The periodontal ligament is the tissue that provides early tooth motion as a result of applied forces during orthodontic treatment: a force-displacement behavior characterized by an instantaneous displacement followed by a creep phase and a stress relaxation phase. Stress relaxation behavior is that which provides the long-term loading to and causes remodelling of the alveolar bone, which is responsible for the long-term permanent displacement of the tooth. In this study, the objective was to assess six viscoelastic models to predict stress relaxation behavior of rabbit periodontal ligament (PDL). Using rabbit stress relaxation data found in the literature, it was found that the modified superposition theory (MST) model best predicts the rabbit PDL behavior as compared to nonstrain-dependent and strain-dependent versions of the Burgers four-parameter and the five-parameter viscoelastic models, as well as predictions by Schapery's viscoelastic model. Furthermore, it is established that using a quadratic form for MST strain dependency provides more stable solutions than the cubic form seen in previous studies.

References

References
1.
Fill
,
T. S.
,
Carey
,
J. P.
,
Toogood
,
R. W.
, and
Major
,
P. W.
,
2011
, “
Experimentally Determined Mechanical Properties of, and Models for, the Periodontal Ligament: Critical Review of Current Literature
,”
J. Dent. Biomech.
,
10
, p.
312980
.10.4061/2011/312980
2.
Fill
,
T. S.
,
Toogood
,
R. W.
,
Major
,
P. W.
, and
Carey
,
J. P.
,
2012
, “
Analytically Determined Mechanical Properties of, and Models for the Periodontal Ligament: Critical Review of Literature
,”
J. Biomech.
,
45
, pp.
9
16
.10.1016/j.jbiomech.2011.09.020
3.
Proffit
,
W. R.
,
Fields
,
H. W.
, and
Sarver
,
D. M.
,
2007
,
Contemporary Orthodontics
,
Mosby Elsevier
,
St. Louis
.
4.
Jónsdóttir
,
S. H.
,
Giesen
,
E. B. W.
, and
Maltha
,
J. C.
,
2006
, “
Biomechanical Behaviour of the Periodontal Ligament of the Beagle Dog During the First 5 Hours of Orthodontic Force Application
,”
Eur. J. Orthod.
,
28
, pp.
547
552
.10.1093/ejo/cjl050
5.
Owman-Moll
,
P.
,
Kurol
,
J.
, and
Lundgren
,
D.
,
1995
, “
Continuous Versus Interrupted Continuous Orthodontic Force Related to Early Tooth Movement and Root Resorption
,”
Angle Orthod.
,
65
, pp.
395
401
.
6.
Bergomi
,
M.
,
Cugnoni
,
J.
,
Botsis
,
J.
,
Belser
,
U. C.
, and
Anselm Wiskott
,
H. W.
,
2010
, “
The Role of the Fluid Phase in the Viscous Response of Bovine Periodontal Ligament
,”
J. Biomech.
,
43
, pp.
1146
1152
.10.1016/j.jbiomech.2009.12.020
7.
Pietrzak
,
G.
,
Curnier
,
A.
,
Botsis
,
J.
,
Scherrer
,
S.
,
Wiskott
,
A.
, and
Belser
,
U.
,
2002
, “
A Nonlinear Elastic Model of the Periodontal Ligament and Its Numerical Calibration for the Study of Tooth Mobility
,”
Comput. Methods Biomech. Biomed. Eng.
,
5
, pp.
91
100
.10.1080/10255840290032117
8.
Embery
,
G.
,
1990
, “
An Update on the Biochemistry of the Periodontal Ligament
,”
Eur. J. Orthod.
,
12
, pp.
77
80
.10.1093/ejo/12.1.77
9.
Carvalho
,
L.
,
Moreira
,
R. A. S.
, and
Simões
,
J. A.
,
2006
, “
Application of a Vibration Measuring Technique to Evaluate the Dynamic Stiffness of Porcine Periodontal Ligament
,”
Technol. Health Care
,
14
, pp.
457
465
.
10.
Picton
,
D. C. A.
, and
Wills
,
D. J.
,
1978
, “
Viscoelastic Properties of the Periodontal Ligament and Mucous Membrane
,”
J. Prosthet. Dent.
,
40
, pp.
263
272
.10.1016/0022-3913(78)90031-8
11.
Moxham
,
B. J.
, and
Berkovitz
,
B. K. B.
,
1979
, “
The Effects of Axially-Directed Extrusive Loads on Movements of the Mandibular Incisor of the Rabbit
,”
Arch. Oral Biol.
,
24
, pp.
