High-Resolution Finite Volume Methods for Extracorporeal Shock Wave Therapy

Extracorporeal Shock Wave Therapy (ESWT) is a noninvasive technique for the treatment of a variety of musculoskeletal conditions such as delayed union of bone fractures, plantar fasciitis, and calcified tendonitis of the shoulder. Shock waves were first used medically in the lithotripsy procedure (ESWL) to pulverize hardened calcified deposits such as kidney stones. This technique was then extended to musculoskeletal conditions as a treatment for calcifications in the shoulder, as these deposits are similar to renal calculi [1]. Later ESWT was shown to improve bone regeneration in the treatment of nonunions, which are bone fractures that fail to heal over time. In electrohydraulic lithotripsy, a shock wave is generated in a liquid bath, focused through the use of an ellipsoid reflector, and then propagates into the body where it ideally strikes the area of interest. Clinicians have indicated that this is not always the case and treatments will sometimes cause unforseen damage in parts of the body. 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.We utilize highresolution finite volume methods to capture the discontinuous pressure wave and model the wave propagation in bone and tissue. This approach has been successfully applied to many problems in acoustic or elastic wave propagation in heterogeneous media [2].