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Technical Briefs

Quantifying Cervical-Spine Curvature Using Bézier Splines

[+] Author and Article Information
Kathleen D. Klinich1

 University of Michigan Transportation Research Institute, 2901 Baxter Rd., Ann Arbor, MI 48109

Sheila M. Ebert

 University of Michigan Transportation Research Institute, 2901 Baxter Rd., Ann Arbor, MI 48109

Matthew P. Reed

 University of Michigan Transportation Research Institute, 2901 Baxter Rd., Ann Arbor, MI 48109kklinich@umich.edu

1

Corresponding author.

J Biomech Eng 134(11), 114503 (Oct 26, 2012) (6 pages) doi:10.1115/1.4007749 History: Received May 02, 2012; Revised August 29, 2012; Posted September 29, 2012; Published October 26, 2012; Online October 26, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The posterior-inferior corner of the C7 vertebral body is aligned with point B0, and the cervical-spine posterior margin coordinates are scaled and rotated so the superior-posterior corner of the dens is at B3 and the neck chord length is 1.0. The shape of the curve between these two points is controlled by the lengths and angles of segments B0–B1 and B2–B3. These segments are tangent to the curve at B0 and B3. The B1 control point has a greater effect on the first half of the curve, while the B2 point has a greater effect on the second half of the curve. The lower photo shows an overlay on a subject’s X-ray of a Bézier spline fit through the digitized posterior margins.

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Figure 2

Four Bézier splines with inferior Bézier angles of 15 deg represent a wide variation in curvature shape and magnitude depending on the value of the superior Bézier angle

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Figure 3

Dimensions used in classifying Bézier curvatures for lordotic/kyphotic cervical spines (left) and S-shaped cervical spines (right)

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Figure 4

Cervical-spine curvature classifications based on superior and inferior Bézier angles; classification abbreviations defined in Fig. 3 and Tables  23

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Figure 5

Distribution of subjects in Bézier space by flexion, neutral, and extension postures

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Figure 6

Mean values and standard deviations of superior versus inferior Bézier angles by age group for flexion, neutral, and extension postures

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Figure 7

Mean values and standard deviations of superior versus inferior Bézier angles by gender for flexion, neutral, and extension postures

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Figure 8

Mean values of superior versus inferior Bézier angles by stature group for flexion, neutral, and extension postures

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