Table of Contents
ISRN Orthopedics
Volume 2012, Article ID 840426, 10 pages
Research Article

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

1Hôpital Nord Ouest site de Villefranche, BP436, 69655 Villefranche Saone, France
2Laboratoire de Physiologie de l’Exercice, Université de Lyon, 42023 Saint Etienne, France
3Group of Applied Research in Orthopaedic, 69005 Lyon, France

Received 3 October 2011; Accepted 31 October 2011

Academic Editors: M. Kawakami and E. Pola

Copyright © 2012 E. Berthonnaud et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.