Accurate constitutive models are required to gain further insight into the mechanical behavior of cardiovascular tissues. In this study, a structural constitutive framework for cardiovascular tissues is introduced that accounts for the angular distribution of collagen fibers. To demonstrate its capabilities, the model is applied to study the biaxial behavior of the arterial wall and the aortic valve. The pressure–radius relationships of the arterial wall accurately describe experimentally observed sigma-shaped curves. In addition, the nonlinear and anisotropic mechanical properties of the aortic valve can be analyzed with the proposed model. We expect that the current model offers strong possibilities to further investigate the complex mechanical behavior of cardiovascular tissues, including their response to mechanical stimuli.

1.
Silver
,
F. H.
,
Christiansen
,
D. L.
, and
Buntin
,
C. M.
, 1989, “
Mechanical Properties of the Aorta: A Review
,”
Crit. Rev. Biomed. Eng.
0278-940X,
17
, pp.
323
358
.
2.
Humphrey
,
J. D.
, 1999, “
An evaluation of pseudoelastic descriptors used in arterial mechanics
,”
J. Biomech. Eng.
0148-0731,
121
, pp.
259
262
.
3.
Humphrey
,
J. D.
, 2002,
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
Springer-Verlag
, New York.
4.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Ogden
,
R. W.
, 2000, “
A New Constitutive Framework For Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elasticity
,
61
, pp.
1
48
.
5.
Fung
,
Y. C.
,
Fronek
,
K.
, and
Patitucci
,
P.
, 1979, “
Pseudoelasticity of Arteries and the Choice of its Mathematical Expression
,”
Am. J. Physiol.
0002-9513,
237
, pp.
H620
H631
.
6.
Chuong
,
C. J.
, and
Fung
,
Y. C.
, 1983. “
Three-Dimensional Stress Distribution in Arteries
,”
J. Biomech. Eng.
0148-0731,
105
, pp.
268
274
.
7.
Vaishnav
,
R. N.
,
Young
,
J. T.
, and
Patel
,
D. J.
, 1973, “
Distribution of Stresses and of Strain–Energy Density Through the Wall Thickness in a Canine Aortic Segment
,”
Circ. Res.
0009-7330,
32
, pp.
577
583
.
8.
Takamizawa
,
K.
, and
Hayashi
,
K.
, 1987, “
Strain Energy Density Function and Uniform Strain Hypothesis For Arterial Mechanics
,”
J. Biomech.
0021-9290,
20
, pp.
7
17
.
9.
Zulliger
,
M. A.
,
Fridez
,
P.
,
Hayashi
,
K.
, and
Stergiopulos
,
N.
, 2004, “
A Strain Energy Function For Arteries Accounting For Wall Composition and Structure
,”
J. Biomech.
0021-9290,
37
, pp.
989
1000
.
10.
Christie
G. W.
, and
Medland
,
I. C.
, 1982, “
A Non-linear Finite Element Stress Analysis of Bioprosthetic Heart Valves
,” in
Finite Elements in Biomechanics
,
R. H.
Gallagher
,
B. R.
Simon
,
P. C.
Johnson
, and
Gross
J. F.
(eds.),
Wiley
, Chichester, pp.
153
179
.
11.
Li
,
J.
,
Luo
,
X. Y.
, and
Kuang
,
Z. B.
, 2001, “
A Nonlinear Anisotropic Model for porcine aortic heart valves
,”
J. Biomech.
0021-9290,
34
, pp.
1279
1289
.
12.
Luo
,
X. Y.
,
Li
,
W. G.
, and
Li
,
J.
, 2003, “
Geometrical Stress-Reducing factors in the Anisotropic Porcine Heart Valves
,”
J. Biomech. Eng.
0148-0731,
125
, pp.
735
744
.
13.
de Hart
,
J.
,
Cacciola
,
G.
