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Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

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Abstract

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.

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Authors and Affiliations

  1. Laboratoire de Mécanique Physique, UMR CNRS 7052 B2OA, Faculté des Sciences et Technologie, Université Paris XII-Val de Marne, 61 Avenue du Général de Gaulle, 94010, Créteil Cédex, France

    Agnès Rémond, Salah Naïli & Thibault Lemaire

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  1. Agnès Rémond
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  2. Salah Naïli
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  3. Thibault Lemaire
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Correspondence to Salah Naïli.

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Rémond, A., Naïli, S. & Lemaire, T. Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study. Biomech Model Mechanobiol 7, 487–495 (2008). https://doi.org/10.1007/s10237-007-0111-0

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  • DOI: https://doi.org/10.1007/s10237-007-0111-0

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