176th Meeting of the Acoustical Society of America 5-9 November 2018, Victoria, BC, Canada.

Our goal is an office-based, handheld ultrasound system to target, detach, break, and/or expel stones and stone fragments from the urinary collecting system to facilitate natural clearance. Repositioning of stones in humans (maximum 2.5 MPa, and 3-second bursts) and breaking of stones in a porcine model (maximum 50 cycles, 20 Hz repetition, 30 minutes, and 7 MPa peak negative pressure) have been demonstrated using the same 350-kHz probe. Repositioning in humans was conducted during surgery with a ureteroscope in the kidney to film stone movement. Independent video review confirmed stone movements (≥ 3 mm) in 15 of 16 kidneys (94%). No serious or unanticipated adverse events were reported. Experiments of burst wave lithotripsy (BWL) effectiveness on breaking human stones implanted in the porcine bladder and kidney demonstrated fragmentation of 7 of 7 stones on post mortem dissection. A 1-week survival study with the BWL exposures and 10 specific pathogen-free pigs, showed all findings were within normal limits on clinical pathology, hematology, and urinalysis. These results demonstrate that repositioning of stones with ultrasonic propulsion and breaking of stones with BWL are safe and effective.

High intensity focused ultrasound (HIFU) is rapidly advancing as an alternative therapy for non-invasively treating specific cancers and other pathological tissues through thermal ablation. A new type of HIFU therapy — boiling histotripsy (BH) — aims at mechanical fractionation of into subcellular fragments, with a range of accompanying thermal effects that can be tuned from none to substantial depending on the requirements of the application. The degree of mechanical tissue damage induced by BH has been shown to depend on the tissue type, with collagenous structures being most resistant, and cellular structures being most sensitive. This has been reported for single BH lesions, but has not been replicated in large volumes. Such tissue selectivity effect has potential uses involving tissue decellularization for biofabrication technologies as well as mechanical ablation by BH while sparing critical structures. The goal of this study was to investigate tissue decellularization effect in larger, clinically relevant liquefied volumes of tissue, and to evaluate the accumulated thermal effect in the volumetric lesions under different exposure parameters. All BH exposures were performed with a 256-element 1.2-MHz array of a magnetic resonance imaging — guided HIFU (MR-HIFU) clinical system (Sonalleve V1, Profound Medical Inc, Mississauga, Canada). The volumetric BH lesions were produced in degassed ex vivo bovine liver using 1–10-ms long pulses with in situ shock amplitudes of 75–100 MPa at the focus and pulse repetition frequencies (PRFs) of 1–10 Hz covering a range of effects from pure mechanical homogenization to thermal ablation. Multimodal analysis of the lesions was then performed, including microstructure (histological), ultrastructure (electron microscopy), and molecular (biochemistry) methods. Results show a range of tissue effects in terms of the degree of tissue selectivity and the amount of heat generated in large BH lesions, thereby demonstrating potential for treatments tailored to different clinical applications.

Proceedings, 176th Meeting of the Acoustical Society of America, 5-9 November 2018, Victoria, BC, Canada.

Burst wave lithotripsy (BWL) is a new non-invasive method for stone comminution using bursts of sub-megahertz ultrasound. A porcine model of urolithiasis and techniques to implement BWL treatment has been developed to evaluate its effectiveness and acute safety. Six human calcium oxalate monohydrate stones (6–7 mm) were hydrated, weighed, and surgically implanted into the kidneys of three pigs. Transcutaneous stone treatments were performed with a BWL transducer coupled to the skin via an external water bath. Stone targeting and treatment monitoring were performed with a co-aligned ultrasound imaging probe. Treatment exposures were applied in three 10-minute intervals for each stone. If sustained cavitation in the parenchyma was observed by ultrasound imaging feedback, treatment was paused and the pressure amplitude was decreased for the remaining time. Peak negative focal pressures between 6.5 and 7 MPa were applied for all treatments. After treatment, stone fragments were removed from the kidneys. At least 50% of each stone was reduced to <2 mm fragments. 100% of four stones were reduced to <4 mm fragments. Magnetic resonance imaging showed minimal injury to the functional renal volume. This study demonstrated that BWL could be used to effectively fragment kidney stones with minimal injury.

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.

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.

Multielement focused ultrasound phased arrays have been used in therapeutic applications to treat large tissue volumes by electronic steering of the focus, to target multiple simultaneous foci, and to correct aberration caused by inhomogeneous tissue pathways. There is an increasing interest in using arrays to generate more complex beam shapes and corresponding acoustic radiation force patterns for manipulation of particles such as kidney stones. Toward this end, experimental and computational tools are needed to enable accurate delivery of desired transducer vibrations and corresponding ultrasound fields. The purpose of this paper was to characterize the vibrations of a 256-element array at 1.5 MHz, implement strategies to compensate for variability, and test the ability to generate specified vortex beams that are relevant to particle manipulation. The characterization of the array output was performed in water using both element-by-element measurements at the focus of the array and holography measurements for which all the elements were excited simultaneously. Both methods were used to quantify each element’s output so that the power of each element could be equalized. Vortex beams generated using both compensation strategies were measured and compared to the Rayleigh integral simulations of fields generated by an idealized array based on the manufacturer’s specifications. Although both approaches improved beam axisymmetry, compensation based on holography measurements had half the error relative to the simulation results in comparison to the element-by-element method.

