UW Applied Mathematics Graduate Student
Extracorporeal Shock Wave Therapy (ESWT) is a noninvasive technique for the treatment of a variety of musculoskeletal conditions such as delayed union of fractures, plantar fascitis and calcified tendonitis of the shoulder. Shock waves were first used medically as lithotripsy to pulverize hardened calcified deposits such as kidney stones. This technique was first use beyond lithotripsy to treat calcifications in the shoulder as these deposits are similar to renal calculi. Later it was shown to improve bone regeneration in the treatment of non-unions. In lithotripsy, a shock wave is generated in a liquid bath, focused through the use of an ellipsoid reflector and it then propagates into the body where it strikes the area of interest. Current numerical models are limited to simplified situations because the structure of the wave is highly nonlinear and therefore difficult to model with traditional finite difference and finite element techniques. I would like to use finite volume methods to capture this nonlinear behavior and model the shock wave propagation in bone and tissue. This approach has been successfully applied to many problems in acoustic or elastic wave propagation in heterogeneous media.