Multi-Scale Micro-Mechanical Poroelastic Modeling of Fluid Flow in Cortical Bone

Abstract

To explore the potential role that load-induced fluid flow plays as a mechano-transduction mechanism in bone adaptation, a lacunar-canalicular scale bone poroelasticity model is developed and exercised. The model uses micromechanics to homogenize the pericanalicular bone matrix, a system of straight circular cylinders in the bone matrix through which bone fluids can flow, as a locally anisotropic poroelastic medium. In this work, a simplified two-dimensional model of a periodic array of lacunae and their surrounding systems of canaliculi is developed and exercised to quantify local fluid flow characteristics in the vicinity of a single lacuna. When the cortical bone model is loaded, microscale stress and strain concentrations occur in the vicinity of individual lacunae and give rise to microscale spatial variations in the pore fluid pressure field. Consequently, loading of cortical bone can induce fluid flow in the canaliculi and exchange of fluid between canaliculi and lacunae. For realistic bone morphology parameters, and a range of loading frequencies, fluid pressures and fluid-solid shear stresses in the canalicular bone are computed and the associated energy dissipation in the models compared to that measured in physical in vitro experiments on human cortical bone. For realistic volume fractions of canaliculi, deformation-induced fluid flow is found to have a much larger characteristic time constant than deformation-induced flow in the Haversian system.