The color Doppler ultrasound twinkling artifact, which highlights kidney stones with rapidly changing color, has the potential to improve stone detection; however, its inconsistent appearance has limited its clinical utility. Recently, it was proposed stable crevice bubbles on the kidney stone surface cause twinkling; however, the hypothesis is not fully accepted because the bubbles have not been directly observed. In this paper, the micron or submicron-sized bubbles predicted by the crevice bubble hypothesis are enlarged in kidney stones of five primary compositions by exposure to acoustic rarefaction pulses or hypobaric static pressures in order to simultaneously capture their appearance by high-speed photography and ultrasound imaging. On filming stones that twinkle, consecutive rarefaction pulses from a lithotripter caused some bubbles to reproducibly grow from specific locations on the stone surface, suggesting the presence of pre-existing crevice bubbles. Hyperbaric and hypobaric static pressures were found to modify the twinkling artifact; however, the simple expectation that hyperbaric exposures reduce and hypobaric pressures increase twinkling by shrinking and enlarging bubbles, respectively, largely held for rough-surfaced stones but was inadequate for smoother stones. Twinkling was found to increase or decrease in response to elevated static pressure on smooth stones, perhaps because of the compression of internal voids. These results support the crevice bubble hypothesis of twinkling and suggest the kidney stone crevices that give rise to the twinkling phenomenon may be internal as well as external.

Multi-element ultrasound arrays are increasingly used in clinical practice for both imaging and therapy. In therapy, they allow electronic steering, aberration correction, and focusing. To avoid grating lobes, an important requirement for such an array is the absence of periodicity in the arrangement of the elements. A convenient solution is the arrangement of the elements along spirals. The objective of this work was to design, fabricate, and characterize an array for boiling histotripsy applications that is capable of generating shock waves in the focus of up to 100 MPa peak pressure while having a reasonable electronic steering range.

The use of shock waves for enhancing thermal effects and mechanically ablating tissue is gaining increased attention in high intensity focused ultrasound (HIFU) applications such as tumor treatment, drug delivery, noninvasive biopsy, and immunotherapy. For abdominal targets, the presence of ribs and inhomogeneous adipose tissue can affect shock formation through aberration, absorption, and diffraction. The goal of this study was to design and validate a phantom for investigating the impact of different tissue structures on shock formation in situ. A transducer with driving electronics was developed to operate at 1.2 MHz with the ability to deliver either short pulses at high powers (up to 5 kW electric power) or continuous output at moderate powers (up to 700 W). Fat and muscle layers were represented by phantoms made from polyvinyl alcohol. Ribs were 3D-printed from a photopolymer material based on 3D CT scan images. Representative targeted tissue was comprised of optically transparent alginate or polyacrylamide gels. The system was characterized by hydrophone measurements free-field in water and in the presence of a body wall or rib phantoms. Shocked waveforms with peak positive/negative pressures of +100 / –20 MPa were measured at the focus in a free field at 1 kW electric source power. When ribs were present, shocks formed at about 50% amplitude at the same power, and higher pressures were measured with ribs positioned closer to the transducer. A uniform body wall structure attenuated shock amplitudes by a smaller amount than non-uniform, and the measurements were insensitive to the axial position of the phantom. Signal magnitude loss at the focus for both the rib phantoms and abdominal wall tissue were consistent with results from real tissues. In addition, boiling histotripsy lesions were generated and visualized in the target gels. The results demonstrate that the presence of ribs and absorptive tissue-mimicking layers do not prevent shock formation at the focus. With real-time lesion visualization, the phantom is suitable for adaptation as a training tool.

Boiling histotripsy (BH) is a method of focused ultrasound surgery that noninvasively applies millisecond-length pulses with high-amplitude shock fronts to generate liquefied lesions in tissue. Such a technique requires unique outputs compared to a focused ultrasound thermal therapy apparatus, particularly to achieve high in situ pressure levels through intervening tissue. This paper describes the design and characterization of a system capable of producing the necessary pressure to transcutaneously administer BH therapy through clinically relevant overlying tissue paths using pulses with duration up to 10 ms. A high-voltage electronic pulser was constructed to drive a 1-MHz focused ultrasound transducer to produce shock waves with amplitude capable of generating boiling within the pulse duration in tissue. The system output was characterized by numerical modeling with the 3-D Westervelt equation using boundary conditions established by acoustic holography measurements of the source field. Such simulations were found to be in agreement with directly measured focal waveforms. An existing derating method for nonlinear therapeutic fields was used to estimate in situ pressure levels at different tissue depths. The system was tested in ex vivo bovine liver samples to create BH lesions at depths up to 7 cm. Lesions were also created through excised porcine body wall (skin, adipose, and muscle) with 3–5 cm thickness. These results indicate that the system is capable of producing the necessary output for transcutaneous ablation with BH.

Therapeutic ultrasound can drive bubble activity that damages soft tissues. To study the potential mechanisms of such injury, transparent agar tissue-mimicking phantoms were subjected to multiple pressure wave bursts of the kind being considered specifically for burst wave lithotripsy. A high-speed camera recorded bubble activity during each pulse. Various agar concentrations were used to alter the phantom's mechanical properties, especially its stiffness, which was varied by a factor of 3.5. However, the maximum observed bubble radius was insensitive to stiffness. During 1000 wave bursts of a candidate burst wave lithotripsy treatment, bubbles appeared continuously in a region that expanded slowly, primarily toward the transducer. Denser bubble clouds are formed at higher pulse repetition frequency. The specific observations are used to inform the incorporation of damage mechanisms into cavitation models for soft materials.

