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Research Papers

Theoretical and Finite Element Modeling of Fine Kirschner Wires in Ilizarov External Fixator

[+] Author and Article Information
A. R. Zamani, S. O. Oyadiji

School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M60 1QD, UK

J. Med. Devices 4(3), 031001 (Aug 31, 2010) (9 pages) doi:10.1115/1.4001815 History: Received November 03, 2009; Revised May 14, 2010; Published August 31, 2010; Online August 31, 2010

The mechanical behavior of the transosseous elements is a defining factor in the overall stiffness, stability, and reliability of an external fixation system. Mechanics involving the application of thin Kirschner wires in Ilizarov apparatus is yet to be fully explained. To address this problem, load-deflection behavior of the pretensioned thin wires laterally loaded by the bone is necessary to be studied. In this paper, the lateral deflections of thin Kirschner wires are studied both theoretically and computationally. Fully three dimensional finite element (FE) modeling and analyses were performed in which the bone was modeled as a hollow cylinder, and the wire-bone interaction was assumed to be frictionless. The mathematical solution resulted in new exact solutions for the deflection as well as final tension in the wires subjected to the lateral loading under a cylinder representing the bone. Results from the FE analyses turned out to be very close to those from the mathematical solution. The results obtained from theory and FE method are comparable to published experimental findings. Some aspects of the pretensioned thin wire behavior in ring fixation systems, e.g., stiffness-tension proportionality, were revealed in the results. The current study adds to the existing knowledge on the general behavior of tensile elements.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Ilizarov ring fixator applied to tibia

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Figure 2

Transverse deflection of a K-wire passing through a cylinder and fixed to an Ilizarov full-ring, where cylinder can slide freely over the wire and the wire assumed to be deformed solely due to tension (i.e., no bending in the wire)

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Figure 3

Free-body diagram of the K-wire showing the forces acting on half of the wire: (a) after pretensioning and prior to lateral loading and (b) after application of both pretension and lateral load

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Figure 4

Pretensioning step for FEA of the wire-bone interaction (F=490 N, unit of stress is Pa)

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Figure 5

Application of a transverse load of P=400 N on pretensioned wires (F=490 N, unit of stress is Pa) by applying equivalent pressure to the upper surface of the cylinder (free bone-wire sliding was allowed)

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Figure 6

Stress levels for frictionless suspending of the bone (as a cylinder) on four K-wires at 90 deg (F=883 N, P=300 N, unit of stress is Pa)

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Figure 7

Stress contours for frictionless suspension of the bone (i.e., cylinder) on four K-wires at 45 deg (F=490 N, P=300 N, unit of stress is Pa).

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Figure 8

Load versus deflection curves for a K-wire under different pretensions (tensile free-sliding model), for (a) a small range and (b) an extended range of transverse loads

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Figure 9

Comparison of load versus deflection curves for a wire under a given pretension with different wire spans modeled by the two tensile models

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Figure 10

Load versus stiffness curves for a wire under a given pretension for different wire spans (tensile free-sliding model), where stiffness is defined as tangent modulus (i.e., K=Kt=∂P/∂y)

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Figure 11

Load versus deflection curves from FE analysis of two different configurations for K-wires angles (90 deg and 45 deg, as seen in Figs.  67, respectively)

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Figure 12

Results for load versus deflection from FEA for a pair of K-wires subjected to lateral compression by the bone (see Fig. 5), compared with analytical solution from Eq. 25, in the absence of friction and pretension

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Figure 13

Results for load versus deflection from FEA for a pair of K-wires subjected to frictionless lateral compression by the bone (see Fig. 5), compared with analytical solution from Eq. 25, at a relatively low clinical pretension (F=490 N)

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Figure 14

Results for load versus deflection from FEA for a pair of wires subjected to frictionless lateral compression by the bone (see Fig. 5), compared with analytical solution from Eq. 25, at medium range clinical pretensions: (a) F=883 N and (b) F=1079 N

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Figure 15

Results for load versus deflection from FEA for a pair of wires subjected to transverse compression by the bone (see Fig. 5), compared with analytical solution from Eq. 25. At a high clinical pretension (F=1275 N), the bone-wire interaction assumed to be frictionless.

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Figure 16

Final tension in a K-wire subjected to frictionless transverse (lateral) compression by a cylinder, as predicted by analytical solution in Eq. 27, at different clinically applied pretensions

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Figure 17

Effect of length on the final tension in the K-wires subjected to frictionless lateral compression by a cylinder, as predicted by analytical solution in Eq. 27, at (a) a low clinical pretension and (b) a high pretension

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Figure 18

Effect of length on the angle of deflection of the K-wires subjected to frictionless lateral compression by a cylinder, as predicted by analytical solution in Eq. 25, at (a) a low clinical pretension and (b) a high pretension

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Figure 19

K-wire stiffness defined as tangent modulus versus tension in the wire under different pretensions and transverse loads from 0 N to 500 N for a 180 mm diameter ring

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Figure 20

A comparison of Load versus deflection curves for a K-wire under different pretensions (in a small range of applied lateral loads) obtained from Eq. 25, and experimental data published by Watson (16)

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