Inertial Collapse Research Articles

A two-criterion model for microvascular bioeffects induced in vivo by contrast microbubbles exposed to medical ultrasound

The mechanical index (MI) assumes that bubbles of all relevant sizes exist in tissue, yet that assumption is approximated only in studies that include use of a microbubble contrast agent. If the MI is taken to be the key dosimetric parameter, then it should allow science-based safety guidance for contrast-enhanced diagnostic ultrasound. However, theoretical predictions based on the MI typically do not concur with the frequency dependence of experimentally measured thresholds for bioeffects. For example, experimental measurements of thresholds for glomerular capillary hemorrhage in rats infused with contrast microbubbles (Miller et al. UMB 2008;34:1678) increase approximately linearly with frequency while the MI assumes a square-root dependence. Here, thresholds for inertial cavitation were computed for linear versions of the acoustic pulses used in that study assuming bubbles containing either air, C3F8, or a 1:1 mixture of the two and surrounded by either blood or kidney tissue. While no single threshold criterion was successful, combining results for one criterion that maximized circumferential stress in the capillary wall with another that ensured an inertial collapse, produced thresholds that were consistent with experimental data. This suggests that development of a contrast-specific safety metric may be achieved by further testing and confirmation in different tissues.

Deformation- and temperature-related processes that occur upon the collapse of a thick cylindrical shell made of steel 20

An experiment has been performed on the collapse of a thick steel cylindrical shell into a continuous cylinder under the action of a sliding detonation wave. The process of the collapse has been recorded via X-ray photography, and it has been found that the time of collapse in one section is equal to 30 μs. The average degree of deformation is 77% and the rate of deformation is 104 s−1. The structure of steel 20 in the transverse section of the cylinder consists of three zones. In the outer zone, the initial ferrite-pearlite structure changes under the effect of compressive shock wave and localized shears. The shock wave leads to the formation of a high-pressure ɛ phase and twins. Upon the subsequent inertial collapse of the shell, substantial shear deformations arise in the surface layer, which are localized in directions located at angles of 60° to the cylindrical surface. The structure of the middle zone changes under the action of severe plastic deformation, which occurs predominantly in the radial direction. The deformation leads to the appearance of an internal pressure and to an increase in the temperature. As a result of the action of three factors (pressure, temperature, and deformation), the temperature of the formation of austenite decreases by several hundred kelvins. In the free ferrite, an α → γ transformation occurs and quenching takes place following a subsequent sharp decrease in pressure (barothermic quenching). The pearlitic regions suffer plastic deformation. The microhardness of the steel with this structure is equal to the microhardness of quenched steel. The structure of the third, i.e., central, zone, changes under the action of a significant increase in temperature caused by the further increase in the degree of deformation. The complete transformation of ferrite into austenite occurs at the center of this zone, which means that the temperature in this zone reaches 850–900°C or greater. The microhardness decreases to values typical of annealed steel.

Inertial collapse of liquid rings

AbstractLiquid rings can be generated in the Leidenfrost state using liquid oxygen of low boiling point ($- 183~\textdegree \mathrm{C} $) and high magnetic susceptibility, allowing one to ‘sculpt’ the liquid into a ring shape using an annular magnet. When the magnetic field is turned off, the ring shrinks back into a puddle with a constant acceleration. A potential flow approach accurately describes the dynamics of closure with an equation reminiscent of the Rayleigh–Plesset equation for the collapse of transient cavities.

The effect of static pressure on the inertial cavitation threshold

The amplitude of the acoustic pressure required to nucleate a gas or vapor bubble in a fluid, and to have that bubble undergo an inertial collapse, is termed the inertial cavitation threshold. The magnitude of the inertial cavitation threshold is typically limited by mechanisms other than homogeneous nucleation such that the theoretical maximum is never achieved. However, the onset of inertial cavitation can be suppressed by increasing the static pressure of the fluid. The inertial cavitation threshold was measured in ultrapure water at static pressures up to 30 MPa (300 bars) by exciting a radially symmetric standing wave field in a spherical resonator driven at a resonant frequency of 25.5 kHz. The threshold was found to increase linearly with the static pressure; an exponentially decaying temperature dependence was also found. The nature and properties of the nucleating mechanisms were investigated by comparing the measured thresholds to an independent analysis of the particulate content and available models for nucleation.

