Monitoring cavitation dynamics evolution in tissue mimicking hydrogels for repeated exposures via acoustic cavitation emissions

Cavitation has been studied for many years for different applications and phenomena as a result of the often-violent conditions generated in the vicinity of cavitation events.^1–3 To facilitate its study, numerous methods of generating cavitation have been developed, including laser, acoustic, and hydrodynamic means.^3–8 Although these have enabled a better understanding of its outcomes and effects, fundamental questions remain. There has recently been a great deal of interest in cavitation in the medical community, where it has been suspected of contributing to tissue damage in traumatic brain injuries and also investigated for use in therapeutic applications such as histotripsy.^9–12 To that end, numerous studies investigating how viscoelastic materials respond to cavitation have been conducted to better inform models of cavitation-induced damage in these materials.^13–16 

For therapeutic applications, a number of cavitation monitoring techniques have been developed to observe the magnitude of induced cavitation. For example, standard diagnostic B-mode ultrasound imaging can be used to detect generated cavitation bubbles as well as the presence of damage generated by them.^17–19 Similarly, passive cavitation imaging (PCI) methods can be used to evaluate cavitation energetics and classify lesions.^20,21 However, current cavitation monitoring techniques such as these are limited in their ability to resolve the cavitation dynamics and level of damage generated by cavitation (e.g., percent tumor-kill), which is essential for monitoring treatment progress in cavitation therapies such as histotripsy.

Histotripsy and boiling histotripsy rely on the repeated application of cavitation to incrementally reduce the target materials, including tissues, to liquid-like homogenates, a process which, by inspection, will alter the mechanical/viscoelastic properties of the target medium.^11,12,22,23 It has been previously demonstrated that the mechanical/viscoelastic properties of a cavitating medium impact the dynamics of generated cavitation, and the material properties of the medium can be determined based on high-speed images of the cavitation dynamics combined with inverse numerical modeling.^24,25 Although such techniques cannot be directly applied to opaque materials, such as tissues, other features of cavitation, namely, the acoustic cavitation emission (ACE) signals (i.e., shockwaves) generated during a bubble's initial growth and subsequent collapses and rebounds, have also been shown to depend on the viscoelastic properties of the nucleation medium.^16,26–32 Viscous and elastic effects exerted on a bubble by the medium can only act to suppress a bubble's growth or otherwise dissipate energy.^4,29,33 This reduces the energy available during the collapse of the bubble and, correspondingly, the energy available to generate the associated ACE signals. As ACE signals can be measured acoustically, they represent an appealing phenomenological candidate for assessing material properties in opaque media, such as tissues, and have been used previously to monitor other kinds of acoustic treatments like lithotripsy.³⁴ Whether measurements of the ACE signals alone are sufficient to directly assess the material properties of the target medium remains to be determined and is beyond the scope of this report. However, it is reasonable to expect that features of the ACE signals will change as a material is incrementally liquefied by repeated exposures to cavitation. It is hypothesized that by monitoring their evolutions, the ACE signals can be used to track the damage state of repeatedly cavitated materials. Further, these trends will also vary across ablation media as the evolution of material properties influencing the cavitation will change depending on the structure of the therapy target. The ACE signals, thus, have the potential to address a key limitation of current cavitation monitoring methods and provide a means to assess the degree of tissue damage generated during cavitation-based ablation therapies such as histotripsy.

While measurements of ACE signals generated by cavitation events may provide an avenue for evaluating the damage states of opaque materials, such as tissues, the feasibility and relative accuracy of doing so must first be demonstrated. Given the direct access afforded by transparent materials regarding monitoring the dynamics of cavitation events, it is desirable to perform such feasibility investigations in them. In this study, we process the ACE signals from acoustically nucleated cavitation in transparent, tissue mimicking hydrogels to identify features of them correlated with the observed dynamics of generated cavitation events. Features of the ACE signals generated during the nucleation, collapse, and rebounds of generated bubbles, including their timings and amplitudes, are processed to correlate with the optically observed features of the cavitation dynamics, including the bubble lifespans and maximum radii. In addition, we investigate how the cavitation dynamics in gels change as a function of cavitation exposure count, which is expected to confer information about the damage state of the gel. We hope that the results from this study will provide an acoustic measure to monitor cavitation dynamics in the opaque media and a means to potentially evaluate the damage states of targeted materials exposed to repeated cavitation.

