Sensitivities of biomechanical assessment methods for fracture healing of long bones

There is a controversy as to whether the biomechanical methods are feasible to assess fracture healing of long bones. This paper investigated the sensitivities of two biomechanical methods, torsion and bending, for assessing fracture healing of long bones; both a simplified beam model and finite element model of an artificial femur were employed. The results demonstrated that, in the initial healing stage, the whole-bone stiffness of the fractured bone is extremely sensitive to the variation of the callus stiffness at the fracture site; when the shear (or Young's) modulus of the callus reaches 15% that of the intact bone, the whole-bone stiffness rises up to 90% that of the intact bone. After that, the whole-bone torsional (or bending) stiffness increases slowly; it becomes less sensitive to the variation of the callus stiffness. These results imply that the whole-bone stiffness is of limited reliability to assess the healing quality particular at late stages of the healing process. The simplified model in this paper provided a theoretical framework to explain why the whole-bone stiffness is insensitive to the healing process of fractured long bones in the late stage of healing. The conclusions obtained from the simplified model were verified with the finite element simulations of the artificial femur.