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Robert Cooperstein, MA, DC
Actual and Projected Innominate Height Changes as a Function of Posterior Innominate Rotation
J Amer Chiropr Assoc 2013 Sept-Oct;50(5):33-36
Abstract: Once again, Dr. Cooperstein challenges the validity of a widely accepted rule.

In the early 1990s, frustrated by the continuous discussion about the reliability of various x-ray line marking procedures but virtually no discussion about their validity, I decided to study the validity of one well-known line marking rule: “When an ilium misaligns in a PI direction, the length of the innominate involved increases on the A-P film.”1 Figure 1 illustrates this belief. The problem is that examiners could be reliable. That is, they could agree on numbers and angles measured on a radiograph. Even so, both could be wrong in terms of what those examiners thought this meant about the patient. I was aware of no evidence that a posteriorly rotated innominate bone became longer, and had seen some that suggested it did not.2

I decided to geometrically calculate innominate height changes as a function of pelvic torsion. The method that I used involved taking measurements from a drawing by Kapandji of the lateral aspect of the innominate bone.3 From these measurements, I obtained (x,y) coordinates for the highest point of the iliac crest, the lowest point of the ischial tuberosity, and the symphysis pubis. By inputting these data onto a spreadsheet, I could then use trigonometry to calculate changes in the vertical length of the innominate bone as it rotated posteriorly. In the first phase of the project, I calculated such changes in a “flesh and blood” subject, as if I were measuring the vertical length using calipers. This resulted in a conference presentation and a publication.4 In the second phase of the project, I calculated the changes in innominate height that would be seen on a radiographic image of the pelvis according to various assumptions about the radiographic method: an AP full-spine film with FFD=72 inches, or a sectional lumbopelvic film with FFD=40 inches (FFD=focal-film distance). This phase of the project also resulted in a conference presentation and a published article on the results,5 for which I won an award.

My results necessarily depended on how pelvic torsion was made to occur for the purpose of the study. Hildebrandt’s pelvic torsion model, in which the paired innominate bones rotated in opposed directions about a symphysis pubis axis, was selected to be the analytic engine.6 He was apparently unaware that this model of pelvic torsion, which he believed he had originated, dated back at least to the time of Pitkin and Pheasant’s seminal article in 1936.7 A review article on pelvic torsion further describes this model and its ramifications.8 To calculate innominate height changes as a function of pelvic torsion, it became necessary to somewhat arbitrarily define a “normal pelvic carrying angle” (PCA) because innominate height changes with posterior rotation turn out to be a function not only of the degree of pelvic torsion but also the PCA. Following well-known authorities Kendal and McCreary,9 I assumed that in normal pelvic carriage, a vertical line would pass through both the ASIS and the symphysis pubis. Figure 3 depicts the analytic engine for this study, again based on Kapandji’s drawing. The dotted line represents the posteriorly rotated innominate bone.

The variables in Figure 3 are defined as follows:

A = normal innominate angle, for ASIS=PSIS

B = normal ischial angle, for ASIS=PSIS

C = innominate subluxation angle, posterior rotation

HCi = crest height, initial

HCt = crest height post-torsion

ΔHC = decreased crest height, post-torsion

HIi = ischial height, initial

HIt = ischial height, post-torsion                                   

ΔHI = decreased ischial height, post-torsion

Rc = radius of the crest

Ri = radius of the ischium

Δ = change                                                                                                    

I derived a trigonometric equation for calculating actual (i.e., as if with calipers, not radiographic) innominate height changes as follows:

Δ innominate height = ΔHc - ΔHi = Rc {cos A - cos(A+C)} - Ri {sin B - sin(B+C)}

Computations were performed for 3 PCAs:

    0° = normal pelvic carrying angle

 -10° = anterior bilateral pelvic tilt (“steep”)

+10° = posterior bilateral pelvic tilt (“flat”)

Having computed “caliper” changes in innominate height with rotation, I could now calculate projected innominate length changes, which turn out to be very sensitive not only to the PCA but also to the FFD and direction of the central ray. I again assumed a 200-mm innominate vertical length. Figure 4 shows how the computations were done. Although a rather massive posterior subluxation is shown for the sake of clarity, the x-ray beam angles are drawn quite accurately for the respective projections.

The projected vertical length of the innominate bone turns out to be a function of three initial conditions: 1) the location of the x-ray tube, in terms of FFD and direction of the central ray; 2) the amount of intrapelvic innominate torsion; and 3) the pelvic carrying angle (PCA). A spreadsheet was used to calculate the projected length of the innominate bone as different values were assigned to the location of the x-ray tube, the degree of intrapelvic torsion, and the PCA of the subject. The overall system is dynamic in the sense that the position of both the virtual film and x-ray tube shift as the innominate bone rotates in the sagittal plane in order to maintain a constant FFD and keep the virtual film pressed against the PSIS even as the virtual innominate bone moves.

