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History of the CBP® Ideal Spinal Model

By Deed E. Harrison, DC

             I used the term CBP® Normal Spinal Model in my title because this model has evolved from my father’s original 1979 Height-to-Length (H/L) model into our present elliptical model. Several people had some input into this model recently, but most of the work was done by my father (Don Harrison, PhD, DC, MSE), Tad Janik, PhD, and I. Thus, I could have used the terms Harrison-Janik or Janik-Harrison spinal model. However, since our profession seems to have an aversion to sir-named items, I will use the generic version, i.e. CBP® Ideal Spinal Model or just ISM.

            There are many different types of spinal models in the literature. In 1987, Yoganandan et al.¹ grouped spinal models into the following four categories:

• Geometrical Considerations,
• Force Considerations,
• Type of Analysis,
• Applications of the Model.

From this description, I note that the CBP® Ideal Spinal Model is a type A model. It is the geometric path of the posterior longitudinal ligament from the occiput to the back of S1.

In 1979 while teaching at NCCC, which became Palmer Chiropractic College-West, my father used two major assumptions (and several smaller assumptions) to derive a sagittal spinal model.^2-4 These were (1) all three spinal regions (cervical lordosis, thoracic kyphosis, & lumbar lordosis) are arcs of circles, and (2) the Delmas⁵ Height to Length ratio, H/L = 0.95 index is ideal for the each region of the sagittal spine. Using some geometry and trigonometry, he arrived at the equation H/L = (sin q)/q = 0.95, which when solved for 2q provided a 63° arc for each spinal region, e.g., C1-T1 (Figure 1).

Figure 1. The 1979 Harrison Spinal Model was a Height-to-Length ratio based on two assumptions: (1) the spinal curvatures are arcs of circles and (2) the Delmas Index is ideal (H/L = 0.95).

         Prior to 1979, there were others,^6,7 who used the same major assumption of arcs of circles for the spinal curvatures, but with different second assumptions. In 1908, Goetz⁶ assumed that the radius of curvature (R) was equal to the length of the arcs (L), yielding 57.3° arcs, while in 1974, Pettibon⁷ assumed that the radius (R) equaled the chord of the arc (C), yielding 60° arcs. Table 1 compares these early spinal models. For years my father thought that he had done something special with his “different” 1979 spinal model, but looking back at the models in Table 1, it can be observed that all three of these models are included in the range of 57°-63° and would differ very little clinically, i.e., segmental angles of curvature (C2-3, C3-4, C4-5, C5-6, C6-7) and/or global angles of curvature from C2 to C7.

In 1993 while studying for his PhD in Mathematics at the University of Alabama in Huntsville, my father met and became friends with Tad Janik, PhD, who was a Mathematician with a numerical analysis background. Dr. Janik became interested in helping my father with one of his life’s goals: to support or improve his ideal spinal model (ISM). They started with a cervical force-element model, but could not complete it because the cervical segmental muscle efforts were not reported in the literature.

For the cervical model, they next turned to determining an average model. From measurements on 400 lateral cervical radiographs from Dwight DeGeorge’s clinic in Saugus, Massachusetts, average segmental angles (C2-C7), global angles between C2 and C7, H/L, and anterior head weight bearing were obtained. These were compared to my father’s old model of H/L = (sin q)/ q, but with out forcing the exact value of 0.95 for normal. My father’s old model predicted the average values within a mean error of 5%. This supported the assumption that the cervical spine was approximately a piece of a circle (arc of a circle); see Figure 2. This was published in 1996.⁴ Although, I was not an author on this 1996 manuscript, I helped answer several of the Spine Reviewers’ comments, which enabled the manuscript to be accepted for publication.

I digress here to include an important point. The measurements on sagittal spinal radiographs are made with posterior body tangents. This method of radiographic line drawing analysis has been reported to be highly reliable.^8-10

Figure 2. The 1996 CBP® C1-T1 Cervical Model was an arc of a circle.4 It provided an “average normal” model based on 400 subjects and an “ideal normal” model based on several hypothetical assumptions. It reported average and ideal normal values for each segmental angle (C2-3, C3-4, C4-5, C5-6, and C6-7) and a normal value for the global angle between posterior tangents on C2 and C7.

Subsequently, we turned our attention to the lumbar spine. Out of several geometric choices (circle, hyperbola, parabola, sine wave, etc), my father and Tad Janik decided to try an ellipse. After trial and error, an ellipse of minor axis to major axis ratio (b/a) of 0.4 and an arc segment of one quadrant of 85° from posterior-inferior of T12 to posterior-superior of S1 was found to closely approximate (least squares error of 1.2 mm) the average lumbar curvature of 50 healthy subjects (Figure 3). This project was published in 1998.¹¹ In a follow-up study, the ability of this lumbar elliptical model to discriminate between healthy subjects and low back pain subjects was studied.¹² Here, the lumbar lordosis of four groups of subjects was measured via radiography and subjected to elliptical modeling using a computer iteration process. The four groups included: 50 healthy subjects, 50 acute low back pain subjects free from pathology, 50 chronic low back pain subjects free from pathology, and a group of 24 chronic low back pain subjects with various lumbar degenerative pathologies. In 11/13 measurements we found statistically significant differences between the groups; including elliptical model parameters. Thus our elliptical lumbar model has been found to have predictive validity.

