Biomechanical Assessment for Healing Progression of Fractured Long Bones: Comparisons of Various Methods Using Beam Models

Abstract

Measurements of various effective stiffnesses have been suggested as non-invasive biomechanical methods to assess healing status of a fractured long bone. This paper has compared the sensitivities of five assessment methods for fracture healing of long bones: torsion, compression, 3-point bending, 4-point bending and cantilever bending. A fractured human femur is modeled by an Euler beam and Castigliano’s theorem is used to obtain the effective stiffnesses of the fractured bone. The variations of the effective stiffnesses of the fractured bone with the healing status of the callus have been investigated. The healing process of the callus is represented by gradual increases of the Young’s modulus. The callus is divided into multiple regions. The narrowing process of the fracture gap is characterized by assigning different Young’s modulus for different regions. Our findings showed that torsional, compressional, and bending stiffnesses all perform similarly with respect to the healing process. Before the rapid increase, all effective stiffness curves show a substantial creeping stage which corresponds to the narrowing process of the fracture gap. A higher value of them indicates bony bridging of healing callus. The effective stiffnesses for cantilever bending and 3-point bending are more sensitive to the fracture location, while torsional and compressional stiffness are independent from the fracture location.