Derivation, Validation, and Prediction of Loading-Induced Mineral Apposition Rates at Endocortical and Periosteal Bone Surfaces Based on Fluid Velocity and Pore Pressure

Abstract

Bones adapt to mechanical forces driven by osteocytes in the lacunae canalicular network (LCN). Osteocytes sense signals such as strain, interstitial fluid flow, and pore pressure. Physiological tissue strain is insufficient to induce bone formation, and fluid flow-based models struggle to predict bone formation at both the periosteal and endocortical surfaces, simultaneously. This prompted the exploration of pore pressures role. The study introduces dissipation energy density as a more significant stimulus, combining various LCN parameters, including the waveforms of both fluid velocity and pore pressure and the number of loading cycles. A pivotal achievement is the mathematical derivation of the Mineral Apposition Rate (MAR), linked proportionally to the square root of the dissipation energy density minus its reference value. This hypothesis is subjected to testing/ validation for both endocortical and periosteal surfaces for an in-vivo study on mouse tibia available in the literature. Computational implementation of this mathematical model adopts a poroelastic finite element analysis approach, treating bone as a porous fluid-filled entity. Crucially, assumptions underpinning the model, such as the impermeability of the periosteum to fluid and the maintenance of a reference zero pressure at the endosteal surface, are corroborated by relevant experimental studies. As a bottom line, the resulting model is the first of its kind, as it has been able to predict MAR at both endocortical and periosteal surfaces, significantly advancing our understanding of cortical bone adaptation to exogenous mechanical loading.