Estimation of pelvic tilt on anteroposterior X-rays—a comparison of six parameters

Abstract

Objective

To compare six different parameters described in literature for estimation of pelvic tilt on an anteroposterior pelvic radiograph and to create a simple nomogram for tilt correction of prosthetic cup version in total hip arthroplasty.

Design

Simultaneous anteroposterior and lateral pelvic radiographs are taken routinely in our institution and were analyzed prospectively. The different parameters (including three distances and three ratios) were measured and compared to the actual pelvic tilt on the lateral radiograph using simple linear regression analysis.

Patients

One hundred and four consecutive patients (41 men, 63 women with a mean age of 31.7 years, SD 9.2 years, range 15.7–59.1 years) were studied.

Results

The strongest correlation between pelvic tilt and one of the six parameters for both men and women was the distance between the upper border of the symphysis and the sacrococcygeal joint. The correlation coefficient was 0.68 for men (P<0.001) and 0.61 for women (P<0.001). Based on this linear correlation, a nomogram was created that enables fast, tilt-corrected cup version measurements in clinical routine use.

Conclusion

This simple method for correcting variations in pelvic tilt on plain radiographs can potentially improve the radiologist’s ability to diagnose and interpret malformations of the acetabulum (particularly acetabular retroversion and excessive acetabular overcoverage) and post-operative orientation of the prosthetic acetabulum.

Mathematical derivation of the nomogram

Referring to Fig. 6(a), the relationship between radiological cup version (α), cup abduction (β), and the cup version angle that is projected onto the body’s mid plane (γ), was expressed by Murray as [13]:

$$\tan \;\alpha = \tan \;\gamma \cdot \cos \;\beta $$

(1)

Fig. 6

The definitions of cup version (α), cup abduction (β), and the cup version angle that is projected onto the body’s mid plane (γ), are shown (a). A pelvic tilt of δ would lead to a decreased cup version α′ (b)

A change in pelvic tilt (Δδ) would lead to a decreased γ′ angle as follows (Fig. 6b):

$$\gamma \prime = \gamma - \Delta \delta $$

(2)

The resulting radiological cup version γ′ can now be expressed as

$$\tan \;\alpha \prime = \tan \;\gamma \prime \cdot \cos \;\beta = \tan {\left( {\gamma - \Delta \delta } \right)} \cdot \cos \beta $$

(3)

Based on the resulting linear regression model of the present study and subtracting the neutral pelvic tilt of 60° [26, 33, 34] (Fig. 1, Table 1), the relationship between change in pelvic tilt (Δδ) and the vertical distance between the upper border of the symphysis and the mid region of the sacrococcygeal joint (distance A) is

$$\Delta \delta _{m} = \frac{{A + 7.1786}} {{0.1829}} - 60^\circ $$

(4)

for men and

$$\Delta \delta _{f} = \frac{{A + 4.4829}} {{0.1578}} - 60^\circ $$

(5)

for women. Inserting Eqs. 4 and 5 for men and women into Eq. 3 yields the following equations of the corrected radiological anteversion (α′)

$$\alpha \prime _{{\text{m}}} = \operatorname{arc} \;tan{\left( {\tan {\left( {\gamma - \frac{{A + 7.1786}}{{0.1829}} + 60^\circ } \right)}\cos \beta } \right)}$$

(6)

for men and

$$\alpha \prime _{{\text{f}}} = \operatorname{arc} \;tan{\left( {\tan {\left( {\gamma - \frac{{A + 4.4829}}{{0.1578}} + 60^\circ } \right)}\cos \beta } \right)}$$

(7)

for women. The acetabular cup version, measured on a radiograph that is centered to the body’s mid axis, is 5° less than measurements centered over the hip [1]. Therefore, the final formulas for creation of the nomograms are

$$\alpha \prime \prime _{{\text{m}}} = \operatorname{arc} \;tan{\left( {\tan {\left( {\gamma - \frac{{A + 7.1786}}{{0.1829}} + 60^\circ } \right)}\cos \beta } \right)} + 5^\circ $$

(8)

for men and

$$\alpha ^{{\prime \prime }}_{{\text{f}}} = \operatorname{arc} \;tan{\left( {\tan {\left( {\gamma - \frac{{A + 4.4829}}{{0.1578}} + 60^\circ } \right)}\cos \beta } \right)} + 5^\circ $$

(9)

for women.