Efficacy of monitoring long-bone fracture healing by measurement of either bone stiffness or resonant frequency: Numerical simulation

Development of noninvasive mechanical tests to monitor fracture healing has been hindered because relationships between bone geometry, measurement conditions, and fracture callus strength are not well understood. Beam theory was used to analyze the effects of fracture length, fracture location, end conditions, and fracture callus stiffness on mechanical properties (resonant frequency, bending stiffness, and torsional stiffness) of healing bone. Actual bone mineral geometry from a human tibia, quantified every 1 mm, was used in the beam analysis. Geometry of the fracture callus segment was uniformly scaled from the values for intact bone. Experimental tests on multisegmented machined rods were used to verify analytical methods. Mechanical properties of the healing bone initially increased very rapidly to 30-70% of the stiffness of intact bone, depending on the configuration. The increases then tapered off dramatically. Lateral bending stiffness was sensitive to changes in callus properties for a larger portion of the healing process than was either torsional stiffness or resonant frequency. Because callus strength increases at half the rate of callus stiffness, measures of whole-bone mechanical properties can provide insight into changes in callus strength until a maximum of less than one-half the strength of intact bone is regained. The analytical method presented is proposed for clinical use to develop individualized models of bone, fracture, and fixation conditions to identify early stages of healing. Because increases in whole-bone mechanical properties are small in the later stages of fracture healing, however, such measures must be used prudently beyond the initial stages.