Computational Modeling of Extracorporeal Shock Wave Therapy

Extracorporeal shock wave therapy (ESWT) is a noninvasive treatment for a variety of musculoskeletal conditions such as bone fractures that fail to heal, calcium deposits in soft tissue and necrotic wounds. The underlying biological mechanisms responsible for healing are not yet well understood, and this partially due to the complex nature of shock wave interaction with bone, soft tissue and the complex 3D geometries present in the skeletal system. I will present a Lagrangian form of the isentropic Euler equations, with the modified Tait equation of state, that we use to model ESWT wave propagation with idealized biological materials and bone models reconstructed from CT scans. We have solved this system of equation using a high-resolution finite volume method that incorporates a spatially varying stress-strain relationship in order to model the different materials. We used adaptive mesh refinement and parallelization available in CHOMBOCLAW to solve the three-dimensional problems. We have used this approach to investigate optimization of treatment angle for nonunions and heterotopic ossifications with the goal of helping clinicians optimize treatment protocols.