All of the experiments were performed in a 3′ × 3′ × 2′ tank of de-ionized water filtered to 2 μm and degassed to 20% oxygen saturation as measured by a ThermoFisher Orion Star A323 oxygen meter (Waltham, MA; Fig. 1). The temperature of the water during all of the experiments was measured to be between 20 and 21 °C. Cavitation was generated in tissue mimicking agarose, gelatin, and polyacrylamide gel phantoms. Agarose and gelatin gels of varying concentrations [agarose, 1% (13 kPa), 2%, and 3% (50 kPa; w/v); gelatin, 5% (4.5 kPa), 10%, and 15% (36 kPa)] were used to simulate tissues of varying Young's moduli, and prepared following preciously described methods.^8,35,36 Polyacrylamide gels were also prepared from a BioRad Acrylamide Kit (No. 1610183; Hercules, CA) in different ratios of reagent A (acrylamide) to reagent B [bis-acrylamide; 2:1 (4.24 kPa), 1:1 (10.9 kPa), and 1:2 (25.43 kPa)]. The stiffness values for the agarose and gelatin samples are referenced from the literature, whereas the stiffness values for the polyacrylamide gels were measured via compression testing. Gel samples were prepared with a cylindrical geometry with a height of 7.5 cm and a diameter of 2.5 cm.

Cavitation was generated using a 360 element, 30 cm aperture diameter hemispherical histotripsy array that was designed and constructed in-house. Each array element was configured to operate in a transmit-receive mode to allow the simultaneous generation of the acoustic pulses necessary to generate cavitation and the acquisition of resulting ACE signals (i.e., shockwaves) emitted therefrom. The individual transducer elements were characterized by measuring the waveform using a fiber-optic hydrophone (HP; Onda HPO-690, Sunnyvale, CA) at a distance of 15 cm axially from the transducer surface.³⁷ The measurements were averaged over 50 pulses to remove the random noise on the fiber tip. On transmit, each element output a 1.5 cycle acoustic pulse with a center frequency of 700 kHz and was capable of generating a peak rarefactional pressure amplitude at the array focus of up to 1.36 MPa. The focal zone of the array was acquired by measuring one-dimensional (1D) beam profiles along three axes using a needle HP (Onda HNR-0500, Sunnyvale, CA) at low driving pressure. The focal zone was defined as the full width at half-maximum (FWHM) of the beam profiles and resulted in a focal zone that measured 2 mm, 2 mm, and 7 mm in the axial, sagittal, and coronal axes, respectively. On receive, each array element was connected to a 12-bit analog-to-digital converter (ADC) with a maximum sampling frequency of up to 50 MHz. Control of the array was accomplished using custom programmed system-on-a-chip (SoC) devices, which were capable of delivering acoustic pulses to generate cavitation and storing received ACE signals from every element of the array after every delivered acoustic pulse.

To deliver repeated cavitation exposure via histotripsy, the per-element peak-negative pressure amplitude was set to 300 kPa by adjusting the supply voltage to 20 V. This value is based on previous measurements using a fiber-optic HP to capture pressure outputs across a spectrum of input voltages using the methods described in Sec. II B. By linear summation of the contributions from individual elements, the resulting estimated peak-negative focal pressure of the entire array was approximately 110 MPa. Acoustic pulses were delivered to the gel samples at a pulse repetition frequency (PRF) of 2 Hz to generate 150 cavitation events per target location. All of the target locations were located centrally within the cylindrical gel samples with a minimum separation between adjacent target sites of 15 mm. The experiments were repeated eight times per gel concentration.

High-speed images of generated cavitation events were acquired using a Phantom v2012 (Vision Research, Wayne, NJ) camera at a fixed frame rate of 333 kHz (3 μs frame period). Images were backlit using custom designed light-emitting diode (LED) flash sources with a flash duration of 300 ns.³⁸ Image sequences spanned a duration of 390 μs (130 frames total) and were timed to capture the first-cycle dynamics (i.e., nucleation through first collapse) of the generated bubbles, as well as their rebounds and eventual dissolutions. Bubbles in acquired images were identified using brightness thresholding and object detection via the regionprops function in MATLAB. This function receives a binary image and identifies an object based on its connectivity (four-connected, adjacent pixels; eight-connected, adjacent or diagonal pixels). Bubbles generated during experiments were typically observed to form as dense clouds of microbubbles, which would merge together into apparently singular large bubbles with ellipsoidal geometries during their subsequent expansions. Major and minor axes of the bubble cloud were determined as the length of the major and minor axes of the ellipse with the same normalized second moment of the identified object in the image. This is performed by evaluating the multivariate normal distribution of all of the points in the image, then constructing its covariance matrix from the first- and second-order central moments of the object, and, finally, calculating the eigenvalues of the matrix which are equal to the major and minor axes of the ellipse. During analyses, bubbles were approximated as singular spherical bubbles whose radii were defined as the square root of the product of the major and minor radii returned from the ellipsoidal fits.

