Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.

1.
Demer
,
L. L.
, and
Yin
,
F. C.
, 1983, “
Passive Biaxial Mechanical Properties of Isolated Canine Myocardium
,”
J. Physiol. (London)
0022-3751,
339
, pp.
615
630
.
2.
Sacks
,
M. S.
, and
Chuong
,
C. J.
, 1993, “
Biaxial Mechanical Properties of Passive Right Ventricular Free Wall Myocardium
,”
J. Biomech. Eng.
0148-0731,
115
(
2
), pp.
202
205
.
3.
Billiar
,
K. L.
, and
Sacks
,
M. S.
, 2000, “
Biaxial Mechanical Properties of the Native and Glutaraldehyde-Treated Aortic Valve Cusp: Part II—A Structural Constitutive Model
,”
J. Biomech. Eng.
0148-0731,
122
(
4
), pp.
327
335
.
4.
Billiar
,
K. L.
, and
Sacks
,
M. S.
, 2000, “
Biaxial Mechanical Properties of the Natural and Glutaraldehyde Treated Aortic Valve Cusp—Part I: Experimental Results
,”
J. Biomech. Eng.
0148-0731,
122
(
1
), pp.
23
30
.
5.
Vaishnav
,
R. N.
,
Young
,
J. T.
,
Janicki
,
J. S.
, and
Patel
,
D. J.
, 1972, “
Nonlinear Anisotropic Elastic Properties of the Canine Aorta
,”
Biophys. J.
0006-3495,
12
(
8
), pp.
1008
1027
.
6.
Lynch
,
H. A.
,
Johannessen
,
W.
,
Wu
,
J. P.
,
Jawa
,
A.
, and
Elliott
,
D. M.
, 2003, “
Effect of Fiber Orientation and Strain Rate on the Nonlinear Uniaxial Tensile Material Properties of Tendon
,”
J. Biomech. Eng.
0148-0731,
125
(
5
), pp.
726
731
.
7.
Lanir
,
Y.
, 1974, “
Two Dimensional Mechanical Properties of Mammalian Skin—II. Experimental Results
,”
J. Biomech.
0021-9290,
7
, pp.
171
182
.
8.
Quapp
,
K. M.
, and
Weiss
,
J. A.
, 1998, “
Material Characterization of Human Medial Collateral Ligament
,”
J. Biomech. Eng.
0148-0731,
120
(
6
), pp.
757
763
.
9.
Bonifasi-Lista
,
C.
,
Lake
,
S. P.
,
Small
,
M. S.
, and
Weiss
,
J. A.
, 2005, “
Viscoelastic Properties of the Human Medial Collateral Ligament Under Longitudinal, Transverse and Shear Loading
,”
J. Orthop. Res.
0736-0266,
23
(
1
), pp.
67
76
.
10.
Holmes
,
J. W.
,
Nunez
,
J. A.
, and
Covell
,
J. W.
, 1997, “
Functional Implications of Myocardial Scar Structure
,”
Am. J. Physiol.
0002-9513,
272
(5 Pt 2), pp.
H2123
2130
.
11.
Costa
,
K. D.
,
Lee
,
E. J.
, and
Holmes
,
J. W.
, 2003, “
Creating Alignment and Anisotropy in Engineered Heart Tissue: Role of Boundary Conditions in a Model Three-Dimensional Culture System
,”
Tissue Eng.
1076-3279,
9
(
4
), pp.
567
577
.
12.
Thomopoulos
,
S.
,
Fomovsky
,
G. M.
, and
Holmes
,
J. W.
, 2005, “
The Development of Structural and Mechanical Anisotropy in Fibroblast Populated Collagen Gels
,”
J. Biomech. Eng.
0148-0731,
127
(
5
), pp.
742
750
.
13.
Barocas
,
V. H.
,
Girton
,
T. S.
, and
Tranquillo
,
R. T.
, 1998, “
Engineered Alignment in Media Equivalents: Magnetic Prealignment and Mandrel Compaction
,”
J. Biomech. Eng.
0148-0731,
120
(
5
), pp.
660
666
.
14.
Grinnell
,
F.
, and
Lamke
,
C. R.
, 1984, “
Reorganization of Hydrated Collagen Lattices by Human Skin Fibroblasts
,”
J. Cell. Sci.
0021-9533,
66
, pp.