,
Schreurs
,
P. J.
, and
Peters
,
G. W.
, 1998, “
A Three-Dimensional Analysis of a Fibre-Reinforced Aortic Valve Prosthesis
,”
J. Biomech.
0021-9290,
31
, pp.
629
638
.
14.
de Hart
,
J.
,
Baaijens
F. P. T.
,
Peters
,
G. W. M.
, and
Schreurs
,
P. J. G.
, 2003, “
A Computational fluid–Structure Interaction Analysis of a Fiber-Reinforced Stentless Aortic Valve
,”
J. Biomech.
0021-9290,
36
, pp.
699
712
.
15.
Humphrey
,
J. D.
, 1999, “
Remodeling of a Collagenous Tissue at Fixed Lengths
,”
J. Biomech. Eng.
0148-0731,
121
, pp.
591
597
.
16.
Boerboom
,
R. A.
,
Driessen
,
N. J. B.
,
Bouten
,
C. V. C.
,
Huyghe
,
J. M.
, and
Baaijens
,
F. P. T.
, 2003, “
A Finite Element Model of Mechanically Induced Collagen Fiber Synthesis and Degradation in the Aortic Valve
,”
Ann. Biomed. Eng.
0090-6964,
31
, pp.
1040
1053
.
17.
Driessen
,
N. J. B.
,
Boerboom
,
R. A.
,
Huyghe
,
J. M.
,
Bouten
,
C. V. C.
, and
Baaijens
F. P. T.
, 2003, “
Computational Analyses of Mechanically Induced Collagen Fiber Remodeling in the Aortic Heart Valve
,”
J. Biomech. Eng.
0148-0731,
125
, pp.
549
557
.
18.
Driessen
,
N. J. B.
,
Wilson
,
W.
,
Bouten
,
C. V. C.
, and
Baaijens
F. P. T.
, 2004, “
A Computational Model for Collagen Fibre Remodelling in the Arterial Wall
,”
J. Theor. Biol.
0022-5193,
226
, pp.
53
64
.
19.
Driessen
,
N. J. B.
,
Bouten
,
C. V. C.
, and
Baaijens
,
F. P. T.
, 2005, “
Improved Prediction of the Collagen Fiber Architecture in the Aortic Heart Valve
,”
J. Biomech. Eng.
0148-0731,
127
(
2
), pp.
329
-
336
.
20.
Finlay
,
H. M.
,
McCullough
,
L.
, and
Canham
,
P. B.
, 1995, “
Three-Dimensional Collagen Organization of Human Brain Arteries at Different Transmural Pressures
,”
J. Vasc. Res.
1018-1172,
32
, pp.
301
312
.
21.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Stadler
,
M.
, 2002, “
A Structural Model For the Viscoelastic Behavior of Arterial Walls: Continuum Formulation and Finite Element Analysis
,”
Eur. J. Mech. A/Solids
0997-7538,
21
, pp.
441
463
.
22.
Sacks
,
M. S.
,
Smith
,
D. B.
, and
Hiester
,
E. D.
, 1998, “
The Aortic Valve Microstructure: Effects of Transvalvular Pressure
,”
J. Biomed. Mater. Res.
0021-9304,
41
, pp.
131
141
.
23.
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
, pp.
23
30
.
24.
Billiar
,
K. L.
, and
Sacks
M. S.
, 2000, “
Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp—Part II: a structural constitutive model
,”
J. Biomech. Eng.
0148-0731,
122
, pp.
327
335
.
25.
Lanir
,
Y.
, 1979, “
A Structural Theory For the Homogeneous Biaxial Stress–Strain Relationships in Flat Collagenous Tissues
,”
J. Biomech.
0021-9290,
12
, pp.
423
436
.
26.
Lanir
,
Y.
, 1983, “
Constitutive Equations for Fibrous Connective Tissues
,”
J. Biomech.
0021-9290,
16
, pp.
1
12
.
27.
Zioupos
,
P.