ACE signals from generated cavitation events were captured using the receive-capable elements (Rx) of the histotripsy array after every delivered acoustic pulse. Signals were acquired at a sampling frequency of 5 MHz. Acquired ACE signals were timed to begin 100 μs prior to nucleation and had a total duration of 500 μs. The timings and amplitudes of each ACE shockwave within the acquired signals were calculated as follows and recorded.

First, the median of the waveforms acquired across all of the 150 treatment pulses is evaluated on an element-by-element basis to isolate the acoustic background signals (e.g., due to reflections from the water surface—note that as the timings of the ACE signals varied from pulse-to-pulse, they were not present in median filtered waveforms). The per-element acoustic background signals were then subtracted from the original waveforms to isolate the ACE signals. For each pulse, the median of the background-subtracted signals across all of the 360 elements was then calculated to eliminate any remaining incoherent noise from the individually acquired waveforms. Peak detection was used next to identify the ACE signals in the resulting waveforms and extract their timings. As cavitation nucleation, collapse, and rebound are unambiguously ordered, the corresponding ACE signal timings identified in the waveforms were uniquely associated with these events by chronological sorting.

HPs represent the ideal standard for capturing acoustic signals, but their use can be limited, particularly, for therapeutic applications where access to the target may be restricted. Although the receive elements of the array are narrow bandwidth receivers and, as such, cannot fully capture the frequency content of the shockwaves like a HP, it is hypothesized that the narrow bandwidth still permits the detection of the requisite ACE features to monitor cavitation dynamics. To that end, in addition to the receiving elements of the array, ACE signals were captured via needle HP (Onda HNR-0500, Sunnyvale, CA). Calibration of the HP and others referenced in this manuscript, were not performed in-house, but were performed by Onda. The HP was positioned 15 cm from the treatment focus to match the focal distance of the array. Signals were acquired at a sampling frequency of 125 MHz. Acquired signals were timed to begin 100 μs prior to nucleation and had a total duration of 500 μs. First, the median signal across all of the pulses was subtracted from each of the raw waveforms to reduce the presence of background signals. Then, the nucleation and collapse shockwave timings and amplitudes were evaluated from the time-gated maxima of the background-subtracted data.

High-speed optical imaging captured the nucleation, growth, collapse, and rebounds of the cavitation events (Fig. 2). Nucleation (i.e., the arrival of the acoustic pulse to the focus) occurs at approximately 100 μs as a cloud of densely populated microbubbles, which then grow and merge into a single, larger bubble during the first 20–40 μs after the arrival of the ultrasound pulse. Then, this larger bubble collapses, after which it is observed to rebound between one and four times before eventually dissolving back into the medium. The first collapse in Fig. 2 occurs at approximately 280 μs, after which the bubbles were observed to rebound three times at 380, 430, and 445 μs. Similar behaviors were observed across all of the nucleation media, however, increasing gels stiffness resulted in smaller initial cloud radii and fewer bubble rebounds following the initial collapse.

During experiments, it was often observed that a “satellite” cloud of bubbles would form around the core bubble cloud (Fig. 2; ∼300–350 μs). The generation of these satellite clouds was observed to occur at nearly fixed timing with respect to bubble nucleation and concurrent with the expected round trip time of flight of the shockwave emitted during cavitation nucleation to the transducer and back (⁠ $150 mm/1.5 mm / μ s=100 μs$ from the array surface to the acoustic focus; 200 μs following nucleation). These secondary cavitation bubbles are, thus, attributed to shock scattering effects wherein the incoming shockwaves undergo a pressure inversion as they are reflected off of the bubbles, which, in turn, results in the nucleation of additional bubbles.^39–41 Although this does not appear to affect the dynamics of the core bubble cloud, the core bubble cloud and the shock scattering bubbles overlap in the two-dimensional (2D) camera perspective, and often could not be distinguished from one another. All of the frames of the image series during and after which shock scattering effects interfered with the ability to accurately assess the bubble cloud size were omitted in the analysis of this study. Similar to observations from nucleation, it is also noted that stiffer gels reduced the sizes of bubbles generated by shock scattering effects.

