Geometric variability of the scoliotic spine using statistics on articulated shape models

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.