Early weight bearing appears to enhance bone fracture healing under Ilizarov circular fixators (ICFs). However, the role of early weight bearing in the healing process remains unclear. This study aims to provide insights into the effects of early weight bearing on healing of bone fractures stabilized with ICFs, with the aid of mathematical modeling. A computational model of fracture site was developed using poro-elastic formulation to simulate the transport of mesenchymal stem cells (MSCs), fibroblasts, chondrocytes, osteoblasts, osteogenic growth factor (OGF), and chondrogenic growth factor (CGF) and MSC differentiation during the early stage of healing, under various combinations of fracture gap sizes (GS), ICF wire pretension forces, and axial loads. 1 h of physiologically relevant cyclic axial loading followed by 23 h of rest in the post-inflammation phase (i.e., callus with granulation tissue) was simulated. The results show that physiologically relevant dynamic loading could significantly enhance cell and growth factor concentrations in the fracture site in a time and spatially dependent manner. 1 h cyclic loading (axial load with amplitude, PA, of 200 N at 1 Hz) increased the content of chondrocytes up to 37% (in all zones of callus), CGF up to 28% (in endosteal and periosteal callus) and OGF up to 50% (in endosteal and cortical callus) by the end of the 24 h period simulated. This suggests that the synergistic effect of dynamic loading-induced advective transport and mechanical stimuli due to early weight bearing is likely to enhance secondary healing. Furthermore, the study suggests that relatively higher PA values or lower ICF wire pretension forces or smaller GS could result in increased chondrocyte and GF content within the callus.

References

References
1.
Schwartsman
,
V.
,
Martin
,
S. N.
,
Ronquist
,
R. A.
, and
Schwartsman
,
R.
,
1992
, “
The Ilizarov Alternative
,”
Clin. Orthop. Relat. Res.
,
278
, pp.
207
216
.https://journals.lww.com/clinorthop/Abstract/1992/05000/The_Ilizarov_Alternative.33.aspx
2.
Tucker
,
H. L.
,
Kendra
,
J. C.
, and
Kinnebrew
,
T. E.
,
1992
, “
Management of Unstable Open and Closed Tibial Fractures Using the Ilizarov Method
,”
Clin. Orthop. Relat. Res.
,
280
, pp.
125
135
.https://journals.lww.com/clinorthop/Abstract/1992/07000/Management_of_Unstable_Open_and_Closed_Tibial.15.aspx
3.
Dendrinos
,
G. K.
,
Kontos
,
S.
,
Katsenis
,
D.
, and
Dalas
,
A.
,
1996
, “
Treatment of High-Energy Tibial Plateau Fractures by the Ilizarov Circular Fixator
,”
J. Bone Jt. Surg. Br.
,
78
(
5
), pp.
710
717
.https://online.boneandjoint.org.uk/doi/abs/10.1302/0301-620X.78B5.0780710
4.
Fragomen
,
A. T.
, and
Rozbruch
,
S. R.
,
2007
, “
The Mechanics of External Fixation
,”
HSS J.
,
3
(
1
), pp.
13
29
.
5.
Larsson
,
S.
,
Kim
,
W.
,
Caja
,
V. L.
,
Egger
,
E. L.
,
Inoue
,
N.
, and
Chao
,
E. Y.
,
2001
, “
Effect of Early Axial Dynamization on Tibial Bone Healing: A Study in Dogs
,”
Clin. Orthop. Relat. Res.
,
388
, pp.
240
251
.
6.
Epari
,
D. R.
,
Taylor
,
W. R.
,
Heller
,
M. O.
, and
Duda
,
G. N.
,
2006
, “
Mechanical Conditions in the Initial Phase of Bone Healing
,”
Clin. Mech.
,
21
(
6
), pp.
646
655
.https://www.sciencedirect.com/science/article/pii/S0268003306000209
7.
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.
,
21
(
4
), pp.
662
669
.
8.
Miramini
,
S.
,
Zhang
,
L.
,
Richardson
,
M.
,
Mendis
,
P.
,
Oloyede
,
A.
, and
Ebeling
,
P.
,
2016
, “
The Relationship Between Interfragmentary Movement and Cell Differentiation in Early Fracture Healing Under Locking Plate Fixation
,”
Australas. Phys. Eng. Sci. Med.
,
39
(
1
), pp.
123
133
.
9.
Goodship
,
A.
, and
Kenwright
,
J.