On stability of inertial collapse of shells filled with viscous fluid

Consideration is given to problems of nonlinear stability of inertial collapse of spherical and cylindrical shells filled with a viscous incompressible fluid homogeneous in density. Using Lyapunov’s direct method, we determine: 1) the necessary and sufficient condition for stability of spherically symmetrical inertial collapse of a thick spherical shell with respect to finite disturbances of symmetry of the same type and 2) absolute stability of cylindrically symmetrical inertial collapse of a cylindrical shell relative to finite disturbances of the same symmetry.

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.

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.

Investigation of noninertial cavitation produced by an ultrasonic horn

This paper reports on noninertial cavitation that occurs beyond the zone close to the horn tip to which the inertial cavitation is confined. The noninertial cavitation is characterized by collating the data from a range of measurements of bubbles trapped on a solid surface in this noninertial zone. Specifically, the electrochemical measurement of mass transfer to an electrode is compared with high-speed video of the bubble oscillation. This gas bubble is shown to be a "noninertial" event by electrochemical surface erosion measurements and "ring-down" experiments showing the activity and motion of the bubble as the sound excitation was terminated. These measurements enable characterization of the complex environment produced below an operating ultrasonic horn outside of the region where inertial collapse can be detected. The extent to which solid boundaries in the liquid cause the frequencies and shapes of oscillatory modes on the bubble wall to differ from their free field values is discussed.

The effect of static pressure on the inertial cavitation threshold and collapse strength.

The conditions within an inertially collapsing bubble are known to produce high temperatures and pressures. Previous investigators have proposed various mechanisms for driving the collapse in order to maximize the energy density of the bubble’s contents. Working in fluids at high static pressures (up to 30 MPa) has shown some promising results. Preliminary data indicate that the strength of the collapse scales with the static pressure in the fluid. We report here the results of a series of rigorous experiments designed to better define this relation at the threshold of inertial cavitation. The hydrostatic pressure dependence of the inertial cavitation threshold in ultrapure water was measured in a radially symmetric standing wave field in a spherical resonator driven at 26 kHz. At this threshold, the collapse strength will be reported in terms of the resulting photon radiance below 400 nm and the relative shock wave amplitude. These experimental results will be compared to predictions of collapse strength. [Work supported by Impulse Devices, Inc.]

Shock-controlled bubble cloud dynamics and light emission.

Cavitation bubble collapse can generate intense concentrations of mechanical energy, sufficient to erode even the hardest metals and to generate light emissions visible to the naked eye. In this talk we describe cavitation bubble cloud experiments carried out in spherical resonators at ambient and acoustic pressures up to 30 MPa. Key to our system is the ability to nucleate with temporal and spatial controls, which we achieve using dielectric breakdown in water from pulsed focused laser beams. Our observations show that the cloud dynamics are controlled by the repetitive emission of shock waves, which propagate outward from the inertial cloud collapse, reflect off of the sphere wall, and then converge on the resonator center. Shock convergence phenomena and light emission from compact cloud collapse will be discussed. [Work supported by the Impulse Devices, Inc.]

Comparing the Marmottant model for ultrasound contrast agents with experimental postexcitation signals.

When insonified with sufficiently large rarefactional pressures, single unconstrained ultrasound contrast agents undergo inertial collapse with postexcitation emissions. Experimental measurements of postexcitation signal data for Definity microbubbles are compared with the Marmottant theoretical model for large amplitude oscillations of ultrasound contrast agents (UCAs). After taking into account the insonifying pulse characteristics, microbubble properties, and size distribution of the population of UCAs, a good comparison between simulated results and experimental data is obtained by determining a threshold maximum radial expansion (Rmax) to indicate the onset of postexcitation activity. Though this threshold Rmax is found to vary depending on insonification frequency, the values obtained are well above the typical free bubble inertial cavitation threshold commonly chosen at 2R0. The close agreement between the experiment and models suggests that lipid shelled UCAs behave as unshelled bubbles during most of a large amplitude cavitation cycle, as proposed in the Marmottant equation. [NIH Grant No. R37EB002641.]

