Hydrodynamic Mechanism for Clumping along the Equatorial Rings of SN1987A and Other Stars.

An explanation for the origin and number of clumps along the equatorial ring of Supernova 1987A has eluded decades of research. Our linear analysis and hydrodynamic simulations of the expanding ring prior to the supernova reveal that it is subject to the Crow instability between vortex cores. The dominant wave number is remarkably consistent with the number of clumps, suggesting that the Crow instability stimulates clump formation. Although the present analysis focuses on linear fluid flow, future nonlinear analysis and the incorporation of additional stellar physics may further elucidate the remnant structure and the evolution of the progenitor and other stars.

Saturation of Vortex Rings Ejected from Shock-Accelerated Interfaces.

Structures evoking vortex rings can be discerned in shock-accelerated flows ranging from astrophysics to inertial confinement fusion. By constructing an analogy between vortex rings produced in conventional propulsion systems and rings generated by a shock impinging upon a high-aspect-ratio protrusion along a material interface, we extend classical, constant-density vortex-ring theory to compressible multifluid flows. We further demonstrate saturation of such vortex rings as the protrusion aspect ratio is increased, thus explaining morphological differences observed in practice.

Dynamics of an oscillating microbubble in a blood-like Carreau fluid.

A numerical model for cavitation in blood is developed based on the Keller-Miksis equation for spherical bubble dynamics with the Carreau model to represent the non-Newtonian behavior of blood. Three different pressure waveforms driving the bubble oscillations are considered: a single-cycle Gaussian waveform causing free growth and collapse, a sinusoidal waveform continuously driving the bubble, and a multi-cycle pulse relevant to contrast-enhanced ultrasound. Parameters in the Carreau model are fit to experimental measurements of blood viscosity. In the Carreau model, the relaxation time constant is 5-6 orders of magnitude larger than the Rayleigh collapse time. As a result, non-Newtonian effects do not significantly modify the bubble dynamics but do give rise to variations in the near-field stresses as non-Newtonian behavior is observed at distances 10-100 initial bubble radii away from the bubble wall. For sinusoidal forcing, a scaling relation is found for the maximum non-Newtonian length, as well as for the shear stress, which is 3 orders of magnitude larger than the maximum bubble radius.

Predicting complex nonspherical instability shapes of inertial cavitation bubbles in viscoelastic soft matter.

Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access to a world full of nonlinear physics, yet most of our quantitative understanding to date has been centered on a spherically symmetric description of the cavitation process in water. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, nonspherical instabilities in soft matter has remained a significant, unresolved challenge, in part due to the additional constitutive complexities introduced by the surrounding nonlinear viscoelastic solid. Here, we provide a new theoretical framework capable of accurately predicting the onset of nonspherical instability shapes of a bubble in a soft material by explicitly accounting for all pertinent nonlinear interactions between the cavitation bubble and the solid surroundings. Comparison with high-resolution experimental images from laser-induced cavitation events in a polyacrylamide hydrogel show excellent agreement. Interestingly, and consistent with experimental findings, our model predicts the emergence of various dynamic instability shapes for circumferential bubble stretch ratios greater than 1, in contrast to most quasistatic investigations. Our new theoretical framework not only provides unprecedented insight into the cavitation dynamics in a soft, nonlinear solid, but also provides a quantitative means of interpreting bubble dynamics relevant to a wide array of engineering and medical applications as well as natural phenomena.

Acoustic cavitation rheometry.

Characterization of soft materials is challenging due to their high compliance and the strain-rate dependence of their mechanical properties. The inertial microcavitation-based high strain-rate rheometry (IMR) method [Estrada et al., J. Mech. Phys. Solids, 2018, 112, 291-317] combines laser-induced cavitation measurements with a model for the bubble dynamics to measure local properties of polyacrylamide hydrogel under high strain-rates from 103 to 108 s-1. While promising, laser-induced cavitation involves plasma formation and optical breakdown during nucleation, a process that could alter local material properties before measurements are obtained. In the present study, we extend the IMR method to another means to generate cavitation, namely high-amplitude focused ultrasound, and apply the resulting acoustic-cavitation-based IMR to characterize the mechanical properties of agarose hydrogels. Material properties including viscosity, elastic constants, and a stress-free bubble radius are inferred from bubble radius histories in 0.3% and 1% agarose gels. An ensemble-based data assimilation is used to further help interpret the obtained estimates. The resulting parameter distributions are consistent with available measurements of agarose gel properties and with expected trends related to gel concentration and high strain-rate loading. Our findings demonstrate the utility of applying IMR and data assimilation methods with single-bubble acoustic cavitation data for measurement of viscoelastic properties.

