A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.

1.
Hunter
,
K. S.
,
Lee
,
P. F.
,
Lanning
,
C. J.
,
Ivy
,
D. D.
,
Kirby
,
K. S.
,
Claussen
,
L. R.
,
Chan
,
K. C.
, and
Shandas
,
R.
, 2008, “
Pulmonary Vascular Input Impedance Is a Combined Measure of Pulmonary Vascular Resistance and Stiffness and Predicts Clinical Outcomes Better Than Pulmonary Vascular Resistance Alone in Pediatric Patients With Pulmonary Hypertension
,”
Am. Heart J.
0002-8703,
155
(
1
), pp.
166
174
.
2.
Humphrey
,
J. D.
, 2002,
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs
,
Springer
,
New York
.
3.
Lammers
,
S. R.
,
Kao
,
P. H.
,
Qi
,
H. J.
,
Hunter
,
K.
,
Lanning
,
C.
,
Albietz
,
J.
,
Hofmeister
,
S.
,
Mecham
,
R.
,
Stenmark
,
K. R.
, and
Shandas
,
R.
, 2008, “
Changes in the Structure-Function Relationship of Elastin and Its Impact on the Proximal Pulmonary Arterial Mechanics of Hypertensive Calves
,”
Am. J. Physiol. Heart Circ. Physiol.
0363-6135,
295
(
4
), pp.
H1451
H1459
.
4.
Jacob
,
M. P.
, 2003, “
Extracellular Matrix Remodeling and Matrix Metalloproteinases in the Vascular Wall During Aging and in Pathological Conditions
,”
Biomed. Pharmacother
0753-3322,
57
(
5–6
), pp.
195
202
.
5.
Patel
,
D. J.
, and
Fry
,
D. L.
, 1969, “
Elastic Symmetry of Arterial Segments in Dogs
,”
Circ. Res.
0009-7330,
24
(
1
), pp.
1
8
.
6.
Doyle
,
J. M.
, and
Dobrin
,
P. B.
, 1971, “
Finite Deformation Analysis of Relaxed and Contracted Dog Carotid-Artery
,”
Microvasc. Res.
0026-2862,
3
(
4
), pp.
400
415
.
7.
Roach
,
M. R.
, and
Burton
,
A. C.
, 1957, “
The Reason for the Shape of the Distensibility Curves of Arteries
,”
Can. J. Biochem. Physiol.
0576-5544,
35
(
8
), pp.
681
690
.
8.
Lanir
,
Y.
, 1979, “
Structural Theory for the Homogeneous Biaxial Stress-Strain Relationships in Flat Collagenous Tissues
,”
J. Biomech.
0021-9290,
12
(
6
), pp.
423
436
.
9.
Elbischger
,
P. J.
,
Cacho
,
R.
,
Bischof
,
H.
, and
Holzapfel
,
G. A.
, 2006,
Modeling and Characterizing Collagen Fiber Bundles
,
IEEE
,
Piscataway, NJ
, p.
1280
.
10.
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
(
5
), pp.
H620
H631
.
11.
Bischoff
,
J. E.
,
Arruda
,
E. M.
, and
Grosh
,
K.
, 2002, “
A Microstructurally Based Orthotropic Hyperelastic Constitutive Law
,”
ASME J. Appl. Mech.
0021-8936,
69
(
5
), pp.
570
579
.
12.
Zhang
,
Y. H.
,
Dunn
,
M. L.
,
Hunter
,
K. S.
,
Lanning
,
C.
,
Ivy
,
D. D.
,
Claussen
,
L.
,
Chen
,
S. J.
, and
Shandas
,
R.
, 2007, “
Application of a Microstructural Constitutive Model of the Pulmonary Artery to Patient-Specific Studies: Validation and Effect of Orthotropy
,”
ASME J. Biomech. Eng.
0148-0731,
129
(
2
), pp.
193
201
.
13.
Zhang
,
Y. H.
,
Dunn
,
M. L.
,
Drexler
,
E. S.
,
McCowan
,
C. N.
,
Slifka
,
A. J.
,
Ivy
,
D. D.
, and
Shandas
,
R.
, 2005, “
A Microstructural Hyperelastic Model of Pulmonary Arteries Under Normo- and Hypertensive Conditions
,”
Ann. Biomed. Eng.
0090-6964,
33
(
8
), pp.
1042
1052
.
14.
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
(
7
), pp.
989
1000
.
15.
Gasser
,
T. C.
,
Ogden
,
R. W.
, and
Holzapfel
,
G. A.
, 2006, “
Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations
,”
J. R. Soc., Interface
1742-5689,
3
(
6
), pp.
15
35
.
16.
Cacho
,
F.
,
Elbischger
,
P. J.
,
Rodriguez
,
J. F.
,
Doblare
,
M.
, and
Holzapfel
,
G. A.
, 2007, “
A Constitutive Model for Fibrous Tissues Considering Collagen Fiber Crimp
,”
Int. J. Non-Linear Mech.
0020-7462,
42
(
2
), pp.
391
402
.
17.
Sacks
,
M. S.
, 2003, “
Incorporation of Experimentally-Derived Fiber Orientation Into a Structural Constitutive Model for Planar-Collagenous Tissues
,”
ASME J. Biomech. Eng.
0148-0731,
125
(
2
), pp.
280
287
.
18.
Comninou
,
M.
, and
Yannas
,
I. V.
, 1976, “
Dependence of Stress-Strain Nonlinearity of Connective Tissues on Geometry of Collagen-Fibers
,”
J. Biomech.
0021-9290,
9
(
7
), pp.
427
433
.
19.