Detecting cavitation in mercury exposed to a high-energy pulsed proton beam

The Oak Ridge National Laboratory Spallation Neutron Source employs a high-energy pulsed proton beam incident on a mercury target to generate short bursts of neutrons. Absorption of the proton beam produces rapid heating of the mercury, resulting in the formation of acoustic shock waves and the nucleation of cavitation bubbles. The subsequent collapse of these cavitation bubbles promote erosion of the steel target walls. Preliminary measurements using two passive cavitation detectors (megahertz-frequency focused and unfocused piezoelectric transducers) installed in a mercury test target to monitor cavitation generated by proton beams with charges ranging from 0.041 to 4.1 muC will be reported on. Cavitation was initially detected for a beam charge of 0.082 muC by the presence of an acoustic emission approximately 250 mus after arrival of the incident proton beam. This emission was consistent with an inertial cavitation collapse of a bubble with an estimated maximum bubble radius of 0.19 mm, based on collapse time. The peak pressure in the mercury for the initiation of cavitation was predicted to be 0.6 MPa. For a beam charge of 0.41 muC and higher, the lifetimes of the bubbles exceeded the reverberation time of the chamber ( approximately 300 mus), and distinct windows of cavitation activity were detected, a phenomenon that likely resulted from the interaction of the reverberation in the chamber and the cavitation bubbles.

Gas content of the medium surrounding a stone has a significant effect on the efficiency of stone breakage in shock wave lithotripsy.

In shock wave lithotripsy inertial collapse of cavitation bubbles produces daughter microbubbles [Y. A. Pishchalnikov et al., BJU Int. 102, 1681–1686 (2008)]. This will cause proliferation of bubbles only if daughter microbubbles survive until the arrival of the next shock wave (SW). While the time interval between SWs is determined by the firing rate of the lithotripter, the dissolution time of microbubbles depends on concentration of dissolved gas in the water. Thus, the same firing rate may produce different cavitation fields depending on the gas concentration. We assessed how the concentration of dissolved gas in the water tank affected SWs and the efficiency of stone comminution. More numerous bubbles generated in nondegassed water caused a dramatic reduction in the trailing negative‐pressure component of the SWs, while the leading positive‐pressure phase remained almost unchanged. It required 3.5 times more SWs to break stones in nondegassed water than in water degassed to 30% (P<0.001). This suggests that changes in temporal profiles of the SWs associated with cavitation are responsible for reduced efficiency of stone comminution observed in dense cavitation fields, regardless of whether these denser cavitation clouds were generated by using a faster rate or higher gas content. [Work supported by NIH‐DK43881.]

The effects of nonlinear wave propagation on the stability of inertial cavitation

In the context of forecasting temperature and pressure fields generated by high-intensity focussed ultrasound, the accuracy of predictive models is critical for the safety and efficacy of treatment. In such fields 'inertial' cavitation is often observed. Classically, estimations of cavitation thresholds have been based on the assumption that the incident wave at the surface of a bubble is the same as in the far-field, neglecting the effect of nonlinear wave propagation. By modelling the incident wave as a solution to Burgers' equation using weak shock theory, the effects of nonlinear wave propagation on inertial cavitation are investigated using both numerical and analytical techniques. From radius-time curves for a single bubble, it is observed that there is a reduction in the maximum size of a bubble undergoing inertial cavitation and that the inertial collapse occurs earlier in contrast with the classical case. Corresponding stability thresholds for a bubble whose initial radius is slightly below the critical Blake radius are calculated, providing a lower bound for the onset of instability. Bifurcation diagrams and frequency-response curves are presented associated with the loss of stability. The consequences and physical implications of the results are discussed with respect to the classical results.

Nanoparticle-targeted photoacoustic cavitation for deep tissue optical imaging.

