Biomechanical Assessment for Healing Progression of Fractured Long Bones: Numerical Investigations of Bending Stiffness and Resonant Frequency

Abstract

Though biomechanical methods have been proposed to assess the healing status of fractured bones for more than two decades, the effective stiffnesses obtained theoretically never match the experimentally measured results for the healing progression. This paper proposed a novel numerical model, the simulation results of which are able to reflect the experimental observations. The callus is divided into 10 regions with different material properties and the gap-narrowing process of the fracture is simulated with the variations of the material properties during the healing progression. The variations of the effective bending stiffness and resonant frequency with the healing progression have been obtained. The bending stiffness and resonant frequency squared of the fractured bone show a substantial creeping part during gradual narrowing of the fracture gap. They start to increase rapidly during bridging of the fracture gap by a bony callus. When the Young’s modulus in the callus region calcified last (i.e., Region 10) reaches 5% that of the reference intact bone, the bending stiffness and resonant frequency squared rise up to 90% those of the reference intact bone. After that they increase slowly and get flat; they become less sensitive to bone growth in the late healing stages. It is the first time that the simulation results demonstrate three distinct stages like in the experimentally measured results. These results imply that the variations of the bending stiffness and resonant frequency squared are not linearly correlated with the healing progression; however, their fast growing phase does indicate bony bridging of the callus.