Simulation of cavitation enhanced temperature elevation in a soft tissue during high-intensity focused ultrasound thermal therapy

Microbubble-enhanced transcranial MR-guided focused ultrasound brain hyperthermia: heating mechanism investigation using finite element method

Recently, our group developed a synergistic brain drug delivery method to achieve simultaneous transcranial hyperthermia and localized blood-brain barrier opening via MR-guided focused ultrasound (MRgFUS). In a rodent model, we demonstrated that the ultrasound power required for transcranial MRgFUS hyperthermia was significantly reduced by injecting microbubbles (MBs). However, the specific mechanisms underlying the power reduction caused by MBs remain unclear. The present study aims to elucidate the mechanisms of MB-enhanced transcranial MRgFUS hyperthermia through numerical studies using the finite element method. The microbubble acoustic emission (MAE) and the viscous dissipation (VD) were hypothesized to be the specific mechanisms. Acoustic wave propagation was used to model the FUS propagation in the brain tissue, and a bubble dynamics equation for describing the dynamics of MBs with small shell thickness was used to model the MB oscillation under FUS exposures. A modified bioheat transfer equation was used to model the temperature in the rodent brain with different heat sources. A theoretical model was used to estimate the bubble shell's surface tension, elasticity, and viscosity losses. The simulation reveals that MAE and VD caused a 40.5% and 52.3% additional temperature rise, respectively. Compared with FUS only, MBs caused a 64.0% temperature increase, which is consistent with our previous animal experiments. Our investigation showed that MAE and VD are the main mechanisms of MB-enhanced transcranial MRgFUS hyperthermia.

Bubble pulsation characteristics in multi-bubble systems affected by bubble size polydispersity and spatial structure

This study seeks to explore the bubble pulsation characteristics in multi-bubble environment with a special focus on the influences of the size polydispersity and the two-dimensional structure of bubbles. Three representative configurations of three interacting bubbles are formed by setting the initial radii of cavitation bubbles and inter-bubble distances appropriately, then the pulsation characteristics of a small bubble are investigated and compared by the bifurcation analysis. The results illustrate that the bubble size polydispersity and two-dimensional structure would greatly affect the bubble pulsations (i.e., the amplitude and nonlinearity of pulsations). Furthermore, the effects of two-dimensional structure are strong at a small inter-bubble distance of the large and small bubbles while the bubble size polydispersity always significantly affects the bubble pulsations for all cases. Moreover, the influences of both bubble size polydispersity and two-dimensional structure can be enhanced as the acoustic pressure increases, which can also become stronger when the large bubble is located at the same side as the small bubble and the initial radius of large bubble increases. Additionally, the effects would also be increased when the tissue viscoelasticity varies within a certain range. The present findings shed new light on the dynamics of multiple polydisperse microbubbles in viscoelastic tissues, potentially contributing to an optimization of their applications with ultrasound excitation.

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.

Resonance behaviors of encapsulated microbubbles oscillating nonlinearly with ultrasonic excitation

The resonance behaviors of a few lipid-coated microbubbles acoustically activated in viscoelastic media were comprehensively examined via radius response analysis. The size polydispersity and random spatial distribution of the interacting microbubbles, the rheological properties of the lipid shell and the viscoelasticity of the surrounding medium were considered simultaneously. The obtained radius response curves present a successive occurrence of linear resonances, nonlinear harmonic and sub-harmonic resonances with the acoustic pressure increasing. The microbubble resonance is radius-, pressure- and frequency-dependent. Specifically, the maximum bubble expansion ratio at the main resonance peak increases but the resonant radius decreases as the ultrasound pressure increases, while both of them decrease with the ultrasound frequency increasing. Moreover, compared to an isolated microbubble case, it is found that large microbubbles in close proximity prominently suppress the resonant oscillations while slightly increase the resonant radii for both harmonic and subharmonic resonances, even leading to the disappearance of the subharmonic resonance with the influences increasing to a certain degree. In addition, the results also suggest that both the encapsulating shell and surrounding medium can substantially dampen the harmonic and subharmonic resonances while increase the resonant radii, which seem to be affected by the medium viscoelasticity to a greater degree rather than the shell properties. This work offers valuable insights into the resonance behaviors of microbubbles oscillating in viscoelastic biological media, greatly contributing to further optimizing their biomedical applications.