Photoacoustic tomography is a non-invasive imaging technique based on broadband acoustic emissions from light absorption in tissue. Light-absorbing gold nanoparticles can be introduced and targeted to specific cell populations, thereby promoting both contrast and the ability to delineate tissue types. For sufficiently high laser fluence, a transient vapor cavity is formed and undergoes inertial collapse, generating enhanced emission and additional contrast. However, the fluence required to achieve this effect usually exceeds the maximum permissible exposure for tissue. By combining ultrasonic and optical pulses, the light and sound thresholds required to repeatedly generate inertial cavitation were reduced to 5 mJ/cm2 and 1 MPa, respectively. Experiments employed a transparent arylimide gel possessing a small (&amp;lt;600 μm) region doped with 80nm diameter gold nanoparticles and simultaneously exposed to pulsed laser light (532 nm) and pulsed ultrasound (1.1 MHz). The amplitude of broadband emissions induced by both light and sound exceeded that produced by light alone by almost two orders of magnitude, thereby facilitating imaging a deeper depth within tissue. Two-dimensional images of doped regions generated from conventional photoacoustic and ultrasound-enhanced emissions are presented and compared. Implications for imaging and HIFU therapy are discussed. [Work is supported by a Boston University Dean’s Catalyst Award.]

Comparison of Spectral and Temporal Criteria for Inertial Cavitation Collapse

Dilute solutions of Optison and Definity were studied using a passive cavitation detector (PCD) with a 2.8-MHz transmitter and 13-MHz receiver. The dilution was such that each received signal should, on average, arise from a single microbubble. Several hundred microbubble responses were acquired at each of three rarefactional pressures (1.6+/-0.2, 2.0+/0.2 and 2.4+/-0.2 MPa). Each microbubble response was grouped with signals presenting post-excitation emissions (100% Inertial Cavitation-Collapse) or those with no evidence of post-excitation emission (0% IC-Collapse). For each incident pressure, we compared discrimination of 100% and 0% IC-Collapse groups with peak-voltage, broadband noise (12-17.6 MHz) and power at the fundamental, 2nd, 3rd, and 4th harmonic peaks. In addition to increased peak-voltage and broadband noise, spectra from 100% IC-Collapse groups consistently presented increased 2nd, 3rd and 4th harmonics compared to the 0% IC-Collapse group. Throughout the studied pressure range, best separation between 0% and 100% IC-Collapse groups was obtained with peak-voltage (4.7+/-1.8dB), broadband noise (4.4+/-1.8dB) and 4th harmonic (5.6+/-2.2dB) for Optison. For Definity, all harmonics (2nd to 4th) increased strongly for the 100% IC-Collapse group (on the order of 6 dB) as well as peak-voltage (5.3+/-1.2dB) and broadband noise (5.8+/-2dB). Results should contribute to relating PCD criteria and IC activity.

Parametrically forced gravity waves in a circular cylinder and finite-time singularity

In this paper we present results on parametrically forced gravity waves in a circular cylinder in the limit of large fluid-depth approximation. The phase diagram that shows the stability-forcing-amplitude threshold and the wave-breaking threshold has been determined in the frequency range of existence of the lowest axisymmetric wave mode. The instability is shown to be supercritical for forcing frequencies at and above the natural frequency and subcritical below in a frequency range where the instability and breaking thresholds do not coincide. Above the instability threshold, the growth in wave amplitude is exponential, but with an initial time delay. The wave-amplitude response curve of stationary wave motions exhibits steady-state wave motion, amplitude modulations and bifurcations to other wave modes at frequencies where the parametric instability boundary of the axisymmetric mode overlaps with the neighbouring modes. The amplitude modulations are either on a slow time scale or exhibit period tripling and intermittent period tripling, without wave breaking. In the wave-breaking regime, a finite-time singularity may occur with intense jet formation, a phenomenon demonstrated by others in fluids of high viscosity and large surface tension. Here, this singular behaviour with jet formation is demonstrated for a low viscosity and low kinematic surface tension liquid. The results indicate that the jet is driven by inertial collapse of the cavity created at the wave trough. Therefore, the jet velocity is determined by the wave fluid velocity but depends, in addition, on kinematic surface tension and viscosity as these affect the last stable wave crest shape and the cavity size.

