Mathematical evaluation of jumping distance in total hip arthroplasty

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.