Holographic extraction of plane waves from an ultrasound beam for acoustic characterization of an absorbing layer of finite dimensions.

For the acoustic characterization of materials, a method is proposed for interpreting experiments with finite-sized transducers and test samples in terms of the idealized situation in which plane waves are transmitted through an infinite plane-parallel layer. The method uses acoustic holography, which experimentally provides complete knowledge of the wave field by recording pressure waveforms at points on a surface intersected by the acoustic beam. The measured hologram makes it possible to calculate the angular spectrum of the beam to decompose the field into a superposition of plane waves propagating in different directions. Because these waves cancel one another outside the beam, the idealized geometry of an infinite layer can be represented by a sample of finite size if its lateral dimensions exceed the width of the acoustic beam. The proposed method relies on holograms that represent the acoustic beam with and without the test sample in the transmission path. The method is described theoretically, and its capabilities are demonstrated experimentally for silicone rubber samples by measuring their frequency-dependent phase velocities and absorption coefficients in the megahertz frequency range.

Bilayer aberration-inducing gel phantom for high intensity focused ultrasound applications.

Aberrations induced by soft tissue inhomogeneities often complicate high-intensity focused ultrasound (HIFU) therapies. In this work, a bilayer phantom made from polyvinyl alcohol hydrogel and ballistic gel was built to mimic alternating layers of water-based and lipid tissues characteristic of an abdominal body wall and to reproducibly distort HIFU fields. The density, sound speed, and attenuation coefficient of each material were measured using a homogeneous gel layer. A surface with random topographical features was designed as an interface between gel layers using a 2D Fourier spectrum approach and replicating different spatial scales of tissue inhomogeneities. Distortion of the field of a 256-element 1.5 MHz HIFU array by the phantom was characterized through hydrophone measurements for linear and nonlinear beam focusing and compared to the corresponding distortion induced by an ex vivo porcine body wall of the same thickness. Both spatial shift and widening of the focal lobe were observed, as well as dramatic reduction in focal pressures caused by aberrations. The results suggest that the phantom produced levels of aberration that are similar to a real body wall and can serve as a research tool for studying HIFU effects as well as for developing algorithms for aberration correction.

Energy shielding by cavitation bubble clouds in burst wave lithotripsy.

Combined laboratory experiment and numerical simulation are conducted on bubble clouds nucleated on the surface of a model kidney stone to quantify the energy shielding of the stone caused by cavitation during burst wave lithotripsy (BWL). In the experiment, the bubble clouds are visualized and bubble-scattered acoustics are measured. In the simulation, a compressible, multi-component flow solver is used to capture complex interactions among cavitation bubbles, the stone, and the burst wave. Quantitative agreement is confirmed between results of the experiment and the simulation. In the simulation, a significant shielding of incident wave energy by the bubble clouds is quantified. The magnitude of shielding can reach up to 90% of the energy of the incoming burst wave that otherwise would be transmitted into the stone, suggesting a potential loss of efficacy of stone comminution. There is a strong correlation between the magnitude of the energy shielding and the amplitude of the bubble-scattered acoustics, independent of the initial size and the void fraction of the bubble cloud within a range addressed in the simulation. This correlation could provide for real-time monitoring of cavitation activity in BWL.

Dependence of inertial cavitation induced by high intensity focused ultrasound on transducer F-number and nonlinear waveform distortion.

Pulsed high intensity focused ultrasound was shown to enhance chemotherapeutic drug uptake in tumor tissue through inertial cavitation, which is commonly assumed to require peak rarefactional pressures to exceed a certain threshold. However, recent studies have indicated that inertial cavitation activity also correlates with the presence of shocks at the focus. The shock front amplitude and corresponding peak negative pressure (p -) in the focal waveform are primarily determined by the transducer F-number: less focused transducers produce shocks at lower p -. Here, the dependence of inertial cavitation activity on the transducer F-number was investigated in agarose gel by monitoring broadband noise emissions with a coaxial passive cavitation detector (PCD) during pulsed exposures (pulse duration 1 ms, pulse repetition frequency 1 Hz) with p- varying within 1-15 MPa. Three 1.5 MHz transducers with the same aperture, but different focal distances (F-numbers 0.77, 1.02, 1.52) were used. PCD signals were processed to extract cavitation probability, persistence, and mean noise level. At the same p -, all metrics indicated enhanced cavitation activity at higher F-numbers; specifically, cavitation probability reached 100% when shocks formed at the focus. These results provide further evidence supporting the excitation of inertial cavitation at reduced p - by waveforms with nonlinear distortion and shocks.

