Numerical Simulations of Cavitating Bubbles in Elastic and Viscoelastic Materials for Biomedical Applications

Citation

Spratt, Jean-Sébastien Alexandre (2024) Numerical Simulations of Cavitating Bubbles in Elastic and Viscoelastic Materials for Biomedical Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/g34e-6p65. https://resolver.caltech.edu/CaltechTHESIS:10162023-141935060

Abstract

The interactions of cavitating bubbles with elastic and viscoelastic materials play a central role in many biomedical applications. This thesis makes use of numerical modeling and data-driven approaches to characterize soft biomaterials at high strain rates via observation of bubble dynamics, and to model burst-wave lithotripsy, a focused ultrasound therapy to break kidney stones.

In the first part of the thesis, a data assimilation framework is developed for cavitation rheometry, a technique that uses bubble dynamics to characterize soft, viscoelastic materials at high strain-rates. This framework aims to determine material properties that best fit observed cavitating bubble dynamics. We propose ensemble-based data assimilation methods to solve this inverse problem. This approach is validated with surrogate data generated by adding random noise to simulated bubble radius time histories, and we show that we can confidently and efficiently estimate parameters of interest within 5% given an iterative Kalman smoother approach and an ensemble- based 4D-Var hybrid technique. The developed framework is applied to experimental data in three distinct settings, with varying bubble nucleation methods, cavitation media, and using different material constitutive models. We demonstrate that the mechanical properties of gels used in each experiment can be estimated quickly and accurately despite experimental inconsistencies, model error, and noisy data. The framework is used to further our understanding of the underlying physics and identify limitations of our bubble dynamics model for violent bubble collapse.

In the second part of the thesis, we simulate burst-wave lithotripsy (BWL), a non- invasive treatment for kidney stones that relies on repeated short bursts of focused ultrasound. Numerical approaches to study BWL require simulation of acoustic waves interacting with solid stones as well as bubble clouds which can nucleate ahead of the stone. We implement and validate a hypoelastic material model, which, with the addition of a continuum damage model and calibration of a spherically- focused transducer array, enables us to determine how effective various treatment strategies are with arbitrary stones. We present a preliminary investigation of the bubble dynamics occurring during treatment, and their impact on damage to the stone. Finally, we propose a strategy to reduce shielding by collapsing bubbles ahead of the stone via introduction of a secondary, low-frequency ultrasound pulse during treatment.

Thesis Files