Vol. 8, No. 1, 2013

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Computational models of material interfaces for the study of extracorporeal shock wave therapy

Kirsten Fagnan, Randall J. LeVeque and Thomas J. Matula

Vol. 8 (2013), No. 1, 159–194

Extracorporeal shock wave therapy (ESWT) is a noninvasive treatment for a variety of musculoskeletal ailments. A shock wave is generated in water and then focused using an acoustic lens or reflector so the energy of the wave is concentrated in a small treatment region where mechanical stimulation in principle enhances healing. In this work we have computationally investigated shock wave propagation in ESWT by solving a Lagrangian form of the isentropic Euler equations in the fluid and linear elasticity in the bone using high-resolution finite volume methods. We solve a full three-dimensional system of equations and use adaptive mesh refinement to concentrate grid cells near the propagating shock. We can model complex bone geometries, the reflection and mode conversion at interfaces, and the propagation of the resulting shear stresses generated within the bone. We discuss the validity of our simplified model and present results validating this approach.

high-resolution finite volume methods, computational biology, shock wave therapy
Mathematical Subject Classification 2010
Primary: 92-08, 92C50, 65M08
Received: 6 December 2010
Accepted: 6 November 2013
Published: 22 January 2014
Kirsten Fagnan
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 943R0256
Berkeley, CA 94720
United States
Randall J. LeVeque
Department of Applied Mathematics
University of Washington
Box 352420
Seattle, WA 98195-2420
United States
Thomas J. Matula
Applied Physics Laboratory
University of Washington
1013 NE 40th Street
Box 355640
Seattle, WA 98105-6698
United States