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Statistical shape models have become essential for medical image registration or segmentation and are used in many biomedical applications. These models are often based on Gaussian distributions learned from a training set. We propose in this paper a shape model which does not rely on the estimation of a Gaussian distribution, but on similarities computed with a kernel function. Our model takes advantage of the one-class support vector machine (OCSVM) to do so. In this context, we propose in this paper a method for reconstructing the spine of scoliotic patients using OCSVM regularization. Current state-of-the-art methods use conventional statistical shape models, and the reconstruction is commonly processed by minimizing a Mahalanobis distance. Nevertheless, when a shape differs significantly from the statistical model, the associated Mahalanobis distance often overstates the need for statistical regularization. We show that OCSVM regularization is more robust and is less sensitive to weak landmarks definition and is hardly influenced by the presence of outliers in the training data. The proposed OCSVM model applied to 3-D spine reconstruction was evaluated on real patient data, and results showed that our approach allows precise reconstruction.

Severe cases of spinal deformities such as scoliosis are usually treated by a surgery where instrumentation (hooks, screws and rods) is installed to the spine to correct deformities. Even if the purpose is to obtain a normal spine curve, the result is often straighter than normal. In this paper, we propose a fast statistical reconstruction algorithm based on a general model which can deal with such instrumented spines. To this end, we present the concept of multilevel statistical model where the data are decomposed into a within-group and a between-group component. The reconstruction procedure is formulated as a second-order cone program which can be solved very fast (few tenths of a second). Reconstruction errors were evaluated on real patient data and results showed that multilevel modeling allows better 3D reconstruction than classical models.

This paper proposes a novel method for fast 3D reconstructions of the scoliotic spine from two planar radiographs. The method uses a statistical model of the shape of the spine for computing the 3D reconstruction that best matches the user input (about 7 control points per radiograph). In addition, the spine was modelled as an articulated structure to take advantage of the dependencies between adjacent vertebrae in terms of location, orientation and shape. The accuracy of the method was assessed for a total of 30 patients with mild to severe scoliosis (Cobb angle [22°, 70°]) by comparison with a previous validated method. Reconstruction time was 90 s for mild patients, and 110 s for severe. Results show an accuracy of ∼0.5mm locating vertebrae, while orientation accuracy was up to 1.5° for all except axial rotation (3.3° on moderate and 4.4° on severe cases). Clinical indices presented no significant differences to the reference method (Wilcoxon test, p ≤ 0.05) on patients with moderate scoliosis. Significant differences were found for two of the five indices (p=0.03) on the severe cases, while errors remain within the inter-observer variability of the reference method. Comparison with state-of-the-art methods shows that the method proposed here generally achieves superior accuracy while requiring less reconstruction time, making it especially appealing for clinical routine use., (Copyright © 2011 IPEM. All rights reserved.)

Three-dimensional models of the spine are commonly used to diagnose, to treat, and to study spinal deformities. Creating these models is however time-consuming and, therefore, expensive. We propose in this paper a reconstruction method that finds the most likely 3D reconstruction given a maximal error bound on a limited set of landmark locations supplied by the user. This problem can be solved using second-order cone programming, leading to a globally convergent method that is considerably faster than currently available methods. A user can, with our current implementation, interactively modify the landmark locations and receive instantaneous feedback on the effect of those changes on the 3D reconstruction instead of blindly selecting landmarks. The proposed method was validated on a set of 53 patients who had adolescent idiopathic scoliosis using real and synthetic tests. Test results showed that the proposed method is considerably faster than currents methods (about forty times faster), is extremely flexible, and offers comparable accuracy.

Three-dimensional models of the spine are extremely important to the assessment of spinal deformities. However, it could be difficult in practical situations to obtain enough accurate information to reconstruct complete 3-D models. This paper presents a set of methods to rebuild complete models either from partial 3-D models or from 2-D landmarks. The spine was modeled as an articulated object to take advantage of its natural anatomical variability. A statistical model of the vertebrae and spine shape was first derived. Then, complete models were computed by finding the articulated spine descriptions that were consistent with the observations while optimizing the prior probability given by the statistical model. The observations used were the absolute positions, orientations, and shapes of the vertebrae when a partial 3-D model was available. The reconstruction of 3-D spine models from 2-D landmarks identified on radiograph(s) was performed by minimizing the Mahalanobis distance and the landmarks reprojection error. The vertebrae estimated from partial models were within 2 mm of the measured values (which is comparable to the accuracy of currently used methods) if at least 25% of the vertebrae were available. Experiments also suggest that the reconstruction from posterior-anterior and lateral radiographs using the proposed method is more accurate than the conventional triangulation method.

This paper introduces a method to analyze the variability of the spine shape and of the spine shape deformations using articulated shape models. The spine shape was expressed as a vector of relative poses between local coordinate systems of neighboring vertebrae. Spine shape deformations were then modeled by a vector of rigid transformations that transforms one spine shape into another. Because rigid transformations do not naturally belong to a vector space, conventional mean and covariance could not be applied. The Fréchet mean and a generalized covariance were used instead. The spine shapes of a group of 295 scoliotic patients were quantitatively analyzed as well as the spine shape deformations associated with the Cotrel-Dubousset corrective surgery (33 patients), the Boston brace (39 patients), and the scoliosis progression without treatment (26 patients). The variability of intervertebral poses was found to be inhomogeneous (lumbar vertebrae were more variable than the thoracic ones) and anisotropic (with maximal rotational variability around the coronal axis and maximal translational variability along the axial direction). Finally, brace and surgery were found to have a significant effect on the Fréchet mean and on the generalized covariance in specific spine regions where treatments modified the spine shape.

Bracing is a widely used treatment of scoliosis, but there is still no consensus about its actual effect. Previous studies were based on global descriptors of the spine shape (Cobb angle, plane of maximal deformity, etc.). We present a new method to analyze braces effects at a finer scale and to find which vertebral levels are significantly affected by this treatment. The proposed method compares a group of patients treated with a brace and a control group. The 3D spine geometry of the patients from the two groups was digitized on two separate occasions: with and without brace (first group) or two times without brace (control group). The modifications of the vertebrae relative poses (combination of relative translation and rotation between consecutive vertebrae) were then extracted from 3D reconstructions. Centrality and dispersion measures of the relative poses modifications were computed using a method that take into account the non-linearity of the rotation matrix. Then, finally, multivariate hypothesis tests were used to compare the centrality and dispersion of the two groups. The method was applied to 28 untreated scoliotic patients and 41 patients treated with a Boston brace. Significant differences (p<0.01) between the centrality and dispersion measures of the relative poses modifications were respectively found from T1 to T6 and from T8 to L1. Those significant differences concords with the back flattening effect and the spatially limited correction found in other studies; however the proposed method offers a more specific evaluation of the localization of those effects.