Three-dimensional finite element analysis of halo pin insertion and loosening
Description
To understand loosening of halo pins at the skull bone interface, a finite element analysis of pin insertion and loosening potential was performed. Phase I included construction and validation of an axisymmetric model of halo pin insertion into bovine skull bone. Phase II examined stress distribution and interfacial separation on three-dimensional models based on plasticity results of Phase I models In Phase I, nonlinear contact and plastic analyses were necessary to model pin insertion. Bovine skull bone orthotropic elastic properties were measured ultrasonically. The average stiffness constants (GPa) were C$\sb{11}$ = 13.2, C$\sb{22}$ = 21.5, C$\sb{33}$ = 15.4, C$\sb{44}$ = 5.6, C$\sb{55}$ = 3.0, C$\sb{66}$ = 3.3, C$\sb{23}$ = 7.9, C$\sb{13}$ = 5.2, and C$\sb{12}$ = 7.6 (1-direction normal to skull). Using the specific experimental data from five specimens, five corresponding finite element models were evaluated. As pins were inserted into the five specimens, surface strain gage measurements were taken. The measured strains (Mean: $-$1315 $\mu\varepsilon$) were compared to the calculated strains (Mean: $-$1234.2 $\mu\varepsilon$) in order to establish validity. The models and the test specimens both exhibited similar pin penetration depth and large plastic deformation including an upraised ridge surrounding the hole. The bovine insertion models also established an inverse relationship between depth of pin penetration and elastic constant C$\sb{11}$ In Phase II, three-dimensional loosening models assumed a 'work hardened' material distribution based on Phase I plasticity results. Ten loosening analyses modeled five insertion torgues (2, 4, 6, 8, and 10 inch-lb), each with two transverse pin forces (100 and 300 N). Bone stresses exceeded yield (180 MPa) and increased due to transverse loading. Average interface nodal separations on each of the five models for the 100 N transverse force were 2.73 $\mu$m, 0.99 $\mu$m, 0.135 $\mu$m, 0.0375 $\mu$m, and 0.0 $\mu$m. The range of results extended from no gap formation (100 N/10.0 inch-lb model) to complete interface separation (300 N/2.0 inch-lb model). Assuming that gap formation at the interface indicates potential loosening, identification of larger gaps in the reduced axial force models supports the clinical practice of maintaining initial torque levels to prevent pin related complications