The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150Nmm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.

1.
Goodship
,
A. E.
,
Watkins
,
P. E.
,
Rigby
,
H. S.
, and
Kenwright
,
J.
, 1993, “
The Role of Fixator Frame Stiffness in the Control of Fracture Healing. An Experimental Study
,”
J. Biomech.
0021-9290,
26
(
9
), pp.
1027
1035
.
2.
Chao
,
E. Y. S.
,
Aro
,
H. T.
,
Lewallen
,
D. G.
, and
Kelly
,
P. J.
, 1989, “
The Effect of Rigidity on Fracture Healing in External Fixation
,”
Clin. Orthop. Relat. Res.
0009-921X,
241
, pp.
24
35
.
3.
Wu
,
J. J.
,
Shyr
,
H. S.
,
Chao
,
E. Y.
, and
Kelly
,
P. J.
, 1984, “
Comparison of Osteotomy Healing Under External Fixation Devices With Different Stiffness Characteristics
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355, Vol.
66
, pp.
1258
1264
.
4.
Klein
,
P.
,
Schell
,
H.
,
Streitparth
,
F.
,
Heller
,
M.
,
Kassi
,
J. P.
,
Kandziora
,
F.
,
Bragulla
,
H.
,
Haas
,
N. P.
, and
Duda
,
G. N.
, 2003, “
The Initial Phase of Fracture Healing is Specifically Sensitive to Mechanical Conditions
,”
J. Orthop. Res.
0736-0266,
21
(
4
), pp.
662
669
.
5.
Augat
,
P.
,
Margevicious
,
K.
,
Simon
,
J.
,
Wolf
,
S.
,
Suger
,
G.
, and
Claes
,
L.
, 1998, “
Local Tissue Properties in Bone Healing: Influence of Size and Stability of the Osteotomy Gap
,”
J. Orthop. Res.
0736-0266,
16
, pp.
475
481
.
6.
McKibbin
,
B.
, 1978, “
The Biology of Fracture Healing in Long Bones
,”
J. Bone Jt. Surg., Br. Vol.
0301-620X, Vol.
60B
(
2
), pp.
150
162
.
7.
Claes
,
L.
,
Heigele
,
C. A.
,
Neidlinger-Wilke
,
C.
,
Kaspar
,
D.
,
Seidl
,
W.
,
Margevicius
,
K.
, and
Augat
,
P.
, 1998, “
Effects of Mechanical Factors on the Fracture Healing Process
,”
Clin. Orthop. Relat. Res.
0009-921X,
355S
, pp.
132
147
.
8.
Goodship
,
A. E.
, 1992, “
Mechanical Stimulus to Bone
,”
Ann. Rheum. Dis.
0003-4967,
51
, pp.
4
6
.
9.
Claes
,
L.
,
Augat
,
P.
,
Suger
,
G.
, and
Wilke
,
H. J.
, 1997, “
Influence of Size and Stability of the Osteotomy Gap on the Success of Fracture Healing
,”
J. Orthop. Res.
0736-0266,
15
(
4
), pp.
577
584
.
10.
Lacroix
,
D.
, and
Prendergast
,
P. J.
, 2002, “
A Mechano-Regulation Model for Tissue Differentiation During Fracture Healing: Analysis of Gap Size and Loading
,”
J. Biomech.
0021-9290,
35
, pp.
1163
1171
.
11.
Kuiper
,
J. H.
,
Ashton
,
B. A.
, and
Richardson
,
J. B.
, 2000, “
Computer Simulation of Fracture Callus Formation and Stiffness Restoration
,”
Proc. Proc. 12th Europ. Soc. Biomech
,
P. J.
Prendergast
,
T. C.
Lee
, and
A. J.
Carr
, eds., p.
61
.
12.
Carter
,
D. R.
,
Beaupré
,
G. S.
,
Giori
,
N. J.
, and
Helms
,
J. A.
, 1998, “
Mechanobiology of Skeletal Regeneration
,”
Clin. Orthop. Relat. Res.