Sasaki
,
N.
, and
Odajima
,
S.
, 1996, “
Elongation Mechanism of Collagen Fibrils and Force-Strain Relations of Tendon at Each Level of Structural Hierarchy
,”
J. Biomech.
0021-9290,
29
(
9
), pp.
1131
1136
.
20.
Buckley
,
C. P.
,
Lloyd
,
D. W.
, and
Konopasek
,
M.
, 1980, “
On the Deformation of Slender Filaments With Planar Crimp: Theory, Numerical Solution and Applications to Tendon Collagen and Textile Materials
,”
Proc. R. Soc. London, Ser. A
0950-1207,
372
, pp.
33
64
.
21.
Sasaki
,
N.
, and
Odajima
,
S.
, 1996, “
Stress-Strain Curve and Young’s Modulus of a Collagen Molecule as Determined by the X-Ray Diffraction Technique
,”
J. Biomech.
0021-9290,
29
(
5
), pp.
655
658
.
22.
Wolinsky
,
H.
, and
Glagov
,
S.
, 1964, “
Structural Basis for Static Mechanical Properties of Aortic Media
,”
Circ. Res.
0009-7330,
14
(
5
), pp.
400
413
.
23.
Rezakhaniha
,
R.
, and
Stergiopulos
,
N.
, 2008, “
A Structural Model of the Venous Wall Considering Elastin Anisotropy
,”
ASME J. Biomech. Eng.
0148-0731,
130
(
3
), p.
031017
.
24.
Sherebrin
,
M. H.
, 1983, “
Mechanical Anisotropy of Purified Elastin From the Thoracic Aorta of Dog and Sheep
,”
Can. J. Physiol. Pharmacol.
0008-4212,
61
(
6
), pp.
539
545
.
25.
Lillie
,
M. A.
, and
Gosline
,
J. M.
, 2002, “
Unusual Swelling of Elastin
,”
Biopolymers
0006-3525,
64
(
3
), pp.
115
126
.
26.
Lillie
,
M. A.
,
David
,
G. J.
, and
Gosline
,
J. M.
, 1998, “
Mechanical Role of Elastin-Associated Microfibrils in Pig Aortic Elastic Tissue
,”
Connect. Tissue Res.
0300-8207,
37
(
1–2
), pp.
121
141
.
27.
Gundiah
,
N.
,
Ratcliffe
,
M. B.
, and
Pruitt
,
L. A.
, 2007, “
Determination of Strain Energy Function for Arterial Elastin: Experiments Using Histology and Mechanical Tests
,”
J. Biomech.
0021-9290,
40
(
3
), pp.
586
594
.
28.
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. Elast.
0374-3535,
61
(
1–3
), pp.
1
48
.
29.
Manuscript in preparation.
30.
deBotton
,
G.
,
Hariton
,
I.
, and
Socolsky
,
E. A.
, 2006, “
Neo-Hookean Fiber-Reinforced Composites in Finite Elasticity
,”
J. Mech. Phys. Solids
0022-5096,
54
(
3
), pp.
533
559
.
31.
Holzapfel
,
G. A.
, 2000,
Nonlinear Solid Mechanics: A Continuum Approach for Engineering
,
Wiley
,
New York
.
32.
Spencer
,
A. J. M.
, 1971, “
Theory of Invariants
,”
Continuum Physics, Volume 1: Mathematics
,
Academic
,
London, UK
, p.
239
.
33.
Basu
,
A. J.
, and
Lardner
,
T. J.
, 1985, “
Deformation of a Planar Sinusoidal Elastic Beam
,”
Z. Angew. Math. Phys.
0044-2275,
36
(
3
), pp.
460
474
.
34.
Garikipati
,
K.
,
Goktepe
,
S.
, and
Miehe
,
C.
, 2008, “
Elastica-Based Strain Energy Functions for Soft Biological Tissue
,”
J. Mech. Phys. Solids
0022-5096,
56
(
4
), pp.
1693
1713
.
35.
Spencer
,
A. J. M.
, 1984, “
Constitutive Theory for Strongly Anisotropic Solids
,”
Continuum Theory of the Mechanics of Fiber-Reinforced Composites
,
Springer-Verlag
,
Vienna, Austria
, p.
1
.
36.
Zou
,
Y.
, and
Zhang
,
Y. H.
, 2009, “
An Experimental and Theoretical Study on the Anisotropy of Elastin Network
,”
Ann. Biomed. Eng.
0090-6964,
37
(
8
), pp.
1572
1583
.
37.
Cusack
,
S.
, and
Miller
,
A.
, 1979, “
Determination of the Elastic-Constants of Collagen by Brillouin Light-Scattering
,”
J. Mol. Biol.
0022-2836,
135
(
1
), pp.
39
51
.
38.
Harley
,
R.
,
James
,
D.
,
Miller
,
A.
, and
White
,
J. W.
, 1977, “
Phonons and Elastic-Moduli of Collagen and Muscle
,”
Nature (London)
0028-0836,
267
(
5608
), pp.
285
287
.
39.
Hurschler
,
C.
,
Provenzano
,
P. P.
, and
Vanderby
,
R.
, 2003, “
Application of a Probabilistic Microstructural Model to Determine Reference Length and Toe-to-Linear Region Transition in Fibrous Connective Tissue
,”
ASME J. Biomech. Eng.
0148-0731,
125
(
3
), pp.
415
422
.
40.
Sacks
,
M. S.
, 1999, “
A Method for Planar Biaxial Mechanical Testing That Includes In-Plane Shear
,”
ASME J. Biomech. Eng.
0148-0731,
121
(
5
), pp.
551
555
.
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