Acoustic Measurements of Nucleus Size Distribution at the Cavitation Threshold.

An understanding of the acoustic cavitation threshold is essential for minimizing cavitation bio-effects in diagnostic ultrasound and for controlling cavitation-mediated tissue ablation in focused ultrasound procedures. The homogeneous cavitation threshold is an intrinsic material property of recognized importance to biomedical ultrasound as well as a variety of other applications requiring cavitation control. However, measurements of the acoustic cavitation threshold in water differ from those predicted by classic nucleation theories. This persistent discrepancy is explained by combining recently developed methods for acoustically nucleating single bubbles at threshold with numerical modeling to obtain a nucleus size distribution consistent with first-principles estimates for ion-stabilized nuclei. We identify acoustic cavitation at threshold as a reproducible subtype of heterogeneous cavitation with a characteristic nucleus size distribution. Knowledge of the nucleus size distribution could inspire new approaches to achieving cavitation control in water, tissue and a variety of other media.

Bubble Cloud Behavior and Ablation Capacity for Histotripsy Generated from Intrinsic or Artificial Cavitation Nuclei.

The study described here examined the effects of cavitation nuclei characteristics on histotripsy. High-speed optical imaging was used to compare bubble cloud behavior and ablation capacity for histotripsy generated from intrinsic and artificial cavitation nuclei (gas-filled microbubbles, fluid-filled nanocones). Results showed a significant decrease in the cavitation threshold for microbubbles and nanocones compared with intrinsic-nuclei controls, with predictable and well-defined bubble clouds generated in all cases. Red blood cell experiments showed complete ablations for intrinsic and nanocone phantoms, but only partial ablation in microbubble phantoms. Results also revealed a lower rate of ablation in artificial-nuclei phantoms because of reduced bubble expansion (and corresponding decreases in stress and strain). Overall, this study demonstrates the potential of using artificial nuclei to reduce the histotripsy cavitation threshold while highlighting differences in the bubble cloud behavior and ablation capacity that need to be considered in the future development of these approaches.

Single-bubble dynamics in histotripsy and high-amplitude ultrasound: Modeling and validation.

A variety of approaches have been used to model the dynamics of a single, isolated bubble nucleated by a microsecond length high-amplitude ultrasound pulse (e.g. a histotripsy pulse). Until recently, the lack of single-bubble experimental radius vs. time data for bubble dynamics under a well-characterized driving pressure has limited model validation efforts. This study uses radius vs. time measurements of single, spherical histotripsy-nucleated bubbles in water to quantitatively compare and validate a variety of bubble dynamics modeling approaches, including compressible and incompressible models as well as different thermal models. A strategy for inferring an analytic representation of histotripsy waveforms directly from experimental radius vs. time and cavitation threshold data is presented. We compare distributions of a calculated validation metric obtained for each model applied to 88 experimental data sets. There is minimal distinction (<1%) among the modeling approaches for compressibility and thermal effects considered in this study. These results suggest that our proposed strategy to infer the waveform, combined with simple models minimizing parametric uncertainty and computational resource demands accurately represent single-bubble dynamics in histotripsy, including at and near the maximum bubble radius. Remaining sources of parametric and model-based uncertainty are discussed.

Shape stability of a gas bubble in a soft solid.

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.

Modeling tissue-selective cavitation damage.

The destructive growth and collapse of cavitation bubbles are used for therapeutic purposes in focused ultrasound procedures and can contribute to tissue damage in traumatic injuries. Histotripsy is a focused ultrasound procedure that relies on controlled cavitation to homogenize soft tissue. Experimental studies of histotripsy cavitation have shown that the extent of ablation in different tissues depends on tissue mechanical properties and waveform parameters. Variable tissue susceptibility to the large stresses, strains, and strain rates developed by cavitation bubbles has been suggested as a basis for localized liver tumor treatments that spare large vessels and bile ducts. However, field quantities developed within microns of cavitation bubbles are too localized and transient to measure in experiments. Previous numerical studies have attempted to circumvent this challenge but made limited use of realistic tissue property data. In this study, numerical simulations are used to calculate stress, strain, and strain rate fields produced by bubble oscillation under histotripsy forcing in a variety of tissues with literature-sourced viscoelastic and acoustic properties. Strain field calculations are then used to predict a theoretical damage radius using tissue ultimate strain data. Simulation results support the hypothesis that differential tissue responses could be used to design tissue-selective treatments. Results agree with studies correlating tissue ultimate fractional strain with resistance to histotripsy ablation and are also consistent with experiments demonstrating smaller lesion size under exposure to higher frequency waveforms. Methods presented in this study provide an approach for modeling tissue-selective cavitation damage in general.

Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media.

Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations.

Experimental considerations to observe two ionizing fronts in systems with a sharp absorption edge.

This paper examines the experimental requirements to observe two shock fronts driven by a single x-ray source in systems with a sharp absorption edge. We consider systems where the peak of the x-ray radiation drive coincides with the K-edge of the carbon, which occurs at a photon energy of 284 eV, causing photons to be deposited in two regions. The low-energy photons (E < 284 eV) penetrate further and drive the main shock, while the higher-energy photons (E > 284 eV) are absorbed in the ablated plasma. These higher-energy photons create an ionization front, which then produces a second shock, termed an edge-shock. Using a different radiation-hydrodynamics code and different opacity and equation of state tables, we replicate the previous work and build upon them to explore the conditions required to form the edge shock. We find that having the material K-edge coincide with the spectral domain of the radiation source is necessary but not sufficient on its own to drive the edge-shock.

Soft-Tissue Aberration Correction for Histotripsy.

Acoustic aberrations caused by natural heterogeneities of biological soft tissue are a substantial problem for histotripsy, a therapeutic ultrasound technique that uses acoustic cavitation to mechanically fractionate and destroy unwanted target tissue without damaging surrounding tissue. These aberrations, primarily caused by sound speed variations, result in severe defocusing of histotripsy pulses, thereby decreasing treatment efficacy. The gold standard for aberration correction (AC) is to place a hydrophone at the desired focal location to directly measure phase aberrations, which is a method that is infeasible in vivo. We hypothesized that the acoustic cavitation emission (ACE) shockwaves from the initial expansion of inertially cavitating microbubbles generated by histotripsy can be used as a point source for AC. In this study, a 500-kHz, 112-element histotripsy phased array capable of transmitting and receiving ultrasound on all channels was used to acquire ACE shockwaves. These shockwaves were first characterized optically and acoustically. It was found that the shockwave pressure increases significantly as the source changes from a single bubble to a dense cavitation cloud. The first arrival of the shockwave received by the histotripsy array was from the outer-most cavitation bubbles located closest to the histotripsy array. Hydrophone and ACE AC methods were then tested on ex vivo porcine abdominal tissue samples. Without AC, the focal pressure is reduced by 49.7% through the abdominal tissue. The hydrophone AC approach recovered 55.5% of the lost pressure. Using the ACE AC method, over 20% of the lost pressure was recovered, and the array power required to induce cavitation was reduced by approximately 31.5% compared to without AC. These results supported our hypothesis that the ACE shockwaves coupled with a histotripsy array with transmit and receive capability can be used for AC for histotripsy through soft tissue.

Bubble-Induced Color Doppler Feedback Correlates with Histotripsy-Induced Destruction of Structural Components in Liver Tissue.

Bubble-induced color Doppler (BCD) is a histotripsy-therapy monitoring technique that uses Doppler ultrasound to track the motion of residual cavitation nuclei that persist after the collapse of the histotripsy bubble cloud. In this study, BCD is used to monitor tissue fractionation during histotripsy tissue therapy, and the BCD signal is correlated with the destruction of structural and non-structural components identified histologically to further understand how BCD monitors the extent of treatment. A 500-kHz, 112-element phased histotripsy array is used to generate approximately 6- × 6- × 7-mm lesions within ex vivo bovine liver tissue by scanning more than 219 locations with 30-1000 pulses per location. A 128-element L7-4 imaging probe is used to acquire BCD signals during all treatments. The BCD signal is then quantitatively analyzed using the time-to-peak rebound velocity (tprv) metric. Using the Pearson correlation coefficient, the tprv is compared with histologic analytics of lesions generated by various numbers of pulses using a significance level of 0.001. Histologic analytics in this study include viable cell count, reticulin-stained type III collagen area and trichrome-stained type I collagen area. It is found that the tprv metric has a statistically significant correlation with the change in reticulin-stained type III collagen area with a Pearson correlation coefficient of -0.94 (p <0.001), indicating that changes in BCD are more likely because of destruction of the structural components of tissue.

Predicting Tissue Susceptibility to Mechanical Cavitation Damage in Therapeutic Ultrasound.