In the agarose gels, images showed that bubble maximum radii initially increased with exposure count before reaching a plateau and then decreased (Fig. 3). The maximum radii stayed mostly constant in the gelatin and polyacrylamide gels with the exception of the 15% gelatin sample, which decreased slowly, plateaued, and increased again toward the end of treatment. For all of the gel types, the initial maximum radii (pulse 1) were also observed to depend on gel stiffness, where stiffer gels resulted in smaller maximum radii, in good agreement with the results from prior studies.^8,42,43 As might be expected based on the initial bubble maximum radius results, the lifespans of bubbles were observed to be the smallest in the stiffer gels. However, while the bubble maximum radii were observed to increase, plateau, and then decrease in the agarose gels, the bubble lifespans were observed to increase monotonically with exposure count (Fig. 4). The bubbles cavitated in the gelatin samples behaved similarly, but the bubbles cavitated in polyacrylamide exhibited decreasing bubble lifespans with increasing exposure count.

An example ACE signal captured via a receive-capable element of the array and a HP, along with the corresponding high-speed optical images of the cavitation bubble cloud which generated them, is displayed in Fig. 5. The portions of the acquired signals associated with bubble nucleation were not generally observed to be compact and often spanned several microseconds in duration. This is likely due to the fact that each bubble is initially generated as a cloud of individual microbubbles, which each emit their own shockwave on nucleation. As may be appreciated from the corresponding image of the nucleation event in Fig. 2, individual bubbles were observed across a region measuring 2–3 mm. The corresponding arrival timings of the individual shockwaves were likewise spread out as a result of the differences in path lengths from individual bubbles back to the array elements. Collapse shockwave signals were generally observed to be singular and compact, in line with observations from imaging showing that individual bubbles merge into a “single” large bubble over the course of their evolutions. Rebound shockwaves were similarly compact.

The shockwave emitted during bubble nucleation first arrived at the transducer array at 200 μs, after which it was reflected back to the focus of the array. On arriving at the array focus at 300 μs, it was reflected off of the extant bubble and led to the nucleation of the shock scattering bubbles noted earlier (Figs. 2 and 5). Shockwave emissions from these shock scattering bubbles and/or reflections of the initial nucleation shockwave off of the remaining core of bubbles were often observed in the acquired signals and can be seen in Fig. 5(a) at approximately 400 μs. The timings of the bubble collapse and rebound shockwaves were not fixed but evolved as a function of exposure count along with the dynamics of generated bubbles that changed as the gel was ablated.

The ACE signals acquired using the array elements and the HP were processed similarly to evaluate bubble lifespan and collapse shockwave amplitudes (Figs. 6 and 7). The assessments of the lifespans of the bubbles from both devices very closely matched the measurements acquired using the high-speed camera. Measurements of the shockwave signals acquired using both devices were observed to be very similar temporally but deviated from one another in amplitude. That is to say, both devices showed multiple, temporally disperse nucleation shockwave emissions and temporally compact, singular shockwave emissions from the collapses and rebounds of the generated bubbles, which is in good agreement with expectations from imaging results. As the array elements are not calibrated receivers, direct measurements of the shockwave pressures based on the signals acquired using them could not be made. As such, comparisons between the array element and HP measurements are reported in terms of the normalized change in measured shockwave signal amplitude (with respect to the first pulse) as a function of exposure count. Whereas the shockwave amplitudes measured by both devices followed roughly similar trends, the HP measurements were typically observed to diverge from the array element measurements and generally seen to exhibit greater pulse-to-pulse variances in signal amplitude. In the agarose gels, collapse shockwave amplitudes were observed to increase early during treatment, plateau, and then increase again during the end of treatment. The notable exception is the 1% agarose gels which continued to plateau at high exposure counts. The shockwave amplitudes measured in the gelatin samples increased early in treatment, plateaued, and decreased toward the end of the exposures. Collapse shockwaves generated in polyacrylamide gels were observed to decrease monotonically across all of the exposures. Collapse shockwave amplitudes were independent of the gel stiffness for agarose and polyacrylamide. In the gelatin hydrogels, shockwave amplitude increased with increasing stiffness.