51
63
.
15.
Lanir
,
Y.
, 1979, “
Rheological Behavior of the Skin—Experimental Results and a Structural Model
,”
Biorheology
0006-355X,
16
, pp.
191
202
.
16.
Sacks
,
M. S.
, 2003, “
Incorporation of Experimentally-Derived Fiber Orientation Into a Structural Constitutive Model for Planar Collagenous Tissues
,”
J. Biomech. Eng.
0148-0731,
125
(
2
), pp.
280
287
.
17.
Chandran
,
P. L.
, and
Barocas
,
V. H.
, 2006, “
Affine vs Non-affine Fibril Kinematics in Collagen Networks: Theoretical Studies of Network Behavior
,”
J. Biomech. Eng.
0148-0731,
128
(
2
), pp.
259
270
.
18.
Chandran
,
P. L.
, and
Barocas
,
V. H.
, 2007, “
Deterministic Material-Based Averaging Theory Model of Tissue-Equivalent Micromechanics
,”
ASME J. Biomech. Eng.
0148-0731,
129
(
2
), pp.
137
147
.
19.
Knezevic
,
V.
,
Sim
,
A. J.
,
Borg
,
T. K.
, and
Holmes
,
J. W.
, 2002, “
Isotonic Biaxial Loading of Fibroblast-Populated Collagen Gels: A versatile, Low-Cost System for the Study of Mechanobiology
,”
Biomech. Model. Mechanobiol.
,
1
, pp.
59
67
.
20.
Brightman
,
A. O.
,
Rajwa
,
B. P.
,
Sturgis
,
J. E.
,
McCallister
,
M. E.
,
Robinson
,
J. P.
, and
Voytik-Harbin
,
S. L.
, 2000, “
Time-Lapse Confocal Reflection Microscopy of Collagen Fibrillogenesis and Extracellular Matrix Assembly in Vitro
,”
Biopolymers
0006-3525,
54
(
3
), pp.
222
234
.
21.
Karlon
,
W. J.
,
Covell
,
J. W.
,
McCulloch
,
A. D.
,
Hunter
,
J. J.
, and
Omens
,
J. H.
, 1998, “
Automated Measurement of Myofiber Disarray in Transgenic Mice With Ventricular Expression of Ras
,”
Anat. Rec.
0003-276X,
252
(
4
), pp.
612
625
.
22.
Karlon
,
W. J.
,
Hsu
,
P. P.
,
Li
,
S.
,
Chien
,
S.
,
McCulloch
,
A. D.
, and
Omens
,
J. H.
, 1999, “
Measurement of Orientation and Distribution of Cellular Alignment and Cytoskeletal Organization
,”
Ann. Biomed. Eng.
0090-6964,
27
(
6
), pp.
712
720
.
23.
Batschelet
,
E.
, 1981,
Circular Statistics in Biology
,
Academic Press
,
London
.
24.
Pryse
,
K. M.
,
Nekouzadeh
,
A.
,
Genin
,
G. M.
,
Elson
,
E. L.
, and
Zahalak
,
G. I.
, 2003, “
Incremental Mechanics of Collagen Gels: New Experiments and a New Viscoelastic Model
,”
Ann. Biomed. Eng.
0090-6964,
31
(
10
), pp.
1287
1296
.
25.
Zahalak
,
G. I.
,
Wagenseil
,
J. E.
,
Wakatsuki
,
T.
, and
Elson
,
E. L.
, 2000, “
A Cell-Based Constitutive Relation for Bio-Artificial Tissues
,”
Biophys. J.
0006-3495,
79
(
5
), pp.
2369
2381
.
26.
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.
0148-0731,
125
(
5
), pp.
719
725
.
27.
Nakagawa
,
S.
,
Pawelek
,
P.
, and
Grinnell
,
F.
, 1989, “
Long-Term Culture of Fibroblasts in Contracted Collagen Gels: Effects on Cell Growth and Biosynthetic Activity
,”
J. Invest. Dermatol.
0022-202X,
93
(
6
), pp.
792
798
.
28.
