Purpose: Osteoarthritis (OA) is a common degenerative disease involving a variety of structural changes in the affected joint. In addition to narrowing of the articular space, recent studies involving statistical shape analysis methods have suggested that specific bone shapes might be associated with the disease. We aim to investigate the feasibility of using the recently introduced framework of functional shapes (Fshape) to extract morphological features of OA that combine shape variability of articular surfaces of the tibia (or femur) together with the changes of the joint space.
Approach: Our study uses a dataset of three-dimensional cone-beam CT volumes of 17 knees without OA and 17 knees with OA. Each knee is then represented as an object (Fshape) consisting of a triangulated tibial (or femoral) articular surface and a map of joint space widths (JSWs) measured at the points of this surface (joint space map, JSM). We introduce a generative atlas model to estimate a template (mean) Fshape of the sample population together with template-centered variables that model the transformations from the template to each subject. This approach has two potential advantages compared with other statistical shape modeling methods that have been investigated in knee OA: (i) Fshapes simultaneously consider the variability in bone shape and JSW, and (ii) Fshape atlas estimation is based on a diffeomorphic transformation model of surfaces that does not require a priori landmark correspondences between the subjects. The estimated atlas-to-subject Fshape transformations were used as input to principal component analysis dimensionality reduction combined with a linear support vector machine (SVM) classifier to identify the morphological features of OA.
Results: Using tibial articular surface as the shape component of the Fshape, we found leave-one-out cross validation scores of ≈91.18 % for the classification based on the bone surface transformations alone, ≈91.18 % for the classification based on the residual JSM, and ≈85.29 % for the classification using both Fshape components. Similar results were obtained using femoral articular surfaces. The discriminant directions identified in the statistical analysis were associated with medial narrowing of the joint space, steeper intercondylar eminence, and relative deepening of the medial tibial plateau.
Conclusions: The proposed approach provides an integrated framework for combined statistical analysis of shape and JSPs. It can successfully extract features correlated to OA that appear consistent with previous studies in the field. Although future large-scale study is necessary to confirm the significance of these findings, our results suggest that the functional shape methodology is a promising new tool for morphological analysis of OA and orthopedics data in general.
Purpose: We develop an Active Shape Model (ASM) framework for automated bone segmentation and anatomical landmark localization in weight-bearing Cone-Beam CT (CBCT). To achieve a robust shape model fit in narrow joint spaces of the foot (0.5 – 1 mm), a new approach for incorporating proximity constraints in ASM (coupled ASM, cASM) is proposed. Methods: In cASM, shape models of multiple adjacent foot bones are jointly fit to the CBCT volume. This coupling enables checking for proximity between the evolving shapes to avoid situations where a conventional single-bone ASM might erroneously fit to articular surfaces of neighbouring bones. We used 21 extremity CBCT scans of the weight-bearing foot to compare segmentation and landmark localization accuracy of ASM and cASM in leave-one-out validation. Each scan was used as a test image once; shape models of calcaneus, talus, navicular, and cuboid were built from manual surface segmentations of the remaining 20 scans. The models were augmented with seven anatomical landmarks used for common measurements of foot alignment. The landmarks were identified in the original CBCT volumes and mapped onto mean bone shape surfaces. ASM and cASM were run for 100 iterations, and the number of principal shape components was increased every 10 iterations. Automated landmark localization was achieved by applying known point correspondences between landmark vertices on the mean shape and vertices of the final active shape segmentation of the test image. Results: Root Mean Squared (RMS) error of bone surface segmentation improved from 3.6 mm with conventional ASM to 2.7 mm with cASM. Furthermore, cASM achieved convergence (no change in RMS error with iteration) after ~40 iterations of shape fitting, compared to ~60 iterations for ASM. Distance error in landmark localization was 25% to 55% lower (depending on the landmark) with cASM than with ASM. The importance of using a coupled model is underscored by the finding that cASM detected and corrected collisions between evolving shapes in 50% to 80% (depending on the bone) of shape model fits. Conclusion: The proposed cASM framework improves accuracy of shape model fits, especially in complexes of tightly interlocking, articulated joints. The approach enables automated anatomical analysis in volumetric imaging of the foot and ankle, where narrow joint spaces challenge conventional shape models.
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