Evaluation of experimental, analytical, and computational methods to determine long-bone bending stiffness.

Methods used to evaluate bone mechanical properties vary widely depending on the motivation and environment of individual researchers, clinicians, and industries. Further, the innate complexity of bone makes validation of each method difficult. Thus, the purpose of the present research was to quantify methodological error of the most common methods used to predict long-bone bending stiffness, more specifically, flexural rigidity (EI). Functional testing of a bi-material porcine bone surrogate, developed in a previous study, was conducted under four-point bending test conditions. The bone surrogate was imaged using computed tomography (CT) with an isotropic voxel resolution of 0.625 mm. Digital image correlation (DIC) of the bone surrogate was used to quantify the methodological error between experimental, analytical, and computational methods used to calculate EI. These methods include the application of Euler Bernoulli beam theory to mechanical testing and DIC data; the product of the bone surrogate composite bending modulus and second area moment of inertia; and finite element analysis (FEA) using computer-aided design (CAD) and CT-based geometric models. The methodological errors of each method were then compared. The results of this study determined that CAD-based FEA was the most accurate determinant of bone EI, with less than five percent difference in EI to that of the DIC and consistent reproducibility of the measured displacements for each load increment. CT-based FEA was most accurate for axial strains. Analytical calculations overestimated EI and mechanical testing was the least accurate, grossly underestimating flexural rigidity of long-bones.