of the cloud along the centerline grew to larger sizes.For 10 Hz PRF, a similar expansion behavior is seen on pulse #2 with the addition of a single expanded rim of cavitation bubbles due to scattering events at the front of the cloud.Later pulse images show bubble clouds with larger bubbles in comparison to 0.1 and 1 Hz.Furthermore, the bubble sizes were consistent along the length of the cloud.As the PRF increased to 100 and 1000 Hz PRF, cloud expansion on pulse #2 showed large increases in the number and size of bubbles throughout the length of the cloud.Similarly, bubble diameters were consistent along the length of the cloud in a densely packed structure.Starting at pulse #10, dense bubble clouds were formed that had consistent size and shape for the remainder of the pulses.

Effects of PRF on ablation
In a third set of experiments, the effects of PRF on ablation for single-cycle histotripsy were quantified.Each PRF successfully ablated the RBC layer within 500 pulses, shown by the complete removal of contrast within the targeted region (figure 10).The low PRFs (1 Hz) demonstrated consistent and precise lesions with very limited  instances of off-target damage as shown by the sharp demarcated boundaries of the lesion with no noticeable damage occurring outside of the final lesion.Lesion areas were elliptical in geometry and closely adhered to the estimated focal area of the transducer with only a slight reduction in area from 0.1 (7.29 ± 1.24 mm 2 ) to 1 Hz (6.44 ± 0.52 mm 2 , p = 0.13).
Lesions generated using 10 Hz PRF (figure 11) had no statistical difference from 0.1 Hz ablations (6.30 ± 0.96 mm 2 , p = 0.41), but generated less consistent ablation geometries with a reduction in ablated focal area in the rear of the cloud in comparison to the lesions generated at 0.1 Hz.For 100 and 1000 Hz PRFs, lesion areas increased beyond what was measured for 0.1 Hz ablations (8.29 ± 1.84 mm 2 and 8.60 ± 2.23 mm 2 for 100 Hz and 1000 Hz, respectively), but the difference was not significant due to inconsistent lesion areas across samples (p = 0.20 and p = 0.14 for 100 Hz and 1000 Hz, respectively), which is represented in the images in figure 11 as well as the larger standard deviations in the quantified ablation areas shown in figure 12 and table 2. The ablation efficiency measured over the first 100 pulses decreased slightly for 1 Hz (0.049 ± 0.007 mm 2 /pulse, p < 0.05), decreased further at 10 Hz (0.043 ± 0.005 mm 2 /pulse, p < 0.05) and 1000 Hz (0.035 ± 0.006 mm 2 /pulse, p < 0.05) in comparison with 0.1 Hz (0.057 ± 0.005 mm 2 /pulse), but saw no statistically significant difference at 100 Hz (0.054 ± 0.007 mm 2 /pulse, p = 0.29).Table 2. RBC ablation area.The average ablated area (mm 2 ) and corresponding standard deviation for each PRF is shown for pulse #100, 200, 300, 400, and 500.The lower PRFs (<10 Hz) generated the most consistent lesion sizes indicated by the similar ablation areas and deviations.In contrast, higher PRFs (>10 Hz) generated larger overall lesions with a higher degree of variability after 500 pulses.

