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 0180deg 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.

1.
Ilizarov
,
G. A.
, 1992,
Transosseous Osteosynthesis
,
Springer
, Berlin, Germany, pp.
63
136
.
2.
Velazquez
,
R. J.
,
Bell
,
D. F.
,
Armstrong
,
P. F.
,
Babyn
,
P.
, and
Tibshirani
,
R.
, 1993, “
Complications of Use of Ilizarov Technique in the Correction of Limb Deformities in Children
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355,
75
, pp.
1148
1156
.
3.
Paley
,
D.
, 2002,
Principles of Deformity Correction
,
Springer
, Berlin, Germany, pp.
291
410
.
4.
Watson
,
M. A.
,
Mathias
,
K. J.
, and
Maffuli
,
N.
, 2000, “
External Ring Fixators: An Overview
,”
Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119,
214
, pp.
459
470
.
5.
Behrens
,
F.
,
Allgower
,
M.
,
Fernandez
,
D. L.
et al.
, 1991, “
External Fixation
,”
Manual of Internal Fixation. Techniques Recommended by the AO-ASIF Group
,
M. E.
Müller
,
M.
Allgower
,
R.
Schneider
, and
H.
Willenegger
, eds.,
Springer
, New York, p.
367
.
6.
Burny
,
F.
,
Bourgouis
,
R.
, and
Donkerwolcke
,
M.
, 1982, “
Elastic External Fixation: A Biomechanical Study of Half Frame
,”
Concepts in External Fixation
,
D.
Seligson
, and
M. H.
Pope
, eds.,
Grune Stratton
, New York, pp.
66
77
.
7.
Goodship
,
A. E.
, and
Kenwright
,
J.
, 1985, “
The Influence of Induced Micro-Movement on the Healing of Experimental Tibia Fractures
,”
J. Bone Jt. Surg., Br. Vol.
0301-620X,
67
, pp.
650
655
.
8.
Kenwright
,
J.
, and
Goodship
,
A. E.
, 1989, “
Controlled Mechanical Stimulation in the Treatment of Tibial Fractures
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
36
47
.
9.
De Bastiani
,
G.
,
Aldegheri
,
R.
, and
Renzi Brivio
,
L.
, 1984, “
The Treatment of Fractures with a Dynamic Axial Fixator
,”
J. Bone Jt. Surg., Br. Vol.
0301-620X,
66
, pp.
538
545
.
10.
De Bastiani
,
G.
,
Aldegheri
,
R.
,
Renzi Brivio
,
L.
, and
Trivella
,
F.
, 1987, “
Limb Lengthening by Callus Distraction (Callotasis)
,”
J. Pediatr. Orthop.
0271-6798,
7
, pp.
129
134
.
11.
Grill
,
F.
, 1989, “
Correction of Complicated Extremity Deformities by External Fixation
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
166
176
.
12.
Aldegheri
,
R.
,
Renzi Brivio
,
L.
, and
Agostini
,
S.
, 1989, “
Callotasis Method of Limb Lengthening
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
137
145
.
13.
Aronson
,
J.
, and
Tursky
,
E. A.
, 1992, “
External Fixation of Femur Fractures in Children
,”
J. Pediatr. Orthop.
0271-6798,
12
, pp.
157
163
.
14.
Reff
,
R. B.
, 1984, “
The Use of External Fixation Devices in the Management of Severe Lower Extremity Trauma and Pelvic Injuries in Children
,”
Clin. Orthop. Relat. Res.
0009-921X,
188
, pp.
21
33
.
15.
Stanitski
,
D. F.
,
Srivastava
,
P.
, and
Stanitski
,
C. L.
, 1998, “
Correction of Proximal Tibial Deformities in Adolescents using the T-Garches External Fixator
,”
J. Pediatr. Orthop.
0271-6798,
18
, pp.
512
517
.
16.
Alonso
,
J.
,
Geissler
,
W.
, and
Hughes
,
J. L.
, 1989, “
External Fixation of Femoral Fractures: Indications and Limitations
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
83
88
.
17.
Chao
,
E. Y. S.
, and
Pope
,
M. H.
, 1982, “
The Mechanical Basis of External Fixation
,”
Concepts in External Fixation
,
D.