Shock formation and nonlinear saturation effects in the ultrasound field of a diagnostic curvilinear probe.

Newer imaging and therapeutic ultrasound technologies may benefit from in situ pressure levels higher than conventional diagnostic ultrasound. One example is the recently developed use of ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe has been used to deliver the acoustic pushing pulses. The probe is a curvilinear array comprising 128 elements equally spaced along a convex cylindrical surface. The effectiveness of the treatment can be increased by using higher transducer output to provide a stronger pushing force; however nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the three-dimensional Westervelt equation with the boundary condition set to match low power measurements of the acoustic pressure field. Nonlinear focal waveforms simulated for different numbers of operating elements of the array at several output power levels were compared to fiber-optic hydrophone measurements and were found to be in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of a diagnostic imaging probe.

Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based bubble dynamics model.

A generalized Rayleigh-Plesset-type bubble dynamics model with a damage mechanism is developed for cavitation and damage of soft materials by focused ultrasound bursts. This study is linked to recent experimental observations in tissue-mimicking polyacrylamide and agar gel phantoms subjected to bursts of a kind being considered specifically for lithotripsy. These show bubble activation at multiple sites during the initial pulses. More cavities appear continuously through the course of the observations, similar to what is deduced in pig kidney tissues in shock-wave lithotripsy. Two different material models are used to represent the distinct properties of the two gel materials. The polyacrylamide gel is represented with a neo-Hookean elastic model and damaged based upon a maximum-strain criterion; the agar gel is represented with a strain-hardening Fung model and damaged according to the strain-energy-based Griffith's fracture criterion. Estimates based upon independently determined elasticity and viscosity of the two gel materials suggest that bubble confinement should be sufficient to prevent damage in the gels, and presumably injury in some tissues. Damage accumulation is therefore proposed to occur via a material fatigue, which is shown to be consistent with observed delays in widespread cavitation activity.

Fragmentation of urinary calculi in vitro by burst wave lithotripsy.

PURPOSE: We developed a new method of lithotripsy that uses short, broadly focused bursts of ultrasound rather than shock waves to fragment stones. We investigated the characteristics of stone comminution by burst wave lithotripsy in vitro. MATERIALS AND METHODS: Artificial and natural stones (mean ± SD size 8.2 ± 3.0 mm, range 5 to 15) were treated with ultrasound bursts using a focused transducer in a water bath. Stones were exposed to bursts with focal pressure amplitude of 6.5 MPa or less at a 200 Hz burst repetition rate until completely fragmented. Ultrasound frequencies of 170, 285 and 800 kHz were applied using 3 transducers, respectively. Time to fragmentation for each stone type was recorded and fragment size distribution was measured by sieving. RESULTS: Stones exposed to ultrasound bursts were fragmented at focal pressure amplitudes of 2.8 MPa or greater at 170 kHz. Fractures appeared along the stone surface, resulting in fragments that separated at the surface nearest to the transducer until the stone was disintegrated. All natural and artificial stones were fragmented at the highest focal pressure of 6.5 MPa with a mean treatment duration of 36 seconds for uric acid stones to 14.7 minutes for cystine stones. At a frequency of 170 kHz the largest artificial stone fragments were less than 4 mm. Exposure at 285 and 800 kHz produced only fragments less than 2 mm and less than 1 mm, respectively. CONCLUSIONS: Stone comminution with burst wave lithotripsy is feasible as a potential noninvasive treatment method for nephrolithiasis. Adjusting the fundamental ultrasound frequency allows for stone fragment size to be controlled.

Acoustic holography as a metrological tool for characterizing medical ultrasound sources and fields.