759
763
.10.1016/0003-9969(79)90036-0
12.
Pini
,
M.
,
Zysset
,
P.
,
Botsis
,
J.
, and
Contro
,
R.
,
2004
, “
Tensile and Compressive Behaviour of the Bovine Periodontal Ligament
,”
J. Biomech.
,
37
, pp.
111
119
.10.1016/S0021-9290(03)00234-3
13.
Dorow
,
C.
,
Krstin
,
N.
, and
Sander
,
F. G.
,
2003
, “
Determination of the Mechanical Properties of the Periodontal Ligament in a Uniaxial Tensional Experiment
,”
J. Orofac. Orthop.
,
64
, pp.
100
107
.10.1007/s00056-003-0225-7
14.
Slomka
,
N.
,
Vardimon
,
A. D.
,
Gefen
,
A.
,
Pilo
,
R.
,
Bourauel
,
C.
, and
Brosh
,
T.
,
2008
, “
Time-Related PDL: Viscoelastic Response During Initial Orthodontic Tooth Movement of a Tooth With Functioning Interproximal Contact-A Mathematical Model
,”
J. Biomech.
,
41
, pp.
1871
1877
.10.1016/j.jbiomech.2008.04.003
15.
Sopakayang
,
R.
, and
De Vita
,
R.
,
2011
, “
A Mathematical Model for Creep, Relaxation and Strain Stiffening in Parallel-Fibered Collagenous Tissues
,”
Med. Eng. Phys.
,
33
, pp.
1056
1063
.10.1016/j.medengphy.2011.04.012
16.
Nishihira
,
M.
,
Yamamoto
,
K.
,
Sato
,
Y.
,
Ishikawa
,
H.
, and
Natali
,
A. N.
,
2003
, “
Mechanics of Periodontal Ligament
,”
Dent. Biomech.
, pp.
20
34
.
17.
Nanda
,
R.
, and
Kuhlberg
,
A.
,
1997
, “
Principles of Biomechanics
,”
Biomechanics in Clinical Orthodontics
,
R.
Nanda
, ed.,
Saunders
,
Philadelphia
, pp.
1
20
.
18.
van Driel
,
W. D.
,
van Lecuwen
,
E. J.
,
von den Hoff
,
J. W.
,
Maltha
,
J. C.
, and
Kuijpers-Jagtman
,
A. M.
,
2000
, “
Time-Dependent Mechanical Behaviour of the Periodontal Ligament
,”
Proc. Inst. Mech. Eng. H
,
214
, pp.
497
504
.
19.
Toms
,
S. R.
,
Lemons
,
J. E.
,
Bartolucci
,
A. A.
, and
Eberhardt
,
A. W.
,
2002
, “
Nonlinear Stress-Strain Behavior of Periodontal Ligament Under Orthodontic Loading
,”
Am. J. Orthod. Dentofacial Orthop.
,
122
, pp.
174
179
.10.1067/mod.2002.124997
20.
Natali
,
A. N.
,
Pavan
,
P. G.
,
Carniel
,
E. L.
, and
Dorow
,
C.
,
2004
, “
Viscoelastic Response of the Periodontal Ligament: An Experimental-Numerical Analysis
,”
Connect. Tissue Res.
,
45
, pp.
222
230
.10.1080/03008200490885742
21.
Komatsu
,
K.
,
Sanctuary
,
C.
,
Shibata
,
T.
,
Shimada
,
A.
, and
Botsis
,
J.
,
2007
, “
Stress-Relaxation and Microscopic Dynamics of Rabbit Periodontal Ligament
,”
J. Biomech.
,
40
, pp.
634
644
.10.1016/j.jbiomech.2006.01.026
22.
Wise
,
G. E.
, and
King
,
G. J.
,
2008
, “
Mechanisms of Tooth Eruption and Orthodontic Tooth Movement
,”
J. Dent. Res.
,
87
, pp.
414
434
.10.1177/154405910808700509
23.
Pilon
,
J. J.
,
Kuijpers-Jagtman
,
A. M.
, and
Maltha
,
J. C.
,
1996
, “
Magnitude of Orthodontic Forces and Rate of Bodily Tooth Movement. An Experimental Study
,”
Am. J. Orthod. Dentofacial Orthop.
,
110
, pp.
16
23
.10.1016/S0889-5406(96)70082-3
24.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer-Verlag
,
New York.
25.
