Michael L. Calvisi

Interaction of lithotripter shockwaves with single inertial cavitation bubbles

The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.

Shape stability and violent collapse of microbubbles in acoustic traveling waves

Acoustically driven bubbles can develop shape instabilities and, if forced sufficiently strongly, distort greatly and break up. Perturbation theory provides some insight as to how these nonspherical shape modes grow initially but loses validity for large deformations. To validate the perturbation theory, we use a numerical model based on the boundary integral method capable of simulating nonspherical, axisymmetric bubbles subject to acoustic driving. The results show that the perturbation theory compares well with numerical simulations in predicting bubble breakup and stability. Thereafter, we compare the peak temperatures and pressures of spherical to nonspherical bubble collapses by forcing them with standing waves and traveling waves, respectively. This comparison is made in parameter ranges of relevance to both single bubble sonoluminescence and multibubble sonoluminescence and sonochemistry. At moderate forcing, spherical and nonspherical collapses achieve similar peak temperatures and pressures but,...

Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies non-spherical cavitation collapse

In this paper we use the boundary integral method to model the non-spherical collapse of bubbles excited by lithotripter shock waves near a rigid boundary. The waves we consider are representative of those developed by shock wave lithotripsy or shock wave therapy devices, and the rigid boundaries we consider are representative of kidney stones and reflective bony tissue. This study differs from previous studies in that we account for the reflection of the incident wave and also the asymmetry of the collapse caused by the presence of the rigid surface. The presence of the boundary causes interference between reflected and incident waves. Quantities such as kinetic energy, Kelvin impulse and centroid translation are calculated in order to illuminate the physics of the collapse process. The main finding is that the dynamics of the bubble collapse depend strongly on the distance of the bubble relative to the wall when reflection is taken into account, but much less so when reflection is omitted from the model. The reflection enhances the expansion and subsequent collapse of bubbles located near the boundary owing to constructive interference between incident and reflected waves; however, further from the boundary, the dynamics of collapse are suppressed owing to destructive interference of these two waves. This result holds regardless of the initial radius of the bubble or its initial state at the time of impact with the lithotripter shock wave. Also, the work done by the lithotripter shock wave on the bubble is shown to predict strongly the maximum bubble volume regardless of the standoff distance and the presence or absence of reflection; furthermore, allowing for non-sphericity, these predictions match almost exactly those of a previously developed spherical model.

Numerical modeling of the 3D dynamics of ultrasound contrast agent microbubbles using the boundary integral method

Ultrasound contrast agents (UCAs) are microbubbles stabilized with a shell typically of lipid, polymer, or protein and are emerging as a unique tool for noninvasive therapies ranging from gene delivery to tumor ablation. While various models have been developed to describe the spherical oscillations of contrast agents, the treatment of nonspherical behavior has received less attention. However, the nonspherical dynamics of contrast agents are thought to play an important role in therapeutic applications, for example, enhancing the uptake of therapeutic agents across cell membranes and tissue interfaces, and causing tissue ablation. In this paper, a model for nonspherical contrast agent dynamics based on the boundary integral method is described. The effects of the encapsulating shell are approximated by adapting Hoff’s model for thin-shell, spherical contrast agents. A high-quality mesh of the bubble surface is maintained by implementing a hybrid approach of the Lagrangian method and elastic mesh techniqu...

Dynamical analysis of the nonlinear response of ultrasound contrast agent microbubbles.

The nonlinear response of spherical ultrasound contrast agent microbubbles is investigated to understand the effects of common shells on the dynamics. A compressible form of the Rayleigh-Plesset equation is combined with a thin-shell model developed by Lars Hoff to simulate the radial response of contrast agents subject to ultrasound. The responses of Albunex, Sonazoid, and polymer shells are analyzed through the application of techniques from dynamical systems theory such as Poincaré sections, phase portraits, and bifurcation diagrams to illustrate the qualitative dynamics and transition to chaos that occurs under certain changes in system parameters. Corresponding calculations of Lyapunov exponents provide quantitative data on the system dynamics. The results indicate that Albunex and polymer shells sufficiently stabilize the response to prevent transition to the chaotic regime throughout typical clinical ranges of ultrasound pressure and frequency. By contrast, Sonazoid shells delay the onset of chaos relative to an unshelled bubble but do not prevent it. A contour plot identifying regions of periodic and chaotic behavior over clinical ranges of ultrasound pressure and frequency is provided for Sonazoid. This work characterizes the nonlinear response of various ultrasound contrast agents, and shows that shell properties have a profound influence on the dynamics.

MECHANICAL MODELS OF CHUA'S CIRCUIT

In this paper we present two different examples of electromechanical realization of Chuas circuit and one of Chuas unfolding circuit. In addition, a novel mechanism is proposed for realizing Chua...

