AJCC April 2000

Normal Elliptical Spinal Model

by Deed Harrison, D.C.

After his undergraduate pre-chiropractic courses at the University of Utah, Dr. Deed Harrison graduated from Life-West in 1996. He is co-author of more than 30 peer-reviewed, indexed, research articles. These include 21 in JMPT, 3 in Chiropractic Technique, and 6 at major Index Medicus journals. He is a reviewer for an Index Medicus Orthopaedic journal. He is a certified instructor for CBP®¨ Seminars, has written two chapters in the CBP®¨ text books, and is Vice-President of CBP®¨ Nonprofit, Inc. He has a private practice in Elko, Nevada.

The Harrison circular cervical model1 and the elliptical lumbar model2-4 are going to be illustrated in the following Figures. Like the cervical model, the Harrison thoracic model is also a piece of a circle. Since circles are special ellipses with minor axis (2b) equal to the major axis (2a), which are diameters of a circle, then the elliptical ratio for circles is a/b = 1. The elliptical ratio for the Harrison normal lumbar ellipse is a/b = 0.4.2-3 Since T1 has facets similar in design to the cervical spine and T2 is statistically the point of inflection between the convex (forward) cervical curve and concave thoracic curvature, while T11 (point of inflection) and T12 are transition segments between the lumbar curve and the thoracic curve, Harrison has drawn posterior tangents on T3 and T10. The hypothesized value for this thoracic absolute rotation angle (T3-T10) varies with the height-to-length ratio (H/L).

If, instead of inserting average values (currently not available for H/L in the thoracic spine), the Delmas5 ideal value (H/L = 0.95) and normal range (0.94 < H/L < 0.96) is inserted in the system of equations in Figure 1, then normal values for theta (one half of the circular arc angle), height of a vertebral body x (in degrees of the arc angle theta), RRA, and ARA can be calculated. Figure 2 illustrates the angles formed by HarrisonÕs Posterior Tangent Method of x-ray analysis. Harrison et al6 have published ideal normal and average normal values for allthe segmental (RRA) and global (ARA) angles depicted in Figure 2.

The original Harrison spinal model was developed for a lecture in 1979 as a height to length index, H/L = sin U/U, while Don Harrison was teaching a 3rd quarter spinal biomechanics course at Northern California College of Chiropractic in Sunnyvale, California. Figure 3 illustrates this model which had a normal assumption. The normal assumption was that the Delmas Index was correct, i.e. H/L = 0.95 and a Ònormal rangesÓ of 0.94 < H/L < 0.96. This ideal assumption can be replaced by average values, which was in fact what Harrison et al. did in their Cervical spine model published in 1996, i.e. H/L = sin U/ U = 0.97.

While deriving their elliptical spinal model of the lumbar lordosis, Harrison et al. also devised a height-to-length ratio for the lumbar ellipse. The length from T12 to S1 can be expressed in terms of the elliptical integral of the second kind E(f,k):7

Since the height of the T12 to S1 segment can be evaluated as:

with k = 1- b2/a2, the height-to-length ratio (H/L)T12-S1 is calculated as:

This formula (H/L) provides the correspondence between all our parameters, the two ratios R = H/L and r = b/a for the minor and major axis ratio, the angle f for the part of a quadrant that our ellipse will assume, and the parameter Q, which is a parameter related to f. This Harrison ideal lumbar model and the average lumbar lordotic model both had a height to length index of 0.96. However, Harrison et al. had unpublished data for the average H/L index from T12 to inferior S1. This value was H/L = 0.91. If the new Harrison thoracic model results in a H/L = 0.97, then the average full spine model could result in a total height-to-length index of 0.95, e.g. [0.97 + 0.97 + 0.91]/3 = 0.95.

SEE TABLES ON NEXT PAGE

References

1. Harrison DD, Janik TJ, Troyanovich SJ, Holland B. Comparisons of lordotic cervical spine curvatures to a theoretical ideal model of the static sagittal cervical spine. Spine 1996;21(6):667-675.

2. Troyanovich SJ, Calliet R, Janik TJ, Harrison DD, Harrison DE. Radiographic mensuration characteristics of the sagittal lumbar spine from a normal population with a method to synthesize prior studies of lordosis. J Spinal Disord 1997; 10(5): 380-86.

3. Janik TJ, Harrison DD, Calliet R, Troyanovich TJ, Harrison DE. Can the Sagittal Lumbar Curvature be Closely Approximated by an Ellipse? J Orthop Res 1998; 16(6):766-770.

4. Harrison DD, Calliet R, Janik TJ, Troyanovich TJ, Harrison DE. Elliptical modeling of the sagittal lumbar lordosis and segmental rotation angles as a method to discriminate between normal and low back pain subjects. J Spinal Disord 1998; 11(5): 430-439.

5. Harrison DE, Harrison DD, Troyanovich SJ. Reliability of Spinal Displacement Analysis on Plane X-rays: A Review of Commonly Accepted Facts and Fallacies with Implications for Chiropractic Education and Technique. J Manipulative Physiol Ther 1998;21:252-66.

6. Delmas A. Types rachidiens de statique corporelle. Revue de Morphophysiologie humaine, 1951. (French)

7. Gradshteyn IS, Ryzhik IM. Table of Integrals, Series and Products. New York, Academic Press, 1993.

8. Stagnara P, De Mauroy JC, Dran G, Fonon GP, Costanzo G, Dimnet J, Pasquet A. Reciprocal angulation of vertebral bodies in a sagittal plane: Approach to references for the evaluation of kyphosis and lordosis. Spine 7:335-342, 1982.

9. Bernhardt M, Bridwell KH. Segmental analysis of the sagittal plane alignment of the normal thoracic and lumbar spines and thoracolumbar junction. Spine 1989;14:717-21.

10. Harrison DD. Spinal Biomechanics: A Chiropractic Perspective. National Library of Medicine #WE 725 H318C, 1986, pgs. 33-41.