Matthew Warnez

Histotripsy-induced cavitation cloud initiation thresholds in tissues of different mechanical properties

Histotripsy is an ultrasound ablation method that depends on the initiation and maintenance of a cavitation bubble cloud to fractionate soft tissue. This paper studies how tissue properties impact the pressure threshold to initiate the cavitation bubble cloud. Our previous study showed that shock scattering off one or more initial bubbles, expanded to sufficient size in the focus, plays an important role in initiating a dense cavitation cloud. In this process, the shock scattering causes the positive pressure phase to be inverted, resulting in a scattered wave that has the opposite polarity of the incident shock. The inverted shock is superimposed on the incident negative pressure phase to form extremely high negative pressures, resulting in a dense cavitation cloud growing toward the transducer. We hypothesize that increased tissue stiffness impedes the expansion of initial bubbles, reducing the scattered tensile pressure, and thus requiring higher initial intensities for cloud initiation. To test this hypothesis, 5-cycle histotripsy pulses at pulse repetition frequencies (PRFs) of 10, 100, or 1000 Hz were applied by a 1-MHz transducer focused inside mechanically tunable tissue-mimicking agarose phantoms and various ex vivo porcine tissues covering a range of Youngs moduli. The threshold to initiate a cavitation cloud and resulting bubble expansion were recorded using acoustic backscatter detection and optical imaging. In both phantoms and ex vivo tissue, results demonstrated a higher cavitation cloud initiation threshold for tissues of higher Youngs modulus. Results also demonstrated a decrease in bubble expansion in phantoms of higher Youngs modulus. These results support our hypothesis, improve our understanding of the effect of histotripsy in tissues with different mechanical properties, and provide a rational basis to tailor acoustic parameters for fractionation of specific tissues.

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 Youngs 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.

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 Youngs 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.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation.

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.

Damage mechanisms for ultrasound-induced cavitation in tissue

In a variety of biomedical applications, cavitation occurs in soft tissue. Although significant amounts of research have been performed on cavitation in water, bubble dynamics, and related bioeffects remain poorly understood. We use numerical simulations of spherical bubble dynamics in soft tissue to assess the extent to which viscoelasticity affects “known” and introduces “new” damage mechanisms. We find that deviatoric stresses – although not an important damage mechanism in water – are significantly enhanced and could be an important bioeffect mechanism in tissue. Both the viscoelastic properties and the nonlinear, large-collapse radius contribute to stress amplification in the surroundings. In addition, temperatures in the surrounding medium increase more in the Zener tissue than in water, due to viscous heating.

Small-bubble transport and splitting dynamics in a symmetric bifurcation

Abstract Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.

Stress and strain fields produced by violent bubble collapse

Cavitation finds a key application in therapeutic ultrasound. For example, histotripsy relies on the rapid expansion of cavitation bubbles to fractionate soft tissue. To fully understand the mechanisms responsible for tissue fractionation, we numerically model cavitation in a tissuelike medium, focusing on the effect of its viscoelastic properties (viscosity, elasticity, and relaxation). It is hypothesized that ablation is caused by high strain rates and stresses exerted on the surrounding tissue as bubbles rapidly expand from nanometer to micron scales. The present study uses robust numerical techniques to compute the stress fields in the surrounding medium produced by single-bubble expansion. Bubble expansion is driven by a waveform that approximates a histotripsy pulse with relevant parameters, and soft tissue surrounding the bubble is modeled as a viscoelastic medium with Neo-Hookean elasticity. We will examine the stress, strain, and temperature fields produced during this process to explain potential damage mechanisms.

Tissue damage produced by cavitation: The role of viscoelasticity

Cavitation may cause damage at the cellular level in a variety of medical applications, e.g., therapeutic and diagnostic ultrasound. While cavitation damage to bodies in water has been studied for over a century, the dynamics of bubbles in soft tissue remain vastly unexplored. One difficulty lies in the viscoelasticity of tissue, which introduces additional physics and time scales. We developed a numerical model to investigate acoustic cavitation in soft tissue, which accounts for liquid compressibility, full thermal effects, and viscoelasticity (including nonlinear relaxation and elasticity). The bubble dynamics are represented by a Keller-Miksis formulation and a spectral collocation method is used to solve for the stresses in the surrounding medium. Our numerical studies of a gas bubble exposed to a relevant waveform indicate that under inertial conditions high pressures and velocities are generated at collapse, though they are lower than those observed in water due to the elasticity and viscosity of t...

A numerical model for large-amplitude spherical bubble dynamics in tissue

In a variety of therapeutic and diagnostic ultrasound procedures (e.g., histotripsy, lithotripsy, and contrast-enhanced ultrasound), cavitation occurs in soft tissue, which behaves in a viscoelastic fashion. While stable bubble oscillations may occur in ultrasound, the most dramatic outcomes (tissue ablation, bleeding, etc.) are usually produced by inertial cavitation. Historically, Rayleigh-Plesset equations have been used to investigate the dynamics of spherical bubbles, including in biomedical applications. For large-amplitude bubble oscillations in tissue, it is clear that compressibility, heat transfer and nonlinear viscoelasticity play important roles. However, no existing model includes all of these effects. To address this need, we use a compressible Rayleigh-Plesset equation (Keller-Miksis) adjoined with heat conduction in conjunction with an upper-convected Zener viscoelastic model, which accounts for relaxation, elasticity, and viscosity. The partial differential equations describing the stress tensor components in the surrounding medium are solved using a spectral collocation method. The method proves to be robust even for strong bubble collapse. Numerical comparisons with previous models are made, comparisons to experiments are included, and the dependence of bubble dynamics on viscoelastic parameters is explored. This model is used to revisit the inertial cavitation threshold in biomedical settings.