Three-Scale Multiphysics Modeling of Transport Phenomena within Cortical Bone

T Lemaire,V Sansalone,S Naili,J Kaiser

doi:10.1155/2015/398970

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.

Highlights

Bone remodeling corresponds to a process by which bone tissue gradually alters its morphology and properties in order to adapt to its external environment [1, 2]
This ability is a key point of the success of different protocols in bone tissue engineering
Interstitial fluid and ionic transport taking place in the fluid compartments of bone is thought to play a major role in the bone ability to transmit physical stimuli toward bone cells and trigger the remodeling process [5, 6]

Summary

Introduction

Bone remodeling corresponds to a process by which bone tissue gradually alters its morphology and properties in order to adapt to its external environment [1, 2]. Cortical bone, which corresponds to the dense tissue located at the periphery of bones, is mostly made of cylindrical structures called osteons These cylinders are crossed by a hierarchical porous network saturated by a fluid with both mechanical and chemical functions. To the best of our knowledge, this theoretical work is the first attempt to describe the multiphysical transport phenomena taking place within the HVC and the LCP at once. These two fluid compartments exchange mass and ions through the permeable outer wall of the HVC. A rewriting of the macroscopic equations when convection and diffusion mechanisms are comparable resulted in checking the Onsager reciprocal relations linking the fluxes and driving forces that govern the coupled transport phenomena

Multiscale Structure of the Cortical Tissue

From the Microscale to the Mesoscale

From the Lamellar Tissue to the Cortical Tissue

Discussion on the Onsager Reciprocal Relations

Concluding Remarks