Histotripsy is a developing focused ultrasound procedure that uses cavitation bubbles to mechanically homogenize soft tissue. To better understand the mechanics of tissue damage, a numerical model of single-bubble dynamics was used to calculate stress, strain and strain rate fields produced by a cavitation bubble exposed to a tensile histotripsy pulse. The explosive bubble growth and its subsequent collapse were found to depend on the properties of the surrounding material and on the histotripsy pulse. Stresses far greater than gigapascals were observed close to the bubble wall, but attenuated by four to six orders of magnitude within 50 µm from the bubble wall, with at least two orders of magnitude attenuation occurring within the first 10 µm from the bubble. Elastic stresses were found to dominate close to the bubble wall, whereas viscous stresses tended to persist farther into the surroundings. A non-dimensional parameter combining tissue, waveform and bubble properties was identified that dictates the dominant stress (viscous vs. elastic) as a function of distance from the bubble nucleus. In a cycle of bubble growth and collapse, characteristic times at which mechanical damage is likely to occur and dominant mechanisms acting at each time were identified.

The effects of heat and mass diffusion on freely oscillating bubbles in a viscoelastic, tissue-like medium.

In certain cavitation-based ultrasound techniques, the relative importance of thermally vs mechanically induced damage is unclear. As a first step to investigate this matter, a numerical model for bubble dynamics in tissue-like, viscoelastic media is presented in which full thermal effects are included inside and outside the bubble, as well as interdiffusion of vapor and non-condensible gas inside the bubble. Soft tissue is assumed to behave according to a Kelvin-Voigt model in which viscous and elastic contributions are additive. A neo-Hookean formulation, appropriate for finite-strain elasticity, accounts for the large deformations produced by cavitation. Numerical solutions to problems of relevance to therapeutic ultrasound are examined, and linear analysis is used to explain the underlying mechanisms. The dependence between the surrounding medium's elasticity (shear modulus) and the extent to which the effects of heat and mass transfer influence bubble dynamics is quantified. In particular, the oscillation properties are related to the eigenvalues determined from linear theory. Regimes under which a polytropic relation describes the heat transfer to sufficient accuracy are identified, for which the complexity and computational expense associated with solving full partial differential equations can be avoided.

Visualizing the Histotripsy Process: Bubble Cloud-Cancer Cell Interactions in a Tissue-Mimicking Environment.

Histotripsy is a non-invasive ultrasonic ablation method that uses cavitation to mechanically fractionate tissue into acellular debris. With a sufficient number of pulses, histotripsy can completely fractionate tissue into a liquid-appearing homogenate with no cellular structures. The location, shape and size of lesion formation closely match those of the cavitation cloud. Previous work has led to the hypothesis that the rapid expansion and collapse of histotripsy bubbles fractionate tissue by inducing large stress and strain on the tissue structures immediately adjacent to the bubbles. In the work described here, the histotripsy bulk tissue fractionation process is visualized at the cellular level for the first time using a custom-built 2-MHz transducer incorporated into a microscope stage. A layer of breast cancer cells were cultured within an optically transparent fibrin-based gel phantom to mimic cells inside a 3-D extracellular matrix. To test the hypothesis, the cellular response to single and multiple histotripsy pulses was investigated using high-speed optical imaging. Bubbles were always generated in the extracellular space, and significant cell displacement/deformation was observed for cells directly adjacent to the bubble during both bubble expansion and collapse. The largest displacements were observed during collapse for cells immediately adjacent to the bubble, with cells moving more than 150-300 µm in less than 100 µs. Cells often underwent multiple large deformations (>150% strain) over multiple pulses, resulting in the bisection of cells multiple times before complete removal. To provide theoretical support to the experimental observations, a numerical simulation was conducted using a single-bubble model, which indicated that histotripsy exerts the largest strains and cell displacements in the regions immediately adjacent to the bubble. The experimental and simulation results support our hypothesis, which helps to explain the formation of the sharp lesions formed in histotripsy therapy localized to the regions directly exposed to the bubbles.

Effects of Temperature on the Histotripsy Intrinsic Threshold for Cavitation.