Discussion
This study investigated the effects of PRF on bubble cloud characteristics and ablation for single-cycle histotripsy.Results showed a decrease in the pressure required to generate histotripsy bubble clouds at PRFs >10 Hz, which we interpret to be due to the restimulation of residual cavitation nuclei at sub-intrinsic threshold pressures followed by the nucleation of new cavitation events prefocally adjacent upon the delivery of successive pulses.In contrast to our initial hypothesis, the results from our RBC ablation studies showed that higher PRFs did not suffer a reduction in treatment efficiency compared to lower PRFs.The likely reason for this finding, highlighted by the results from the bubble cloud characteristics analysis, is that very dense bubble clouds and significant bubble expansion were generated at these high PRFs.Expanded bubbles filled the entire focal region on every pulse, as seen in the late time point imaging (figure 9), even with the higher pulse-to-pulse spatial correlation of bubble nucleation locations across pulses (figure 8(a)).This finding is contrary to the decreases in ablation efficiency previously reported in shock-scattering histotripsy (Wang et al 2012), in which bubble clouds did not fill the entire focal region on each pulse and resulted in reduced ablation efficiency for higher PRFs.
While prior literature on shock-scattering histotripsy (Wang et al 2012, Duryea et al 2015, Shi et al 2018) led to our hypothesis that single-cycle histotripsy would likewise see a reduction in ablation efficiency at high PRF, the effects of PRF on single-cycle histotripsy ablation had not previously been explored.Prior evidence has shown that high PRF pulsing for shock-scattering histotripsy is affected by the cavitation memory effect, leading to incomplete or less efficient ablation of a given focal volume.Although the results of this study showed increased cavitation memory effects at higher PRFs for these single-cycle histotripsy treatments (figure 8(a)), this effect did not translate to a large reduction in ablation efficiency (figure 12 and table 2).High-speed optical imaging (figures 6 and 9) suggests that this difference between our findings and prior shock-scattering studies is due to the differences in the bubble cloud characteristics.For instance, prior shock-scattering histotripsy studies showed bubble clouds at higher PRFs were more sparsely packed with bubbles distributed over a larger focal area (Wang et al 2012).In comparison, the single-cycle histotripsy bubble clouds generated at higher PRFs in this study were very densely packed over a smaller focal region, with a much larger portion of the focus exposed to the expanding histotripsy bubbles (figures 6 and 9).Upon the arrival of subsequent pulses, cavitation events can be restimulated in approximately the same locations for high PRFs.Prior shock-scattering studies reported that this effect results in large volumes of the focus never being exposed to bubble activity with pockets of cavitation activity separated by untreated regions of intact tissue (Wang et al 2012, Duryea et al 2015, Shi et al 2018).For single-cycle histotripsy clouds generated in this study, the restimulation of the residual nuclei still resulted in complete and efficient ablation because of the dense cloud structure (figures 10 and 11).Furthermore, the slightly decreased bubble cloud densities reported in this study for 100 and 1000 Hz PRFs (figure 8(b)) did not translate to a reduction in ablation in comparison to low PRFs due to the generation of a sufficiently dense cloud that had greater bubble expansion due to the restimulation of the residual nuclei.Therefore, the general finding of this study suggests that single-cycle histotripsy is capable of maintaining high ablation efficiency in high PRF conditions.However, since high PRFs restimulate residual nuclei in approximately the same locations, this finding likely only holds for cases in which a very dense histotripsy bubble cloud is formed on the first pulse.Prior work has shown that increasing the transducer f-number (Vlaisavljevich et al 2017) or decreasing transducer frequency (Edsall et al 2021) can both result in decreases in bubble cloud density.It is therefore likely that ablation efficiency could decrease at higher PRFs for single-cycle histotripsy in cases where a sufficiently dense bubble cloud is not generated, which is an important consideration when interpreting the findings of this study.
The higher PRFs tested in this work decreased the pressure required to generate a histotripsy bubble cloud.For 0.1-10 Hz PRFs, sub-intrinsic threshold pressures (<26 MPa) generated sporadic, isolated cavitation events; however, for PRFs of 100 Hz at pressures >20 MPa and 1000 Hz at pressures >14 MPa, once a cavitation event occurred, it persisted for the duration of the test.Because these initial cavitation events at high PRFs did not consistently occur on the same pulse number, there was a higher degree of variability in reporting the cavitation thresholds for higher PRFs (figure 5).It is worth noting, that pulses without cavitation still cause deformation in the hydrogel, which may not have fully recovered by the time the subsequent pulse is delivered, particularly as the PRF is increased to faster rates.This preconditioning of the material may be a factor in the decrease in threshold and may vary depending on the material properties of the medium.Based on the results from this study, residual nuclei were not restimulated every pulse.For instance, p t for 100 Hz PRF was significantly greater than the respective p − min , and bubble clouds were not consistently observed until 24 MPa.This difference between p t and p − min decreased to an insignificant level for 1000 Hz tests.This finding suggests that residual nuclei generated in isolated cavitation events at these low pressures (∼10-17 MPa) had likely dissolved before the arrival of the subsequent pulse at 100 Hz, but had not yet dissolved before subsequent pulses at 1000 Hz, enabling the nuclei to be restimulated by successive