,
1985
, “
The Influence of Induced Micromovement Upon the Healing of Experimental Tibial Fractures
,”
Bone Jt. J.
,
67
(
4
), pp.
650
655
.https://online.boneandjoint.org.uk/doi/abs/10.1302/0301-620X.67B4.4030869
10.
Witt
,
F.
,
Duda
,
G. N.
,
Bergmann
,
C.
, and
Petersen
,
A.
,
2014
, “
Cyclic Mechanical Loading Enables Solute Transport and Oxygen Supply in Bone Healing: An In Vitro Investigation
,”
Tissue Eng. Part A
,
20
(
3–4
), pp.
486
493
.https://www.liebertpub.com/doi/abs/10.1089/ten.TEA.2012.0678
11.
O'Hara
,
B.
,
Urban
,
J.
, and
Maroudas
,
A.
,
1990
, “
Influence of Cyclic Loading on the Nutrition of Articular Cartilage
,”
Ann. Rheum. Dis.
,
49
(
7
), pp.
536
539
.
12.
Mauck
,
R. L.
,
Hung
,
C. T.
, and
Ateshian
,
G. A.
,
2003
, “
Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering
,”
J. Biomech. Eng.
,
125
(
5
), pp.
602
614
.http://biomechanical.asmedigitalcollection.asme.org/article.aspx?articleid=1410679
13.
Mavčič
,
B.
, and
Antolič
,
V.
,
2012
, “
Optimal Mechanical Environment of the Healing Bone Fracture/Osteotomy
,”
Int. Orthop.
,
36
(
4
), pp.
689
695
.
14.
Gardner
,
M. J.
,
Ricciardi
,
B. F.
,
Wright
,
T. M.
,
Bostrom
,
M. P.
, and
van der Meulen
,
M. C.
,
2008
, “
Pause Insertions During Cyclic In Vivo Loading Affect Bone Healing
,”
Clin. Orthop. Relat. Res.
,
466
(
5
), pp.
1232
1238
.
15.
Watson
,
M.
,
Mathias
,
K.
,
Maffulli
,
N.
,
Hukins
,
D.
, and
Shepherd
,
D.
,
2007
, “
Finite Element Modelling of the Ilizarov External Fixation System
,”
Proc. Inst. Mech. Eng., Part H
,
221
(
8
), pp.
863
871
.
16.
Lacroix
,
D.
, and
Prendergast
,
P.
,
2002
, “
A Mechano-Regulation Model for Tissue Differentiation During Fracture Healing: Analysis of Gap Size and Loading
,”
J. Biomech.
,
35
(
9
), pp.
1163
1171
.
17.
Isaksson
,
H.
,
Van Donkelaar
,
C. C.
,
Huiskes
,
R.
, and
Ito
,
K.
,
2006
, “
Corroboration of Mechanoregulatory Algorithms for Tissue Differentiation During Fracture Healing: Comparison With In Vivo Results
,”
J. Orthop. Res.
,
24
(
5
), pp.
898
907
.
18.
Duda
,
G. N.
,
Bartmeyer
,
B.
,
Sporrer
,
S.
,
Taylor
,
W. R.
,
Raschke
,
M.
, and
Haas
,
N. P.
,
2003
, “
Does Partial Weight Bearing Unload a Healing Bone in External Ring Fixation?
,”
Langenbeck's Arch. Surg.
,
388
(
5
), pp.
298
304
.
19.
Duda
,
G. N.
,
Sollmann
,
M.
,
Sporrer
,
S.
,
Hoffmann
,
J. E.
,
Kassi
,
J.-P.
,
Khodadadyan
,
C.
, and
Raschke
,
M.
,
2002
, “
Interfragmentary Motion in Tibial Osteotomies Stabilized With Ring Fixators
,”
Clin. Orthop. Relat. Res.
,
396
, pp.
163
172
.
20.
Duda
,
G. N.
,
Sporrer
,
S.
,
Sollmann
,
M.
,
Hoffmann
,
J. E.
,
Kassi
,
J.-P.
,
Khodadadyan
,
C.
, and
Raschke
,
M.
,
2003
, “
Interfragmentary Movements in the Early Phase of Healing in Distraction and Correction Osteotomies Stabilized With Ring Fixators
,”
Langenbeck's Arch. Surg.
,
387
(
11–12
), pp.
433
440
.https://link.springer.com/article/10.1007/s00423-002-0340-8
21.
Miramini
,
S.
