Mathematical evaluation of jumping distance in total hip arthroplasty: influence of abduction angle, femoral head offset, and head diameter

Abstract

Background and purpose: The jumping distance (JD) is the degree of lateral translation of the femoral head center required before dislocation occurs. The smaller the distance, the higher the theoretical risk of dislocation. The aim of our study was to evaluate this jumping distance and its variation according to the characteristics of the implant, and also the theoretical gain in using large head diameters of above 38 mm.

Methods: The JD was calculated as a function of the cup anteversion and abduction angles, the head diameter, and the head offset (defined as the distance between the center of the femoral head and the cup opening plane). Head diameters of 28, 32, 36, 40, 44 and 48 mm were analyzed. The abduction angle was increased from 0 degrees to 80 degrees with a 10 degree increment. The anteversion angle was increased from 0 degrees to 40 degrees with a 5 degree increment.

Results: The jumping distance was found to decrease as the cup abduction angle increased (0.25 mm each 1 degree for 32-mm head diameter). It increased by 0.05 mm for a 1 degree increase in the anteversion angle. The jumping distance increased as the head diameter increased (0.4 mm each mm diameter for a 45 degree abduction angle). The net gain obtained by increasing the diameter, however, decreased when abduction angle increased (0.25 each mm diameter for 60 degree abduction). The JD decreased by 0.92 mm for each 1-mm increase in head offset, showing that head offset was the most important parameter influencing the JD.

Interpretation: The theoretical gain in stability obtained by using a large femoral head (above 36 mm) is negligible in cases where there is a high cup abduction angle. An increase in offset of the femoral head substantially reduces the jumping distance and it should therefore be avoided.

Figure 1.

The jumping distance is the lateral translation (AB) of the center of the femoral head (t) before dislocation occurs. F is the load force and y is the planar cup inclination angle measured in the frontal plane.

Figure 2.

Definition of the angular parameters used for positioning of the cup. O is the center of the cup, Oz is the cranio-caudal axis, Oy is the lateral-medial axis, and Ox is the postero-anterior axis. Starting at the reference position (I), a first rotation of value a (cup abduction angle) is performed around the anterior-posterior axis (II). A second rotation of value b (cup anteversion angle) is performed around the cranialcaudal axis (III).

Figure 3.

The femoral head offset is the distance from the center of the head (O) to the opening plane of the cup (purple line). If the head center is outside the cup, the offset is positive (A); otherwise it is negative and is called inset (B). The use of large heads above 38 mm in diameter generally imposes the use of an offset because the cup is usually a truncated hemisphere of 165° for the large heads.

Figure 4.

Variation in jumping distance according to the cup abduction angle

Figure 5.

Variation in jumping distance according to acetabular ante-version angle.

Figure 6.

Combined influence of head offset and diameter on the jumping distance. 45° abduction and 15° anteversion cup angles are used.

Figure 7.

Influence of femoral offset on jumping distance.

Figure 8.

Dependency of jumping distance on head diameter for current commercial designs. For diameters above 38 mm, the cup is an incomplete truncated hemisphere, causing a positive offset, which in turn causes a dip in the jumping distance.