Geometric Structure of 3D Spinal Curves: Plane Regions and Connecting Zones

Abstract

<jats:p>This paper presents a new study of the geometric structure of 3D spinal curves. The spine is considered as an heterogeneous beam, compound of vertebrae and intervertebral discs. The spine is modeled as a deformable wire along which vertebrae are beads rotating about the wire. 3D spinal curves are compound of plane regions connected together by zones of transition. The 3D spinal curve is uniquely flexed along the plane regions. The angular offsets between adjacent regions are concentrated at level of the middle zones of transition, so illustrating the heterogeneity of the spinal geometric structure. The plane regions along the 3D spinal curve must satisfy two criteria: (i) a criterion of minimum distance between the curve and the regional plane and (ii) a criterion controlling that the curve is continuously plane at the level of the region. The geometric structure of each 3D spinal curve is characterized by the sizes and orientations of regional planes, by the parameters representing flexed regions and by the sizes and functions of zones of transition. Spinal curves of asymptomatic subjects show three plane regions corresponding to spinal curvatures: lumbar, thoracic and cervical curvatures. In some scoliotic spines, four plane regions may be detected.</jats:p>

Three-dimensional reconstructions of Lenke 1A curves

“…The emergence of 3D analysis to evaluate scoliosis [6, 7, 13, 16–21] has allowed a more comprehensive and more correct approach, thanks to the top view.…”

“…Among all parameters that have been defined to describe 3D deformation in scoliosis, we retain the plane of major curvature (PMC), the best-fit planes, and the regional planes [6, 14, 22]. This study was conducted with the regional planes, and our results show that there is no correlation between the Cobb angle simply measured on a front radiograph in standing position and the angle measured on the matching regional plane.…”

“…The relation was based on the use of epipolar planes. The 3D spinal curves were projected on fixed plane, and regional planes were detected along this rough spinal curve [6, 7]. Three or four planes were then identified.…”

“…For Berthonnaud et al, the spine is considered as a heterogeneous beam and is modeled as a deformable wire along which vertebrae can be seen as beads turning on this wire [6]. In our modeling, the 3D spinal curve is a compound of plane regions connected together by zones of transition.…”

“…Biplanar radiography involves the setting of specific devices to get simultaneous exposures, and this has been used for clinical applications. The geometric structure of a 3D spinal curve can be characterized by the size and orientation of regional planes, by the parameters representing flexed regions and by the size and function of zones of transition [6]. …”