,
Zhang
,
L.
,
Richardson
,
M.
,
Mendis
,
P.
, and
Ebeling
,
P.
,
2016
, “
Influence of Fracture Geometry on Bone Healing Under Locking Plate Fixations: A Comparison Between Oblique and Transverse Tibial Fractures
,”
Med. Eng. Phys.
,
38
(
10
), pp.
1100
1108
.
22.
Aronson
,
J.
,
Johnson
,
E.
, and
Harp
,
J. H.
,
1989
, “
Local Bone Transportation for Treatment of Intercalary Defects by the Ilizarov Technique: Biomechanical and Clinical Considerations
,”
Clin. Orthop. Relat. Res.
,
243
, pp.
71
79
.https://journals.lww.com/clinorthop/Abstract/1989/06000/Local_Bone_Transportation_for_Treatment_of.11.aspx
23.
Zhang
,
L.
,
Miramini
,
S.
,
Smith
,
D. W.
,
Gardiner
,
B. S.
, and
Grodzinsky
,
A. J.
,
2015
, “
Time Evolution of Deformation in a Human Cartilage Under Cyclic Loading
,”
Ann. Biomed. Eng.
,
43
(
5
), pp.
1166
1177
.
24.
Barker
,
M.
, and
Seedhom
,
B.
,
2001
, “
The Relationship of the Compressive Modulus of Articular Cartilage With Its Deformation Response to Cyclic Loading: Does Cartilage Optimize Its Modulus so as to Minimize the Strains Arising in It Due to the Prevalent Loading Regime?
,”
Rheumatology
,
40
(
3
), pp.
274
284
.
25.
Miramini
,
S.
,
Zhang
,
L.
,
Richardson
,
M.
,
Pirpiris
,
M.
,
Mendis
,
P.
,
Oloyede
,
K.
, and
Edwards
,
G.
,
2015
, “
Computational Simulation of the Early Stage of Bone Healing Under Different Configurations of Locking Compression Plates
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
8
), pp.
900
913
.
26.
Peiffer
,
V.
,
Gerisch
,
A.
,
Vandepitte
,
D.
,
Van Oosterwyck
,
H.
, and
Geris
,
L.
,
2011
, “
A Hybrid Bioregulatory Model of Angiogenesis During Bone Fracture Healing
,”
Mech. Model. Mechanobiol.
,
10
(
3
), pp.
383
395
.
27.
Geris
,
L.
,
Gerisch
,
A.
,
Vander Sloten
,
J.
,
Weiner
,
R.
, and
Van Oosterwyck
,
H.
,
2008
, “
Angiogenesis in Bone Fracture Healing: A Bioregulatory Model
,”
J. Theor. Biol.
,
251
(
1
), pp.
137
158
.
28.
McCartney
,
W.
,
Mac Donald
,
B.
, and
Hashmi
,
M.
,
2005
, “
Comparative Performance of a Flexible Fixation Implant to a Rigid Implant in Static and Repetitive Incremental Loading
,”
J. Mater. Process. Technol.
,
169
(
3
), pp.
476
484
.
29.
Zhang
,
L.
,
Gardiner
,
B. S.
,
Smith
,
D. W.
,
Pivonka
,
P.
, and
Grodzinsky
,
A. J.
,
2008
, “
IGF Uptake With Competitive Binding in Articular Cartilage
,”
J. Biol. Syst.
,
16
(
2
), pp.
175
195
.
30.
Gardiner
,
B.
,
Smith
,
D.
,
Pivonka
,
P.
,
Grodzinsky
,
A.
,
Frank
,
E.
, and
Zhang
,
L.
,
2007
, “
Solute Transport in Cartilage Undergoing Cyclic Deformation
,”
Comput. Methods Biomech. Biomed. Eng.
,
10
(
4
), pp.
265
278
.
31.
Bailon-Plaza
,
A.
, and
Van Der Meulen
,
M. C.
,
2001
, “
A Mathematical Framework to Study the Effects of Growth Factor Influences on Fracture Healing
,”
J. Theor. Biol.
,
212
(
2
), pp.
191
209
.
32.
Isaksson
,
H.
,
van Donkelaar
,
C. C.
,
Huiskes
,
R.
, and
Ito
,
K.
,
2008
, “
A Mechano-Regulatory Bone-Healing Model Incorporating Cell-Phenotype Specific Activity
,”
J. Theor. Biol.
,
252
(
2
), pp.
