The macroscopic viscoelastic behavior of collagen gel was studied through relaxation time distribution spectrum obtained from stress relaxation tests and viscoelastic constitutive modeling. Biaxial stress relaxation tests were performed to characterize the viscoelastic behavior of collagen gel crosslinked with Genipin solution. Relaxation time distribution spectrum was obtained from the stress relaxation data by inverse Laplace transform. Peaks at the short (0.3 s–1 s), medium (3 s–90 s), and long relaxation time (>200 s) were observed in the continuous spectrum, which likely correspond to relaxation mechanisms involve fiber, inter-fibril, and fibril sliding. The intensity of the long-term peaks increases with higher initial stress levels indicating the engagement of collagen fibrils at higher levels of tissue strain. We have shown that the stress relaxation behavior can be well simulated using a viscoelastic model with viscous material parameters obtained directly from the relaxation time spectrum. Results from the current study suggest that the relaxation time distribution spectrum is useful in connecting the macro-level viscoelastic behavior of collagen matrices with micro-level structure changes.

References

References
1.
Kastelic
,
J.
Galeski
,
A.
, and
Baer
,
E.
,
1978
, “
The Multicomposite Structure of Tendon
.”
Connect. Tissue Res.
,
6
, pp.
11
23
.10.3109/03008207809152283
2.
Fratzl
,
P.
,
2008
,
Collagen: Structure and Mechanics
,
Springer
,
New York
.
3.
Sherman
,
P.
,
1970
,
Industrial Rheology
,
Academic
,
New York
.
4.
Ferry
,
J. D.
,
1980
,
Viscoelastic Properties of Polymers
,
Wiley
,
New York
.
5.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer
,
New York
.
6.
Peleg
,
M.
, and
Pollak
,
N.
,
1982
, “
The Problem of Equilibrium Conditions in Stress Relaxation Analyses of Solid Foods
,”
J. Texture Studies
,
13
, pp.
1
11
.10.1111/j.1745-4603.1982.tb00873.x
7.
Malkin
,
Y. A.
,
2006
, “
The Use of a Continuous Relaxation Spectrum for Describing the Viscoelastic Properties of Polymers
,”
J. Polym. Sci. A
,
48
, pp.
39
45
.10.1134/S0965545X06010068
8.
Sodhi
,
N. S.
,
Sasaki
,
T.
,
Lu
,
Zh.
, and
Kohyama
,
K.
,
2010
, “
Phenomenological Viscoelasticity of Some Rice Starch Gels
,”
Food Hydrocolloids
,
24
, pp.
512
517
.10.1016/j.foodhyd.2009.12.009
9.
Mao
,
R.
,
Tang
,
J.
, and
Swanson
,
B. G.
,
2000
, “
Relaxation Time Spectrum of Hydrogels by CONTIN Analysis
,”
J. Food Sci.
,
65
, pp.
374
381
.10.1111/j.1365-2621.2000.tb16010.x
10.
Li
,
W.
,
Dobraszczyk
,
B. J.
, and
Schofield
,
J. D.
,
2003
, “
Stress Relaxation Behavior of Wheat Dough, Gluten and Gluten Protein Fractions
,”
Cereal Chemistry
,
80
, pp.
333
338
.10.1094/CCHEM.2003.80.3.333
11.
Xu
,
B.
,
Chow
,
M. J.
, and
Zhang
,
Y.
,
2011
, “
Experimental and Modeling Study of Collagen Scaffolds With the Effects of Crosslinking and Fiber Alignment
,”
Int. J. Biomater.
, Vol.
2011
.10.1155/2011/172389
12.
Sacks
,
M. S.
,
2000
, “
Biaxial Mechanical Evaluation of Planar Biological Materials
,”
J. Elasticity
,
61
, pp.
199
246
.10.1023/A:1010917028671
13.
Zou
,
Y.
, and
Zhang
,
Y.
,
2010
, “
The Orthotropic Viscoelastic Behavior of Aortic Elastin
.”
Biomech. Model. Mechanobiol.
,
10
, pp.
613
625
.10.1007/s10237-010-0260-4
14.
Gasser
,
T. C.
,
Ogden
,
R. W.
, and
Holzapfel
,
G. A.
,
2006
, “
Hyperelastic Modeling of Arterial Layers With Distributed Collagen Fibre Orientations
,”
J. R. Soc., Interface
,
3
, pp.
15
35
.10.1098/rsif.2005.0073
15.
Provencher
,
S. W.
,
1982
, “
CONTIN: A General Purpose Constrained Regularization Program for Inverting Noisy Linear Algebraic and Integral Equations
,”
Comput. Phys. Commun.
,
27
, pp.
229
242
.10.1016/0010-4655(82)90174-6
16.
Komatsu
,
K.
,
2010
, “
Mechanical Strength and Viscoelastic Response of the Periodontal Ligament in Relation to Structure
,”
J. Dental Biomech.
,
1
(1), pp.
1
18
.10.4061/2010/502318
17.
Wagenseil
,
J. E.
,
Wakatsuki
,
T.
,
Okamoto
,
R. J.
,
Zahalak
,
G. I.
, and
Elson
,
E.
L,
2003
, “
One-Dimensional Viscoelastic Behavior of Fibroblast Populated Collagen Matrices
,”
J. Biomech. Eng.
,
125
, pp.
719
725
.10.1115/1.1614818
18.
Toms
,
S. R.
,
Dakin
,
G. J.
,
Lemons
,
J. E.
, and
Eberhardt
,
A. W.
,
2002
, “
Quasi-Linear Vicoelastic Behavior of the Human Periodontal Ligament
,”
J. Biomech.
,
35
, pp.
1411
1415
.10.1016/S0021-9290(02)00166-5
19.
Sundararaghavan
,
H. G.
,
Monteiro
,
G. A.
,
Firestein
,
B. L.
, and
Shreiber
,
D. J.
,
2009
, “
Neurite Growth in 3D Collagen Gels With Gradients of Mechanical Properties
,”
Biotechnol. Bioeng.
,
102
,
632
643
.10.1002/bit.22074
20.
Bailey
,
A. J.
,
2001
, “
Molecular Mechanisms of Ageing in Connective Tissues
,”
Mech. Ageing Dev.
,
122
, pp.
735
755
.10.1016/S0047-6374(01)00225-1
21.
Gupta
,
H. S.
,
Seto
,
J.
,
Krauss
,
S.
,
Boesecke
,
P.
, and
Screen
,
H. R. C.
,
2010
, “
In situ Multi-Level Analysis of Viscoelastic Deformation Mechanisms in Tendon Collagen
,”
J. Struct. Biol.
,
169
, pp.
183
191
.10.1016/j.jsb.2009.10.002
22.
Rigozzi
,
S.
,
Stemmer
,
A.
,
Muller
,
R.
, and
Snedeker
,
J. G.
,
2001
, “
Mechanical Response of Individual Collagen Fibrils in Loaded Tendon as Measured by Atomic Force Microscopy
,”
J. Struct. Biol.
,
176
, pp.
9
15
.10.1016/j.jsb.2011.07.002
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