High Efficiency Molecular Delivery with Sequential Low-Energy Sonoporation Bursts

Microbubbles interact with ultrasound to induce transient microscopic pores in the cellular plasma membrane in a highly localized thermo-mechanical process called sonoporation. Theranostic applications of in vitro sonoporation include molecular delivery (e.g., transfection, drug loading and cell labeling), as well as molecular extraction for measuring intracellular biomarkers, such as proteins and mRNA. Prior research focusing mainly on the effects of acoustic forcing with polydisperse microbubbles has identified a “soft limit” of sonoporation efficiency at 50% when including dead and lysed cells. We show here that this limit can be exceeded with the judicious use of monodisperse microbubbles driven by a physiotherapy device (1.0 MHz, 2.0 W/cm2, 10% duty cycle). We first examined the effects of microbubble size and found that small-diameter microbubbles (2 µm) deliver more instantaneous power than larger microbubbles (4 & 6 µm). However, owing to rapid fragmentation and a short half-life (0.7 s for 2 µm; 13.3 s for 6 µm), they also deliver less energy over the sonoporation time. This translates to a higher ratio of FITC-dextran (70 kDa) uptake to cell death/lysis (4:1 for 2 µm; 1:2 for 6 µm) in suspended HeLa cells after a single sonoporation. Sequential sonoporations (up to four) were consequently employed to increase molecular delivery. Peak uptake was found to be 66.1 ± 1.2% (n=3) after two sonoporations when properly accounting for cell lysis (7.0 ± 5.6%) and death (17.9 ± 2.0%), thus overcoming the previously reported soft limit. Substitution of TRITC-dextran (70 kDa) on the second sonoporation confirmed the effects were multiplicative. Overall, this study demonstrates the possibility of utilizing monodisperse small-diameter microbubbles as a means to achieve multiple low-energy sonoporation bursts for efficient in vitro cellular uptake and sequential molecular delivery.

Theoretical study of BOLD response to sinusoidal input

This is a theoretical study of a compelling model of blood oxygen level-dependent (BOLD) response dynamics, measured in functional magnetic resonance imaging (fMRI). The novelty of this study involves the way the model is driven sinusoidally, in order to avoid onset and offset transients that pose difficulties in data analysis and interpretation. The driving frequency ranges over the natural time scales of the hemodynamic response (0.01-1 Hz), which also corresponds to the period in typical boxcar stimulus designs. At low stimulus amplitude, the predicted BOLD response is quasi-linear. The amplitude exhibits a mild peak near the modulation frequency 0.1 Hz, and falls rapidly for higher frequencies. The phase lag relative to the stimulus is a monotonically increasing function of the modulation frequency. These findings illustrate the dynamical nature of the BOLD response, and could be used to optimize experimental designs that admit sinusoidal modulation. Higher stimulus amplitude elicits nonlinear behavior characterized by a double peak during the positive deflection of the BOLD response. This finding is particularly interesting, because similar double peaks are seen frequently in BOLD data.

Experimental Study of EEG and Bold Responses to Sinusoidal Contrast Modulation

This paper reports pilot experiments and modeling studies on the dynamics of the BOLD response to sinusoidal input steady-state visual evoked potentials were generated with a contrast-reversing grating. The absolute contrast of the grating was modulated sinusoidally, across a range of frequencies relevant to block and event-related designs. The amplitude of the neural response was found to track the stimulus closely, with some interesting differences at higher frequencies. The BOLD responses were quasi-sinusoidal, without the onset or offset transients typical in block designs. A hemodynamic model, based upon the balloon model with delayed compliance, and a linear model of inward flow, was fit to the BOLD data using the contrast waveform as input The hemodynamic model fit the BOLD data well, but required different model parameters for each stimulus frequency. This implies that the differential equations comprising the hemodynamic model do not capture adequately the dynamics of the BOLD response across multiple time scales.

Shape mode stability of lipid-coated ultrasound contrast agent microbubbles

Ultrasound contrast agents (UCAs) are shell encapsulated microbubbles developed originally for ultrasound imaging enhancement. More recently, UCAs are being exploited for therapeutic applications such as drug and gene delivery. Ultrasound transducer pulses can induce spherical (radial) UCA oscillations, translation, and nonspherical shape oscillations, the latter of which can lead to breakup. Breakup can facilitate drug or gene delivery, but should be minimized for imaging purposes to increase residence time and maximize diagnostic effect. Therefore, an understanding of the interplay between the acoustic driving and shape mode stability of UCAs is important for both diagnostic and therapeutic applications. The present work couples a radial model of a lipid-coated microbubble with a model for bubble translation and nonspherical shape oscillation to predict shape mode stability for ultrasound driving frequencies and pressure amplitudes of clinical interest. In addition, calculations of the stability of indi...