Multiscale and multiphysics computational models of processes in shock wave lithotripsy

Fovargue, Daniel

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March 22, 2019

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Fovargue, Daniel
- Affiliation: College of Arts and Sciences, Department of Mathematics

Abstract

This thesis presents two computational models applied to processes in shock wave lithotripsy. The first is a multiphysics model of the focusing of an acoustic pulse and the subsequent shock wave formation that occurs in a refracting electromagnetic lithotripter. This model solves both the linear elasticity equations and the Euler equations with a Tait equation of state in arbitrary subsets of the full computational domain. It is implemented within BEARCLAW and uses a finite-volume Riemann solver approach. The model is validated using a standard lens design and is shown to accurately predict the effects of a lens modification. This model is also extended to include a kidney stone simulant in the domain in which a simple isotropic damage law is included. The second computational model is a 3D multiscale fracture model which predicts crack formation and propagation within a kidney stone simulant by utilizing a continuum-mesoscopic interaction. The simulant included in the model is realistic in that the data representing the stone is drawn from MicroCT image data. At the continuum scale the linear elasticity equations are solved while incorporating an anisotropic damage variable, again using a finite-volume Riemann solver within BEARCLAW. At the mesoscale, damage accumulates based on experimentally informed probability distributions and on predefined surfaces representing a granular structure. In addition to the computational models, some experimental results are discussed. These include probability distributions of fracture properties found from MicroCT images of kidney stone simulants and corresponding image processing procedures.

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