Rectified growth of histotripsy bubbles

The histotripsy spectrum: differences and similarities in techniques and instrumentation

Since its inception about two decades ago, histotripsy - a non-thermal mechanical tissue ablation technique - has evolved into a spectrum of methods, each with distinct potentiating physical mechanisms: intrinsic threshold histotripsy, shock-scattering histotripsy, hybrid histotripsy, and boiling histotripsy. All methods utilize short, high-amplitude pulses of focused ultrasound delivered at a low duty cycle, and all involve excitation of violent bubble activity and acoustic streaming at the focus to fractionate tissue down to the subcellular level. The main differences are in pulse duration, which spans microseconds to milliseconds, and ultrasound waveform shape and corresponding peak acoustic pressures required to achieve the desired type of bubble activity. In addition, most types of histotripsy rely on the presence of high-amplitude shocks that develop in the pressure profile at the focus due to nonlinear propagation effects. Those requirements, in turn, dictate aspects of the instrument design, both in terms of driving electronics, transducer dimensions and intensity limitations at surface, shape (primarily, the F-number) and frequency. The combination of the optimized instrumentation and the bio-effects from bubble activity and streaming on different tissues, lead to target clinical applications for each histotripsy method. Here, the differences and similarities in the physical mechanisms and resulting bioeffects of each method are reviewed and tied to optimal instrumentation and clinical applications.

Mechanisms of nuclei growth in ultrasound bubble nucleation

This paper interrogates the intersections between bubble dynamics and classical nucleation theory (CNT) towards constructing a model that describes intermediary nucleation events between the extrema of cavitation and boiling. We employ Zeldovich's hydrodynamic approach to obtain a description of bubble nuclei that grow simultaneously via hydrodynamic excitation by the acoustic field and vapour transport. By quantifying the relative dominance of both mechanisms, it is then possible to discern the extent to which viscosity, inertia, surface tension and vapour transport shape the growth of bubble nuclei through non-dimensional numbers that naturally arise within the theory. The first non-dimensional number Φ12/Φ2 is analogous to the Laplace number, representing the balance between surface tension and inertial constraints to viscous effects. The second non-dimensional number δ represents how enthalpy transport into the bubble can reduce nucleation rates by cooling the surrounding liquid. This formulation adds to the current understanding of ultrasound bubble nucleation by accounting for bubble dynamics during nucleation, quantifying the physical distinctions between "boiling" and "cavitation" bubbles through non-dimensional parameters, and outlining the characteristic timescales of nucleation according to the growth mechanism of bubbles throughout the histotripsy temperature range. We observed in our simulations that viscous effects control the process of ultrasound nucleation in water-like media throughout the 0-120 °C temperature range, although this dominance decreases with increasing temperatures. Enthalpy transport was found to reduce nucleation rates for increasing temperatures. This effect becomes significant at temperatures above 30 °C and favours the creation of fewer nuclei that are larger in size. Conversely, negligible enthalpy transport at lower temperatures can enable the nucleation of dense clusters of small nuclei, such as cavitation clouds. We find that nuclei growth as modelled by the Rayleigh-Plesset equation occurs over shorter timescales than as modelled by vapour-dominated growth. This suggests that the first stage of bubble nuclei growth is hydrodynamic, and vapour transport effects can only be observed over longer timescales. Finally, we propose that this framework can be used for comparison between different experiments in bubble nucleation, towards standardisation and dosimetry of protocols.

Inertial Cavitation Behaviors Induced by Nonlinear Focused Ultrasound Pulses

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

Modeling the Physics of Bubble Nucleation in Histotripsy

This work aims to establish a theoretical framework for the modeling of bubble nucleation in histotripsy. A phenomenological version of the classical nucleation theory was parametrized with histotripsy experimental data, fitting a temperature-dependent activity factor that harmonizes theoretical predictions and experimental data for bubble nucleation at both high and low temperatures. Simulations of histotripsy pressure and temperature fields are then used in order to understand spatial and temporal properties of bubble nucleation at varying sonication conditions. This modeling framework offers a thermodynamic understanding on the role of the ultrasound frequency, waveforms, peak focal pressures, and duty cycle on patterns of ultrasound-induced bubble nucleation. It was found that at temperatures lower than 50 °C, nucleation rates are more appreciable at very large negative pressures such as -30 MPa. For focal peak-negative pressures of -15 MPa, characteristic of boiling histotripsy, nucleation rates grow by 20 orders of magnitude in the temperature interval 60 °C-100 °C.

Estimating the mechanical energy of histotripsy bubble clouds with high frame rate imaging

Mechanical ablation with the focused ultrasound therapy histotripsy relies on the generation and action of bubble clouds. Despite its critical role for ablation, quantitative metrics of bubble activity to gauge treatment outcomes are still lacking. Here, plane wave imaging was used to track the dissolution of bubble clouds following initiation with the histotripsy pulse. Information about the rate of change in pixel intensity was coupled with an analytic diffusion model to estimate bubble size. Accuracy of the hybrid measurement/model was assessed by comparing the predicted and measured dissolution time of the bubble cloud. Good agreement was found between predictions and measurements of bubble cloud dissolution times in agarose phantoms and murine subcutaneous SCC VII tumors. The analytic diffusion model was extended to compute the maximum bubble size as well as energy imparted to the tissue due to bubble expansion. Regions within tumors predicted to have undergone strong bubble expansion were collocated with ablation. Further, the dissolution time was found to correlate with acoustic emissions generated by the bubble cloud during histotripsy insonation. Overall, these results indicate a combination of modeling and high frame rate imaging may provide means to quantify mechanical energy imparted to the tissue due to bubble expansion for histotripsy.

The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

A phenomenological implementation of Classical Nucleation Theory (CNT) is employed to investigate the connection between high intensity focused ultrasound (HIFU) pressure and temperature fields with the energetic requirements of bubble nucleation. As a case study, boiling histotripsy in tissue-mimicking phantoms is modelled. The physics of key components in the implementation of CNT in HIFU conditions such as the derivation of nucleation pressure thresholds and approximations regarding the surface tension of the liquid are reviewed and discussed. Simulations show that the acoustic pressure is the ultimate trigger for millisecond bubble nucleation in boiling histotripsy, however, HIFU heat deposition facilitates nucleation by lowering nucleation pressure thresholds. Nucleation thus occurs preferentially at the regions of highest heat deposition within the HIFU field. This implies that bubble nucleation subsequent to millisecond HIFU heat deposition can take place at temperatures below 100 °C as long as the focal HIFU peak negative pressure exceeds the temperature-dependent nucleation threshold. It is also found that the magnitude of nucleation pressure thresholds decreases with decreasing frequencies. Overall, results indicate that it is not possible to separate thermal and mechanical effects of HIFU in the nucleation of bubbles for timescales of a few milliseconds. This methodology provides a promising framework for studying time and space dependencies of the energetics of bubble nucleation within a HIFU field.

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

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

The influence of gas diffusion on bubble persistence in shock-scattering histotripsy

Bubble cloud persistence reduces the efficacy of mechanical liquefaction with shock-scattering histotripsy. In this study, the contribution of gas transfer to bubble longevity was investigated in silico by solving the equations for bubble oscillations and diffusion in parallel. The bubble gas content increased more than 5 orders of magnitude during the expansion phase, arresting the inertial collapse. The residual gas bubble required more than 15 ms for passive dissolution post excitation, consistent with experimental observation. These results demonstrate gas diffusion is an important factor in the persistence of histotripsy-induced cavitation.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields

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.