A novel fracture mechanics model explaining the axial penetration of bone-like porous, compressible solids by various orthopaedic implant tips

Abstract

Many features of orthopaedic implants have been previously examined regarding their influence on migration in trabecular bone under axial loading, with screw thread design being one of the most prominent examples. There has been comparatively little investigation, however, of the influence that implant tip design has on migration under axial loads. We present a novel fracture mechanics model that explains how differences in tip design affect the force required for axial penetration of porous, compressible solids similar to trabecular bone. Three tip designs were considered based on typical 5 mm diameter orthopaedic locking screws: flat and conical tip designs, as well as a novel elastomeric tip. Ten axial penetration trials were conducted for each tip design. In order to isolate the effect of tip design on axial migration from that of the threads, smooth steel rods were used. Tip designs were inserted into polyurethane foam commonly used to represent osteoporotic trabecular bone tissue (ASTM Type 10, 0.16 g/cc) to a depth of 10 mm at a rate of 2 mm/min, while force and position were recorded. At maximum depth, elastomeric tips were found to require the greatest force for axial migration (mean of 248.24 N, 95% Confidence Interval [CI]: 238.1–258.4 N), followed by conical tips (mean of 143.46 N, 95% CI: 142.1–144.9 N), and flat tips (mean of 113.88 N, 95% CI: 112.2–115.5 N). This experiment was repeated in cross-section while recording video of material compaction through a transparent window. Strain fields for each tip design were then generated from these videos using digital image correlation (DIC) software. A novel fracture mechanics model, combining the Griffith with porous material compaction, was developed to explain the performance differences observed between the three tip designs. This model predicted that steady-state stress would be roughly the same (~ 4 MPa) across all designs, a finding consistent with the experimental results. The model also suggested that crack formation and friction are negligible mechanisms of energy absorption during axial penetration of porous compressible solids similar to trabecular bone. Material compaction appears to be the dominant mechanism of energy absorption, regardless of tip design. The cross-sectional area of the compacted material formed during migration of the implant tip during axial penetration was shown to be a strong determinant of the force required for migration to occur (Pearson Coefficient = 0.902, p <.001). As such, implant tips designed to maximize the cross-sectional area of compacted material – such as the elastomeric and conical tips in the present study – may be useful in reducing excessive implant migration under axial loads in trabecular bone.