Textural versus electrostatic exclusion‐enrichment effects in the effective chemical transport within the cortical bone: A numerical investigation

Abstract

Interstitial fluid within bone tissue is known to govern the remodelling signals' expression. Bone fluid flow is generated by skeleton deformation during the daily activities. Due to the presence of charged surfaces in the bone porous matrix, the electrochemical phenomena occurring in the vicinity of mechanosensitive bone cells, the osteocytes, are key elements in the cellular communication. In this study, a multiscale model of interstitial fluid transport within bone tissues is proposed. Based on an asymptotic homogenization method, our modelling takes into account the physicochemical properties of bone tissue. Thanks to this multiphysical approach, the transport of nutrients and waste between the blood vessels and the bone cells can be quantified to better understand the mechanotransduction of bone remodelling. In particular, it is shown that the electrochemical tortuosity may have stronger implications in the mass transport within the bone than the purely morphological one.

Three-Scale Multiphysics Modeling of Transport Phenomena within Cortical Bone

“…This subsection briefly recalls the main results of the two-scale treatment of multiphysical transport within the lacunocanalicular system as presented in [24].…”

“…The first upscaling procedure to derive the transport phenomena at the mesoscale from the microscopic description is based on the asymptotic periodic homogenization process as proposed in [23,30,31]. The two-level homogenization procedure for the same Poisson-Boltzmann equation (1) and Brinkman equations (2) can be found in [23,29], whereas the upscaling of the Nernst-Planck equations is given in [24]. In particular, it was shown in these references that the fluid pressure , the salinity , and the streaming potential = do not vary at the microscale whereas the double layer potential is purely microscopic.…”

“…The complete expression of the effective diffusion tensor at the mesoscale D ± is detailed in [24]. This quantity combines textural and electrical effects.…”

“…In geoscience, fluid and ionic transport in monoporous media is a classical application of upscaling methods to derive effective transport coefficients [18][19][20][21][22]. Similarly, hydrochemical transport phenomena in the LCP were extensively studied by our group [23,24] highlighting their effects on bone physiology [25,26]. This paper stems from those results and extends them to the osteonal scale, focusing on the fluid and ionic transport along the osteon.…”

“…This paper stems from those results and extends them to the osteonal scale, focusing on the fluid and ionic transport along the osteon. An asymptotic homogenization technique is used to upscale a coupled description of the transport phenomena toward the tissue scale [23,24]. The outcome is an explicit description of the velocity and the ionic flux along the osteon which turns out to be ruled by generalized forms of the Darcy law and macroscopic convectiondiffusion equations.…”