Features of the ACE signals, including the bubble lifespan and collapse shockwave amplitudes, were evaluated for correlations with observations of the bubble maximum radii from the high-speed images. In the gelatin and polyacrylamide gels, small relationships may be present toward the beginning of treatment; however, following these first several pulses, no identifiable relationship between the aforementioned features could be identified. In the agarose gels, all of the combinations of the features were observed to transition partway through treatment. The bubble lifespans and collapse shockwave amplitudes as measured using the array elements were both observed to show a segmented-linear relationship with the bubble maximum radius [Figs. 8(a) and 8(d)]. However, both were non-uniquely related to bubble maximum radius as the lifespan and collapse shockwave amplitude increased monotonically with exposure count, whereas the bubble maximum radius did not. During early exposures, the bubble lifespan was observed to increase linearly with increasing maximum radius, however, after the plateau in bubble maximum radius, the bubble lifespan was observed to increase with decreasing bubble maximum radius [Fig. 8(a)]. The rates of lifespan increase vs bubble maximum radius on both sides of the plateau were seen to differ by less than 30% across all three gel concentrations. The collapse shockwave amplitudes were observed to follow similar trends to the bubble lifespan with increasing exposure count [Fig. 8(d)] and seen to increase with increasing bubble maximum radius (pre-plateau). The collapse shockwave amplitude was also observed to show a segmented-linear relationship with the bubble lifespan [Fig. 8(g)]. During early exposures (pre-plateau), the collapse shockwave amplitude increased slowly with increasing collapse time. In the post-plateau region, the collapse shockwave amplitude increased more quickly with increasing collapse time. The critical point in the collapse shockwave amplitude vs bubble lifespan curve was observed to be concurrent with the plateau in the bubble maximum radius.

In this study, it was observed that features from repeated cavitation events generated in hydrogel phantoms demonstrated trends dependent on cavitation exposure. The evolution of cavitation features could be detected via high-speed imaging and ACE signals captured by the transducer array elements, which also emit ultrasound to generate cavitation. Cavitation lifespans, maximum radii, and shockwave amplitudes were all observed to decrease with increasing stiffness of the nucleation medium. However, the observed trends in the gels varied by gel type and structure.

One possible explanation for the differences in observed evolutions of the cavitation dynamics between the studied hydrogels is a dependence of the changing material properties on their respective structures. First, agarose hydrogels are porous gels.³⁵ During early exposures, the hydrogel is structurally intact and an effectively solid material that can exert strong restrictions on bubble growth. Repeated cavitation exposures fracture the gel, weakening this effect, thus, allowing bubbles to grow larger. As this process continues, however, gel fragments break apart from the surrounding structure, releasing the liquid encapsulated in the gel's pores, and breaking down further to a liquid homogenate. As this gel-liquid develops, the target volume locally becomes increasingly viscous, which leads to increased energy dissipation during bubble growth, resulting in smaller bubble maximum radii. At the same time, viscous effects would slow bubble collapses, which could, thus, allow bubble lifespans to increase even while bubble maximum radii begin to decrease. This behavior would be consistent with a transition from a regime where the dynamics are dominated by elastic effects to one where they are dominated by viscous effects (Table I). Another potential explanation is that the cavitation dynamics and their changes due to damage are dependent on the porosity of the agarose hydrogels.⁴⁴ The initial bubble dynamics would still be dominated by elastic effects, but as the gel is liquefied, the growth of bubbles within would force the now-fluid material into the surrounding, porous gel structure. While poroelastic relaxation typically occurs on a much longer time scale than viscoelastic relaxation, the forcing of this fluid into/out of the surrounding porous structure during bubble expansion and collapse could act similarly and in addition to the inherent fluid viscosity to restrict bubble growth and slow bubble collapse.^45,46 Additionally, the magnitude of the effect would depend explicitly on the fluid displacement volume and, hence, would scale with bubble size. That is to say, it would be most dominant as the bubble approached its maximum radius but smaller toward the beginning and end of the bubble lifespan when the bubble is smaller and, therefore, displaces less fluid.

