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 μs) 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.