Seligson
and
M. H.
Pope
, eds.,
Grune Stratton
, New York, pp.
13
39
.
18.
Broekhuizen
,
A. H.
, 2000, “
The Stabilitiy of Orthofix External Fixation: A Comparative Evaluation
,”
Orthofix External Fixaton in Trauma and Orthopaedics
,
G.
De Bastiani
,
A. G.
Apley
, and
A.
Goldberg
, eds.,
Springer
, London, pp.
71
76
.
19.
Behrens
,
F.
, and
Johnson
,
W.
, 1989, “
Unilateral External Fixation: Methods to Increase and Reduce Frame Stiffness
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
48
56
.
20.
Briggs
,
B. T.
, and
Chao
,
E. Y. S.
, 1982, “
The Mechanical Performance of the Standard Hoffmann-Vidal External Fixation Apparatus
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355,
64
, pp.
566
573
.
21.
Draper
,
E. R. C.
,
Strachan
,
R. K.
,
Hughes
,
S. P. F.
,
Nichol
,
A. C.
, and
Paul
,
J. P.
, 1997, “
Design and Performance of an Experimental External Fixator with Variable Axial Stiffness and a Compressive Force Transducer
,”
Med. Eng. Phys.
1350-4533,
19
, pp.
690
695
.
22.
Goh
,
J.
,
Thambyah
,
A.
,
Noor Ghani
,
A.
, and
Bose
,
K.
, 1997, “
Evaluation of a Simple and Low-Cost External Fixator
,”
Injury
0020-1383,
28
, pp.
29
34
.
23.
Sladicka
,
S.
, and
Duffin
,
S. R.
, 1998, “
A Biomechanical Strength Comparison of External Fixators
,”
J. Trauma: Inj., Infect., Crit. Care
1079-6061,
44
, pp.
965
969
.
24.
Matsuura
,
M.
,
Lounici
,
S.
,
Inoue
,
N.
,
Walulik
,
S.
, and
Chao
,
E. Y. S.
, 2003, “
Assessment of External Fixator Reusability Using Load- and Cycle-Dependent Tests
,”
Clin. Orthop. Relat. Res.
0009-921X,
476
, pp.
275
281
.
25.
Yang
,
L.
,
Nayagam
,
S.
, and
Saleh
,
M.
, 2003, “
Stiffness Characteristics and Inter-Fragmentary Displacements with Different Hybrid External Fixators
,”
Clin. Biomech.
,
18
, pp.
166
172
.
26.
Dirschl
,
D. R.
, and
Obremskey
,
W. T.
, 2002, “
Mechanical Strength and Wear of Used EBI External Fixators
,”
Orthopedics
0147-7447,
25
, pp.
1059
1062
.
27.
Johnson
,
W. D.
, and
Fischer
,
D. A.
, 1983, “
Skeletal Stabilization with a Multiplane External Fixation Device: Biomechanical Evaluation and Finite Element Model
,”
Clin. Orthop. Relat. Res.
0009-921X,
180
, pp.
34
43
.
28.
Shahar
,
R.
, 2000, “
Relative Stiffness and Stress of Type I and Type II External Fixators: Acrylic Versus Stainless-Steel Connecting Bars A Theoretical Approach
,”
Vet. Surg.
0161-3499,
29
, pp.
59
69
.
29.
Lauer
,
S. K.
,
Aron
,
D. N.
, and
Evans
,
M. D.
, 2000, “
Finite Element Method Evaluation: Articulations and Diagonals in an 8-pin Type 1B External Skeletal Fixator
,”
Vet. Surg.
0161-3499,
29
, pp.
28
37
.
30.
Radke
,
H.
,
Aron
,
D. N.
,
Applewhite
,
A.
, and
Zhang
,
G.
, 2006, “
Biomechanical Analysis of Unilateral External Skeletal Fixators Combined with IM-Pin and Without IM-Pin Using Finite-Element Method
,”
Vet. Surg.
0161-3499,
35
, pp.
15
23
.
31.
Koo
,
T. K.
,
Chao
,
E. Y.
, and
Mak
,
A. F.
, 2005, “
Fixation Stiffness of Dynafix Uilateral External Fixator in Neutral and Non-neutral Configurations
,”
Biomed. Mater. Eng.
