Quantifying Cervical-Spine Curvature Using Bézier Splines

Abstract

Knowledge of the distributions of cervical-spine curvature is needed for computational studies of cervical-spine injury in motor-vehicle crashes. Many methods of specifying spinal curvature have been proposed, but they often involve qualitative assessment or a large number of parameters. The objective of this study was to develop a quantitative method of characterizing cervical-spine curvature using a small number of parameters. 180 sagittal X-rays of subjects seated in automotive posture with their necks in neutral, flexed, and extended postures were collected in the early 1970s. Subjects were selected to represent a range of statures and ages for each gender. X-rays were reanalyzed using advanced technology and statistical methods. Coordinates of the posterior margins of the vertebral bodies and dens were digitized. Bézier splines were fit through the coordinates of these points. The interior control points that define the spline curvature were parameterized as a vector angle and length. By defining the length as a function of the angle, cervical-spine curvature was defined with just two parameters: superior and inferior Bézier angles. A classification scheme was derived to sort each curvature by magnitude and type of curvature (lordosis versus S-shaped versus kyphosis; inferior or superior location). Cervical-spine curvature in an automotive seated posture varies with gender and age but not stature. Average values of superior and inferior Bézier angles for cervical spines in flexion, neutral, and extension automotive postures are presented for each gender and age group. Use of Bézier splines fit through posterior margins offers a quantitative method of characterizing cervical-spine curvature using two parameters: superior and inferior Bézier angles.