Mathematical Modeling of Bone Tissue Regeneration Processes under Mechanical Stimulation

This study addresses the mathematical formulation of a relevant mechanobiology problem concerning the regulatory effect of mechanical stimulation on reparative bone tissue regeneration. Based on poroelasticity theory, a mathematical model was developed to describe changes in the physic-mechanical properties of key biological tissue morphotypes involved in bone regeneration under stationary dynamic loading. A finite-element algorithm was also created to implement the model digitally. The proposed approaches were applied to computer simulations of a biomechanical structure representing an idealized fracture of a human long tubular bone and the surrounding callus tissue. The results were compared with published data from other poroelastic models, demonstrating their consistency. An investigation was conducted into the influence of key dynamic loading parameters on the mechanical property recovery of the callus. The presented bone regeneration model exhibits mathematically adequate behavior and sufficient predictive capability, enabling its further development and application in biophysical research and biomedical practice.