Boiling histotripsy (BH) is a high-intensity focused ultrasound (HIFU)–based method of mechanical tissue fractionation that utilizes millisecond-long bursts of HIFU shock waves to cause boiling at the focus in milliseconds. The subsequent interaction of the incoming shocks with the vapor bubble mechanically lyses surrounding tissue and cells. The acoustic parameter space for BH has been investigated previously and an inverse dependence between the HIFU frequency and the dimensions of a BH lesion has been observed. The primary goal of the present study was to investigate in more detail the ablation rate and reliability of BH in the frequency range relevant to treatment of deep abdominal tissue targets (1–2 MHz). The second goal was to investigate the effect of focal peak pressure levels and shock amplitude on BH lesion formation, given a constant duty factor, a constant ratio of the pulse duration to the time to reach boiling and a constant number of BH pulses. A custom-built 12-element sector array HIFU transducer with F-number = 1.05 was used in all experiments. BH pulses at 5 different frequencies (1, 1.2, 1.5, 1.7 and 1.9 MHz) were delivered to optically transparent polyacrylamide gel phantoms and ex vivo bovine liver and myocardium tissue to observe cavitation and boiling bubble activity with high-speed photography and B-mode ultrasound imaging, correspondingly. In gel phantoms, a cavitation bubble cloud was shown to form prefocally and to shield the focus in all exposures at 1 and 1.2 MHz and in the highest amplitude exposures at 1.5–1.7 MHz; shielding was not observed at 1.9 MHz. In ex vivo tissue, this shielding effect was observed in 25% of exposures when peak negative in situ pressure exceeded 10.2 MPa at 1 MHz and 14.5 MPa at 1.5 MHz. When shielding occurred, the exposures resulted in mild tissue disruption in the prefocal region, but not liquefaction. The dimensions of liquefied lesions followed the inverse proportionality trend with frequency; consequently, the frequency range of 1.2–1.5 MHz appeared to be preferable for BH exposures in terms of the compromise between the ablation rate and reliability. The lesion size was independent of the duration of the BH pulses (or the total "HIFU on" time), provided that the number of pulses was constant and boiling was induced within each pulse. Thus, the use of shorter (1 ms vs. 10 ms), higher amplitude BH pulses allowed up to 10-fold reduction in treatment time for a given duty factor.

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.

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

A theoretical study of the growth of a spherical vapor bubble in a spherically symmetric superheated region is described. The modeling of bubble dynamics is based on considering the hydrodynamic and thermal processes inside a bubble and the surrounding liquid.

Ultrasonic atomization has been used in air humidifiers and is also involved in therapeutic applications of intense ultrasound such as boiling histotripsy. An as-yet unexplained phenomenon occurs when a focused ultrasound beam in water creates an acoustic fountain in the form of a drop chain, which explodes in less than a millisecond. In the present paper, we seek to develop a nonlinear theory to explain this phenomenon. We hypothesize that standing wave harmonics are generated inside the water drops due to acoustic nonlinearities, which, along with localized heat deposition in the drop center, may generate a superheated vapor bubble that causes the explosion.

In this work, an effective transcranial imaging technique is proposed to compensate for distortions of ultrasound (US) field caused by skull bone. The results of an experimental study using skull phantoms and 2D synthetic array are presented. The method was used to visualize mm-sized spherical scatterers made from styrofoam as well as a soft silicone tube mimicking a blood vessel. It is shown that the proposed technique is capable to compensate for field distortion and results in improved imaging through the skull.

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.

In medical and industrial ultrasound, it is often necessary to measure the acoustic properties of a material. A specific medical application requires measurements of sound speed, attenuation, and nonlinearity to characterize livers being evaluated for transplantation. For this application, a transmission-mode caliper device is proposed in which both transmit and receive transducers are directly coupled to a test sample, the propagation distance is measured with an indicator gage, and receive waveforms are recorded for analysis. In this configuration, accurate measurements of nonlinearity present particular challenges: diffraction effects can be considerable while nonlinear distortions over short distances typically remain small. To enable simple estimates of the nonlinearity coeffcient from a quasi-linear approximation to the lossless Burgers’ equation, the calipers utilize a large transmitter and plane waves are measured at distances of 15–50 mm. Waves at 667 kHz and pressures between 0.1 and 1 MPa were generated and measured in water at different distances; the nonlinearity coeffcient of water was estimated from these measurements with a variability of approximately 10%. Ongoing efforts seek to test caliper performance in other media and improve accuracy via additional transducer calibrations.

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation of tissue. In this work, an inverse problem of determining transducer parameters to enable formation of shocks with desired amplitude at the focus is solved. The solution was obtained by performing multiple direct simulations of the parabolic Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sources as well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocks are formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90–100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University.

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.

Purpose
We have developed a new method of lithotripsy that uses short, broadly focused bursts of ultrasound rather than shock waves to fragment stones. This study investigated the characteristics of stone comminution by burst wave lithotripsy in vitro.

Materials and Methods
Artificial and natural stones (mean 8.2±3.0 mm, range 5–15 mm) were treated with ultrasound bursts using a focused transducer in a water bath. Stones were exposed to bursts with focal pressure amplitude 𕟮.5 MPa at 200 Hz burst repetition rate until completely fragmented. Ultrasound frequencies of 170 kHz, 285 kHz, and 800 kHz were applied using 3 different transducers. The time to achieve 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 𕟴.8 MPa at 170 kHz. Fractures appeared along the stone surface, resulting in fragments separating 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 treatment durations between a mean of 36 seconds for uric acid to 14.7 minutes for cystine stones. At a frequency of 170 kHz, the largest artificial stone fragments were <4 mm. Exposures at 285 kHz produced only fragments <2 mm, and 800 kHz produced only fragments <1 mm.