However, unlike the agarose, gelatin is comprised of many interwoven fibers that form a less porous, more elastic system. Specifically, gelatin can experience greater strain while still remaining in the elastic deformation domain.⁴⁷ Although the focus of the ablation treatment zone will be liquified to a gel homogenate, like agarose, the surrounding gel structure will experience elastic deformation. However, without sufficient time to fully relax, successive cavitation exposures compound the elastic deformation. This maximal elastic restriction keeps the maximum radii from changing during treatment. However, the bubble lifespan increases because less of the expansion energy is allocated toward the expansion of the bubble, which is a result of the deformation induced by previous cavitation events.

Similar to agarose, polyacrylamide is a globular hydrogel that has very high water content/swellability.⁴⁸ With nearly constant observed maximum radii and a decreasing bubble lifespan, it can be inferred that bubble expansion and collapse occur more quickly. Bubble wall velocity is primarily dependent on viscosity with larger viscosities leading to lower bubble wall velocities. Because the bubble wall velocity increases with exposure count, it can be deduced that the viscosity at the treatment focus is decreasing with pulse number. However, as bubble wall velocity increases, so do the effects of high-strain rate on the bubble expansion and collapse. Polyacrylamide expresses higher stiffness in a high-strain rate state than it does in a quasi-static state.²⁴ Therefore, the decrease to viscosity results in greater apparent stiffness and greater elastic suppression to bubble growth as exposure count increases. These act in such a manner that the maximum radii stay roughly constant throughout the ablation treatment.

It is useful to study various hydrogels with different structures in anticipation of repeating these studies in vitro and in vivo because the ACE signal evolutions from different structures can be suggestive of features in tissues with similar material properties. For example, identifying trends in fibrous gelatin hydrogels will likely be informative into patterns that may be observed in muscle tissue while porous agarose may more closely mimic the material property evolutions to be noticed in the liver or kidney. Histological evaluations of damage from various animal models provide evidence for such effects where it has been shown that stiffer tissues are more resistant to cavitation-induced damage and certain components of tissues (e.g., cellular membranes and intracellular structures) are more readily destroyed by cavitation than others (e.g., cell nuclei and the extracellular matrix).^11,12,41

Whereas the observed trends in the evolutions of the cavitation dynamics are suggestive of transitions in the viscoelastic properties of the gels and prior studies have demonstrated that repeated exposure to cavitation does ultimately liquefy materials, a key limitation of this study was that direct measurements of the properties of the cavitation-damaged gels could not be made to track them. Experimental limitations also prevented the use of the previously described inverse methods for evaluating material properties based on imaging observations of the cavitation dynamics of single bubbles. In particular, it has previously been demonstrated that the per-pulse probability of acoustically nucleating single bubbles, even under ideal nucleation conditions, is on the order of only 15%–20% and, thus, could not reasonably have been accomplished repeatedly to allow inverse material property assessments over the full 150 exposures of the experiments.⁸ Thus, although it can reasonably deduced that the observed changes in cavitation dynamics and ACE signal evolutions were the result of changes in the material properties of the target media as the input nucleation conditions were held constant across exposures, how the specific viscoelastic material properties of the cavitation media changed as a function of exposure remains to be quantitatively determined.

It was also noticed that evaluations of bubble lifespan matched very closely between the ACE signals measured by HP and acoustic array receive elements. The HP and array elements were able to detect the characteristic asymptotic growth of the shockwave amplitude, but the relative increase in amplitude as a function of exposure count differed, and the amplitudes measured with the HP exhibited significantly greater variation across pulses. One likely cause for the difference in amplitude results between measurement devices is related to the number of receivers, 360 array elements vs 1 HP. That is to say, the assessed shockwave amplitude from the array elements was taken as the average of 360 measurements from a spatially distributed set of receivers, whereas the HP was a single measurement from a single location. Taking the average of 360 signals would significantly reduce any inherent noise in individual signals that would not be possible to account for in the single HP measurement. Further, and perhaps more importantly, as noise in the HP signals was not a limiting factor, the array elements are spatially well distributed. The noted asymmetries in the generated bubbles would likewise have produced asymmetries in the resulting shockwave signals which, assuming stochastically oriented pulse-to-pulse collapse asymmetries, would have introduced pulse-to-pulse variabilities in the measured signals from the single-point HP measurement but would have been averaged out in the case of the spatially distributed array element measurements.

