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Modeling of the Sagittal Cervical Spine as a Method to Discriminate Hypolordosis: Results of Elliptical and Circular Modeling in 72 Asymptomatic Subjects, 52 Acute Neck Pain Subjects, and 70 Chronic Neck Pain Subjects

Harrison, Donald D., PhD, DC, MSE*; Harrison, Deed E., DC; Janik, Tadeusz J., PhD; Cailliet, Rene, MD§; Ferrantelli, Joseph R., DC; Haas, Jason W., DC**; Holland, Burt, PhD††

doi: 10.1097/01.brs.0000144449.90741.7c
Cervical Spine

Study Design. Computer analysis of digitized vertebral body corners on lateral cervical radiographs.

Objectives. Using elliptical and circular modeling, the geometric shape of the path of the posterior bodies of C2–C7 was sought in normal, acute pain, and chronic pain subjects. To determine the least squares error per point for paths of geometric shapes, minor axis to major axis elliptical ratios (b/a), Cobb angles, sagittal balance of C2 above C7, and posterior tangent segmental and global angles.

Summary of Background Data. When restricted to cervical lordotic configurations, normal, acute pain, and chronic pain subjects have not been compared for similarities or differences of these parameters. Conventional Cobb angles provide only a comparison of the endplates of the distal vertebrae, while geometric modeling provides the shape of the entire sagittal curves, the orientation of the spine, and segmental angles.

Methods. Radiographs of 72 normal subjects, 52 acute neck pain subjects, and 70 chronic neck pain subjects were digitized. For normal subjects, the inclusion criteria were no kyphotic cervical segments, no cranial-cervical symptoms, and less than ± 10 mm horizontal displacement of C2 above C7. In pain subjects, inclusion criteria were no kyphotic cervical segments and less than 25 mm of horizontal displacement of C2 above C7. Measurements included segmental angles, global angles of lordosis (C1–C7 and C2–C7), height-to-length ratios, anterior weight bearing, and from modeling, circular center, and radius of curvature.

Results. In the normal group, a family of ellipses wasfound to closely approximate the posterior body margins of C2–C7 with a least squares error of less than 1 mm per vertebral body point. The only ellipse/circle found to include T1, with a least squares error of less than 1 mm, was a circle. Compared with the normal group, the pain group’s mean radiographic angles were reduced and the radius of curvature was larger. For normal, acute, and chronic pain groups, the mean angles between posterior tangents on C2–C7 were 34.5°, 28.6°, and 22.0°, C2–C7Cobb angles were 26.8°, 16.5°, and 12.7°, and radius of curvature were r = 132.8 mm, r = 179 mm, and r = 245.4 mm, respectively.

Conclusions. The mean cervical lordosis for all groups could be closely modeled with a circle. Pain groups had hypolordosis and larger radiuses of curvature compared with the normal group. Circular modeling may be a valuable tool in the discrimination between normal lordosis and hypolordosis in normal and pain subjects.

Using kyphosis and anterior head translation as exclusion criteria, a family of ellipses was found to closely approximate the posterior body margins of C2–C7 in normal subjects. While the conventional Cobb angle provides only a cross-sectional analysis of end segments of the spinal curves, more insight can be obtained applying a slightly higher mathematical analysis such as circular and elliptical modeling. Additionally, in neck pain subjects, hypolordosis was quantified using this circular modeling.

From *Biomechanics Laboratory, Department of Sciences of Physical Activity, Universite du Quebec a Trois Rivieres, Quebec, Canada; †Private Practice, Elko, NV; ‡Comp Math research consultant, Huntsville, AL; §Professor Emeritus, University of Southern California School of Medicine, Los Angeles, CA; ¶Private Practice, New Port Richey, FL; **Private Practice, Windsor, CO; and ‡‡Department of Statistics, Temple University, Philadelphia, PA.

Acknowledgment date: August 26, 2003. First revision date: October 28, 2003. Second revision date: November 24, 2003. Acceptance date: December 22, 2003.

The manuscript submitted does not contain information about medical device(s)/drug(s).

Other funds were received in support of this work. No benefits in any form have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript.

Address correspondence and reprint requests to Deed E. Harrison, DC, 123 Second Street, Elko, NV 89801; E-mail:

© 2004 Lippincott Williams & Wilkins, Inc.