Conclusions
Stone comminution with burst wave lithotripsy is feasible as a potential noninvasive treatment method for nephrolithiasis. Adjusting the fundamental ultrasound frequency allows control of stone fragment size.

Burst wave lithotripsy is a novel technology that uses focused, sinusoidal bursts of ultrasound to fragment kidney stones. Prior research laid the groundwork to design an extracorporeal, image-guided probe for in-vivo testing and potentially human clinical testing. Toward this end, a 12-element 330 kHz array transducer was designed and built. The probe frequency, geometry, and shape were designed to break stones up to 1 cm in diameter into fragments <2 mm. A custom amplifier capable of generating output bursts up to 3 kV was built to drive the array. To facilitate image guidance, the transducer array was designed with a central hole to accommodate co-axial attachment of an HDI P4-2 probe. Custom B-mode and Doppler imaging sequences were developed and synchronized on a Verasonics ultrasound engine to enable real-time stone targeting and cavitation detection, Preliminary data suggest that natural stones will exhibit Doppler %u201Ctwinkling%u201D artifact in the BWL focus and that the Doppler power increases as the stone begins to fragment. This feedback allows accurate stone targeting while both types of imaging sequences can also detect cavitation in bulk tissue that may lead to injury.

Pulsed high-intensity focused ultrasound (pHIFU) has been shown to enhance vascular permeability, disrupt tumor barriers and enhance drug penetration into tumor tissue through acoustic cavitation. Monitoring of cavitation activity during pHIFU treatments and knowing the ultrasound pressure levels sufficient to reliably induce cavitation in a given tissue are therefore very important. Here, three metrics of cavitation activity induced by pHIFU and evaluated by confocal passive cavitation detection were introduced: cavitation probability, cavitation persistence and the level of the broadband acoustic emissions.

These metrics were used to characterize cavitation activity in several ex vivo tissue types (bovine tongue and liver and porcine adipose tissue and kidney) and gel phantoms (polyacrylamide and agarose) at varying peak-rare factional focal pressures (1–12 MPa) during the following pHIFU protocol: frequency 1.1 MHz, pulse duration 1 ms and pulse repetition frequency 1 Hz. To evaluate the relevance of the measurements in ex vivo tissue, cavitation metrics were also investigated and compared in the ex vivo and in vivo murine pancreatic tumors that develop spontaneously in transgenic KrasLSL.G12 D/+; p53 R172 H/+ ; PdxCretg/ (KPC) mice and closely re-capitulate human disease in their morphology.

The cavitation threshold, defined at 50% cavitation probability, was found to vary broadly among the investigated tissues (within 2.5–10 MPa), depending mostly on the water-lipid ratio that characterizes the tissue composition. Cavitation persistence and the intensity of broadband emissions depended both on tissue structure and lipid concentration. Both the cavitation threshold and broadband noise emission level were similar between ex vivo and in vivo pancreatic tumor tissue. The largest difference between in vivo and ex vivo settings was found in the pattern of cavitation occurrence throughout pHIFU exposure: it was sporadic in vivo, but it decreased rapidly and stopped over the first few pulses ex vivo. Cavitation activity depended on the interplay between the destruction and circulation of cavitation nuclei, which are not only used up by HIFU treatment but also replenished or carried away by circulation in vivo. These findings are important for treatment planning and optimization in pHIFU-induced drug delivery, in particular for pancreatic tumors.

Nonlinear propagation effects are present in most fields generated by high intensity focused ultrasound (HIFU) sources. In some newer HIFU applications, these effects are strong enough to result in the formation of high amplitude shocks that actually determine the therapy and provide a means for imaging. However, there is no standard approach yet accepted to address these effects. Here, a set of combined measurement and modeling methods to characterize nonlinear HIFU fields in water and predict acoustic pressures in tissue is presented. A characterization method includes linear acoustic holography measurements to set a boundary condition to the model and nonlinear acoustic simulations in water for increasing pressure levels at the source. A derating method to determine nonlinear focal fields with shocks in situ is based on the scaling of the source pressure for data obtained in water to compensate for attenuation losses in tissue. The accuracy of the methods is verified by comparing the results with hydrophone and time-to-boil measurements. Major effects associated with the formation of shocks are overviewed. A set of metrics for determining thermal and mechanical bioeffects is introduced and application of the proposed tools to strongly nonlinear HIFU applications is discussed.

Shock wave lithotripsy (SWL) is the most common procedure for treatment of kidney stones. SWL noninvasively delivers high-energy focused shocks to fracture stones into passable fragments. We have recently observed that lower-amplitude, sinusoidal bursts of ultrasound can generate similar fracture of stones. This work investigated the characteristics of stone fragmentation for natural (uric acid, struvite, calcium oxalate, and cystine) and artificial stones treated by ultrasound bursts. Stones were fixed in position in a degassed water tank and exposed to 10-cycle bursts from a 200-kHz transducer with a pressure amplitude of p ≤ 6.5 MPa, delivered at a rate of 40–200 Hz. Exposures caused progressive fractures in the stone surface leading to fragments up to 3 mm. Treatment of artificial stones at different frequencies exhibited an inverse relationship between the resulting fragment sizes and ultrasound frequency. All artificial and natural types of stones tested could be fragmented, but the comminution rate varied significantly with stone composition over a range of 12–630 mg/min. These data suggest that stones can be controllably fragmented by sinusoidal ultrasound bursts, which may offer an alternative treatment strategy to SWL.

