Deformation-induced hierarchical flows and drag forces in bone canaliculi and matrix microporosity

Existing theories for interstitial flows in bone have only examined the contributions from different flow systems separately, such as the flows through the microporosity, the canaliculi, and the Haversian canals. An overall model encompassing the hierarchical microstructure is important to our understanding of the actual physics of flows in bone. The flow-induced drag forces and streaming electrical potentials could interact with the osteocytes to effect biological responses. A finite element model was developed to study the contributions from various hierarchical flow channels in bone. Cortical bone is modelled as a fully hydrated biphasic poroelastic material with a superposing network of one-dimensional channels radiating from the Haversian canals representing the canaliculi. Interfacial cross-flows between these one-dimensional channels and the neighbouring poroelastic matrix are driven by the pressure differences between the matrix and the channel. The model was subjected to stress fields simulating uniform compression and pure bending. The effects of the interfacial permeability and the solid content within the channels on the drag forces in the channels were assessed. Abrupt changes in these drag forces occurred as the channel solidity approached that of the microporosity. The results were quite sensitive to the interfacial permeability, i.e. the interconnectivity between the canalicular system and the matrix microporosity. This biomechanical model should be useful to the study of mechanotransduction in bone.