Figure 3. The 1998 CBP® Lumbar Model was an arc of an ellipse, with b/a = 0.4.11 It provided an “average normal” model based on 50 subjects and an “ideal normal” model based on several hypothetical assumptions. It reported average and ideal normal values for each segmental angle (T12-L1, L1-2, L2-3, L3-4, L4-5, and L5-S1) and an ideal value for the global angle between posterior tangents on L1 and L5.

In 2002¹³and 2003¹⁴, we published two thoracic spine models (Figure 4). Both were portions of an ellipse, with an approximate b/a ratio of 0.7 (as compared to the 1998 lumbar b/a ratio of 0.4). As in the CBP® cervical and lumbar modeling projects, we published average and ideal normal values for each thoracic segmental angle and for global angles of kyphosis. All these modeling studies were performed with a computer iteration process, originated by Dr. Tad Janik. This iteration process attempts to pass geometric shapes through the posterior body margins that were digitized on lateral radiographs by my father, Tad Janik, and I.

Figure 4. The 200213 & 200314 CBP® Thoracic Models were arcs of ellipses, with b/a = 0.7. These provided an “average normal” model based on 80 subjects and an “ideal normal” model based on several hypothetical assumptions. It reported average and ideal normal values for each segmental angle (T1-2, T2-3, T3-4, T4-5, T5-6, T6-7, T7-8, T8-9, T9-10, T10-11, and T11-12) and a normal value for the global angle between posterior tangents from T1-T12, T2-T11, and T3-T10.

Recently, we have revisited our cervical model. The 1996 cervical model data were obtained from “by-hand” line drawing measurements of lateral cervical radiographs, whereas the lumbar and thoracic modeling was performed with computer iterations, in the least squares sense, from digitized vertebral body corners. We wondered if our recent more mathematical approach would affect our old cervical model. We obtained 266 out of the original (from 1996⁴) 400 subjects and digitized these radiographs. We obtained a circular model very similar to our 1996 result, with some interesting differences. This project is in press for 2004 at Spine.¹⁵ Importantly, in this same study, our cervical circular model was able to discriminate between healthy subjects and neck pain subjects.¹⁵ Here, the cervical lordosis of healthy subjects was compared to acute neck pain and chronic neck pain subjects. For all subjects in each of three groups, subjects were free from significant pathology, did not have segmental or total kyphosis, and had minimal anterior head translation. In this manner, the determination and pain relevance of hypo-lordosis was sought. The x-ray measurements were found to be statistically significant different between the groups; including the circular model parameter or radius of curvature.

            This finally leads us to a full spine model that could be a compilation of all past CBP® average normal and ideal spinal models. However, when attempted, the thoracic and lumbar models did not fit properly at T12. We discovered that our 1998 lumbar model, which was derived from subjects in Normal, Illinois, had a posterior translation of T12 compared to S1 due to overweight female subjects.¹¹ By way of a literature review, we found that subjects with a body mass index (BMI= weight (Kg)/Height (m)²) in the overweight range, will have a net increase in their lumbar lordosis.^16,17 Subsequently, we modeled the lumbar spines of 50 normal subjects obtained from Dr. Phil Paulk’s clinic in Stockbridge, Georgia with a more normal BMI. These were the same subjects that we had used to derive our thoracic models and thus continuity was found at T12 between the thoracic ellipse and the new lumbar elliptical model (b/a = 0.32). This new model is in review at present.¹⁸

Importantly, our new cervical model was an almost perfectly fit at T1 with the T1-S1 model. Figure 5 illustrates that there is a near vertical alignment of C1-T1-T12, and S1. Optimal sagittal balance of the cervical, thoracic, and lumbo-pelvic spine is a highly discussed topic in the literature.^19-25 An anterior or posterior displaced sagittal balance has been linked to the development of a number of health disorders including: neck pain and upper back pain, low back pain, increased muscle loads, increased stresses on spinal discs, accelerated spinal degeneration, spondylolisthesis, and scoliosis.^19-25 Lastly, if one remembers his/her geometry, a circle is a special ellipse (with b/a = radius/radius = 1), and thus, the CBP® full spine normal model is composed of separate ellipses for the different spinal regions.

Figure 5. The CBP® Full-spine Normal Model is the path of the posterior longitudinal ligament through the posterior body margins. It is composed of separate ellipses in the different spinal regions (cervicals, thoracics, & lumbars). It has near perfect sagittal balance of vertical alignment of C1-T1-T12-S1. This model provides normal sagittal plane curves and normal values for all segmental angles and global angles. The sagittal curves have points of inflection (mathematic term for change in direction from concavity to convexity) at inferior of T1 and inferior of T12.

Summary

            The CBP® average normal and ISM is a validated ‘evidence based’ model. This model is useful clinically as an outcome of spinal rehabilitative care, in comparison studies of healthy subjects to different spinal disorder populations, in surgical outcome studies, and in analytical modeling studies to use as an initial starting position of neutral spinal geometry.