Acoustic holography is a powerful technique for characterizing ultrasound sources and the fields they radiate, with the ability to quantify source vibrations and reduce the number of required measurements. These capabilities are increasingly appealing for meeting measurement standards in medical ultrasound; however, associated uncertainties have not been investigated systematically. Here errors associated with holographic representations of a linear, continuous-wave ultrasound field are studied. To facilitate the analysis, error metrics are defined explicitly, and a detailed description of a holography formulation based on the Rayleigh integral is provided. Errors are evaluated both for simulations of a typical therapeutic ultrasound source and for physical experiments with three different ultrasound sources. Simulated experiments explore sampling errors introduced by the use of a finite number of measurements, geometric uncertainties in the actual positions of acquired measurements, and uncertainties in the properties of the propagation medium. Results demonstrate the theoretical feasibility of keeping errors less than about 1%. Typical errors in physical experiments were somewhat larger, on the order of a few percent; comparison with simulations provides specific guidelines for improving the experimental implementation to reduce these errors. Overall, results suggest that holography can be implemented successfully as a metrological tool with small, quantifiable errors.

Modeling and experimental analysis of acoustic cavitation bubbles for Burst Wave Lithotripsy.

A combined modeling and experimental study of acoustic cavitation bubbles that are initiated by focused ultrasound waves is reported. Focused ultrasound waves of frequency 335 kHz and peak negative pressure 8 MPa are generated in a water tank by a piezoelectric transducer to initiate cavitation. The resulting pressure field is obtained by direct numerical simulation (DNS) and used to simulate single bubble oscillation. The characteristics of cavitation bubbles observed by high-speed photography qualitatively agree withs the simulation result. Finally, bubble clouds are captured using acoustic B-mode imaging that works in synchronization with high-speed photography.

Comparative Characterization of Nonlinear Ultrasound Fields Generated by Sonalleve V1 and V2 MR-HIFU Systems.

A Sonalleve magnetic resonance-guided high-intensity focused ultrasound (MR-HIFU) clinical system (Profound Medical, Mississauga, ON, Canada) has been shown to generate nonlinear ultrasound fields with shocks up to 100 MPa at the focus as required for HIFU applications such as boiling histotripsy of hepatic and renal tumors. The Sonalleve system has two versions V1 and V2 of the therapeutic array, with differences in focusing angle, focus depth, arrangement of elements, and the size of a central opening that is twice larger in the V2 system compared to the V1. The goal of this study was to compare the performance of the V1 and V2 transducers for generating high-amplitude shock-wave fields and to reveal the impact of different array geometries on shock amplitudes at the focus. Nonlinear modeling of the field in water using boundary conditions reconstructed from holography measurements shows that at the same power output, the V2 array generates 10-15-MPa lower shock amplitudes at the focus. Consequently, substantially higher power levels are required for the V2 system to reach the same shock-wave exposure conditions in histotripsy-type treatments. Although this difference is mainly caused by the smaller focusing angle of the V2 array, the larger central opening of the V2 array has a nontrivial impact. By excluding coherently interacting weakly focused waves coming from the central part of the source, the presence of the central opening results in a somewhat higher effective focusing angle and thus higher shock amplitudes at the focus. Axisymmetric equivalent source models were constructed for both arrays, and the importance of including the central opening was demonstrated. These models can be used in the "HIFU beam" software for simulating nonlinear fields of the Sonalleve V1 and V2 systems in water and flat-layered biological tissues.

Functional and Morphological Changes Associated with Burst Wave Lithotripsy-Treated Pig Kidneys.

Purpose: Burst wave lithotripsy (BWL) is a new technique for comminution of urinary stones. This technology is noninvasive, has a low positive pressure magnitude, and is thought to produce minor amounts of renal injury. However, little is known about the functional changes related to BWL treatment. In this study, we sought to determine if clinical BWL exposure produces a functional or morphological change in the kidney. Materials and Methods: Twelve female pigs were prepared for renal clearance assessment and served as either sham time controls (6) or were treated with BWL (6). In the treated group, 1 kidney in each pig was exposed to 18,000 pulses at 10 pulses/s with 20 cycles/pulse. Pressure levels related to each pulse were 12 and -7 MPa. Inulin (glomerular filtration rate, GFR) and para-aminohippuric acid (effective renal plasma flow, eRPF) clearance was measured before and 1 hour after treatment. Lesion size analysis was performed to assess the volume of hemorrhagic tissue injury created by each treatment (% FRV). Results: No visible gross hematuria was observed in any of the collected urine samples of the treated kidneys. BWL exposure also did not lead to a change in GFR or eRPF after treatment, nor did it cause a measurable amount of hemorrhage in the tissue. Conclusion: Using the clinical treatment parameters employed in this study, BWL did not cause an acute change in renal function or a hemorrhagic lesion.

