Communications in Applied Mathematics and Computational Science

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

Kirsten Fagnan, Randall LeVeque, and Thomas Matula

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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.

Article information

Commun. Appl. Math. Comput. Sci., Volume 8, Number 1 (2013), 159-194.

Received: 6 December 2010
Accepted: 6 November 2013
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 92-08: Computational methods 92C50: Medical applications (general) 65M08: Finite volume methods

high-resolution finite volume methods computational biology shock wave therapy


Fagnan, Kirsten; LeVeque, Randall; Matula, Thomas. Computational models of material interfaces for the study of extracorporeal shock wave therapy. Commun. Appl. Math. Comput. Sci. 8 (2013), no. 1, 159--194. doi:10.2140/camcos.2013.8.159.

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