References

1. Yoganandan et al. Mathematical and finite element analysis of spine injuries. Crit Rev Biomed Eng 1987; 15:29-90.

2. Harrison DD. Class Notes for a 3^rd quarter Spinal Biomechanics course. Sunnyvale, CA: Northern California College of Chiropractic, 1979.
3. Harrison DD, Janik TJ, Troyanovich SJ, Harrison DE, Colloca CJ. Evaluations of the Assumptions Used to Derive an Ideal Normal Cervical Spine Model.  J Manipulative Physiol Ther 1997;20(4): 246-256.
4. 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.
5. Delmas A. Types rachidiens de statique corporelle. Revue de Morphophysiologie, 1951.
6. Goetz HF. Graphic Representation of the curves of the Spinal Column. JAOA 1908; 7(5)
7. Pettibon BR, Loomis . Pettibon Biomechanics (22 articles in a series). Today's Chiropractic. 1973-1975.
8. Harrison DE, Harrison DD, Cailliet R, Troyanovich SJ, Janik TJ. Cobb Method or Harrison Posterior Tangent Method: Which is Better for Lateral Cervical Analysis? Spine 2000; 25: 2072-78.
9. Harrison DE, Cailliet R, Harrison DD, Janik TJ, Holland B. Centroid, Cobb or Harrison Posterior Tangents: Which to Choose for Analysis of Thoracic Kyphosis? Spine 2001; 26(11): E227-E234.
10. Harrison DE, Harrison DD, Janik TJ, Harrison SO, Holland B. Determination of Lumbar Lordosis: Cobb Method, Centroidal Method, TRALL or Harrison Posterior Tangents? Spine 2001; 26(11): E236-E242.
11. Janik TJ, Harrison DD, Cailliet R, Troyanovich SJ, Harrison DE. Can the Sagittal Lumbar Curvature be Closely Approximated by an Ellipse? J Orthop Res 1998; 16(6):766-70.
12. Harrison DD, Cailliet R, Janik TJ, Troyanovich SJ, Harrison DE, Holland B. 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.
13. Harrison DE, Janik TJ, Harrison DD, Cailliet R, Harmon S. Can the Thoracic Kyphosis be Modeled with a Simple Geometric Shape? The Results of Circular and Elliptical Modeling in 80 Asymptomatic Subjects. J Spinal Disord Tech 2002; 15(3): 213-220.
14. Harrison DD, Harrison DE, Janik TJ, Cailliet R, Haas JW. Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of the Thoracic Kyphosis? Spine 2003; 28(5): 463-469.
15. Harrison DD, Harrison DE, Janik TJ, Cailliet R, Haas JW, Ferrantelli J, Holland B. Modeling of the Sagittal Cervical Spine as a Method to Discriminate Hypo-Lordosis: Results of Elliptical and Circular Modeling in 72 Asymptomatic Subjects, 52 Acute Neck Pain Subjects, and 70 Chronic Neck Pain Subjects. Spine 2004; in press.
16. Tuzun C, Yorulmaz I, Cindas A, Vata S. Low back pain and posture. Clin Rheumatol 1999;18:308-312.
17. Ridola C, Palma A, Ridola G, Sanflippo A, Almasio PL, Zummo G. Changes in the lumbosacral segment of the spine due to overweight in adults. Preliminary remarks. Ital J Anat Embryol 1994;99:133-143.
18. Harrison DD, Harrison DE, Colloca CJ, Cailliet R, Janik TJ, Haas JW. Normal Spinal Model from T1 to S1:  Results of Elliptical Modeling in 50 Normal Subjects. 2004; in review.
19. Beck A, Killus J. Normal posture of spine determined by mathematical and statistical methods. Aerospace Medicine 1973;44(11):1277-1281.
20. Jackson RP, McManus AC. Radiographic analysis of sagittal plane alignment and balance in standing volunteers and patients with low back pain matched for age, sex, and size. Spine 1994;19:1611-1618.
21. Kawakami M, Tamaki T, Ando M, Yamada H, Hashizume H, Yoshida M. Lumbar sagittal balance influences the clinical outcome after decompression and posterolateral spinal fusion for degenerative lumbar spondylolisthesis. Spine 2002;27:59-64.
22. Kiefer A, Shirazi-Adl A, Parnianpour M. Synergy of the human spine in neutral postures. Eur Spine J 1998; 7:471-479.
23. Kumar MN, Baklanov A, Chopin D. Correlation between sagittal plane changes and adjacent segment degeneration following lumbar spine fusion. Eur Spine J 2001; 10:314-319.
24. Harrison DE, Colloca CJ, Keller TS, Harrison DD, Janik TJ. Prediction of sagittal plane loads and stresses in the lumbar spine. A comparison of neutral posture and anterior translation of the thoracic cage. Eur Spine J 2004: in press.
25. Ganju A, Ondra SL, Shaffrey CI. Cervical Kyphosis. Techniques in Orthopaedics 2003;17(3):345-354.

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