Girton
,
T. S.
,
Oegema
,
T. R.
, and
Tranquillo
,
R. T.
, 1999, “
Exploiting Glycation to Stiffen and Strengthen Tissue Equivalents for Tissue Engineering
,”
J. Biomed. Mater. Res.
0021-9304,
46
(
1
), pp.
87
92
.
29.
Fung
,
Y. C.
, 1972, “
Stress-Strain-History Relations of Soft Tissues in Simple Elongation
,”
Biomechanics: Its Foundations and Objectives
,
Y. C.
Fung
,
N.
Perrone
, and
M.
Anliker
, eds.,
Prentice-Hall
,
San Diego, CA
, pp.
181
208
.
30.
Abramowitch
,
S. D.
,
Woo
,
S. L.
,
Clineff
,
T. D.
, and
Debski
,
R. E.
, 2004, “
An Evaluation of the Quasi-Linear Viscoelastic Properties of the Healing Medial Collateral Ligament in a Goat Model
,”
Ann. Biomed. Eng.
0090-6964,
32
(
3
), pp.
329
335
.
31.
Allen
,
T. D.
,
Schor
,
S. L.
, and
Schor
,
A. M.
, 1984, “
An Ultrastructural Review of Collagen Gels, a Model System for Cell-Matrix, Cell-Basement Membrane and Cell-Cell Interactions
,”
Scan Electron Microsc.
0586-5581,
1
, pp.
375
390
.
32.
Chandran
,
P. L.
, and
Barocas
,
V. H.
, 2004, “
Microstructural Mechanics of Collagen Gels in Confined Compression: Poroelasticity, Viscoelasticity, and Collapse
,”
J. Biomech. Eng.
0148-0731,
126
(
2
), pp.
152
166
.
33.
Holmes
,
J. W.
,
Borg
,
T. K.
, and
Covell
,
J. W.
, 2005, “
Structure and Mechanics of Healing Myocardial Infarcts
,”
Annu. Rev. Biomed. Eng.
1523-9829,
7
, pp.
223
253
.
34.
Thomopoulos
,
S.
,
Williams
,
G. R.
,
Gimbel
,
J. A.
,
Favata
,
M.
, and
Soslowsky
,
L. J.
, 2003, “
Variation of Biomechanical, Structural, and Compositional Properties Along the Tendon to Bone Insertion Site
,”
J. Orthop. Res.
0736-0266,
21
(
3
), pp.
413
419
.
35.
Meshel
,
A. S.
,
Wei
,
Q.
,
Adelstein
,
R. S.
, and
Sheetz
,
M. P.
, 2005, “
Basic Mechanism of Three-Dimensional Collagen Fibre Transport by Fibroblasts
,”
Nat. Cell Biol.
1465-7392,
7
(
2
), pp.
157
164
.
36.
Grinnell
,
F.
, and
Bennett
,
M. H.
, 1982, “
Ultrastructural Studies of Cell-Collagen Interactions
,”
Methods Enzymol.
0076-6879,
82
, Pt A, pp.
535
544
.
37.
Guidry
,
C.
, and
Grinnell
,
F.
, 1985, “
Studies on the Mechanism of Hydrated Collagen Gel Reorganization by Human Skin Fibroblasts
,”
J. Cell. Sci.
0021-9533,
79
, pp.
67
81
.
38.
Zaleskas
,
J. M.
,
Kinner
,
B.
,
Freyman
,
T. M.
,
Yannas
,
I. V.
,
Gibson
,
L. J.
, and
Spector
,
M.
, 2004, “
Contractile Forces Generated by Articular Chondrocytes in Collagen-Glycosaminoglycan Matrices
,”
Biomaterials
0142-9612,
25
(
7–8
), pp.
1299
1308
.
39.
Marquez
,
J. P.
,
Genin
,
G. M.
,
Zahalak
,
G. I.
, and
Elson
,
E. L.
, 2005, “
The Relationship Between Cell and Tissue Strain in Three-Dimensional Bio-Artificial Tissues
,”
Biophys. J.
0006-3495,
88
, pp.
778
789
.
40.
Wakatsuki
,
T.
,
Kolodney
,
M. S.
,
Zahalak
,
G. I.
, and
Elson
,
E. L.
, 2000, “
Cell Mechanics Studied by a Reconstituted Model Tissue
,”
Biophys. J.
0006-3495,
79
(
5
), pp.
2353
2368
.
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