0009-921X,
355S
, pp.
41
55
.
13.
Claes
,
L. E.
, and
Heigele
,
C. A.
, 1999, “
Magnitudes of Local Stress and Strain Along Bony Surfaces Predict the Course and Type of Fracture Healing
,”
J. Biomech.
0021-9290,
32
, pp.
255
266
.
14.
Gardner
,
T. N.
,
Stoll
,
T.
,
Marks
,
L.
,
Mishra
,
S.
, and
Tate
,
M. K.
, 2000, “
The Influence of Mechanical Stimulus on the Pattern of Tissue Differentiation in a Long Bone Fracture—an FEM Study
,”
J. Biomech.
0021-9290,
33
, pp.
415
425
.
15.
Bailón-Plaza
,
A.
, and
van der Meulen
,
M. C.
, 2003, “
Beneficial Effects of Moderate, Early Loading and Adverse Effects of Delayed or Excessive Loading on Bone Healing
,”
J. Biomech.
0021-9290,
36
(
8
), pp.
1069
1077
.
16.
Ament
,
C.
, and
Hofer
,
E. P.
, 2000, “
A Fuzzy Logic Model of Fracture Healing
,”
J. Biomech.
0021-9290,
33
, pp.
961
968
.
17.
Isaksson
,
H.
,
Wilson
,
W.
,
van Donkelaar
,
C. C.
,
Huiskes
,
R.
, and
Ito
,
K.
, “
Comparison of Biophysical Stimuli for Mechano-Regulation of Tissue Differentiation During Fracture Healing
,”
J. Biomech.
0021-9290, DOI 10.1016/j.jbiomech.2005.01.037.
18.
Prendergast
,
P. J.
,
Huiskes
,
R.
, and
Soballe
,
K.
, 1997, “
Biophysical Stimuli on Cells During Tissue Differentiation at Implant Interfaces
,”
J. Biomech.
0021-9290,
6
, pp.
539
548
.
19.
García-Aznar
,
J.
,
Kuiper
,
J.
,
Doblaré
,
M.
, and
Richardson
,
J.
, “
Computational Simulation of Fracture Healing.
,”
Proceedings of the 13th Conference of European Society of Biomechanics
,
Wroclaw, Poland
, pp.
394
395
.
20.
Gómez-Benito
,
M. J.
,
García-Aznar
,
J. M.
,
Kuiper
,
J. H.
, and
Doblaré
,
M.
, 2005, “
Influence of Fracture Gap Size on the Pattern of Long Bone Healing: A Computational Study
,”
J. Theor. Biol.
0022-5193,
235
(
1
), pp.
105
119
.
21.
Kaplan
,
S. J.
,
Hayes
,
W. C.
,
Mudan
,
P.
,
Lelli
,
J. L.
, and
White
,
A. A.
, 1985, “
Monitoring the Healing of a Tibial Osteotomy in the Rabbit Treated With External Fixation
,”
J. Orthop. Res.
0736-0266,
3
(
3
), pp.
325
330
.
22.
Prat
,
J.
,
Juan
,
J.
,
Vera
,
P.
,
Hoyos
,
J.
,
Dejoz
,
R.
,
Peris
,
J. L.
,
Sanchez-Lacuesta
,
J.
, and
Comin
,
M.
, 1994, “
Load Transmission Through the Callus Site With External Fixation Systems: Theoretical and Experimental Analysis
,”
J. Biomech.
0021-9290,
27
(
4
), pp.
469
478
.
23.
Bishop
,
N. E.
,
Tami
,
I.
,
Schneider
,
E.
, and
Ito
,
K.
, 2002, “
In Vivo Comparison of Early Fracture Healing Under Deviatoric and Volumetric Deformation
,”
Acta of Bioengin. Biomech.
,
4
(
S1
), pp.
754
755
.
24.
