Ramp loading in Russian doll poroelasticity

Aporoelastic model for porous materials with a nested pore space structure is developed to represent the interstitial fluid flow in bone tissue. The nested porosity model is 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 in a ramp loading in the case where the fluid and solid constituents are assumed to be compressible. The compressibility assumption is appropriate for hard tissues while the incompressibility assumption is appropriate for soft tissues. The influence of blood pressure in the PV is included in the analysis. A formula for the fluid that moves between the two porosities is developed. The analysis showed the coupling of the two porosities and their influence on each other and concluded that the PV pore pressure has an influence less than 3% on the PLC pore pressure while the absence of the PV pore pressure will affect the fluid exchange between the PV and PLC by less than 6% (the blood pressure range is 40–60 mmHg). Also the analysis has shown that the draining time of the PLC is inversely proportional to its permeability. The significance of 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.