  The ability of Anisotropic Minkowski Functionals (AMFs) to capture local
anisotropy while evaluating topological properties of the underlying gray-level
structures has been previously demonstrated. We evaluate the ability of this
approach to characterize local structure properties of trabecular bone
micro-architecture in ex vivo proximal femur specimens, as visualized on
multi-detector CT, for purposes of biomechanical bone strength prediction. To
this end, volumetric AMFs were computed locally for each voxel of volumes of
interest (VOI) extracted from the femoral head of 146 specimens. The local
anisotropy captured by such AMFs was quantified using a fractional anisotropy
measure; the magnitude and direction of anisotropy at every pixel was stored in
histograms that served as a feature vectors that characterized the VOIs. A
linear multi-regression analysis algorithm was used to predict the failure load
(FL) from the feature sets; the predicted FL was compared to the true FL
determined through biomechanical testing. The prediction performance was
measured by the root mean square error (RMSE) for each feature set. The best
prediction performance was obtained from the fractional anisotropy histogram of
AMF Euler Characteristic (RMSE = 1.01 +- 0.13), which was significantly better
than MDCT-derived mean BMD (RMSE = 1.12 +- 0.16, p<0.05). We conclude that such
anisotropic Minkowski Functionals can capture valuable information regarding
regional trabecular bone quality and contribute to improved bone strength
prediction, which is important for improving the clinical assessment of
osteoporotic fracture risk.