230
246
.
33.
Zhang
,
L.
,
Miramini
,
S.
,
Richardson
,
M.
,
Mendis
,
P.
, and
Ebeling
,
P.
,
2017
, “
The Role of Impairment of Mesenchymal Stem Cell Function in Osteoporotic Bone Fracture Healing
,”
Australas. Phys. Eng. Sci. Med.
,
40
(
3
), pp.
603
610
.
34.
Andreykiv
,
A.
,
Van Keulen
,
F.
, and
Prendergast
,
P.
,
2008
, “
Simulation of Fracture Healing Incorporating Mechanoregulation of Tissue Differentiation and Dispersal/Proliferation of Cells
,”
Mech. Model. Mechanobiol.
,
7
(
6
), pp.
443
461
.
35.
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.
,
36
(
8
), pp.
1069
1077
.
36.
Huiskes
,
R.
,
Van Driel
,
W.
,
Prendergast
,
P.
, and
Søballe
,
K.
,
1997
, “
A Biomechanical Regulatory Model for Periprosthetic Fibrous-Tissue Differentiation
,”
J. Mater. Sci.: Mater. Med.
,
8
(
12
), pp.
785
788
.
37.
Prendergast
,
P.
,
Huiskes
,
R.
, and
Søballe
,
K.
,
1997
, “
Biophysical Stimuli on Cells During Tissue Differentiation at Implant Interfaces
,”
J. Biomech.
,
30
(
6
), pp.
539
548
.
38.
Zhang
,
L.
,
Gardiner
,
B. S.
,
Smith
,
D. W.
,
Pivonka
,
P.
, and
Grodzinsky
,
A.
,
2007
, “
The Effect of Cyclic Deformation and Solute Binding on Solute Transport in Cartilage
,”
Arch. Biochem. Biophys.
,
457
(
1
), pp.
47
56
.
39.
Isaksson
,
H.
,
Wilson
,
W.
,
van Donkelaar
,
C. C.
,
Huiskes
,
R.
, and
Ito
,
K.
,
2006
, “
Comparison of Biophysical Stimuli for Mechano-Regulation of Tissue Differentiation During Fracture Healing
,”
J. Biomech.
,
39
(
8
), pp.
1507
1516
.
40.
Zhang
,
G.
,
2004
, “
Geometric and Material Nonlinearity in Tensioned Wires of an External Fixator
,”
Clin. Mech.
,
19
(
5
), pp.
513
518
.https://www.sciencedirect.com/science/article/pii/S0268003304000233
41.
Zamani
,
A.
, and
Oyadiji
,
S.
,
2009
, “
Analytical Modelling of Kirschner Wires in Ilizarov Circular External Fixator as Pretensioned Slender Beams
,”
J. R. Soc. Interface
,
6
(
32
), pp.
243
256
.
42.
Antoci
,
V.
,
Voor
,
M. J.
,
Antoci
,
V.
, and
Roberts
,
C. S.
,
2007
, “
Effect of Wire Tension on Stiffness of Tensioned Fine Wires in External Fixation: A Mechanical Study
,”
Am. J. Orthop.
,
36
(
9
), p.
473
.https://www.amjorthopedics.com/article/effect-wire-tension-stiffness-tensioned-fine-wires-external-fixation-mechanical-study
43.
Evans
,
R. C.
, and
Quinn
,
T. M.
,
2006
, “
Dynamic Compression Augments Interstitial Transport of a Glucose-Like Solute in Articular Cartilage
,”
Biophys. J.
,
91
(
4
), pp.
1541
1547
.
44.
Angele
,
P.
,
Yoo
,
J.
,
Smith
,
C.
,
Mansour
,
J.
,
Jepsen
,
K.
,
Nerlich
,
M.
, and
Johnstone
,
B.
,
2003
, “
Cyclic Hydrostatic Pressure Enhances the Chondrogenic Phenotype of Human Mesenchymal Progenitor Cells Differentiated In Vitro
,”
J. Orthop. Res.
,
21
(
3
), pp.
451
457
.
45.
Elder
,
S. H.
,
Kimura
,
J.
,
Soslowsky
,
L. J.
,
Lavagnino
,
M.
, and
Goldstein
,
S. A.
,
2000
, “
Effect of Compressive Loading on Chondrocyte Differentiation in Agarose Cultures of Chick Limb‐Bud Cells
,”
J. Orthop. Res.
,
18
(
1
), pp.
