A new method to evaluate bone rigidity and strength using tomographic bone images obtained via QCT (Quantitative Computed Tomography) is introduced. A newly developed computer program named VA-BATTS is used for image processing, bone segmentation, mesh creation, material assignment and calculation of far field normal and shear stresses as well as other cross sectional properties. In order to calculate torsional and transverse shear stresses in prismatic bodies having inhomogenous material properties, a new two-dimensional finite element formulation to estimate is presented. The formulation combines the torsional and transverse shear problem solutions and adds terms to account for the material inhomogeneity into one Weak Form of the problem, further discretized to yield a numerical approximation of the shear stresses problem. Results were validated using analytical models as well as three dimensional commercial code test cases yielding mean errors over the entire domain of less than 1%. This semi-automated application is publicly distributed and can be downloaded from https://simtk.org/home/va-batts.

VA-BATTS implements an elliptical stress failure criterion to predict bone strength. To validate, fifty-two fresh frozen femurs were tested under combined three-point bending and torsion to failure. VA-BATTS was able to predict bone failure under combined bending and torsion (R²=0.68) as well as bone torsional (R²=0.80) and bending (R²=0.50) rigidity. Using multivariate analysis that combined the elliptical stress failure and the torsional and bending rigidities, the prediction confidence level was raised (R²=0.87), comparable to existing more complex three dimensional finite element studies. The elliptical stress criterion suggests that the distal femur is weaker, in absolute terms, than the midshaft femur suggesting an explanation of the increased rate of distal femur fractures in patients with Spinal Cord Injury. In general, the newly introduced method proved to yield more accurate predictions compared to DXA derived Bone Mineral Density measurements (R²=0.56). Fracture patterns were analyzed to show mostly spiral patterns where torsional loads were applied.

In addition, the accuracy of three point bending experiments was examined. Three parameters that may introduce errors in the predictions - transverse shear, local deformation (indentation) as well as cross sectional deformation effect – were studied using a parametric finite element model. The model shows that depending on the geometric properties of the bone, errors as high as 75% may be introduced in the estimation of the bone elastic modulus. Bone rigidity estimates may now be corrected using the correction factors supplied in this study.