Although HPs are the gold standard for measuring shockwave signals, their utility for doing so is often limited, particularly in therapeutic applications. Namely, HPs require an unobstructed acoustic path to the focus to accurately resolve and measure emitted shockwaves, which is not always available (e.g., due to bone blockages or other obstructions). Additionally, the need for more HPs for accurate ACE signal detection or to account for spatial asymmetries in their magnitudes is in conflict with the general need to maximize the acoustically active area of therapy transducers to improve their power output and ensure cavitation can be generated. While the array elements may lack the bandwidth of HPs, they are guaranteed to have acoustically accessible paths to all targets in which cavitation can be generated and using them as receivers can simplify the design and operation of procedures involving it.

As the primary applications envisioned for this work are related to monitoring therapeutic cavitation-based ablation therapies, such as histotripsy, the transducer used during experiments was also not tailored to generate spherical bubbles but was rather designed with a hemispherical geometry amenable to enabling transmission of sound into the body. Consequently, this resulted in an asymmetric focal pressure field and, likewise, the generation of ellipsoidal bubbles (as may be seen in Figs. 3 and 6, particularly during the early portions of bubble expansion), which can have significant impacts on the bubble dynamics and emitted shockwaves.⁴⁹ Furthermore, it was observed that the aspect ratios of the ellipsoids (major axis radius/minor axis radius) generally increased with exposure count, increasing from approximately 1.15 to 1.25 after 150 exposures (values at R_max), which is likely to have contributed to the unexpected behaviors in bubble maximum radius, lifespan, and shockwave amplitudes and, thus, may need to be accounted for to allow material property assessments based on measurements of the shockwave emissions. Nevertheless, that the asymmetries evolved coherently with increasing exposure count does provide further indication of material property transitions in the targeted gels as the other variables of the experiments, including the input energy of the acoustic pulses used to nucleate cavitation, and the temperature and dissolved gas concentrations of the prepared gel samples and water bath were held constant across all of the experiments.

Another value to developing damage monitoring techniques would be the ability to induce variable amounts of damage to a target. The ongoing clinical trials of histotripsy in the treatment of liver tumors have the goal of inducing 100% ablation (i.e., the creation of a homogenous ablation zone generating 100% cell death).⁵⁰ However, preliminary results of immune studies have suggested that partial ablation of cancer tumors may lead to better outcomes relative to complete ablation. One possible mechanism for this is that the cavitation fractionates otherwise unrecognizable antigens and cellular markers such that the immune system of the patient triggers an autoimmune response in conjunction with the ablation treatment. While further study is necessary to validate this hypothesis, it represents a scenario where accurate assessment of induced damage would be critical for optimizing treatment outcomes.

In this study, we observed that repeated exposures to cavitation in varying hydrogel samples led to characteristic changes in the cavitation dynamics, features of which could then be detected in the resulting shockwave emissions. Bubble maximum radii, lifespans, and collapse shockwave amplitudes were observed to express evolutions dependent on the structure and stiffness of the nucleation medium.

The observed trends in the optically observed cavitation dynamics and acoustically measured shockwave signals are suggestive of elastic-to-viscous dominated transitions in the nucleation media's properties. In agarose, the observed trends in the optically observed cavitation dynamics and acoustically measured shockwave signals are suggestive of elastic-to-viscous dominated transition in the nucleation media's properties. However, in gelatin, the observed trends indicate that gelatin's greater elasticity remains dominant throughout treatment. Trends observed in polyacrylamide gels can be well explained by high-strain rate effects becoming dominant as the media become more damaged. Future work to develop treatment monitoring techniques based on measurements of ACE signals will have to be material specific as induced damage and the resulting shockwaves are affected differently.

It was demonstrated that ACE signals measured by the receive-capable elements of the acoustic array are capable of capturing the requisite information for evaluating features of cavitation dynamics such as the bubble lifespan. Assessments of the relative changes in collapse shockwave amplitudes based on measurements from the array elements were observed to vary from those made using the HPs. However, observations from imaging showed asymmetries during the bubble collapses, which likely introduced asymmetries in the collapse shockwaves and, consequently, introduced large pulse-to-pulse variabilities in HP measurements. These results suggest that although the array elements lack the bandwidth of the HPs, their numbers and spatially well-distributed nature confer particular advantages for monitoring ACE signals from asymmetrically collapsing bubbles.

This work was supported by the Office of Naval Research (Grant No. N00014-17-1-2058, Dr. T. Bentley) and the Focused Ultrasound Foundation (Grant No. 24332).