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RESEARCH PAPERS

# A Theoretical and Experimental Investigation of Lateral Deformations in a Unilateral External Fixator

[+] Author and Article Information
Kerem Ün

Department of Electrical-Electronic Engineering, University of Çukurova, Adana 01330, Turkeykeremun@cu.edu.tr

İbrahim D. Akçalı

Department of Mechanical Engineering, University of Çukurova, Adana 01330, Turkey

Mahir Gülşen

Department of Orthopaedics and Traumatology, University of Çukurova, Adana 01330, Turkey

J. Med. Devices 1(2), 165-172 (Sep 11, 2006) (8 pages) doi:10.1115/1.2735972 History: Received February 16, 2006; Revised September 11, 2006

## Abstract

The objective of this work is to set up, validate, and analyze a theoretical model of an external fixator for its deformation characteristics in order to draw reliable conclusions relevant to the design and effective clinical implementation of such medical devices. External fixators are mechanical devices widely used in the treatment of fractured bones and correction of limb deformities. Lateral deformation at the fracture site is known to delay bone healing, and investigation of lateral deformation characteristics of such devices experiencing forces acting perpendicular to the bone axis is important from the standpoint of their design as well as their clinical effectiveness. A mathematical model of a three-dimensional (3D) unilateral fixator with multipin fragment attachments has been developed using Castigliano’s method. The relative lateral deformations of the fragment ends at the fracture site induced by loads applied perpendicular to bone axes are calculated with the model. The model has been subjected to experimental verification for a uniplanar unilateral external fixator under comparable conditions with the theory. It has been found out that the effects of fixator size, shape, and geometry on the level of relative lateral displacement of the fracture site are similar in both the theoretical and experimental models. Stiffness is a maximum if the force is applied in the same plane as the proximal pin plane. Placing the distal pin group at a $90deg$ position relative to the proximal pin plane has been observed to increase the stiffness about 10%. In loading directions perpendicular to proximal the pin plane, stiffness is minimum. The angle difference between the load direction and the resulting displacement direction follows a sinusoidal pattern with an amplitude of $10deg$ for loading angles in the $0–180deg$ range. Selecting the distance of proximal pins to the fracture site smaller than the distance of distal pins to the fracture site has been found to decrease relative lateral deformation. The model and the experiment have simultaneously demonstrated that lower values of effective pin lengths and higher values of pin connector lengths lead to higher stiffness. Increasing the number of pins also contributes to the higher values of fixator stiffness.

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## Figures

Figure 1

Depiction of the physical model. Geometric parameters are defined and the various parts of the fixator system are labeled with numbers

Figure 2

Spring model of the fixator system

Figure 3

Experimental setup with the fixator and the PVC pipe fragments

Figure 4

The y and z components (Vy and Vz, respectively) of lateral displacement as determined from theory plotted for different α values. The magnitude of the lateral displacement is the distance from the (Vy=0,Vz=0) point.

Figure 5

The y and z components (Vy and Vz, respectively) of lateral displacement as determined from theory (solid line) and experiment (dots) plotted at various loading angles ϕ. The magnitude of the lateral displacement is the distance from the (Vy=0,Vz=0) point.

Figure 6

Figure 7

Percent change with respect to the reference value of lateral deformation as a function of parameter b (the distance between the fracture site and the proximal fixator pins)

Figure 8

Percent change with respect to the reference value of lateral deformation as a function of parameter c (the distance between the fracture site and the distal fixator pins)

Figure 9

Percent change with respect to the reference value of lateral deformation as a function of parameter d (the distance between force application point and the distal fixator pins)

Figure 10

Percent change with respect to the reference value of lateral deformation as a function of parameter f (effective pin length)

Figure 11

Percent change with respect to the reference value of lateral deformation as a function of parameter r (the horizontal length of the connectors)

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