An improved mathematical modeling of bone remodeling: the role of stability in predicting bone health

In this paper, we propose an improved mathematical model that can describe bone remodeling. This process involves the activities of osteoblasts, osteoclasts, osteocytes, and bone mass density. Bone remodeling is an important process that maintains bones in the human body by balancing formation and resorption. The proposed model is formulated as a system of differential equations that incorporate recruitment rates and porosity interaction. The local stability analysis was carried out using the Routh-Hurwitz criteria. The global stability analysis is conducted by using Lyapunov functions. The stability analysis provides the conditions for stable remodeling. Numerical simulations are illustrated to validate stability conditions and demonstrate the effects of parameter variations on cell populations and bone density. The results provide a framework for understanding bone-remodeling mechanisms and have potential applications for predicting bone health.