The results are depicted in Figure 5, which shows changes in actual and projected innominate height (for both full-spine and lumbopelvic projections) as a function of posterior innominate rotation. Separate charts are provided for normal, steep, and flat PCAs. It may be observed that:

  • Actual and projected innominate length is a monotonically increasing function of posterior innominate rotation for both normal and steep PCAs (but not for a flat PCA). Full-spine radiography produces magnitudes about double that of lumbopelvic radiography for any given degree of posterior innominate rotation because the innominate bone is more askew to the central ray.
  • For a flat PCA, actual innominate length decreases with posterior rotation. Paradoxically, full-spine radiography shows a monotonic increase of innominate height with posterior rotation. However, lumbopelvic radiography shows maximum innominate height at 0° posterior rotation, and then decreases with posterior rotation, contrary to the conventional wisdom.

The data suggest that the x-ray line marking rule that has the taller innominate on the AP radiograph posteriorly rotated is in need of some refinement, to put it politely. Less tactfully put, it is simply wrong. The more anteriorly tipped the pelvis, and the more superior the central ray relative to the pelvis, the greater the validity of this dictum. However, the projected vertical-length measurement of the posteriorly rotated innominate bone may decrease in cases where the subject bears a flat PCA when using sectional radiography. Full-spine radiography, with an FFD of 72 inches and the central ray directed toward T6, tends to establish the dictum, whereas sectional lumbopelvic radiography using an FFD of 40 inches and a central ray directed one inch below the iliac crest tends to refute it. Projected innominate length differentials are minimal for subjects with flat PCAs, or even go against the “rule” when using sectional radiography: The posterior innominate may project shorter than its contralateral counterpart. It should also be noted that whether the innominate height changes are negative or positive, in many cases the millimetric values are arguably too small to be considered significant relative to congenital anatomic variation.


Table 1. Projected innominate length differences, 2° opposed bilateral innominate rotations, full-spine radiography.


posterior rotation 20

anterior rotation 20



2.2 mm

-2.4 mm

4.6 mm


3.3 mm

-3.5 mm

6.8 mm


0.9 mm

-1.2 mm

2.1 mm


Table 1 provides a few representative possibilities for subluxation values of 2°, anterior and posterior, again assuming a 200-mm pelvic length and full-spine radiography. These magnitudes may not lie within the bounds of high-tech published anatomical studies on sacroiliac motion.10 That stated, it can be seen that projected innominate length differentials can attain almost 7 mm at the 2° subluxation value, assuming a steep PCA and full-spine radiography, and of course opposed rotations of both innominate bones.

It should be noted that these considerations do not provide a rationale for using full-spine as opposed to sectional radiography. The choice between these two protocols involves many other considerations other than the hypothetical utility of x-ray line marking and radiographic positional asymmetry, including but not limited to the occasional need to rule out pathology and visualize congenital variants.

Many patients, of course, might be best served by taking no x-rays at all for relatively benign complaints, given the scarcity of clinical evidence that the information provided by biomechanical x-rays (a term describing x-rays taken for the purpose of obtaining misalignment listings) improves the outcome of care.


1. Gonstead HA. Gonstead Chiropractic Science and Art: The Chiropractic Methodology of Clarence S. Gonstead. Mount Horeb WI: Schichi Publications; 1980.

2. Jeffery KR. X-ray analysis of differential leg length & pelvic distortion: Anglo-European College of Chiropractic dissertation. 1981.

3. Kapandji A. The Physiology of the Joints, Vol 3. Edinburgh London and New York: Churchill Livingstone; 1974.

4. Cooperstein R, editor. Innominate vertical length differentials as a function of pelvic torsion and pelvic carrying angle. Proceedings of the 5th Annual Conference on Research and Education; 1990; Sacramento, CA: Consortium for Chiropractic Research.

5. Cooperstein R, editor. Roentgenometric assessment of innominate vertical length differentials. Proceedings of the 7th Annual Conference on Research and Education; 1992; Palm Springs, CA: Consortium for Chiropractic Research.

6. Hildebrandt RW. Chiropractic Spinography. 2nd ed. Baltimore: Williams & Wilkins; 1985.

7. Pitkin H, Pheasant H. Sacrarthrogenetic telalgia. II A study of sacral mobility. J Bone Jt Surg. 1936;18(2):365-75.

8. Cooperstein R, Lisi A. Pelvic torsion: anatomical considerations, construct validity, and chiropractic examination procedures. Topics in Clinical Chiropractic. 2000;7(3):38-49.

9. Kendall FP, McCreary EK. Muscle Testing and Function. 3rd ed. Baltimore, MD: Williams & Wilkins; 1983.

10. Goode A, Hegedus EJ, Sizer P, Brismee JM, Linberg A, Cook CE. Three-dimensional movements of the sacroiliac joint: a systematic review of the literature and assessment of clinical utility. J Manip Physiol Ther. 2008;16(1):25-38.