PMID: 9165394Jun 1, 1997Paper

Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations

Journal of Biomechanics
C R JacobsD R Carter

Abstract

Over 100 years ago, Wolff hypothesized that cancellous bone altered both its apparent density and trabecular orientation in response to mechanical loads. A mathematical counterpart of this principle is derived by adding a remodeling rule for the rate-of-change of the full anisotropic stiffness tensor (all 21 independent terms) to the density rate-of-change rule adapted from an existing isotropic theory. As a result, anisotropy and density patterns develop such that the local stiffness tensor is optimal for the given series of applied loadings. The method does not rely on additional morphological measures of trabecular orientation. Furthermore, assumptions of material symmetry are not required, and any observed regions of orthotropy, transverse isotropy, or isotropy are a result entirely of the functional adaptation of the bone and not the consequence of a modeling assumption. This approach has been implemented with the finite element method and applied to a two-dimensional model of the proximal femur with encouraging results.

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Citations

Mar 22, 2005·Biomechanics and Modeling in Mechanobiology·A Menzel
Jun 9, 2005·Biomechanics and Modeling in Mechanobiology·J M García-AznarM Doblare
Mar 18, 2008·Biomechanics and Modeling in Mechanobiology·J Martínez-ReinaM Doblaré
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Sep 12, 2012·Computer Methods in Biomechanics and Biomedical Engineering·Serkan Inceoğlu, Prasath Mageswaran
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