Kelly
,
D. J.
, and
Prendergast
,
P. J.
, 2005, “
Mechano-Regulation of Stem Cell Differentiation and Tissue Regeneration in Osteochondral Defects
,”
J. Biomech.
0021-9290,
38
(
7
), pp.
1413
1422
.
25.
Lacroix
,
D.
, and
Prendergast
,
P. J.
, 2002, “
Three-Dimensional Simulation of Fracture Repair in the Human Tibia
,”
Comput. Methods Biomech. Biomed. Eng.
1025-5842,
5
(
5
), pp.
369
376
.
26.
Simon
,
U.
,
Augat
,
P.
,
Forster
,
E.
,
Breuer
,
H.
, and
Claes
,
L.
, 2004, “
Fracture Healing Under Non-Axisymmetrical Loading Conditions
,”
Proc. Sixth International Symposium on Computer Methods in Biomechanics and Biomedical Engineering
.
27.
Postacchini
,
F.
,
Gumina
,
S.
,
Perugia
,
D.
, and
De Martino
,
C.
, 1995, “
Early Fracture Callus in the Diaphysis of Human Long Bones
,”
Clin. Orthop. Relat. Res.
0009-921X,
310
, pp.
218
228
.
28.
Bland
,
Y. S.
,
Critchlow
,
M. A.
, and
E.
,
A. D.
, 1999, “
The Expression of the Fibrillar Collagen Genes During Fracture Healing
,”
Histochem. J.
0018-2214,
31
, pp.
797
809
.
29.
Wilsman
,
N. J.
,
Farnum
,
C. E.
,
Leiferman
,
E. M.
,
Fry
,
M.
, and
Barreto
,
C.
, 1996, “
Differential Growth by Growth Plates as a Function of Multiple Parameters of Chondrocytic Kinetics
,”
J. Orthop. Res.
0736-0266,
14
, pp.
927
936
.
30.
Beaupré
,
G. S.
,
Orr
,
T. E.
, and
Carter
,
D. R.
, 1990, “
An Approach for Time-Dependent Bone Modeling and Remodeling—Theoretical Development
,”
J. Orthop. Res.
0736-0266,
8
, pp.
551
651
.
31.
Beaupré
,
G. S.
,
Orr
,
T. E.
, and
Carter
,
D. R.
, 1990, “
An Approach for Time-Dependent Bone Modeling and Remodeling—Application: A Preliminary Remodeling Simulation
,”
J. Orthop. Res.
0736-0266,
8
, pp.
662
670
.
32.
Hibbit, Karlsson and Sorensen, Inc.
, 2002,
Theory Manual, v. 6.3
HKS Inc. Pawtucket, RI, USA.
33.
Mücke
,
E.
, 1993, “
Shapes and Implementations in Three-Dimensional Geometry
,” Ph.D. thesis, University of Illinois at Urbana-Champaign.
34.
Augat
,
P.
,
Burger
,
J.
,
Schorlemmer
,
S.
,
Henke
,
T.
,
Peraus
,
M.
, and
Claes
,
L.
, 2003, “
Shear Movement at the Fracture Site Delays Healing in a Diaphyseal Fracture Model
,”
J. Orthop. Res.
0736-0266,
21
, pp.
1011
1017
.
35.
Einhorn
,
T. A.
, 1998, “
The Cell and Molecular Biology of Fracture Healing
,”
Clin. Orthop. Relat. Res.
0009-921X,
355
, pp.
S7
S21
.
36.
Duda
,
G. N.
,
Eckert-Hübner
,
K.
,
Sokiranski
,
R.
,
Kreutner
,
A.
,
Miller
,
R.
, and
Claes
,
L.
, 1998, “
Analysis of Inter-Fragmentary Movement as a Function of Musculoskeletal Loading Conditions in Sheep
,”
J. Biomech.
0021-9290,
31
(
3
), pp.
201
210
.
37.
Yang
,
L.
,
Nayagam
,
S.
, and
Saleh
,
M.