Bubble proliferation in shock wave lithotripsy

Stone breakage is less efficient when lithotripter shock waves (SWs) are delivered at 2 Hz compared to slower 0.5–1-Hz pulse repetition rates (PRFs). This correlates with increased number of transient cavitation bubbles observed along the SW path at fast PRF. The dynamics of this bubble proliferation throughout the bubble lifecycle is investigated in this report. Cavitation bubbles were studied in the free-field of a shock wave lithotripter using fine temporal and microscopic spatial resolution (high-speed camera Imacon-200). A typical cavitation bubble became visible (radius&amp;gt;10 μm) under the tensile phase of the lithotripter pulse, and at its first inertial collapse emitted a secondary SW and formed a micro-jet, which then could break up forming ∼25 micro-bubbles. Subsequent rebound and collapse of the parent bubble appeared to produce a further 40–120 daughter bubbles visible following the rebound. Preexisting bubbles hit by the lithotripter SW also formed micro-jets and broke up into micro-bubbles that grew and coalesced, producing irregular-shaped bubbles that, in turn, broke into micro-bubbles upon subsequent inertial collapse. A conventional NTSC-rate camcorder was used to track cavitation bubbles from pulse-to-pulse, showing that a single bubble can give rise to a cavitation cloud verifying high-speed video results. [Work supported by NIH-DK43881.]

Ultra-high-speed imaging of bubbles interacting with cells and tissue

Ultrasound contrast microbubbles are exploited in molecular imaging, where bubbles are directed to target cells and where their high-scattering cross section to ultrasound allows for the detection of pathologies at a molecular level. In therapeutic applications vibrating bubbles close to cells may alter the permeability of cell membranes, and these systems are therefore highly interesting for drug and gene delivery applications using ultrasound. In a more extreme regime bubbles are driven through shock waves to sonoporate or kill cells through intense stresses or jets following inertial bubble collapse. Here, we elucidate some of the underlying mechanisms using the 25-Mfps camera Brandaris128, resolving the bubble dynamics and its interactions with cells. We quantify acoustic microstreaming around oscillating bubbles close to rigid walls and evaluate the shear stresses on nonadherent cells. In a study on the fluid dynamical interaction of cavitation bubbles with adherent cells, we find that the nonspherical collapse of bubbles is responsible for cell detachment. We also visualized the dynamics of vibrating microbubbles in contact with endothelial cells followed by fluorescent imaging of the transport of propidium iodide, used as a membrane integrity probe, into these cells showing a direct correlation between cell deformation and cell membrane permeability.

Ultrasonic contrast agent shell rupture detected by inertial cavitation and rebound signals

Determining the rupture pressure threshold of ultrasound contrast agent microbubbles has significant applications for contrast imaging, development of therapeutic agents, and evaluation of potential bioeffects. Using a passive cavitation detector, this work evaluates rupture based on acoustic emissions from single, encapsulated, gas-filled microbubbles. Sinusoidal ultrasound pulses were transmitted into weak solutions of Optison at different center frequencies (0.9, 2.8, and 4.6 MHz), pulse durations (three, five, and seven cycles of the center frequencies), and peak rarefactional pressures (0.07 to 5.39 MPa). Pulse repetition frequency was 10 Hz. Signals detected with a 13-MHz, center-frequency transducer revealed postexcitation acoustic emissions (between 1 and 5 micros after excitation) with broadband spectral content. The observed acoustic emissions were consistent with the acoustic signature that would be anticipated from inertial collapse followed by "rebounds" when a microbubble ruptures and thus generates daughter/free bubbles that grow and collapse. The peak rarefactional pressure threshold for detection of these emissions increased with frequency (e.g., 0.53, 0.87, and 0.99 MPa for 0.9, 2.8, and 4.6 MHz, respectively; five-cycle pulse duration) and decreased with pulse duration. The emissions identified in this work were separated from the excitation in time and spectral content, and provide a novel determination of microbubble shell rupture.