pulses.This observation suggests that the size and number of residual nuclei remaining from an antecedent pulse, along with the duration between pulses, dictates the pressure level at which sub-intrinsic bubble clouds can be formed.For instance, due to the convergence of p t with p − min at 1000 Hz, we hypothesize that the threshold would not decrease much further for PRFs >1000 Hz, being limited to p − min .It should be noted, however, that lower p − min values may be observed for longer exposures with more applied pulses, which would lead to a lower p − min and therefore further decrease the cavitation cloud threshold.Additionally, this result suggests that different cavitation thresholds would be expected for singlecycle histotripsy pulsing in different tissue types at higher PRFs due to differences in the size of residual nuclei, which would be in contrast to prior work showing a consistent histotripsy intrinsic threshold for water-based tissues tested at very low PRF (Vlaisavljevich et al 2015a).For example, in mediums with stronger mechanical properties that impede bubble growth and therefore produce smaller residual nuclei after each pulse, we would hypothesize that the resulting cavitation cloud threshold would not decrease to as low a pressure as in a softer tissue where initial bubbles would have greater expansion.Future work should evaluate these hypotheses by investigating the single-cycle histotripsy cavitation cloud thresholds in a wide range of tissue types and tissuemimicking gel phantoms.
High PRF pulsing has also been associated with decreases in treatment precision (Wang et al 2012, Duryea et al 2014, Duryea et al 2015, Shi et al 2018).Evidence from this study suggests that high PRF treatments using single-cycle pulsing will increase the number of off-target cavitation events while also causing a consistent focal shift in the cloud location.The shift in bubble cloud and lesion area seen for high PRFs in figure 6 can be explained by the generation of a grouping of bubbles consistently forming for PRFs ³10 Hz at the front of the cloud on pulse #2 (figure 6).Furthermore, the significant increase in the correlation coefficient for high PRFs indicates that these half-rings, or rims, of cavitation bubbles form from shock-scattering events and are then restimulated in subsequent pulses, extending the cloud in length (figure 8(a)).Future work is needed, however, to fully quantify the degree of focal shifting for a wide range of transducer geometries, center frequencies, and tissue mediums.A final source of imprecision is the decrease in repeatability seen in high PRF treatments.For the 100 and 1000 Hz cases, the size and shape of the ablation zones had inconsistencies across samples (figure 11), which is also indicated by the larger standard deviations for the 1000 Hz case in figure 12 and table 2. This is further explained by an increase in off-target cavitation seen in high-speed imaging (figure 11).While successfully ablating a similar or larger area compared to the low PRF condition, lesions generated at 1000 Hz PRF showed increased off-target ablation and varied in lesion geometry between samples.This loss of shape and adherence to the focal region was not seen in lower PRFs (0.1-1 Hz).Additionally, it is worth noting that the 100 and 1000 Hz lesions in figure 11 have a circular geometry within the focal lesion.This was, in part, observed to be caused by the vortex of fluid flow generated by the collapse of the bubble cloud within the liquified RBC phantom over multiple pulses.However, additional studies are needed in order to better characterize the potential role of enhanced streaming and fluid vorticity that appeared to contribute to this enhanced tissue breakdown at the higher PRFs in this study.
Translating these results into the clinic, this study suggests that high PRF single-cycle histotripsy treatments can greatly reduce treatment times without decreases in ablation efficiency.Additionally, the fast ablation afforded by higher PRFs may allow for the treatment of larger tissue volumes in a single histotripsy session.For most volumetric ablation histotripsy applications, such as targeting large tumors (Schuster et al 2018, Ruger et al 2022, Vidal-Jove et al 2022), the predictable changes in the bubble cloud size and location shown in this study are not to be expected to deter the use of high PRFs, as long as these changes are integrated into volumetric ablation delivery methods.However, for high-precision treatments such as histotripsy thrombolysis (Maxwell et al 2009, Maxwell et al 2011a, Hendley et al 2022) or biofilm ablation in medical catheters (Childers et al 2022), these changes in bubble cloud activity may have more significant effects that could limit the maximum PRF for those applications.Therefore, further investigation may be warranted to improve repeatability and predictability for ultra-high PRF treatments when applied for high-precision applications.A previously developed approach to mitigate the cavitation memory effects has been developed, in which bursts of low amplitude pulses are delivered between the histotripsy therapy pulses, effectively eliminating a residual nuclei's potential to be restimulated by the subsequent treatment pulse (Wang et al 2012, Duryea et al 2014, Duryea et al 2015).Further work is warranted to utilize these and other methods to develop optimized treatment protocols that utilize high PRFs for both rapid volumetric ablation and high-precision histotripsy applications.Finally, as mentioned earlier, the results of this study are based on a relatively low F-number transducer (Transverse 0.61/Elevational 0.71) and a single frequency (500 kHz) making recommendations for PRFs in clinical applications difficult without further testing.It is therefore essential that future studies consider the effects of these and additional parameters on bubble cloud characteristics, particularly bubble cloud density and bubble expansion, when considering the potential effects of PRF on histotripsy tissue ablation for specific devices and clinical applications.

