Principal Deformations Modes of Articulated Models for the Analysis of 3D Spine Deformities

Abstract

Articulated models are commonly used for recognition tasks in robotics and in gait analysis, but can
also be extremely useful to develop analytical methods targeting spinal deformities studies. The threedimensional
analysis of these deformities is critical since they are complex and not restricted to a given
plane. Thus, they cannot be assessed as a two-dimensional phenomenon. However, analyzing large databases
of 3D spine models is a difficult and time-consuming task. In this context, a method that automatically extracts
the most important deformation modes from sets of articulated spine models is proposed.
The spine was modeled with two levels of details. In the first level, the global shape of the spine was
expressed using a set of rigid transformations that superpose local coordinates systems of neighboring vertebrae.
In the second level, anatomical landmarks measured with respect to a vertebra’s local coordinate
system were used to quantify vertebra shape. These articulated spine models do not naturally belong to a
vector space because of the vertebral rotations. The Fréchet mean, which is a generalization of the conventional
mean to Riemannian manifolds, was thus used to compute the mean spine shape. Moreover, a
generalized covariance computed in the tangent space of the Fréchet mean was used to construct a statistical
shape model of the scoliotic spine. The principal deformation modes were then extracted by performing a
principal component analysis (PCA) on the generalized covariance matrix.
The principal deformations modes were computed for a large database of untreated scoliotic patients.
The obtained results indicate that combining rotation, translation and local vertebra shape into a unified
framework leads to an effective and meaningful analysis method for articulated anatomical structures. The
computed deformation modes also revealed clinically relevant information. For instance, the first mode of
deformation is associated with patients’ growth, the second is a double thoraco-lumbar curve and the third
is a thoracic curve. Other experiments were performed on patients classified by orthopedists with respect to
a widely used two-dimensional surgical planning system (the Lenke classification) and patterns relevant to
the definition of a new three-dimensional classification were identified. Finally, relationships between local
vertebrae shapes and global spine shape (such as vertebra wedging) were demonstrated using a sample of
3D spine reconstructions with 14 anatomical landmarks per vertebra.
KeyWords: Shape Analysis, Articulated Models, Spinal Deformities, Scoliosis, 3D Reconstruction, Surgical Classifications.