Vol. 6, No. 1-4, 2011

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ISSN: 1559-3959
Dissipation energy as a stimulus for cortical bone adaptation

Natarajan Chennimalai Kumar, Iwona Jasiuk and Jonathan Dantzig

Vol. 6 (2011), No. 1-4, 303–319
Abstract

We present a finite element study of a poroelastic rectangular beam subjected to oscillatory bending loads. This geometric model is chosen for simplicity, as an idealized representation of cortical bone. We then propose the use of the dissipation energy of the poroelastic flow as a mechanical stimulus for bone adaptation, and show that it can predict the effect of frequency of the applied load. Surface adaptation in the model depends on the weighted average of the mechanical stimulus in a “zone of influence” near each surface point, in order to incorporate the non-locality in the mechanotransduction of osteocytes present in the lacunae. We show that the dissipation energy stimulus and the resulting increase in second moment of inertia of the cross section increase linearly with frequency in the low frequency range (less than 10 Hz) and saturate at the higher frequency range (greater than 10 Hz). Similar non-linear adaptation frequency response also has been observed in numerous experiments. Our framework is readily extended to the modeling of cortical bone using actual bone geometries.

Keywords
poroelasticity, dissipation energy, interstitial fluid flow, cortical bone adaptation, finite element modeling, evolution law
Milestones
Received: 22 May 2010
Revised: 8 December 2010
Accepted: 12 December 2010
Published: 28 June 2011
Authors
Natarajan Chennimalai Kumar
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
1206 West Green Street
Urbana, IL 61801
United States
Iwona Jasiuk
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
1206 West Green Street
Urbana, IL 61801
United States
http://www.mechse.uiuc.edu/faculty/ijasiuk
Jonathan Dantzig
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
1206 West Green Street
Urbana, IL 61801
United States