Diego GARZON

This study presents a computational model that integrates bone remodeling dynamics with damage accumulation, focusing on both physiological and pathological conditions. Building upon Komarova’s classical model of osteoclast and osteoblast interactions, this work introduces fatigue-induced damage using a stress-life (S-N) approach. By simulating bone responses under sinusoidal and random mechanical loads, the model captures the cyclical nature of bone turnover. The results show that under normal physiological conditions, bone is able to repair microdamage and maintain structural integrity. However, in pathological scenarios such as osteoporosis and tumors, the remodeling cycle is disrupted, leading to an increase in damage accumulation and eventual structural failure. Through numerical simulations, the study also demonstrates the significant impact of fatigue on bone health, showing that repetitive mechanical loads, even below critical stress levels, can result in bone degradation over time. By capturing the accumulation of microdamage and its repair, the model offers potential applications in personalized medicine to assess fracture risks in varying stress and health scenarios. This approach provides a framework for understanding how different stress patterns contribute to bone damage and offers insights into the progression of bone diseases. The model could be extended using metabolic and age-related characteristics and serves as a potential tool for personalized medicine, helping to predict bone failure risks in individuals when they are submitted to repetitive mechanical loads.

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.