Estimates of the Peak Pressures in Bone Pore Water

Abstract

The maximum pore fluid pressures due to uniaxial compression are determined for both the vascular porosity (Haversian and Volkmann's canals) and the lacunar-canalicular porosity of live cortical bone. It is estimated that the peak pore water pressure will be 19 percent of the applied axial stress in the vascular porosity and 12 percent of the applied axial stress in the lacunar-canalicular porosity for an impulsive step loading. However, the estimated relaxation time for the vascular porosity (1.36 microseconds) is three orders of magnitude faster than that estimated for the lacunar-canalicular porosity (4.9 ms). Thus, under physiological loading, which has a stress rise time generally larger than 1 ms, pressures higher than the vascular pressure cannot be sustained in the vascular porosity due to the swift pressure relaxation in this porosity (unless the fluid drainage through the boundary is obstructed). The model also predicts a slight hydraulic stiffening of the bulk modulus due to longer draining time of the lacunar-canalicular porosity. The undrained bulk modulus is 6 percent higher than the drained bulk modulus in this case.

Evaluation of the Growth Environment of a Hydrostatic Force Bioreactor for Preconditioning of Tissue-Engineered Constructs

“…72,73 They postulated that the mineralization was a result of stresses caused by the externally applied hydrostatic pressure. 73 In addition, the applied hydrostatic pressure of around 270 kPa is a pressure that osteocytes are subjected to in the canalicula-lacuna network of load-bearing bones, 6 and, hence, the applied hydrostatic pressure is of physiological importance for natural occurring bone formation. Previous studies have also shown that the application of various magnitudes of cyclic hydrostatic pressure to isolated bone cells, cell constructs, and ex-vivo organotypically cultured bone fragments resulted in enhanced calcium deposition and bone formation.…”

“…4,5 Osteocytes in the canaliculalacuna network of load-bearing bones are subjected to physiological pressures of approximately 270 kPa, 6 which was the maximum hydrostatic pressure that was applied in this study to investigate its effect on bone formation. Moreover, the heartbeat of chick embryos delivers a dynamic pressure of 4 kPa, 7 the blood pressure is usually between 8-24 kPa, 8 the hydrostatic pressure in the cerebrospinal fluid is around 1.2 kPa 9 and the interstital fluid pressure is around 0.27 kPa.…”

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

“…Under physiologically possible rapid rise-time loadings of bone, the pore fluid pressure may rise considerably in the PLC (Zhang et al 1998). The decay time for this pore pressure rise is much larger in the PLC than it is in the PV (Johnson et al 1982;Johnson 1984).…”

“…These drainage and imbibing processes occur on a pressure time scale that is much larger than the short pressure adjustment relaxation time for the PV and therefore have minimum influence on the pressure in the PV. The change in interstitial pore fluid pressure in the PV owing to inflow or outflow of bone fluid from the PLC is insignificant because of the time period of pressure adjustment that is much shorter (estimates of these time periods are in Zhang et al 1998) than the pressure adjustment time period for the PLC. While the bone fluid in the PLC is significantly affected for a longer time by the mechanical loading of the whole bone, the bone fluid pressure in the PV is hardly affected because the PV relaxes the pressure pulse by diffusion so rapidly.…”

“…There are four reported estimates of the permeability of the PLC. A theory-based estimate of the intrinsic permeability of the PLC was provided by Zhang et al (1998) as k = 1.47 × 10 −20 m 2 . An experimentally based estimate was provided later by Smit et al (2002), k = 2.2 × 10 −22 m 2 .…”