Radiographic quantification of dynamic hip screw migration

Abstract

Purpose

This study aimed to propose a technique to quantify dynamic hip screw (DHS®) migration on serial anteroposterior (AP) radiographs by accounting for femoral rotation and flexion.

Methods

Femoral rotation and flexion were estimated using radiographic projections of the DHS® plate thickness and length, respectively. The method accuracy was evaluated using a synthetic femur fixed with a DHS® and positioned at pre-defined rotation and flexion settings. Standardised measurements of DHS® migration were trigonometrically adjusted for femoral rotation and flexion, and compared with unadjusted estimates in 34 patients.

Results

The mean difference between the estimated and true femoral rotation and flexion values was 1.3° (95 % CI 0.9–1.7°) and −3.0° (95 % CI – 4.2° to −1.9°), respectively. Adjusted measurements of DHS® migration were significantly larger than unadjusted measurements (p = 0.045).

Conclusion

The presented method allows quantification of DHS® migration with adequate bias correction due to femoral rotation and flexion.

Appendix : Detailed presentation of formulae to estimate femoral rotation angle

The relationship between the projected thickness of the DHS® plate (T_proj) and the femoral rotation angle (α) is described by two sets of formulae (Fig. 5):

Fig. 5

Representation of DHS® plate projection (Tproj) with and without rotation. Abbreviations: T = true plate thickness (T₁ = 7.23 mm, T₂ = 5.8 mm); W = true plate width = 19 mm; C = radius of plate curvature (30.8 mm); α = rotation angle (defined as 90 –α₁ – α₂); φ = threshold rotation angle, i.e., the value of rotation above which the DHS® plate curvature influences the relationship between T_proj and α. T₃ and W₃ define the thickness and width, respectively, of a fictive plate defined according to the rotation angle α

Above a femoral rotation threshold angle of 18°, the DHS® plate curvature radius (C) does not influence the relationship between T_proj and α. Femoral rotation is then calculated as follows (Fig. 5b) :

$$ \mathrm{Femoral}\ \mathrm{rotation}\ \alpha\ \left(\mathrm{degree}\right)=\kern0.5em 90\kern0.5em -\kern0.5em {\alpha}_1\kern0.5em -\kern0.75em {\alpha}_2 $$

(6)

$$ {\alpha}_1\left(\mathrm{degree}\right)= \arctan \left(\frac{{\mathrm{T}}_2}{\mathrm{W}}\right)\times \frac{180}{\pi } $$

(7)

$$ {\alpha}_2\left(\mathrm{degree}\right)=\mathrm{arcos}\left(\frac{{\mathrm{T}}_{\mathrm{proj}}}{\sqrt{{\mathrm{T}}_2{}^2+{\mathrm{W}}^2}}\right)\times \frac{180}{\pi } $$

(8)

For rotation angles ranging from 0 to 18°, the projection of the plate curvature must be considered. The formula presented above can be applied on a “fictive plate” defined by its width, W₃ and thickness, T₃ in relation to the rotation angle as follows (Fig. 5c):

$$ \mathrm{Rotation}\ \mathrm{angle}\ \alpha\ \left(\mathrm{degree}\right)=90-\left( \arctan \frac{{\mathrm{T}}_3}{{\mathrm{W}}_3}+ \arccos\ \frac{{\mathrm{T}}_{\mathrm{proj}}}{\sqrt{{\mathrm{T}}_3{}^2+{\mathrm{W}}_3{}^2}}\right)\times \frac{180}{\pi } $$

(9)

$$ {\mathrm{W}}_3=\raisebox{1ex}{$\mathrm{W}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.+\mathrm{C}\times \sin \propto $$

(10)

$$ {\mathrm{T}}_3={\mathrm{T}}_1-\mathrm{C}\ \mathrm{x}\left(1- \cos \propto \right) $$

(11)