Design and Characterization of an Ultrasound Transducer for Combined Histotripsy-Thrombolytic Therapy.

Chronic thrombi of the deep veins of the leg are resistant to dissolution or removal by current interventions and can act as thrombogenic sources. Histotripsy, a focused ultrasound therapy, uses the mechanical activity of bubble clouds to liquefy target tissues. In vitro experiments have shown that histotripsy enhances thrombolytic agent recombinant tissue plasminogen activator in a highly retracted clot model resistant to lytic therapy alone. Although these results are promising, further refinement of the acoustic source is necessary for in vivo studies and clinical translation. The source parameters for use in vivo were defined, and a transducer was fabricated for transcutaneous exposure of porcine and human iliofemoral deep-vein thrombosis (DVT) as the target. Based on the design criteria, a 1.5-MHz elliptical source with a 6-cm focal length and a focal gain of 60 was selected. The source was characterized by fiber-optic hydrophone and holography. High-speed photography showed that the cavitation cloud could be confined to dimensions smaller than the specified vessel lumen. The source was also demonstrated in vitro to create confined lesions within clots. The results support that this design offers an appropriate clinical prototype for combined histotripsy-thrombolytic therapy.

Development of Tough Hydrogel Phantoms to Mimic Fibrous Tissue for Focused Ultrasound Therapies.

Tissue-mimicking gels provide a cost-effective medium to optimize histotripsy treatment parameters with immediate feedback. Agarose and polyacrylamide gels are often used to evaluate treatment outcomes as they mimic the acoustic properties and stiffness of a variety of soft tissues, but they do not exhibit high toughness, a characteristic of fibrous connective tissue. To mimic pathologic fibrous tissue found in benign prostate hyperplasia (BPH) and other diseases that are potentially treatable with histotripsy, an optically transparent hydrogel with high toughness was developed that is a hybrid of polyacrylamide and alginate. The stiffness was established using shear wave elastography (SWE) and indentometry techniques and was found to be representative of human BPH ex vivo prostate tissue. Different phantom compositions and excised ex vivo BPH tissue samples were treated with a 700-kHz histotripsy transducer at different pulse repetition frequencies. Post-treatment, the hybrid gels and the tissue samples exhibited differential reduction in stiffness as measured by SWE. On B-mode ultrasound, partially treated areas were present as hyperechoic zones and fully liquified areas as hypoechoic zones. Phase contrast microscopy of the gel samples revealed liquefaction in regions consistent with the target lesion dimensions and correlated to findings identified in tissue samples via histology. The dose required to achieve liquefaction in the hybrid gel was similar to what has been observed in ex vivo tissue and greater than that of agarose of comparable or higher Young's modulus by a factor >10. These results indicate that the developed hydrogels closely mimic elasticities found in BPH prostate ex vivo tissue and have a similar response to histotripsy treatment, thus making them a useful cost-effective alternative for developing and evaluating different treatment protocols.

Improving Burst Wave Lithotripsy Effectiveness for Small Stones and Fragments by Increasing Frequency: Theoretical Modeling and Ex Vivo Study.

Introduction and Objective: In clinical trial NCT03873259, a 2.6-mm lower pole stone was treated transcutaneously and ex vivo with 390-kHz burst wave lithotripsy (BWL) for 40 minutes and failed to break. The stone was subsequently fragmented with 650-kHz BWL after a 4-minute exposure. This study investigated how to fragment small stones and why varying the BWL frequency may more effectively fragment stones to dust. Methods: A linear elastic theoretical model was used to calculate the stress created inside stones from shock wave lithotripsy (SWL) and different BWL frequencies mimicking the stone's size, shape, lamellar structure, and composition. To test model predictions about the impact of BWL frequency, matched pairs of stones (1-5 mm) were treated at (1) 390 kHz, (2) 830 kHz, and (3) 390 kHz followed by 830 kHz. The mass of fragments >1 and 2 mm was measured over 10 minutes of exposure. Results: The linear elastic model predicts that the maximum principal stress inside a stone increases to more than 5.5 times the pressure applied by the ultrasound wave as frequency is increased, regardless of the composition tested. The threshold frequency for stress amplification is proportionate to the wave speed divided by the stone diameter. Thus, smaller stones may be likely to fragment at a higher frequency, but not at a lower frequency below a limit. Unlike with SWL, this amplification in BWL occurs consistently with spherical and irregularly shaped stones. In water tank experiments, stones smaller than the threshold size broke fastest at high frequency (p = 0.0003), whereas larger stones broke equally well to submillimeter dust at high, low, or mixed frequencies. Conclusions: For small stones and fragments, increasing frequency of BWL may produce amplified stress in the stone causing the stone to break. Using the strategies outlined here, stones of all sizes may be turned to dust efficiently with BWL.

