Investigating the Difference in Cortical Bone Adaptation at Endocortical and Periosteal Surfaces by Fluid Flow Analysis

Abstract

Load-induced fluid flow in lacunar-canalicular porosity in bone has been suggested to play an essential role in bone adaptation. The applied load causes the fluid inside the lacunar-canalicular system to flow. The osteocytes are believed to sense the shear stress exerted due to the fluid flow and drive new bone formation. The energy dissipated in moving fluid may be considered as a stimulus for bone adaptation. The endocortical bone surfaces are also believed to adapt differently compared to the periosteal surfaces. We investigate such differences and present a finite element poroelasticity-based mathematical model on estimating bone formation rate at mid-diaphysis of a C57BL6 mouse tibia subjected to cantilever loading. A weighted average of dissipation energy in the zone of influence has been considered in accordance with the literature. The model predicts bone formation rate (BFR) at the periosteal surface as well as on the endocortical surface. As desired, the model can differentiate between a continuous cyclic loading and a rest-inserted cyclic loading. The model establishes that the difference in bone formation at the two surfaces, viz. endocortical and periosteal, may be due to the difference in dissipation energy density only, caused by different boundary conditions at the two surfaces.