The use of projection methods is increasingly accepted as a standard way of characterizing the 3D fields generated by medical ultrasound sources. When combined with hydrophone measurements of pressure amplitude and phase over a surface transverse to the wave propagation, numerical projection can be used to reconstruct 3D fields that account for operational details and imperfections of the source. Here, we use holography measurements to characterize the fields generated by two array transducers with different geometries and modes of operation. First, a seven-element, high-power therapy transducer is characterized in the continuous-wave regime using holography measurements and nonlinear forward-projection calculations. Second, a C5-2 imaging probe (Philips Healthcare) with 128 elements is characterized in the transient regime using holography measurements and linear projection calculations. Results from the numerical projections for both sources are compared with independent hydrophone measurements of select waveforms, including shocked focal waveforms for the therapy transducer. Accurate 3D field representations have been confirmed, though a notable sensitivity to hydrophone calibrations is revealed. Uncertainties associated with this approach are discussed toward the development of holography measurements combined with numerical projections as a standard metrological tool.

Previous studies have provided insight into the physical mechanisms of stone fracture in shock wave lithotripsy. Broadly focused shocks efficiently generate shear waves in the stone leading to internal tensile stresses, which in concert with cavitation at the stone surface, cause cracks to form and propagate. Here, we propose a separate mechanism by which stones may fragment from sinusoidal ultrasound bursts without shocks. A numerical elastic wave model was used to simulate propagation of tone bursts through a cylindrical stone at a frequency between 0.15 and 2 MHz. Results suggest that bursts undergo mode conversion into surface waves on the stone that continually create significant stresses well after the exposure is terminated. Experimental exposures of artificial cylindrical stones to focused burst waves in vitro produced periodic fractures along the stone surface. The fracture spacing and resulting fragment sizes corresponded well with the spacing of stresses caused by surface waves in simulation at different frequencies. These results indicate surface waves may be an important factor in fragmentation of stones by focused tone bursts and suggest that the resulting stone fragment sizes may be controlled by ultrasound frequency.

High-intensity focused ultrasound (HIFU) is a treatment modality that relies on the delivery of acoustic energy to remote tissue sites to induce thermal and/or mechanical tissue ablation. To ensure the safety and efficacy of this medical technology, standard approaches are needed for accurately characterizing the acoustic pressures generated by clinical ultrasound sources under operating conditions. Characterization of HIFU fields is complicated by nonlinear wave propagation and the complexity of phased-array transducers. Previous work has described aspects of an approach that combines measurements and modeling, and here we demonstrate this approach for a clinical phased-array transducer. First, low amplitude hydrophone measurements were performed in water over a scan plane between the array and the focus. Second, these measurements were used to holographically reconstruct the surface vibrations of the transducer and to set a boundary condition for a 3-D acoustic propagation model. Finally, nonlinear simulations of the acoustic field were carried out over a range of source power levels. Simulation results were compared with pressure waveforms measured directly by hydrophone at both low and high power levels, demonstrating that details of the acoustic field, including shock formation, are quantitatively predicted.

Histotripsy treatments use high-amplitude shock waves to fractionate tissue. Such treatments have been demonstrated using both cavitation bubbles excited with microsecond-long pulses and boiling bubbles excited for milliseconds. A common feature of both approaches is the need for bubble growth, where at 1 MHz cavitation bubbles reach maximum radii on the order of 100 microns and boiling bubbles grow to about 1 mm. To explore how histotripsy bubbles grow, a model of a single, spherical bubble that accounts for heat and mass transport was used to simulate the bubble dynamics. Results suggest that the asymmetry inherent in nonlinearly distorted waveforms can lead to rectified bubble growth, which is enhanced at elevated temperatures. Moreover, the rate of this growth is sensitive to the waveform shape, in particular the transition from the peak negative pressure to the shock front. Current efforts are focused on elucidating this behavior by obtaining an improved calibration of measured histotripsy waveforms with a fiber-optic hydrophone, using a nonlinear propagation model to assess the impact on the focal waveform of higher harmonics present at the source's surface, and photographically observing bubble growth rates.

High intensity focused ultrasound (HIFU) is a rapidly growing medical technology with many clinical applications. The safety and efficacy of these applications require accurate characterization of ultrasound fields produced by HIFU systems. Current nonlinear numerical models based on the KZK and Westervelt wave equations have been shown to serve as quantitatively accurate tools for HIFU metrology. One of the critical parts of the modeling is to set a boundary condition at the source. In previous studies we proposed using measurements of low-amplitude fields to determine the source parameters. In this paper, two approaches of setting the boundary condition are reviewed: The acoustic holography method utilizes two-dimensional scanning of pressure amplitude and phase and numerical back-propagation to the transducer surface. An equivalent source method utilizes one-dimensional pressure measurements on the beam axis and in the focal plane. The dimensions and surface velocity of a uniformly vibrating transducer then are determined to match the one-dimensional measurements in the focal region. Nonlinear simulations are performed for increasing pressure levels at the source for both approaches. Several examples showing the accuracy and capabilities of the proposed methods are presented for typical HIFU transducers with different geometries.