, and
Barbenel
,
J. C.
, 1994, “
Mechanics of Native Bovine Pericardium. I. The Multiangular Behaviour of Strength and Stiffness of the Tissue
,”
Biomaterials
0142-9612,
15
, pp.
366
373
.
28.
Zioupos
,
P.
, and
Barbenel
,
J. C.
, 1994, “
Mechanics of Native Bovine Pericardium. II. A Structure Based Model for the Anisotropic Mechanical Behaviour of the Tissue
,”
Biomaterials
0142-9612,
15
, pp.
374
382
.
29.
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
, pp.
280
287
.
30.
Humphrey
,
J. D.
, and
Yin
,
F. C.
, 1987, “
A New Constitutive Formulation For Characterizing the Mechanical Behavior of Soft Tissues
,”
Biophys. J.
0006-3495,
52
, pp.
563
570
.
31.
Barocas
,
V. H.
, and
Tranquillo
,
R. T.
, 1997, “
An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment, and Cell Contact Guidance
,”
J. Biomech. Eng.
0148-0731,
119
, pp.
137
145
.
32.
Driessen
,
N. J. B.
,
Peters
,
G. W. M.
,
Huyghe
,
J. M.
,
Bouten
,
C. V. C.
, and
Baaijens
,
F. P. T.
, 2003, “
Remodelling of Continuously Distributed Collagen Fibres in Soft Connective Tissues
,”
J. Biomech.
0021-9290,
36
, pp.
1151
1158
.
33.
van Oijen
,
C. H. G. A.
, 2003, “
Mechanics and Design of Fiber-Reinforced Vascular Prostheses
,” Ph.D thesis, Technische Universiteit Eindhoven, http://alexandria.tue.nl/extra2/200311647.pdfhttp://alexandria.tue.nl/extra2/200311647.pdf.
34.
Hurschler
,
C.
,
Provenzano
,
P. P.
, and
Vanderby
,
R.
Jr.
, 2003, “
Application of a Probabilistic Microstructural Model to Determine Reference Length and Toe-to-Linear Region Transition in Fibrous Connective Tissue
,”
J. Biomech. Eng.
0148-0731,
125
, pp.
415
422
.
35.
Bathe
,
K. J.
, 1996,
Finite Element Procedures
,
Prentice–Hall
, Englewood Cliffs, NJ.
36.
Segal
,
A.
, 1984,
SEPRAN user manual, standard problems and programmers guide
,
Ingenieursbureau SEPRA
, Leidschendam, the Netherlands.
37.
van de Vosse
,
F. N.
,
de Hart
,
J.
,
van Oijen
,
C. H. G. A.
,
Bessems
,
D.
,
Gunther
,
T. W. M.
,
Segal
,
A.
,
Wolters
,
B. J. B. M.
,
Stijnen
,
J. M. A.
, and
Baaijens
,
F. P. T.
, 2003. “
Finite-Element-Based Computational Methods For Cardiovascular Fluid–Structure Interaction
,”
J. Eng. Math.
0022-0833,
47
, pp.
335
368
.
38.
de Hart
,
J.
, 2002, “
Fluid–Structure Interaction in the Aortic Heart Valve: a Three-Dimensional Computational Analysis
,” Ph.D. thesis, Technische Universiteit Eindhoven, http://alexandria.tue.nl/extra2/200210650.pdfhttp://alexandria.tue.nl/extra2/200210650.pdf.
39.
Sacks
,
M. S.
,
Smith
,
D. B.
, and
Hiester
E. D.
, 1997, “
A Small Angle Light Scattering Device for Planar Connective Tissue Microstructural Analysis
,”
Ann. Biomed. Eng.
0090-6964,
25
, pp.
678
689
.
40.
