Adaptive bone regeneration modeling: dependence of specific strain energy parameter on density under triangular loading

This study addresses the critical problem of assessing secondary stability through predictive modeling of bone tissue regeneration in patients with varying initial bone densities, which is essential for successful post-traumatic and post-surgical rehabilitation. The research employs the Carter–Hayes model implemented in the FEBio software package, with variation of the specific strain energy parameter φ0 (threshold value for bone-growth or resorption). The parameter φ0 was analyzed across trabecular bone densities of 300–850 kg/m³ under two representative volume element boundary conditions: uniform compression and partially free boundaries. These conditions simulate different implant fixation scenarios: rigid and mobile fixation systems. The obtained results reveal a nonlinear bonedensity-dependence of φ0 with a critical transition at 500 kg/m³, enabling differentiated approach to predicting regeneration processes. Simulation results demonstrate that increased mechanically loaded zones exhibit active trabecular structure formation, fully consistent with classical Wolff's law of functional bone adaptation. The practical significance of this work lies in the ability to precisely tailor the φ0 parameter for individual patients based on their initial bone density data, which opens new prospects for developing personalized rehabilitation programs and improving preoperative planning methods while accounting for the implant fixation type. The obtained data provide a foundation for further research aimed at integrating mechanical and biological aspects of bone remodeling.