High-speed photomicrography was used to study the translational dynamics of single microbubbles in microvessels of ex vivo rat mesenteries. The microbubbles were insonated by a single 2 microsecond ultrasound pulse with a center frequency of 1 MHz and peak negative pressures spanning the range of 0.8-4 MPa. The microvessel diameters ranged from 10-80 micrometers. The high-speed image sequences show evidence of ultrasound-activated microbubble translation away from the nearest vessel wall; no microbubble showed a net translation toward the nearest vessel wall. Microbubble maximum translation displacements exceeded 20 micrometers. Microjets with the direction of the jets identifiable were also observed; all microjets appear to have been directed away from the nearest vessel wall. These observations appear to be characteristic of a strong coupling between ultrasound-driven microbubbles and compliant microvessels. Although limited to mesenteric tissues, these observations provide an important step in understanding the physical interactions between microbubbles and microvessels.

Histotripsy describes treatments in which high-amplitude acoustic pulses are used to excite bubbles and erode tissue. Though tissue erosion can be directly attributed to bubble activity, the genesis and dynamics of bubbles remain unclear. Histotripsy lesions that show no signs of thermal coagulative damage have been generated with two different acoustic protocols: relatively long acoustic pulses that produce local boiling within milliseconds and relatively short pulses that are higher in amplitude but likely do not produce boiling. While these two approaches are often distinguished as 'boiling' versus 'cavitation', such labels can obscure similarities. In both cases, a bubble undergoes large changes in radius and vapor is transported into and out of the bubble as it oscillates. Moreover, observations from both approaches suggest that bubbles grow to a size at which they cease to collapse violently. In order to better understand the dynamics of histotripsy bubbles, a single-bubble model has been developed that couples acoustically excited bubble motions to the thermodynamic state of the surrounding liquid. Using this model for bubbles exposed to histotripsy sound fields, simulations suggest that two mechanisms can act separately or in concert to lead to the typically observed bubble growth. First, nonlinear acoustic propagation leads to the evolution of shocks and an asymmetry in the positive and negative pressures that drive bubble motion. This asymmetry can have a rectifying effect on bubble oscillations whereby the bubble grows on average during each acoustic cycle. Second, vapor transport to/from the bubble tends to produce larger bubbles, especially at elevated temperatures. Vapor transport by itself can lead to rectified bubble growth when the ambient temperature exceeds 100C ('boiling') or local heating in the vicinity of the bubble leads to a superheated boundary layer.

Recent studies in high intensity focused ultrasound (HIFU) have shown significant interest in generating purely mechanical damage of tissue without thermal coagulation. Here, an approach using millisecond bursts of ultrasound shock waves and repeated localized boiling is presented. In HIFU fields, nonlinear propagation effects lead to formation of shocks only in a small focal region. Significant enhancement of heating due to absorption at the shocks leads to boiling temperatures in tissue in milliseconds as calculated based on weak shock theory. The heated and potentially necrotized region of tissue is small compared to the volume occupied by the mm-sized boiling bubble it creates. If the HIFU pulse is only slightly longer than the time-to-boil, thermal injury is negligible compared to the mechanical injury caused by the exploding boiling bubble and its further interaction with shocks. Experiments performed in transparent gels and various ex vivo and in vivo tissues have confirmed the effectiveness of this emulsification method. In addition, since mm-sized boiling bubbles are highly echogenic, tissue emulsification can be easily monitored in real-time using B-mode ultrasound imaging.

Clinical therapeutic ultrasound systems rely on the delivery of known acoustic pressures to treatment sites. Assessing the safety and efficacy of these systems relies upon characterization of ultrasound sources in order to determine the acoustic fields they produce and to understand performance changes over time. While direct hydrophone measurements of intense acoustic fields are possible, data acquisition throughout a treatment volume can be time-consuming and is only applicable to the specific source conditions tested. Moreover, measuring intense acoustic fields poses challenges for the hydrophone. An alternate approach combines low-amplitude pressure measurements with modeling of the nonlinear pressure field at various transducer power levels. In this work, low-intensity measurements were acquired for several therapeutic transducers. Pressure amplitude and phase were measured on a plane near the test transducer; the Rayleigh integral was used to back-propagate the acoustic field and mathematically reconstruct relative vibrations of the transducer surface. Such holographic reconstructions identified the vibratory characteristics of different types of transducers, including a 256-element clinical array. These reconstructions can be used to define boundary conditions for modeling and to record characteristics of transducer performance.

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.

Interactions between bubbles and nearby boundaries have been studied for some time; however, the direct interactions between bubbles and tissue boundaries, especially blood vessel walls, have not been studied to a large extent. In this work highspeed microscopy was used to study the dynamical interaction between microbubbles and microvessels of ex vivo rat mesentery subjected to a single pulse of ultrasound. Ultrasound contrast agent microbubbles were injected into the blood vessels of rat mesentery subsequent to having the blood flushed out. India ink was used to increase the contrast between microvessels and surrounding tissues. Tissue samples were aligned at the focus of both an ultrasound transducer with a center frequency of 1 MHz and an inverted microscope coupled to a high speed camera. Fourteen high-speed microphotographic images were acquired for each experiment using 50 ns shutter speeds. Observations of the coupled dynamics between bubbles and vessels ranging from 10 micrometer to 100 micrometer diameters under the exposure of ultrasound of peak negative pressure within the range of 1 MPa to 7.8 MPa suggest that the vessel wall dilates during bubble expansion, and invaginates during bubble contraction. A significant finding is that the ratio of invagination to distension is usually >1 and large circumferential strains can be imposed on the vessel wall during vessel invagination. In addition, the surrounding tissue response was also quantified. Based on these studies, we hypothesize that vessel invagination is the dominant mechanism for the initial induction of vascular damage via cavitation.