Wang
,
C. Y.
,
Su
,
M. Z.
,
Chang
,
H. H.
,
Chiang
,
Y. C.
,
Tao
,
S. H.
,
Cheng
,
J. H.
,
Fuh
,
L. J.
, and
Lin
,
C. P.
,
2012
, “
Tension-Compression Viscoelastic Behaviors of the Periodontal Ligament
,”
J. Formosan Med. Assoc.
,
111
, pp.
471
481
.10.1016/j.jfma.2011.06.009
26.
Komatsu
,
K.
,
Shibata
,
T.
,
Shimada
,
A.
,
Viidik
,
A.
, and
Chiba
,
M.
,
2004
, “
Age-Related and Regional Differences in the Stress-Strain and Stress-Relaxation Behaviours of the Rat Incisor Periodontal Ligament
,”
J. Biomech.
,
37
, pp.
1097
1106
.10.1016/j.jbiomech.2003.11.013
27.
Findley
,
W. N.
,
Lai
,
J. S.
, and
Onaran
,
K.
,
1976
, “
Linear Viscoelastic Constitutive Equations
,”
Creep and Relaxation of Nonlinear Viscoelastic Materials
,
North-Holland
,
New York
, pp.
57
64
.
28.
Shepherd
,
T. N.
,
Zhang
,
J.
,
Ovaert
,
T. C.
,
Roeder
,
R. K.
, and
Niebur
,
G. L.
,
2011
, “
Direct Comparison of Nanoindentation and Macroscopic Measurements of Bone Viscoelasticity
,”
J. Mech. Behav. Biomed. Mater.
,
4
, pp.
2055
2062
.10.1016/j.jmbbm.2011.07.004
29.
Findley
,
W. N.
,
Lai
,
J. S.
, and
Onaran
,
K.
,
1976
, “
Multiple Integral Representation
,”
Creep and Relaxation of Nonlinear Viscoelastic Materials
,
North-Holland
,
New York
, pp.
172
175
.
30.
Schapery
,
R. A.
,
1966
, “
An Engineering Theory of Nonlinear Viscoelasticity With Applications
,”
Int. J. Solids Struct.
,
2
, pp.
407
425
.10.1016/0020-7683(66)90030-8
31.
Provenzano
,
P. P.
,
Lakes
,
R. S.
,
Corr
,
D. T.
, and
Vanderby
,
R.
, Jr.
,
2002
, “
Application of Nonlinear Viscoelastic Models to Describe Ligament Behavior
,”
Biomech. Model. Mechanobiol.
,
1
, pp.
45
57
.10.1007/s10237-002-0004-1
32.
Findley
,
W. N.
,
Lai
,
J. S.
, and
Onaran
,
K.
,
1976
, “
Nonlinear Creep (or Relaxation) Under Variable Stress (or Strain)
,”
Creep and Relaxation of Nonlinear Viscoelastic Materials
,
North-Holland
,
New York
, pp.
229
233
.
33.
Marangalou
,
J. H.
,
Ghalichi
,
F.
, and
Mirzakouchaki
,
B.
,
2009
, “
Numerical Simulation of Orthodontic Bone Remodeling
,”
Orthodont. Waves
,
68
, pp.
64
71
.10.1016/j.odw.2008.12.002
34.
Romanyk
,
D. L.
,
Liu
,
S. S.
,
Lipsett
,
M. G.
,
Toogood
,
R. W.
,
Lagravère
,
M. O.
,
Major
,
P. W.
, and
Carey
,
J. P.
, “
Towards a Viscoelastic Model for the Unfused Midpalatal Suture: Development and Validation Using the Midsagittal Suture in New Zealand White Rabbits
,”
J. Biomech.
, (in press).
35.
Favino
,
M.
,
Krause
,
R.
, and
Steiner
,
J.
,
2012
, “
An Efficient Preconditioning Strategy for Schur Complements Arising From Biphasic Models
,”
Proceedings of the 9th IASTED International Conference on Biomedical Engineering, BioMed 2012
, pp.
700
705
.
36.
Blake
,
M.
,
Woodside
,
D. G.
, and
Pharoah
,
M. J.
,
1995
, “
A Radiographic Comparison of Apical Root Resorption After Orthodontic Treatment With the Edgewise and Speed Appliances
,”
Am. J. Orthodont. Dentofac. Orthoped.
,
108
, pp.
76
84
.10.1016/S0889-5406(95)70069-2
37.
Purslow
,
P. P.
,
Wess
,
T. J.
, and
Hukins
,
D. W. L.
,
1998
, “
Collagen Orientation and Molecular Spacing During Creep and Stress-Relaxation in Soft Connective Tissues
,”
J. Exp. Biol.
,
201
, pp.
135
142
.
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