GPU-accelerated study of the inertial cavitation threshold in viscoelastic soft tissue using a dual-frequency driving signal

Inertial cavitation thresholds under two forms of ultrasonic excitation (the single- and dual-frequency ultrasound modes) are studied numerically. The Gilmore-Akulichev model coupled with the Zener viscoelastic model is used to model the bubble dynamics. The threshold pressures are determined with two criteria, one based on the bubble radius and the other on the bubble collapse speed. The threshold behavior is investigated for different initial bubble sizes, acoustic signal modes, frequencies, tissue viscosities, tissue elasticities, and all their combinations. Due to the large number of parameters and their many combinations (around 1.5 billion for each threshold criterion), all simulations were executed on graphics processing units to speed up the calculations. We used our own code written in the C++ and CUDA C languages. The results obtained demonstrate that using the dual-frequency signal mode can help to reduce the inertial cavitation threshold (in comparison to the single-frequency mode). The criterion based on the bubble size gives a lower threshold than the criterion using the bubble collapse speed. With an increase of the elasticity, the threshold pressure also increases, whereas changing the viscosity has a very small impact on the optimal threshold, unlike the elasticity. A detailed analysis of the optimal ultrasound frequencies for a dual-frequency driving signal found that for viscosities less than 0.02 Pa·s, the first optimal frequency, in general, is much smaller than the second optimal frequency, which can reach 1 MHz. However, for high viscosities, both optimal frequencies are similar and varied in the range 0.01-0.05 MHz. Overall, this study presents a detailed analysis of inertial cavitation in soft tissue under dual-frequency signal excitation. It may be helpful for the further development of different applications of biomedical ultrasound.

Enhancing cavitation dynamics and its mechanical effects with dual-frequency ultrasound

Objective. Acoustic cavitation and its mechanical effects (e.g. stress and strain) play a primary role in ultrasound applications. Introducing encapsulated microbubbles as cavitation nuclei and utilizing dual-frequency ultrasound excitation are highly effective approaches to reduce cavitation thresholds and enhance cavitation effects. However, the cavitation dynamics of encapsulated microbubbles and the resultant stress/strain in viscoelastic tissues under dual-frequency excitation are poorly understood, especially for the enhancement effects caused by a dual-frequency approach. The goal of this study was to numerically investigate the dynamics of a lipid-coated microbubble and the spatiotemporal distributions of the stress and strain under dual-frequency excitation. Approach. The Gilmore–Zener bubble model was coupled with a shell model for the nonlinear changes of both shell elasticity and viscosity to accurately simulate the cavitation dynamics of lipid-coated microbubbles in viscoelastic tissues. Then, the spatiotemporal evolutions of the cavitation-induced stress and strain in the surrounding tissues were characterized quantitatively. Finally, the influences of some paramount parameters were examined to optimize the outcomes. Main results. We demonstrated that the cavitation dynamics and associated stress/strain were prominently enhanced by a dual-frequency excitation, highlighting positive correlations between the maximum bubble expansion and the maximum stress/strain. Moreover, the results showed that the dual-frequency ultrasound with smaller differences in its frequencies and pressure amplitudes could enhance the bubble oscillations and stress/strain more efficiently, whereas the phase difference manifested small influences under these conditions. Additionally, the dual-frequency approach seemed to show a stronger enhancement effect with the shell/tissue viscoelasticity increasing to a certain extent. Significance. This study might contribute to optimizing the dual-frequency operation in terms of cavitation dynamics and its mechanical effects for high-efficient ultrasound applications.

Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei

Numerical modelling of acoustic cavitation threshold in water is presented taking into account non-condensable bubble nuclei, which are composed of water vapor and non-condensable air. The cavitation bubble growth and collapse dynamics are modeled by solving the Rayleigh-Plesset or Keller-Miksis equation, which is combined with the energy equations for both the bubble and liquid domains, and directly evaluating the phase-change rate from the liquid and bubble side temperature gradients. The present work focuses on elucidating acoustic cavitation in water with a wide range of cavitation thresholds (0.02-30 MPa) reported in the literature. Computations for different nucleus sizes and acoustic frequencies are performed to investigate their effects on bubble growth and cavitation threshold. The numerical predictions are observed to be comparable to the experimental data in the previous works and show that the cavitation threshold in water has a wide range depending on the bubble nucleus size.

Dynamics of bubble-bubble interactions experiencing viscoelastic drag

The subject of the present theoretical study is the dynamics of bubble-bubble interactions in a viscoelastic medium. First, new equations for calculating the viscoelastic drag exerted on bubbles during their translational motion in a viscoelastic medium are derived. The drag equations are incorporated in the bubble-bubble interaction model in which, thereby, both the translational and radial motions of the bubbles are affected by the viscoelastic features of the medium. Second, the derived equations are applied to investigate how the viscoelastic properties of the medium can affect the dynamics of multiple bubbles, as well as how the bubbles can affect each other. It was discovered that the bubble-bubble interaction can significantly influence the dynamics of a single bubble. As the distance between the bubbles increases, their effect on each other decreases, and at a distance of several millimeters, this effect can be neglected. Moreover, it was concluded that with increasing elasticity and viscosity of the medium, as well with decreasing relaxation time, the effects of other bubbles on the current bubble's radial motion can become negligible. The translational motion of the bubbles was investigated for different viscoelastic models. The elasticity resists the motion of bubbles in space, resulting in a dynamical steady state of the distance between the bubbles at high elasticity values. The relaxation time of the medium was also found to be important in terms of the bubbles' translational movement.