, 2003, “
Stiffness Characteristics and Inter-Fragmentary Displacements With Different Hybrid External Fixators
,”
Clin. Biomech. (Bristol, Avon)
0268-0033,
18
(
2
), pp.
166
172
.
38.
Carpenter
,
J. E.
,
Hipp
,
J. A.
,
Gerhart
,
T. N.
,
Rudman
,
C. G.
,
Hayes
,
W. C.
, and
Trippel
,
S. B.
, 1992, “
Failure of Growth Hormone to Alter Biomechanics of Fracture-Healing in a Rabbit Model
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355,
74A
(
3
), pp.
359
367
.
39.
Jenkis
,
P.
, and
Nokes
,
L.
, 1994, “
The Use of Gauges to Measure Bone Fracture Healing. A Review
,”
Curr. Orthop.
,
8
, pp.
116
118
.
40.
Crelin
,
E. S.
,
White
,
A. A.
,
Panjabi
,
M. M.
, and
Southwick
,
W. O.
, 1978, “
Microscopic Changes in Fractures Rabbit Tibias
,”
Conn Med.
0010-6178,
42
(
9
), pp.
561
569
.
41.
Ashhurst
,
D. E.
, 1986, “
The Influence of Mechanical Stability on the Healing of Experimental Fractures in the Rabbit: A Microscopical Study
,” Ser. B,
313
, pp.
271
302
.
42.
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
.
43.
Williams
,
E. A.
,
Rand
,
J. A.
,
An
,
K. N.
,
Chao
,
E. Y. S.
, and
Kelly
,
P. J.
, 1989, “
The Early Healing of Tibial Osteotomies Stabilized by One-Plane and Two-Plane External Fixation
,”
J. Bone Jt. Surg., Am. Vol.
0021-9355, Vol.
69
, pp.
355
365
.
44.
Goodship
,
A. E.
,
Lanyon
,
L. E.
,
Nicopoulos
,
A.
, and
O’Connor
,
J. A.
, 1978, “
A Technique for Investigating the Response of Bone to Changes in its Mechanical Environment
,”
J. Physiol. (London)
0022-3751,
277
, p.
39
.
45.
Gardner
,
T. N.
, and
Mishra
,
S.
, 2003, “
The Biomechanical Environment of a Bone Fracture and its Influence Upon the Morphology of Healing
,”
Med. Eng. Phys.
1350-4533,
25
, pp.
455
464
.
46.
Martin
,
R. B.
,
Burr
,
D. B.
, and
Sharkey
,
N. A.
, 1998,
Skeletal Tissue Mechanics
,
Springer-Verlarg
,
New York
.
47.
Griffin
,
L. V.
,
Gibeling
,
J. C.
,
Martin
,
R.
,
Gibson
,
V.
, and
Stover
,
S.
, 1997, “
Model of Flexural Fatigue Damage Accumulation for Cortical Bone
,”
J. Orthop. Res.
0736-0266,
15
(
4
), pp.
607
614
.
48.
Sasaki
,
N.
, and
Odajima
,
S.
, 1996, “
Elongation Mechanism of Collagen Fibrils and Force-Strain Relations of Tendon at Each Level of Structural Hierarchy
,”
J. Biomech.
0021-9290,
29
, pp.
1131
1136
.
49.
Farquhar
,
T.
,
Dawson
,
P.
, and
Torzilli
,
P.
, 1990, “
A Microstructural Model for the Anisotropic Drained Stiffness of Articular Cartilage
,”
ASME J. Biomech. Eng.
0148-0731,
112
, pp.
414
425
.
50.
Simha
,
N. K.
,
Fedewa
,
M.
,
Leo
,
P. H.
,
Lewis
,
J. L.
, and
Oegema
,
T.
, 1999, “
A Composites Theory Predicts the Dependence of Stiffness of Cartilage Culture Tissues on Collagen Volume Fraction
,”
J. Biomech.
0021-9290,
32
, pp.
503
509
.
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