Application of the Strain Energy Density Criterion for Patient-Specific Geometry-Based Fracture Healing Simulation

Abstract

Background/Objectives: Strain energy density-based algorithms are widely applied in modelling bone healing, yet their use under patient-specific geometry-based conditions remains underdeveloped. This study proposes a patient-specific geometry-based framework for fracture healing simulation and investigates how different postoperative loading conditions influence the mechanical environment of callus remodeling. Methods: Using postoperative radiographic data of a 63-year-old male patient with a distal diaphyseal tibial fracture and concomitant proximal and distal fibular fractures, a three-dimensional finite element model of the tibia was reconstructed, imported into a multiphysics simulation environment, and coupled with an iterative numerical algorithm. A uniform initial callus density of 750 kg/m3 was assumed as a simplified and homogenized representation of the healing tissue. The effects of different mechanical loading conditions (partial weight-bearing, physiological loading, and supraphysiological loading) on the mechanical response and density evolution of the callus were evaluated. Results: Partial weight-bearing resulted in insufficient mechanical stimulation and progressive density loss within the callus. Physiological loading generated strain energy density levels consistent with known osteogenic ranges and contributed to continuous cortical shell formation and overall density increase. Supraphysiological loading was associated with overload-related resorption and spatial heterogeneity, which may reduce callus stability. Conclusions: The findings suggest that loading magnitude may influence the simulated remodeling response of the callus under the assumptions of the present model. These results indicate that intermediate loading conditions were associated with a more pronounced remodeling response compared to reduced or excessive loading for the investigated case. The comparison with postoperative clinical imaging showed qualitative agreement in the spatial distribution of mineralized and less mineralized regions, supporting the feasibility of the proposed patient-specific geometry-based SED-based framework.