A novel lower bound for tip-apex distance

The cut-out of the cephalomedullary nail is among the most common post-surgery complications for intertrochanteric fractures. As a risk predictor, a tip-apex distance (TAD) below 25 mm, observed from orthogonal fluoroscopic views, is recommended in the literature. This study aims to demonstrate that TAD < 25 mm is a mathematically insufficient risk definition and to complement the TAD upper bound with an appropriate lower bound, with the introduction of a novel distance parameter, TADX, based on the orthogonal projection of the nail tip on the central femoral midline.

Through a mathematical simulation software, all the possible points that lie inside the AP and lateral views of the proximal femoral hemisphere are utilized to create a 3D grid that is sorted into geometrically safe and risk-bearing regions. Extending this methodology, TAD < 25 mm, 10 mm < TAD < 25 mm, and the ideal tip position volumes are simulated. Finally, intersection volumes are created by a combination of different candidate lower TADX bounds and TAD < 25 mm upper bound to determine satisfactory TADX limits.

Simulation of TAD-bound zones exposed that TAD is only a mathematically suitable parameter for defining the upper boundary but not the lower boundary for the optimal region. However, using a TADX lower limit creates a 3D volume that is much closer to the optimal tip region volumetrically and can still be as quickly calculated from 2D AP and lateral views.

According to the mathematical simulations, the use of a TADX lower bound of 9 mm for small, 7.5 mm for medium, and 7 mm for large femoral heads in conjunction with a TAD upper bound of 25 mm is suggested.