Manifold learning for automatically predicting articular cartilage morphology in the knee with data from the osteoarthritis initiative (OAI)

Osteoarthritis (OA) is a degenerative, debilitating disease with a large socio-economic impact. This study looks to manifold learning as an automatic approach to harness the plethora of data provided by the Osteoarthritis Initiative (OAI). We construct several Laplacian Eigenmap embeddings of articular cartilage appearance from MR images of the knee using multiple MR sequences. A region of interest (ROI) defined as the weight bearing medial femur is automatically located in all images through non-rigid registration. A pairwise intensity based similarity measure is computed between all images, resulting in a fully connected graph, where each vertex represents an image and the weight of edges is the similarity measure. Spectral analysis is then applied to these pairwise similarities, which acts to reduce the dimensionality non-linearly and embeds these images in a manifold representation. In the manifold space, images that are close to each other are considered to be more "similar" than those far away. In the experiment presented here we use manifold learning to automatically predict the morphological changes in the articular cartilage by using the co-ordinates of the images in the manifold as independent variables for multiple linear regression. In the study presented here five manifolds are generated from five sequences of 390 distinct knees. We find statistically significant correlations (up to R² = 0.75), between our predictors and the results presented in the literature.