title: 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).
authors: Department of Biomedical Engineering, School of Engineering of the City College and the Graduate School of the City University of New York, New York, NY 10031, USA. scowin@earthlink.net
authors: Stephen C
authors: SC
authors: Cowin
authors: Gaffar
authors: G
authors: Gailani
authors: Mohammed
authors: M
authors: Benalla
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D001794:Blood Pressure / Q000502:physiology; D001842:Bone and Bones / Q000033:anatomy & histology* / Q000098:blood supply / Q000502:physiology*; D004548:Elasticity; D045604:Extracellular Fluid / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D040542:Mechanotransduction, Cellular / Q000502:physiology; D008954:Models, Biological; D010539:Permeability