Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones

Abstract

The governing equations for the theory of poroelastic materials with hierarchical pore space architecture and compressible constituents undergoing small deformations are developed. These equations are applied to the problem of determining the exchange of pore fluid between the vascular porosity (PV) and the lacunar-canalicular porosity (PLC) in bone tissue due to cyclic mechanical loading and blood pressure oscillations. The result is basic to the understanding of interstitial flow in bone tissue that, in turn, is basic to understanding of nutrient transport from the vasculature to the bone cells buried in the bone tissue and to the process of mechanotransduction by these cells. A formula for the volume of fluid that moves between the PLC and PV in a cyclic loading is obtained as a function of the cyclic mechanical loading and blood pressure oscillations. Formulas for the oscillating fluid pore pressure in both the PLC and the PV are obtained as functions of the two driving forces, the cyclic mechanical straining and the blood pressure, both with specified amplitude and frequency. The results of this study also suggest a PV permeability greater than 10 −9 m 2 and perhaps a little lower than 10 −8 m 2 . Previous estimates of this permeability have been as small as 10 −14 m 2 .

Properties of water confined in hydroxyapatite nanopores as derived from molecular dynamics simulations

“…However, the role of nanopores on the fluid flow within the bone has been largely overlooked, most likely because the description of fluid flow has been so far restricted to a double-porosity approach involving vasculature (Haversian system) and submicrometer pores of canalicular network [8,9]. In the framework of porous media theory, the bone interstitial fluid flow is macroscopically described by a Darcy law obtained by upscaling a description of the flow at the pore scale to the macroscopic scale organ [10,11].…”

Molecular Dynamics Simulations of Hydroxyapatite Nanopores in Contact with Electrolyte Solutions: The Effect of Nanoconfinement and Solvated Ions on the Surface Reactivity and the Structural, Dynamical, and Vibrational Properties of Water

“…It is commonly accepted that bone can be described by three main levels of porosity [23], which are nested hierarchically one inside another as a set of Russian dolls in microcirculatory pathways [24]. The macroscopic porous network corresponds to the vascular (or Haversian) porosity, which consists of the Havers and Volkmann canals (typical diameter of 50 µm).…”

Mathematical Problems in the Theory of Bone Poroelasticity

“…The theory of multiporous media, as originally developed for the mechanics of naturally fractured reservoirs, has found applications in blood perfusion. The double porosity model would consider the bone fluid pressure in the vascular porosity and the bone fluid pressure in the lacunar-canalicular porosity [1], [2], [3]. An extensive review of the results in the theory of bone poroelasticity can be found in the survey papers [1], [2].…”

“…Poroelasticity is a well-developed theory for the interaction of fluid and solid phases of a fluid saturated porous medium. It is an effective and useful model for deformation-driven bone fluid movement in bone tissue [1], [2], [3].…”