Atrial fibrillation (AF) is a cardiac arrhythmia that highly increases the risk of stroke and is associated with significant but still unexplored changes in the mechanical behavior of the tissue. Planar biaxial tests were performed on tissue specimens from pigs at the healthy stage and after ventricular tachypacing (VTP), a procedure applied to reproduce the relevant features of AF. The local arrangement of the fiber bundles in the tissue was investigated on specimens from rabbit atria by means of circularly polarized light. Based on this, mechanical data were fitted to two anisotropic constitutive relationships, including a four-parameter Fung-type model and a microstructurally-motivated model. Accounting for the fiber-induced anisotropy brought average R2 = 0.807 for the microstructurally-motivated model and average R2 = 0.949 for the Fung model. Validation of the fitted constitutive relationships was performed by means of FEM simulations coupled to FORTRAN routines. The performances of the two material models in predicting the second Piola-Kirchhoff stress were comparable, with average errors <3.1%. However, the Fung model outperformed the other in the prediction of the Green-Lagrange strain, with 9.2% maximum average error. To increase model generality, a proper averaging procedure accounting for nonlinearities was used to obtain average material parameters. In general, a stiffer behavior after VTP was noted.

References

References
1.
Roger
,
V. L.
,
Go
,
A. S.
,
Lloyd-Jones
,
D. M.
,
Adams
,
R. J.
,
Berry
,
J. D.
,
Brown
,
T. M.
,
Carnethon
,
M. R.
,
Dai
,
S.
, de
Simone
,
G.
,
Ford
,
E. S.
,
Fox
,
C. S.
,
Fullerton
,
H. J.
,
Gillespie
,
C.
,
Greenlund
,
K. J.
,
Hailpern
,
S. M.
,
Heit
,
J. A.
,
Ho
,
P. M.
,
Howard
,
V. J.
,
Kissela
,
B. M.
,
Kittner
,
S. J.
,
Lackland
,
D. T.
,
Lichtman
,
J. H.
,
Lisabeth
,
L. D.
,
Makuc
,
D. M.
,
Marcus
,
G. M.
,
Marelli
,
A.
,
Matchar
,
D. B.
,
McDermott
,
M. M.
,
Meigs
,
J. B.
,
Moy
,
C. S.
,
Mozaffarian
,
D.
,
Mussolino
,
M. E.
,
Nichol
,
G.
,
Paynter
,
N. P.
,
Rosamond
,
W. D.
,
Sorlie
,
P. D.
,
Stafford
,
R. S.
,
Turan
,
T. N.
,
Turner
,
M. B.
,
Wong
,
N. D.
,
Wylie-Rosett
,
J.
, A. H. A. S. Committee, and S. S. Subcommittee, 2011, “
Heart Disease and Stroke Statistics-2011 Update: A Report From the American Heart Association
,”
Circulation
,
123
(
4
), pp.
e18
e209
.
2.
Brundel
,
B. J. J. M.
,
Melnyk
,
P.
,
Rivard
,
L.
, and
Nattel
,
S.
, 2005, “
The Pathology of Atrial Fibrillation in Dogs
,”
J. Vet. Cardiol.
,
7
(
2
), pp.
121
129
.
3.
Wolf
,
P. A.
,
Mitchell
,
J. B.
,
Baker
,
C. S.
,
Kannel
,
W. B.
, and
D’Agostino
,
R. B.
, 1998, “
Impact of Atrial Fibrillation on Mortality, Stroke, and Medical Costs
,”
Arch. Intern. Med.
,
158
(
3
), pp.
229
234
.
4.
Heeringa
,
J.
, 2010, “
Atrial Fibrillation: Is the Prevalence Rising?
,”
Europace
,
12
(
4
), pp.
451
452
.
5.
Kourliouros
,
A.
,
Savelieva
,
I.
,
Kiotsekoglou
,
A.
,
Jahangiri
,
M.
, and
Camm
,
J.
, 2009, “
Current Concepts in the Pathogenesis of Atrial Fibrillation
,”
Am. Heart J.
,
157
(
2
), pp.
243
252
.
6.
Schoonderwoerd
,
B. A.
,
Gelder
,
I. C. V.
,
Veldhuisen
,
D. J. V.
,
den Berg
,
M. P. V.
, and
Crijns
,
H. J. G. M.
, 2005, “
Electrical and Structural Remodeling: Role in the Genesis and Maintenance of Atrial Fibrillation
,”
Prog. Cardiovasc. Dis.
,
48
(
3
), pp.
153
168
.
7.
Nattel
,
S.
, 2002, “
Therapeutic Implications of Atrial Fibrillation Mechanisms: Can Mechanistic Insights Be Used to Improve AF Management?
,”
Cardiovasc. Res.
,
54
(
2
), pp.
347
360
.
8.
Burstein
,
B.
, and
Nattel
,
S.
, 2008, “
Atrial Fibrosis: Mechanisms and Clinical Relevance in Atrial Fibrillation
,”
J. Am. Coll. Cardiol.
,
51
(
8
), pp.
802
809
.
9.
Jaber
,
W. A.
,
Maniu
,
C.
,
Krysiak
,
J.
,
Shapiro
,
B. P.
,
Meyer
,
D. M.
,
Linke
,
W. A.
, and
Redfield
,
M. M.
, 2008, “
Titin Isoforms, Extracellular Matrix, and Global Chamber Remodeling in Experimental Dilated Cardiomyopathy: Functional Implications and Mechanistic Insight
,”
Circ. Heart Fail.
