Mathematics Colloquium: Algorithms for shock wave propagation in tissue, bones and kidney stones
3:10 p.m. WEBS B0012
Randall J. LeVeque
Abstract: Extracorporal shock wave lithotripsy (ESWL) is a well established non-invasive clinical procedure for breaking up kidney stones by the external application of shock waves that (ideally) focus on the kidney stone with minimal collatoral damage. Recently lithotripter devices have been applied to treat a variety of other medical conditions where the goal is to stimulate rather than to pulverize. Applications of extracorporal shock wave therapy (ESWT) include treatment of plantar fasciitis, tennis elbow, hip necrosis, and non-unions (bone fractures that do not heal on their own). Numerical algorithms for modeling nonlinear elastic wave propagation including shock waves are being developed in two and three space dimensions to aid in the study of the mechanisms of ESWL and ESWT. High resolution finite volume methods using Riemann solvers are employed along with adaptive mesh refinement. These methods work well for wave propagation problems in heterogeneous media and can accurately capture the transmission and reflection of waves at material interfaces (e.g. tissue/bone), which is an essential aspect of this problem. I will discuss these methods and some of the applications being studied in work with student Kirsten Fagnan in connection with experiments being performed in the UW Center for Industrial and Medical Ultrasound and clinical work at the UW Medical School.