Session F03: Bubbles: Biomedical, Cavitation and Acoustics (3:55pm - 4:40pm CST)

Maximum Size of an Explosively Growing Bubble

Tissue damage produced by cavitation bubbles is an inherent part of a variety of therapeutic ultrasound procedures, including lithotripsy and histotripsy. Past studies suggest that the size of the damaged region scales with the maximum bubble radius achieved during the process. In this work, we investigate the dependence between the maximum radius of a spherical gas bubble driven by an incident pressure pulse and the parameters entering the problem, including the waveform properties and the material properties. Theoretical scaling for the bubble size and velocity is developed and verified with numerical solutions to Rayleigh-Plesset-based equations for spherical bubble dynamics. The implications of the results to therapeutic ultrasound will be discussed at the meeting.   

Numerical modeling of encapsulated microbubbles with a coupled level set and volume-of-fluid method

The coupled level set and volume-of-fluid (CLSVOF) method is an efficient approach used to simulate multiphase flows in which fluids of different phases are separated by a complex, evolving interface. This method leverages the advantages of both the level set (LS) and volume-of-fluid (VOF) approaches by combining the strong mass conservation properties of the VOF method, while retaining the accurate interface representation of the LS method. In this work, the flow field is discretized by a single-field, finite difference formulation of the weakly compressible Navier-Stokes equations on a stationary grid. A coupled second-order operator split algorithm is used to advect the volume fraction and level set function, and the interface is reconstructed using the least-squares volume-of-fluid interface reconstruction algorithm (LVIRA). A numerical code has been developed for 2D and axisymmetric cases, and its performance has been validated through a series of test cases, such as the oscillation of a spherical bubble in response to changes in ambient pressure. An elastic layer is incorporated at the gas-liquid interface to simulate the nonspherical dynamics of ultrasonically-forced encapsulated microbubbles, which are used for ultrasound imaging and intravenous drug delivery.   

Optimal control of the nonspherical oscillation of encapsulated microbubbles for ultrasound imaging and drug delivery

Encapsulated microbubbles (EMBs) were originally developed as contrast agents for ultrasound imaging but are more recently emerging as vehicles for intravenous drug and gene delivery. Ultrasound can excite nonspherical oscillations, or shape modes, that can enhance the acoustic signature of an EMB and also incite rupture, which promotes drug and gene delivery at targeted sites (e.g., tumors). Therefore, the ability to control shape modes can improve the efficacy of both diagnosis and treatment mediated by EMBs. This work uses optimal control theory to determine the ultrasound input that maximizes a desired nonspherical EMB response (e.g., to enhance scattering or rupture), while minimizing the total acoustic input in order to enhance patient safety and reduce unwanted side effects. The optimal control problem is applied to nonspherical models of both a free gas bubble and an EMB, which are solved numerically through pseudospectral collocation methods using commercial optimization software. Single frequency and broadband acoustic forcing schemes are explored and compared. The encapsulation greatly increases the acoustic effort required to incite rupture. Furthermore, the acoustic effort required to incite rupture depends on the shape mode that is forced to become unstable.   

An Eulerian Framework for Numerical Simulations of Cavitating Bubble-Clouds near Viscoelastic Materials

Given the broad range of spatio-temporal scales involved, simulating cavitating bubble clouds and their interactions with soft materials is challenging. However, such simulations are necessary to predict many physical phenomena, with particular applications in biomedical engineering. These applications include shock-wave and burst-wave lithotripsy (BWL), histrotripsy, blunt trauma and traumatic brain injury. BWL, a therapy for ablating kidney stones, can entail particularly complex physical processes. This treatment focuses large-amplitude ultrasound waves near the stone to break it up. During therapy, bubble clouds can form and cavitate around the stone, affecting treatment efficacy. Modeling of bubble-cloud--stone--soft-material interactions is required to optimize stone comminution against surrounding soft tissue damage. The open-source solver MFC (Bryngelson et al., Comp.\ Phys.\ Comm., 2020) models the bubble cloud cavitation using a phase-averaging sub-grid model, and has been extended to include a hypoelastic Kelvin--Voigt model for linear elastic solids, both fully coupled to the background fluid dynamics. We demonstrate the capabilities of MFC to model BWL.