Analytical modelling of Kirschner wires in Ilizarov circular external fixator as pretensioned slender beams

Abstract

Transfixing thin Kirschner wires (K-wires) are the key components of the Ilizarov fixator regarding its axial stiffness, which affects the mechanobiological environment in which bone is healed. Mechanically speaking, K-wires are slender beams that are axially tensioned, then fixed and transversely loaded. The existing solutions to such a problem either do not accommodate any axial loading prior to transverse loading, or do not account for the change in the axial load (reaction) due to transverse loading. Their applicability is also limited vis-à-vis applied loads and beam dimensions. This work seeks to address those problems by providing a mathematical formulation for a pretensioned slender beam that accounts for the change in the beam tension due to lateral loading. Central loading of a pretensioned beam was studied and new polynomial equations have been derived, the roots of which yield the final tension for a (i) long, slender and heavily loaded beam and (ii) relatively thicker beam subjected to a lower load. Results were produced and discussed for the specific application of pretensioned K-wires in circular (ring) external fixators in orthopaedics (such as Ilizarov's), which were checked (validated) via two-and three-dimensional finite-element analyses.

Bone fracture healing under Ilizarov fixator: Influence of fixator configuration, fracture geometry, and loading

“…The non‐linear relationship between axial load and IFM can be seen in Figure , which is because of stress‐stiffening effect of the pre‐tensioned wires . This non‐linearity is geometric as reported in many studies and depends on the level of transverse movements of the wire. This explains the difference in the non‐linearities under different ring sizes.…”

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

“…And many other configurations have been introduced and studied. Arakelian et al (2011) introduced a novel 3-DoF (Kim et al, 2002); (b) Dynafix fixator (Kim et al, 2002); (c) Ilizarov apparatus (Zamani and Oyadiji, 2009); (d) Ortho-SUV Frame (Solomin, 2013); (e) Taylor Spatial Frame (Mackie Orthopaedics, 2016). planar parallel manipulator with larger rotation capability.…”

A Mesoscopic Analytical Model to Predict the Onset of Wrinkling in Plain Woven Preforms under Bias Extension Shear Deformation

“…The Euler-Bernoulli theory is used to analyze such a hypothesized beam [ 16 , 17 ]. Moreover, as the proposed model takes the effect of tension on the yarns into account, instead of a first-order analysis that is based on the superposition principle and considers the deflection of the beam independent of the applied tension, the second-order analysis [ 18 ] is undertaken, which accounts for the effect of tension on the overall flexural rigidity of yarns, .…”

“…When considering the assumptions made, the deflection of the yarn as a beam at its mid-span and under arbitrary vertical force F can be written as [ 18 ]: where T , , and S are tension along the yarn, the effective flexural rigidity of yarn in its longitudinal direction, and the length of yarn in the representative PWCP element ( Figure 3 ), respectively.…”