In medical ultrasound, acoustically excited bubbles are relevant to both imaging and therapeutic applications and have been implicated in causing vascular damage. A current paradigm for understanding interactions between bubbles and vessels considers the distention of small vessels and the impingement of bubble jets on vessel walls to be the most likely damage mechanisms. However, recent high-speed photographs suggest a type of interaction that is characterized by a prominent invagination of the vessel wall (i.e., an inward deflection toward the lumen) that appears to exceed any accompanying distention.

To elucidate mechanisms for such behavior, a confined flow geometry between an oscillating bubble and a nearby boundary is modeled and compared to fully spherical flow. From a Bernoulli-type equation for an incompressible and inviscid liquid, the pressure attributable to a bubble at a nearby boundary is found to become biased toward negative values as the flow becomes more confined and less spherical. Such negative values are consistent with invagination. Using radial bubble dynamics inferred from a high-speed photographic sequence of a bubble in a vessel, the aforementioned model was used to simulate the pressure radiated by the bubble at the vessel wall. At the 1 MHz acoustic frequency, the simulated negative pressure is 2.5 times the positive pressure; in turn, the observed vessel displacement inward was about 6 times the corresponding outward displacement.

Bubble-enhanced heating is a current topic of interest associated with high intensity focused ultrasound (HIFU). For HIFU treatments designed to utilize acoustic radiation from bubbles as a heating mechanism, it has been reported that useful bubble activity diminishes at elevated temperatures. To better understand and quantify this behavior, a model has been implemented that couples the thermodynamic state of a strongly driven spherical bubble with thermal conditions in the surrounding liquid. This model has been validated over a range of temperature conditions against experimental data from the collapses and rebounds of millimeter-sized bubbles.

With this model, the response of a micron-sized bubble was simulated under exposure to MHz/MPa HIFU excitation, while various surrounding liquid temperatures were considered. Characterizing the bubble response through the power spectral density of pressure radiated from the bubble, model calculations suggest that bubble collapses are significantly attenuated at temperatures above about 70°C. For instance, the acoustically radiated energy at 80°C is an order of magnitude less than that at 20°C. These results suggest that the efficacy of bubble-enhanced heating may be limited to temperatures below 70°C. Moreover, temperature will affect hydrophone measurements used to passively assess cavitation activity.

New lithotripters with narrower foci and higher peak pressures than the original Dornier HM3 electrohydraulic lithotripter have proven to be less effective and less safe. Hence, accurate measurements of the focal characteristics of lithotripter shock waves are important. The current technique for measuring beamwidth requires a collection of single-point measurements over multiple shock waves, thereby introducing error as a result of any shock-to-shock variability.

This work reports on the construction of a hydrophone array sensor and on array measurements of individual lithotripter shock waves. Beamwidths for an electrohydraulic lithotripter with a broad-focus HM3-style reflector and a narrow-focus modified reflector were measured using both new and worn electrodes as well as two different electrical charging potentials. The array measured the waveform, beamwidth, and focal location of individual shock waves. The HM3-style reflector produced repeatable focal waveforms and beam profiles at an 18 kV charging potential with new and worn electrodes. Corresponding measurements suggest a narrower beamwidth than reported previously from averaged point measurements acquired under the same conditions. In addition, a lack of consistency in the measured beam profiles at 23 kV underscores the value of measuring individual shock waves.

In extracorporeal electrohydraulic lithotripters, a hemi-ellipsoidal metal reflector is used to focus a spherical wave generated by an electrical discharge. The spark source is positioned at one of the ellipsoid foci (F1); this makes the reflected wave focused at the other focus (F2). Despite the common assumption that the reflector behaves as a rigid mirror, the true reflection phenomenon includes the generation and reverberation of elastic waves in the reflector, which reradiate to the medium. Although these waves are much lower in amplitude than the specularly reflected wave, they may influence cavitation at F2. To explore such effects, waves in water and a brass reflector were modeled in finite differences based on the linearized equations of elasticity. The bubble response was simulated based on a Rayleigh-type equation for the bubble radius. In addition, the role of acoustic nonlinearity was estimated by numerical modeling. It is shown that the elastic waves in the reflector give rise to a long "ringing" tail, which results in nonmonotonic behavior of the bubble radius during its inertial growth after shock wave passage. This numerical result is qualitatively confirmed by experimental observations of bubble behavior using high-speed photography.

A current topic of interest for high intensity focused ultrasound (HIFU) treatments involves the relative roles of bubbles and nonlinear acoustic propagation as heating mechanisms. At high amplitudes, nonlinear propagation leads to the generation of boiling bubbles within milliseconds; at lower amplitudes, cavitation bubbles can enhance heating through viscous dissipation, acoustic radiation, and heat conduction. In this context, understanding the physics attendant to HIFU bubbles requires consideration of gas–vapor bubble dynamics, including thermal effects in the nearby liquid. To this end, recent experimental observations with high-speed photography suggest that bubbles undergo a brief period of growth after application of HIFU has stopped. To explain this observation, a model is implemented that couples the thermodynamic state of a strongly driven bubble with thermal conditions in the surrounding liquid. From model simulations, liquid heating in the vicinity of a HIFU bubble is estimated. Calculations suggest that thermal conduction and viscous dissipation can lead to the evolution of a nontrivial thermal boundary layer. Development of a boundary layer that reaches superheated temperatures would explain the aforementioned experimental observation. As such, cavitation bubbles and boiling bubbles share important characteristics during HIFU.

