Computational Model of Bone Remodeling Integrating Osteocyte Mechanotransduction and Microdamage-Driven Self-Repair

Bone remodeling is a fundamental physiological process that maintains skeletal integrity through a tightly regulated balance between bone resorption and formation. Mathematical modeling provides a powerful framework for understanding the complex regulatory mechanisms underlying this process, particularly the interplay between biomechanical stimuli and cellular dynamics. This study introduces a new mathematical model of bone remodeling designed to capture the temporal evolution of key bone cell populations and their response to mechanical stimuli within a simplified yet biologically informed architecture. We formulate a system of coupled nonlinear ordinary differential equations to describe the dynamics of osteoclasts, osteoblasts, and osteocytes within a single basic multicellular unit (BMU). The model incorporates feedback regulation via strain energy density, allowing mechanical input to influence cellular activity and bone surface transitions. Initial conditions are assigned to reflect the sequential activation of bone remodeling phases. Physiological parameters are adopted from well-established literature, while non-sourced parameters are tuned to ensure model stability and biological plausibility. The simulations reproduce the canonical sequence of bone remodeling: initiation, resorption, reversal, and formation. The model captures the coupling between mechanical loading and cellular activity, demonstrating how osteocyte signaling can modulate the recruitment of osteoclasts and osteoblasts. The results also highlight the system's capacity to stabilize around a dynamic equilibrium, sensitive to both internal parameters and external mechanical inputs. This model offers a minimal yet comprehensive representation of bone remodeling dynamics within a single BMU, integrating mechanical and biological controls into a unified mathematical structure. It provides a foundation for future extensions toward spatially distributed models and applications in mechanobiological simulation and computational bone health assessment.