Sauren
,
A. A. H. J.
, 1981, “
The Mechanical Behaviour of the Aortic Valve
,” Ph.D. thesis, Technische Hogeschool Eindhoven http://alexandria.tue.nl/extra3/proefschrift/PRF3B/8105502.pdfhttp://alexandria.tue.nl/extra3/proefschrift/PRF3B/8105502.pdf.
41.
Sacks
,
M. S.
, 2004, personal communication.
42.
Vesely
,
I.
, 1998, “
The Role of Elastin in Aortic Valve Mechanics
,”
J. Biomech.
0021-9290,
31
, pp.
115
123
.
43.
Sauren
,
A. A.
,
van Hout
,
M. C.
,
van Steenhoven
,
A. A.
,
Veldpaus
,
F. E.
, and
Janssen
,
J. D.
, 1983, “
The Mechanical Properties of Porcine Aortic Valve Tissues
,”
J. Biomech.
0021-9290,
16
, pp.
327
337
.
44.
Billiar
,
K. L.
, and
Sacks
,
M. S.
, 1997, “
A Method to Quantify the Fiber Kinematics of Planar Tissues under Biaxial Stretch
,”
J. Biomech.
0021-9290,
30
, pp.
753
756
.
45.
Peeters
,
E. A.
,
Bouten
,
C. V.
,
Oomens
,
C. W.
, and
Baaijens
,
F. P.
, 2003, “
Monitoring the Biomechanical Response of Individual Cells under Compression: a New Compression Device
,”
Med. Biol. Eng. Comput.
0140-0118,
41
, pp.
498
503
.
46.
Thubrikar
,
M. J.
, 1990,
The Aortic Valve
,
CRC Press
, Boca Raton, FL.
47.
Vesely
,
I.
, and
Noseworthy
,
R.
, 1992, “
Micromechanics of the Fibrosa and the Ventricularis in Aortic Valve Leaflets
,”
J. Biomech.
0021-9290,
25
, pp.
101
113
.
48.
Thubrikar
,
M. J.
,
Aouad
,
J.
, and
Nolan
,
S. P.
, 1986, “
Comparison of the in vivo and in vitro mechanical properties of aortic valve leaflets
,”
J. Thorac. Cardiovasc. Surg.
0022-5223,
92
, pp.
29
36
.
49.
Vesely
,
I.
, 1996, “
Reconstruction of Loads in the Fibrosa and Ventricularis of Porcine Aortic Valves
,”
ASAIO J.
0162-1432
42
, pp.
M739
M746
.
50.
Fung
,
Y. C.
, 1990,
Biomechanics: Motion, Flow, Stress and Growth
,
Springer-Verlag
, New York.
51.
Gloeckner
,
D. C.
,
Sacks
,
M. S.
,
Fraser
,
M. O.
,
Somogyi
,
G. T.
,
de Groat
,
W. C.
, and
Chancellor
,
M. B.
, 2002, “
Passive Biaxial Mechanical Properties of the Rat Bladder Wall After Spinal Cord Injury
,”
J. Urol.
,
167
, pp.
2247
2252
.
52.
Sacks
,
M. S.
, and
Chuong
,
C. J.
, 1998, “
Orthotropic mechanical properties of chemically treated bovine pericardium
,”
Ann. Biomed. Eng.
0090-6964,
26
, pp.
892
902
.
53.
Sacks
,
M. S.
and
Gloeckner
,
D. C.
, 1999, “
Quantification of the Fiber Architecture and Biaxial Mechanical Behavior of Porcine Intestinal Submucosa
,”
J. Biomed. Mater. Res.
0021-9304,
46
(
1
), pp.
1
10
.
54.
Yin
,
F. C.
,
Strumpf
,
R. K.
,
Chew
,
P. H.
, and
Zeger
,
S. L.
, 1987, “
Quantification of the Mechanical Properties of Noncontracting Canine Myocardium Under Simultaneous Biaxial Loading
,”
J. Biomech.
0021-9290,
20
(
6
), pp.
577
589
.
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