Bubbles generated by acoustic cavitation or boiling are often observed during high intensity focused ultrasound (HIFU) medical treatments. In this work, high-speed video imaging, a 20-MHz focused acoustic transducer, and the driving voltage to our 2-MHz HIFU source are used to distinguish between cavitation and boiling in a tissue-mimicking gel phantom at peak focal intensities up to 30,000 W/cm². Bubble dynamics are modeled using a reduced order model that accounts for evaporation and condensation, heat and gas transfer across the interface, and temperature changes in the surrounding liquid. The model includes vapor trapping, whereby the noncondensable gas slows diffusion of vapor to the interface, thereby limiting condensation. At the transducer focus, evidence of cavitation is observed in the first millisecond before disappearing. Boiling is observed several milliseconds later, after sufficient heating of the focal volume to 100&$176;C. The disappearance of cavitation can be explained in part by the observed motion of bubbles away from the focal region due to radiation-pressure forces and in part by the softening of bubble collapses by vapor trapping. Thus, at clinical HIFU amplitudes, bubble dynamics and their impact on image-feedback and/or therapy change dramatically in only milliseconds.

The responses of bubbles subjected to a lithotripsy shock wave have been investigated numerically and experimentally to elucidate the role of heat and mass transfer in the underlying dynamics of strongly excited bubbles. Single spherical bubbles were modeled as gas–vapor bubbles by accounting for liquid compressibility, heat transfer, vapor transport, vapor trapping by noncondensable gases, diffusion of noncondensable gases, and heating of the liquid at the bubble wall. For shock-wave excitations, the model predicts bubble growth and collapse, followed by rebounds whose durations are significantly affected by vapor trapping. To experimentally test these predictions, bubble rebound durations were measured using passive cavitation detectors, while high-speed photographs were captured to evaluate the local cavitation field and to estimate radius–time curves for individual bubbles. Data were acquired for bubbles in water with varying temperature and dissolved gas content. Measurements verify that vapor trapping is an important mechanism that is sensitive to both temperature and dissolved gas content. While this work focuses primarily on individual bubbles, some bubble cloud effects were observed. Analysis with a simple multibubble model provides noteworthy insights.

For treatments that use high-intensity focused ultrasound (HIFU), it is important to understand the behavior of bubbles in the context of both large acoustic pressures and elevated temperatures in the surrounding medium. Based upon clinical and experimental observations, any preexisting cavitation nuclei in tissue or blood are likely to be less than 1 micron. For HIFU conditions characterized by megahertz frequencies and pressures on the order of megaPascals, gas bubbles less than a micron in radius can grow explosively. Calculations for a single, spherical bubble imply that the resulting bubble motions are significantly influenced by evaporation and condensation processes. Consequently, at both high and low ambient temperatures, HIFU-driven bubbles may best be described as gas-vapor bubbles that can exhibit rectified transfer of both heat and noncondensable gases. Moreover, increased vapor pressures associated with ambient temperatures at or above "boiling" may not lead to unbounded bubble growth as expected for a quasistatic bubble in a superheated medium. Instead, calculations suggest that growth of boiling bubbles can be confined.

In therapeutic applications of biomedical ultrasound, it is important to understand the behavior of cavitation bubbles. Herein, the dynamics of a single, spherical bubble in water are modeled using the Gilmore equation closed by an energy balance on bubble contents for calculation of pressures inside the bubble. Moreover, heat and mass transfer at the bubble wall are incorporated using the Eller–Flynn zeroth-order approximation for gas diffusion, an estimation of non-equilibrium phase change based on the kinetic theory of gases, and assumed shapes for the spatial temperature distribution in the surrounding liquid. Bubble oscillations predicted by this model are investigated in response to a lithotripter shock wave. Model results indicate that vapor trapped inside the bubble during collapse plays a significant role in the afterbounce behavior and is sensitively dependent upon the ambient liquid temperature. Initial experiments have been conducted to quantify the afterbounce behavior of a single bubble as a function of ambient temperature; however, the results imply that many bubbles are present and collectively determine the collapse characteristics.

In therapeutic applications of biomedical ultrasound, it is important to understand the behavior of cavitation bubbles. For applications that use high-intensity focused ultrasound (HIFU), both large negative acoustic pressures and heating can independently lead to bubble formation. Although neglected previously, heating during HIFU is expected to affect the growth and dissolution of bubbles by both raising the vapor pressure and promoting outgassing from gas-saturated tissues. Herein, the dynamics of a single, spherical bubble in water have been modeled using the Gilmore equation closed with an energy balance on bubble contents for calculation of pressures inside the bubble. Moreover, heat and mass transfer at the bubble wall are incorporated using the Eller–Flynn zeroth-order approximation for gas diffusion, an estimation of non-equilibrium phase change based on the kinetic theory of gases, and assumed shapes for the spatial temperature distribution in the surrounding liquid [Yasui, J. Phys. Soc. Jpn. 65, 2830-2840 (1996)]. This model allows explicit coupling of the ambient heating during HIFU to the thermodynamic state of an oscillating bubble and is currently being used to explore the growth rates of initially small, undetectable bubbles exposed to various HIFU treatment protocols.