Histotripsy is an ultrasound ablation method that depends on the initiation of a dense cavitation bubble cloud to fractionate soft tissue. Previous work has demonstrated that a cavitation cloud can be formed by a single acoustic pulse with one high amplitude negative cycle, when the negative pressure amplitude exceeds a threshold intrinsic to the medium. The intrinsic thresholds in soft tissues and tissue phantoms that are water-based are similar to the intrinsic threshold of water over an experimentally verified frequency range of 0.3-3 MHz. Previous work studying the histotripsy intrinsic threshold has been limited to experiments performed at room temperature (~20°C). In this study, we investigate the effects of temperature on the histotripsy intrinsic threshold in water, which is essential to accurately predict the intrinsic thresholds expected over the full range of in vivo therapeutic temperatures. Based on previous work studying the histotripsy intrinsic threshold and classical nucleation theory, we hypothesize that the intrinsic threshold will decrease with increasing temperature. To test this hypothesis, the intrinsic threshold in water was investigated both experimentally and theoretically. The probability of generating cavitation bubbles was measured by applying a single pulse with one high amplitude negative cycle at 1 MHz to distilled, degassed water at temperatures ranging from 10°C-90°C. Cavitation was detected and characterized by passive cavitation detection and high-speed photography, from which the probability of cavitation was measured vs. pressure amplitude. The results indicate that the intrinsic threshold (the negative pressure at which the cavitation probability=0.5) significantly decreases with increasing temperature, showing a nearly linear decreasing trend from 29.8±0.4 MPa at 10˚C to 14.9±1.4 MPa at 90˚C. Overall, the results of this study support our hypothesis that the intrinsic threshold is highly dependent upon the temperature of the medium, which may allow for better predictions of cavitation generation at body temperature in vivo and at the elevated temperatures commonly seen in high intensity focused ultrasound (HIFU) regimes.

Effects of ultrasound frequency and tissue stiffness on the histotripsy intrinsic threshold for cavitation.

Histotripsy is an ultrasound ablation method that depends on the initiation of a cavitation bubble cloud to fractionate soft tissue. Previous work has indicated that a cavitation cloud can be formed by a single pulse with one high-amplitude negative cycle, when the negative pressure amplitude directly exceeds a pressure threshold intrinsic to the medium. We hypothesize that the intrinsic threshold in water-based tissues is determined by the properties of the water inside the tissue, and changes in tissue stiffness or ultrasound frequency will have a minimal impact on the histotripsy intrinsic threshold. To test this hypothesis, the histotripsy intrinsic threshold was investigated both experimentally and theoretically. The probability of cavitation was measured by subjecting tissue phantoms with adjustable mechanical properties and ex vivo tissues to a histotripsy pulse of 1-2 cycles produced by 345-kHz, 500-kHz, 1.5-MHz and 3-MHz histotripsy transducers. Cavitation was detected and characterized by passive cavitation detection and high-speed photography, from which the probability of cavitation was measured versus pressure amplitude. The results revealed that the intrinsic threshold (the negative pressure at which probability = 0.5) is independent of stiffness for Young's moduli (E) <1 MPa, with only a small increase (∼2-3 MPa) in the intrinsic threshold for tendon (E = 380 MPa). Additionally, results for all samples revealed only a small increase of ∼2-3 MPa when the frequency was increased from 345 kHz to 3 MHz. The intrinsic threshold was measured to be between 24.7 and 30.6 MPa for all samples and frequencies tested in this study. Overall, the results of this study indicate that the intrinsic threshold to initiate a histotripsy bubble cloud is not significantly affected by tissue stiffness or ultrasound frequency in the hundreds of kilohertz to megahertz range.

Effects of tissue stiffness, ultrasound frequency, and pressure on histotripsy-induced cavitation bubble behavior.

Histotripsy is an ultrasound ablation method that controls cavitation to fractionate soft tissue. In order to effectively fractionate tissue, histotripsy requires cavitation bubbles to rapidly expand from nanometer-sized initial nuclei into bubbles often larger than 50 µm. Using a negative pressure high enough to initiate a bubble cloud and expand bubbles to a sufficient size, histotripsy has been shown capable of completely fractionating soft tissue into acelluar debris resulting in effective tissue removal. Previous work has shown that the histotripsy process is affected by tissue mechanical properties with stiffer tissues showing increased resistance to histotripsy fractionation, which we hypothesize to be caused by impeded bubble expansion in stiffer tissues. In this study, the hypothesis that increases in tissue stiffness cause a reduction in bubble expansion was investigated both theoretically and experimentally. High speed optical imaging was used to capture a series of time delayed images of bubbles produced inside mechanically tunable agarose tissue phantoms using histotripsy pulses produced by 345 kHz, 500 kHz, 1.5 MHz, and 3 MHz histotripsy transducers. The results demonstrated a significant decrease in maximum bubble radius (Rmax) and collapse time (tc) with both increasing Young's modulus and increasing frequency. Furthermore, results showed that Rmax was not increased by raising the pressure above the intrinsic threshold. Finally, this work demonstrated the potential of using a dual-frequency strategy to modulate the expansion of histotripsy bubbles. Overall, the results of this study improve our understanding of how tissue stiffness and ultrasound parameters affect histotripsy-induced bubble behavior and provide a rational basis to tailor acoustic parameters for treatment of the specific tissues of interest.