Department of Mechanical Engineering2024-11-1020221863-993310.1007/s00068-020-01514-x2-s2.0-85092306822http://dx.doi.org/10.1007/s00068-020-01514-xhttps://hdl.handle.net/20.500.14288/16376Purpose: 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. Method: 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. Results: 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. Conclusions: 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.Emergency medicineJournal Article1863-99415785690000018000