Assessment of mechanical stability factors through parametric multibody modeling of the ESIN technique in paediatric femoral shaft fractures

The Elastic Stable Intramedullary Nailing (ESIN) technique is widely used for treating paediatric femoral shaft fractures. The biomechanical effectiveness of the implant depends on several geometric and surgical factors. However, the lack of quantitative insight into geometric influence on implant performance hinders treatment optimization. This study aimed to develop a parametric model to evaluate, using a multibody approach, the influence of the main geometric factors on the overall implant stability. Two titanium nails (Stryker and Synthes) were characterized through four-point bending test, conducted according to ASTM F1264-24, to obtain force-displacement curves and elastic modulus values. A flexible nail model was then created in Adams View, subjected to the same bending test and tuned to match the experimental results. Subsequently, a parametric model of the implant-fracture system was then developed, featuring two retrogradely inserted nails within a fractured femoral diaphysis with a transverse fracture, represented by two adjacent hollow bone segments. After validation against bending and torsion test data from the literature, the model was used to assess stability under controlled displacement of the proximal segment, while fixing the distal one. The following key geometrical parameters were varied: nail curvature amplitude, nail insertion angle, fracture location and misalignment between nail curvature apex and fracture site. For each variation, translational stiffness was computed in both frontal and sagittal planes. Specifically, for the stability on the frontal plane a full-factorial design of experiment, with three levels per parameter (27 trials), was performed. Furthermore, a statistical analysis (ANOVA) was conducted to identify the parameters which significantly affect the system stability. Experimental tests showed similar elastic modulus values for the two considered nails (110 and 103 GPa). The implant-fracture model was able to accurately reproduce the reported experimental bending stiffness, although torsional stiffness was underestimated. This could be ascribed to the nail tip sinking into cancellous bone which was not implemented in the model. Simulations results revealed that increased nail curvature improved stiffness in both frontal and sagittal planes. In particular, the distal fracture led to the lowest stability along the medio-lateral direction, whereas the highest stability along the antero-posterior one. Also, greater insertion angles enhanced medio-lateral stiffness but slightly reduced antero-posterior stability. Misalignment between curvature apex and fracture site reduced stiffness in both directions. Overall, sagittal stiffness resulted lower than frontal, namely, 4-20 versus 40-70 N/mm, respectively. Finally, the ANOVA showed that fracture location was the only parameter with a statistically significant influence (p-value = 0.027). In conclusion, the proposed model confirms the biomechanical sensitivity of the ESIN system to implant geometry and fracture location. The findings highlight the importance of aligning the nail curvature apex with the fracture site to maximize stability, while the markedly lower sagittal stiffness suggests a critical directional weakness with relevant clinical implications for paediatric femoral fracture stabilization.