78
86
.
46.
Carroll
,
S.
,
Buckley
,
C.
, and
Kelly
,
D.
,
2014
, “
Cyclic Hydrostatic Pressure Promotes a Stable Cartilage Phenotype and Enhances the Functional Development of Cartilaginous Grafts Engineered Using Multipotent Stromal Cells Isolated From Bone Marrow and Infrapatellar Fat Pad
,”
J. Mech.
,
47
(
9
), pp.
2115
2121
. https://www.sciencedirect.com/science/article/pii/S0021929013006271
47.
Vinardell
,
T.
,
Rolfe
,
R. A.
,
Buckley
,
C. T.
,
Meyer
,
E. G.
,
Ahearne
,
M.
,
Murphy
,
P.
, and
Kelly
,
D. J.
,
2012
, “
Hydrostatic Pressure Acts to Stabilise a Chondrogenic Phenotype in Porcine Joint Tissue Derived Stem Cells
,”
Eur. Cell Mater.
,
23
(
23
), pp.
121
132
.
48.
Sakao
,
K.
,
Takahashi
,
K. A.
,
Arai
,
Y.
,
Inoue
,
A.
,
Tonomura
,
H.
,
Saito
,
M.
,
Yamamoto
,
T.
,
Kanamura
,
N.
,
Imanishi
,
J.
,
Mazda
,
O.
, and
Kubo
,
T.
,
2008
, “
Induction of Chondrogenic Phenotype in Synovium-Derived Progenitor Cells by Intermittent Hydrostatic Pressure
,”
Osteoarthritis Cartilage
,
16
(
7
), pp.
805
814
.
49.
Huang
,
C. Y. C.
,
Hagar
,
K. L.
,
Frost
,
L. E.
,
Sun
,
Y.
, and
Cheung
,
H. S.
,
2004
, “
Effects of Cyclic Compressive Loading on Chondrogenesis of Rabbit Bone‐Marrow Derived Mesenchymal Stem Cells
,”
Stem Cells
,
22
(
3
), pp.
313
323
.
50.
Claes
,
L.
,
Wilke
,
H.
,
Augat
,
P.
,
Rübenacker
,
S.
, and
Margevicius
,
K.
,
1995
, “
Effect of Dynamization on Gap Healing of Diaphyseal Fractures Under External Fixation
,”
Clin. Mech.
,
10
(
5
), pp.
227
234
.https://www.sciencedirect.com/science/article/pii/0268003395997998
51.
Claes
,
L.
,
Blakytny
,
R.
,
Göckelmann
,
M.
,
Schoen
,
M.
,
Ignatius
,
A.
, and
Willie
,
B.
,
2009
, “
Early Dynamization by Reduced Fixation Stiffness Does Not Improve Fracture Healing in a Rat Femoral Osteotomy Model
,”
J. Orthop. Res.
,
27
(
1
), pp.
22
27
.
52.
Glatt
,
V.
,
Miller
,
M.
,
Ivkovic
,
A.
,
Liu
,
F.
,
Parry
,
N.
,
Griffin
,
D.
,
Vrahas
,
M.
, and
Evans
,
C.
,
2012
, “
Improved Healing of Large Segmental Defects in the Rat Femur by Reverse Dynamization in the Presence of Bone Morphogenetic Protein-2
,”
J. Bone Jt. Surg..
,
94
(
22
), p.
2063
.
53.
Glatt
,
V.
,
Bartnikowski
,
N.
,
Quirk
,
N.
,
Schuetz
,
M.
, and
Evans
,
C.
,
2016
, “
Reverse Dynamization: Influence of Fixator Stiffness on the Mode and Efficiency of Large-Bone-Defect Healing at Different Doses of rhBMP-2
,”
J. Bone Jt. Surg..
,
98
(
8
), p.
677
.
54.
Tägil
,
M.
, and
Aspenberg
,
P.
,
1999
, “
Cartilage Induction by Controlled Mechanical Stimulation In Vivo
,”
J. Orthop. Res.
,
17
(
2
), pp.
200
204
.
55.
Lacroix
,
D.
,
Prendergast
,
P.
,
Li
,
G.
, and
Marsh
,
D.
,
2002
, “
Biomechanical Model to Simulate Tissue Differentiation and Bone Regeneration: Application to Fracture Healing
,”
Med. Biol. Eng. Comput.
,
40
(
1
), pp.
14
21
.
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