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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 398970, 10 pages
http://dx.doi.org/10.1155/2015/398970
Research Article

Three-Scale Multiphysics Modeling of Transport Phenomena within Cortical Bone

1Laboratoire Modélisation et Simulation Multi Echelle (MSME UMR 8208 CNRS), Université Paris-Est, 61 Avenue du Général de Gaulle, 94010 Créteil, France
2Comsol France, 5 Place Robert Schuman, 38000 Grenoble, France

Received 1 July 2015; Accepted 8 September 2015

Academic Editor: Seungik Baek

Copyright © 2015 T. Lemaire et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Bone tissue can adapt its properties and geometry to its physical environment. This ability is a key point in the osteointegration of bone implants since it controls the tissue remodeling in the vicinity of the treated site. Since interstitial fluid and ionic transport taking place in the fluid compartments of bone plays a major role in the mechanotransduction of bone remodeling, this theoretical study presents a three-scale model of the multiphysical transport phenomena taking place within the vasculature porosity and the lacunocanalicular network of cortical bone. These two porosity levels exchange mass and ions through the permeable outer wall of the Haversian-Volkmann canals. Thus, coupled equations of electrochemohydraulic transport are derived from the nanoscale of the canaliculi toward the cortical tissue, considering the intermediate scale of the intraosteonal tissue. In particular, the Onsager reciprocity relations that govern the coupled transport are checked.