Blood vessel deformations on microsecond time scales by ultrasonic cavitation.

Transient interactions among ultrasound, microbubbles, and microvessels were studied using high-speed photomicrography. We observed liquid jets, vessel distention (motion outward against the surrounding tissue), and vessel invagination (motion inward toward the lumen). Contrary to current paradigms, liquid jets were directed away from the nearest vessel wall and invagination exceeded distention. These observations provide insight into the mechanics of bubble-vessel interactions, which appear to depend qualitatively upon the mechanical properties of biological tissues.

A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound.

Cavitation often occurs in therapeutic applications of medical ultrasound such as shock-wave lithotripsy (SWL) and high-intensity focused ultrasound (HIFU). Because cavitation bubbles can affect an intended treatment, it is important to understand the dynamics of bubbles in this context. The relevant context includes very high acoustic pressures and frequencies as well as elevated temperatures. Relative to much of the prior research on cavitation and bubble dynamics, such conditions are unique. To address the relevant physics, a reduced-order model of a single, spherical bubble is proposed that incorporates phase change at the liquid-gas interface as well as heat and mass transport in both phases. Based on the energy lost during the inertial collapse and rebound of a millimeter-sized bubble, experimental observations were used to tune and test model predictions. In addition, benchmarks from the published literature were used to assess various aspects of model performance. Benchmark comparisons demonstrate that the model captures the basic physics of phase change and diffusive transport, while it is quantitatively sensitive to specific model assumptions and implementation details. Given its performance and numerical stability, the model can be used to explore bubble behaviors across a broad parameter space relevant to therapeutic ultrasound.

Observations of the collapses and rebounds of millimeter-sized lithotripsy bubbles.

Bubbles excited by lithotripter shock waves undergo a prolonged growth followed by an inertial collapse and rebounds. In addition to the relevance for clinical lithotripsy treatments, such bubbles can be used to study the mechanics of inertial collapses. In particular, both phase change and diffusion among vapor and noncondensable gas molecules inside the bubble are known to alter the collapse dynamics of individual bubbles. Accordingly, the role of heat and mass transport during inertial collapses is explored by experimentally observing the collapses and rebounds of lithotripsy bubbles for water temperatures ranging from 20 to 60 °C and dissolved gas concentrations from 10 to 85% of saturation. Bubble responses were characterized through high-speed photography and acoustic measurements that identified the timing of individual bubble collapses. Maximum bubble diameters before and after collapse were estimated and the corresponding ratio of volumes was used to estimate the fraction of energy retained by the bubble through collapse. The rebounds demonstrated statistically significant dependencies on both dissolved gas concentration and temperature. In many observations, liquid jets indicating asymmetric bubble collapses were visible. Bubble rebounds were sensitive to these asymmetries primarily for water conditions corresponding to the most dissipative collapses.

Factors Affecting Tissue Cavitation during Burst Wave Lithotripsy.

Burst wave lithotripsy (BWL) is a technology under clinical investigation for non-invasive fragmentation of urinary stones. Under certain ranges of ultrasound exposure parameters, this technology can cause cavitation in tissue leading to renal injury. This study sought to measure the focal pressure amplitude needed to cause cavitation in vivo and determine its consistency in native tissue, in an implanted stone model and under different exposure parameters. The kidneys of eight pigs were exposed to transcutaneous BWL ultrasound pulses. In each kidney, two locations were targeted: the renal sinus and the kidney parenchyma. Each was exposed for 5 min at a set pressure level and parameters, and cavitation was detected using an active cavitation imaging method based on power Doppler ultrasound. The threshold was determined by incrementing the pressure amplitude up or down after each 5-min interval until cavitation occurred/subsided. The pressure thresholds were remeasured postsurgery, targeting an implanted stone or collecting space (in sham). The presence of a stone or sham surgery did not significantly impact the threshold for tissue cavitation. Targeting parenchyma instead of kidney collecting space and lowering the ultrasound pulse repetition frequency both resulted in an increased pressure threshold for cavitation.