0959-2989,
15
, pp.
433
444
.
32.
Augat
,
A.
,
Burger
,
J.
,
Schorlemmer
,
S.
,
Peraus
,
M.
,
Henke
,
T.
, and
Claes
,
L.
, 2003, “
Shear Movement at the Fracture Site Delays Healing in Diaphyseal Fracture Model
,”
J. Orthop. Res.
0736-0266,
21
, pp.
1011
1017
.
33.
Langhaar
,
H. L.
, 1962,
Energy Methods in Applied Mechanics
, Chap. 4,
Wiley
, New York.
34.
Shigley
,
J. E.
, 1986,
Mechanical Engineering Design
,
1st Metric ed.
,
McGraw–Hill
, New York, pp.
113
116
.
35.
Popov
,
E. P.
, 1968,
Introduction to Mechanics of Solids
,
Prentice–Hall
, Engelwood Cliffs, N.J., Chap. 13.
36.
Beer
,
F. P.
, and
Johnston
,
E. R.
Jr.
, 1987,
Mechanics of Materials
,
SI Metric ed.
,
McGraw–Hill
, New York, Chap. 10.
37.
Hartog
,
J. P. D.
, 1987,
Advanced Strength of Materials
,
Dover
, New York, Chap. 7.
38.
Meirovitch
,
L.
, 1967,
Analytical Methods in Vibrations
,
Macmillan
, London, UK, Chap. 1.
39.
Pugh
,
K. J.
,
Wolinsky
,
P. R.
,
Dawson
,
J. M.
, and
Stahlman
,
G. C.
, 1999, “
The Biomechanics of Hybrid External Fixation
,”
J. Orthop. Trauma
0890-5339,
13
, pp.
20
26
.
40.
Pugh
,
K. J.
,
Wolinsky
,
P. R.
,
Pienkowski
,
D.
,
Banit
,
D.
, and
Dawson
,
J. M.
, 1999, “
Comparative Biomechanics of Hybrid External Fixation
,”
J. Orthop. Trauma
0890-5339,
13
, pp.
418
425
.
41.
Drijber
,
F. L. I. P.
,
Finlay
,
J. B.
, and
Dempsey
,
A. J.
, 1992, “
Evaluation of Linear Finite-Element Analysis Models’ Assumptions for External Fixation Devices
,”
J. Biomech.
0021-9290,
25
, pp.
849
855
.
42.
Gülşen
,
M.
,
Akçalı
,
İ. D.
,
Tosun
,
H.
, and
Tan
,
İ.
, 1993, “
Theoretical and Experimental Analysis of the Multi-Half-Pin Spatial External Fixation System
,”
Proceedings of the 6th General Meeting of Societe Internationale de Chirurgie Ortopedique et de Traumatologie
, Seoul, S. Korea, 28 August–3 September 1993, p.
252
.
43.
Gülşen
,
M.
,
Akçalı
,
İ. D.
, and
Mutlu
,
H.
, 1991, “
Analysis of the Mechanical Behavior of a Spatial Half-Frame External Fixator
,”
Proceedings of the 12th National Congress of Orthopaedics and Traumatology
, Kusadasi, Turkey (in Turkish), 21–24 April 1991, pp.
464
468
.
44.
Mutlu
,
H.
,
Akçalı
,
İ. D.
,
Gülşen
,
M.
, and
Tosun
,
H.
, 1994, “
An Analytical and Experimental Investigation of Lateral Deformations of an External Fixator
,”
Prooceedings of the 6th International Congress of Machine Design and Manufacturing
, Ankara, Turkey (in Turkish), 21–23 September 1996, pp.
553
563
.
45.
Kim
,
Y. H.
,
Inoue
,
N.
, and
Chao
,
E. Y. S.
, 2002, “
Kinematic Simulation of Fracture Reduction and Bone Deformity Correction Under Unilateral External Fixation
,”
J. Biomech.
0021-9290,
35
, pp.
1047
1058
.
46.
Mutlu
,
H.
,
Akçalı
,
İ. D.
, and
Gülşen
,
M.
, 2006, “
A Mathematical Model for the Use of a Gough-Stewart Platform Mechanism as a Fixator
,”
J. Eng. Math.
0022-0833,
54
, pp.
119
143
.
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