Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis

As fractures heal, immature callus formed in the hematoma is calcified by osteoblasts and altered to mature bone. Although the bone strength in the fracture-healing process cannot be objectively measured in clinical settings, bone strength can be predicted by specimen-specific finite element modeling (FEM) of quantitative computed tomography (qCT) scans. FEM predictions of callus strength would enable an objective treatment plan. The present study establishes an equation that converts material properties to bone density and proposes a specimen-specific FEM. In 10 male New Zealand white rabbits, a 10-mm long bone defect was created in the center of the femur and fixed by an external fixator. The callus formed in the defect was extracted after 3-6 weeks, and formed into a (5 × 5 × 5 mm³) cube. The bone density measured by qCT was related to the Young's modulus and the yield stress measured with a mechanical tester. For validation, a 10-mm long bone defect was created in the central femurs of another six New Zealand white rabbits, and fixed by an external fixator. At 3, 4, and 5 weeks, the femur was removed and subjected to Computed tomography (CT) scanning and mechanical testing. A specimen-specific finite element model was created from the CT data. Finally, the bone strength was measured and compared with the experimental value. The bone mineral density σ was significantly and nonlinearly correlated with both the Young's modulus E and the yield stress σ. The material-property conversion equations were E = 0.2391e^8.00ρ and ρ = 30.49σ^2.41. Moreover, the experimental bone strength was significantly linearly correlated with the prospective FEM. We demonstrated the Young's moduli and yield stresses for different bone densities, enabling a FEM of the bone-healing process. An FEM based on these material properties is expected to yield objective clinical judgment criteria.