Diffeomorphic morphometry of the tibio-femoral joint for quantitative assessment of osteoarthritis*

We present an application of the framework of Large Diffeomorphic Deformation Metric Mapping (LDDMM) for statistical analysis of moprhological variants of knee anatomy associated with osteoarthritis (OA).
The LDDMM models the morphological variability by associating each population member – here, a tibial surface – with a diffeomorphic transformation that maps the shape of that member to a common template (mean shape). Compared to conventional Active Shape Models, LDDM has the significant advantage in that it does not require a priori point correspondences between the surfaces in the population. We also investigated an extension of LDDMM (functional shapes, fshapes) that jointly considers the variations in shape and variations in a function on the shape (signal) – here, the signal was a map of tibio-femoral joint space width.
The diffeomorphic modeling was applied to 34 CT scans of normal and OA subjects. To validate that the resulting model captures the morphology of OA, we measured the acuracy of a Suport Vector Machine (SVM) classifier using either only the shape features or the joint shape+signal features. We achieved correct classification (OA vs. normal) in 91% of subjects using shape features and in 85% of subjects using shape+signal.