"HIFU Beam:" A Simulator for Predicting Axially Symmetric Nonlinear Acoustic Fields Generated by Focused Transducers in a Layered Medium.

"HIFU beam" is a freely available software tool that comprises a MATLAB toolbox combined with a user-friendly interface and binary executable compiled from FORTRAN source code (HIFU beam. (2021). Available: http://limu.msu.ru/node/3555?language=en). It is designed for simulating high-intensity focused ultrasound (HIFU) fields generated by single-element transducers and annular arrays with propagation in flat-layered media that mimic biological tissues. Numerical models incorporated in the simulator include evolution-type equations, either the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation or one-way Westervelt equation, for radially symmetric ultrasound beams in homogeneous and layered media with thermoviscous or power-law acoustic absorption. The software uses shock-capturing methods that allow for simulating strongly nonlinear acoustic fields with high-amplitude shocks. In this article, a general description of the software is given along with three representative simulation cases of ultrasound transducers and focusing conditions typical for therapeutic applications. The examples illustrate major nonlinear wave effects in HIFU fields including shock formation. Two examples simulate propagation in water, involving a single-element source (1-MHz frequency, 100-mm diameter, 90-mm radius of curvature) and a 16-element annular array (3-MHz frequency, 48-mm diameter, and 35-mm radius of curvature). The third example mimics the scenario of a HIFU treatment in a "water-muscle-kidney" layered medium using a source typical for abdominal HIFU applications (1.2-MHz frequency, 120-mm diameter, and radius of curvature). Linear, quasi-linear, and shock-wave exposure protocols are considered. It is intended that "HIFU beam" can be useful in teaching nonlinear acoustics; designing and characterizing high-power transducers; and developing exposure protocols for a wide range of therapeutic applications such as shock-based HIFU, boiling histotripsy, drug delivery, immunotherapy, and others.

Inertial Cavitation Behaviors Induced by Nonlinear Focused Ultrasound Pulses.

Inertial cavitation induced by pulsed high-intensity focused ultrasound (pHIFU) has previously been shown to successfully permeabilize tumor tissue and enhance chemotherapeutic drug uptake. In addition to HIFU frequency, peak rarefactional pressure ( p- ), and pulse duration, the threshold for cavitation-induced bioeffects has recently been correlated with asymmetric distortion caused by nonlinear propagation, diffraction and formation of shocks in the focal waveform, and therefore with the transducer F -number. To connect previously observed bioeffects with bubble dynamics and their attendant physical mechanisms, the dependence of inertial cavitation behavior on shock formation was investigated in transparent agarose gel phantoms using high-speed photography and passive cavitation detection (PCD). Agarose phantoms with concentrations ranging from 1.5% to 5% were exposed to 1-ms pulses using three transducers of the same aperture but different focal distances ( F -numbers of 0.77, 1.02, and 1.52). Pulses had central frequencies of 1, 1.5, or 1.9 MHz and a range of p- at the focus varying within 1-18 MPa. Three distinct categories of bubble behavior were observed as the acoustic power increased: stationary near-spherical oscillation of individual bubbles, proliferation of multiple bubbles along the pHIFU beam axis, and fanned-out proliferation toward the transducer. Proliferating bubbles were only observed under strongly nonlinear or shock-forming conditions regardless of frequency, and only where the bubbles reached a certain threshold size range. In stiffer gels with higher agarose concentrations, the same pattern of cavitation behavior was observed, but the dimensions of proliferating clouds were smaller. These observations suggest mechanisms that may be involved in bubble proliferation: enhanced growth of bubbles under shock-forming conditions, subsequent shock scattering from the gel-bubble interface, causing an increase in the repetitive tension created by the acoustic wave, and the appearance of a new growing bubble in the proximal direction. Different behaviors corresponded to specific spectral characteristics in the PCD signals: broadband noise in all cases, narrow peaks of backscattered harmonics in the case of stationary bubbles, and broadened, shifted harmonic peaks in the case of proliferating bubbles. The shift in harmonic peaks can be interpreted as a Doppler shift from targets moving at speeds of up to 2 m/s, which correspond to the observed bubble proliferation speeds.