Conclusion
This study systematically investigated the effects of pulse repetition frequency on single-cycle histotripsy bubble cloud characteristics and ablation.The results support the hypotheses that higher PRF leads to less precise tissue ablation; however, results differed from those found for multi-cycle histotripsy, showing that higher PRF treatments maintained ablation efficiencies comparable to low PRF conditions.While future work is needed to improve the predictability and precision of high PRF treatments, the results of this work support the adoption of high PRF pulsing regimes for single-cycle histotripsy.These high-rate pulsing strategies could reduce treatment times and allow for the targeting of larger volumes in a single treatment session.It is our hope that the findings of this study will inform the selection of histotripsy treatment parameters for future preclinical and clinical studies.

Figure 1 .
Figure1.Experimental setup.The experimental setup consisted of a 500 kHz single-cycle histotripsy transducer mounted to a custom 3D positioning system that manipulated an agarose gel phantom to the focus of the transducer.High-speed optical imaging was aligned to the focus with a constant light source.Bubble clouds were imaged on every pulse and triggered with the amplifier for the transducer.

Figure 2 .
Figure 2. Example waveform and pressure field.An example waveform from the 500 kHz histotripsy transducer (a) and the normalized 2D pressure field (b) was captured using a custom fiber optic hydrophone at the maximum pressure prior to cavitation and a high-resolution rod hydrophone, respectively.

Figure 3 .
Figure 3. Bubble cloud analysis.Examples of bubble cloud images from pulse #100 converted to binary and analyzed for bubble cloud characteristics including bubble size, bubble cloud area, and bubble cloud density.Additionally, binarized images were analyzed for pulse-to-pulse spatial correlation of pixels.

Figure 4 .
Figure 4. Cavitation threshold imaging.The effects of PRF on the cavitation threshold were visualized using high-speed imaging of potential cavitation events occurring at a range of pressures (18-32 MPa) for each PRF (0.1, 1, 10, 100, and 1000 Hz) at pulse #100.Cavitation clouds were formed at sub-threshold pressures for high PRFs.

Figure 5 .
Figure5.Cavitation threshold analysis.S-curves associated with the fitted sigmoidal function were plotted for each sample (n = 3) and each PRF (0.1, 1, 10, 100, and 1000 Hz) for pressures ranging 0-36 MPa at +2 MPa intervals.The cavitation threshold decreased for high PRFs but had a less precise threshold than the lower PRFs which more closely resembled behavior following the intrinsic threshold.

Figure 7 .
Figure7.Bubble cloud characteristics analysis.The mean bubble diameter (a) and total cloud area (b) were calculated using highspeed imaging taken at 6.5 μs after pulse arrival for each PRF (0.1, 1, 10, 100, and 1000 Hz) and plotted as a function of pulse number.After pulse #2 as PRF increased, the mean bubble diameter and total cloud area increased.

Figure 8 .
Figure 8. Bubble cloud characteristics analysis.The correlation coefficient (a) and average cloud density (b) were calculated using high-speed imaging takenat 6.5 μs after pulse arrival for each PRF (0.1, 1, 10, 100, and 1000 Hz).After the first pulse, the correlation coefficient increased, but the cloud density decreased significantly for 10 Hz PRFs.

Figure 10 .
Figure 10.Low PRF RBC ablation.High-speed optical imaging of 500 pulses of RBC ablation for 0.1 and 1 Hz PRFs at 35 MPa were taken at specific time points to show cloud formation (6.5 μs), expansion (52 μs), and resulting lesion (900 μs) for each pulse.

Figure 12 .
Figure 12.RBC analysis.The ablated area in RBC gel phantoms for each PRF (0.1, 1, 10, 100, and 1000 Hz) were plotted as a function of pulse number for the entire 500 pulse exposure.Results show that 100 and 1000 Hz PRFs generated larger total ablation areas.

Table 1 .
Cavitation threshold results.The cavitation threshold (p t ), transition variable (σ), and minimum pressure at which cavitation was observed (p − min ) for each sample along with the mean cavitation threshold (p t_mean ), mean transition variable (σ mean ) and mean minimum pressure (p − mean ) is shown for each PRF.