,
1
(
3
), pp.
192
199
.
10.
Heeringa
,
J.
,
van der Kuip
,
D. A. M.
,
Hofman
,
A.
Kors
,
J. A.
, van
Herpen
,
G.
,
Stricker
,
B. H. C.
,
Stijnen
,
T.
,
Lip
,
G. Y. H.
, and
Witteman
,
J. C. M.
, 2006, “
Prevalence, Incidence and Lifetime Risk of Atrial Fibrillation: The Rotterdam Study
,”
Eur. Heart J.
,
27
(
8
), pp.
949
953
.
11.
Lévy
,
S.
, 1997, “
Factors Predisposing to the Development of Atrial Fibrillation
,”
Pacing Clin. Electrophysiol.
,
20
(
10
, Pt 2), pp.
2670
2674
.
12.
Everett
,
T. H.
,
Wilson
,
E. E.
,
Verheule
,
S.
,
Guerra
,
J. M.
,
Foreman
,
S.
, and
Olgin
,
J. E.
, 2006, “
Structural Atrial Remodeling Alters the Substrate and Spatiotemporal Organization of Atrial Fibrillation: A Comparison in Canine Models of Structural and Electrical Atrial Remodeling
,”
Am. J. Physiol. Heart. Circ. Physiol.
,
291
(
6
), pp.
H2911
H2923
.
13.
Anyukhovsky
,
E. P.
,
Sosunov
,
E. A.
,
Chandra
,
P.
,
Rosen
,
T. S.
,
Boyden
,
P. A.
,
Danilo
,
P.
, and
Rosen.
,
M. R.
, 2005, “
Age-Associated Changes in Electrophysiologic Remodeling: A Potential Contributor to Initiation of Atrial Fibrillation
,”
Cardiovasc. Res.
,
66
(
2
), pp.
353
363
.
14.
Morillo
,
C. A.
,
Klein
,
G. J.
,
Jones
,
D. L.
, and
Guiraudon
,
C. M.
, 1995, “
Chronic Rapid Atrial Pacing. Structural, Functional, and Electrophysiological Characteristics of a New Model of Sustained Atrial Fibrillation
,”
Circulation
,
91
(
5
), pp.
1588
1595
.
15.
Gaspo
,
R.
,
Bosch
,
R. F.
,
Talajic
,
M.
, and
Nattel
,
S.
, 1997, “
Functional Mechanisms Underlying Tachycardia-Induced Sustained Atrial Fibrillation in a Chronic Dog Model
,”
Circulation
,
96
(
11
), pp.
4027
4035
.
16.
Lin
,
C. S.
,
Lai
,
L. P.
,
Lin
,
J. L.
,
Sun
,
Y. L.
,
Hsu
,
C. W.
,
Chen
,
C. L.
,
Mao
,
S. J. T.
, and
Huang
,
S. K. S.
, 2007, “
Increased Expression of Extracellular Matrix Proteins in Rapid Atrial Pacing-Induced Atrial Fibrillation
,”
Heart Rhythm
,
4
(
7
), pp.
938
949
.
17.
Cardin
,
S.
,
Pelletier
,
P.
,
Libby
,
E.
,
Bouter
,
S. L.
,
Xiao
,
L.
,
Kääb
,
S.
,
Demolombe
,
S.
,
Glass
,
L.
, and
Nattel
,
S.
, 2008, “
Marked Differences Between Atrial and Ventricular Gene-Expression Remodeling in Dogs With Experimental Heart Failure
,”
J. Mol. Cell. Cardiol.
,
45
(
6
), pp.
821
831
.
18.
Shimano
,
M.
,
Tsuji
,
Y.
,
Inden
,
Y.
,
Kitamura
,
K.
,
Uchikawa
,
T.
,
Harata
,
S.
,
Nattel
,
S.
, and
Murohara
,
T.
, 2008, “
Pioglitazone, a Peroxisome Proliferator-Activated Receptor-Gamma Activator, Attenuates Atrial Fibrosis and Atrial Fibrillation Promotion in Rabbits With Congestive Heart Failure
,”
Heart Rhythm
,
5
(
3
), pp.
451
459
.
19.
Li
,
D.
,
Fareh
,
S.
,
Leung
,
T. K.
, and
Nattel
,
S.
, 1999, “
Promotion of Atrial Fibrillation by Heart Failure in Dogs: Atrial Remodeling of a Different Sort
,”
Circulation
,
100
(
1
), pp.
87
95
.
20.
Verheule
,
S.
,
Wilson
,
E.
,
Everett
,
T.
,
Shanbhag
,
S.
,
Golden
,
C.
, and
Olgin
,
J.
, 2003, “
Alterations in Atrial Electrophysiology and Tissue Structure in a Canine Model of Chronic Atrial Dilatation due to Mitral Regurgitation
,”
Circulation
,
107
(
20
), pp.
2615
2622
.
21.
Omens
,
J. H.
,
May
,
K. D.
, and
McCulloch
,
A. D.
, 1991, “
Transmural Distribution of Three-Dimensional Strain in the Isolated Arrested Canine Left Ventricle
,”
Am. J. Physiol.
,
261
(
3
, Pt 2), pp.
H918
H928
.
22.
Novak
,
V. P.
,
Yin
,
F. C.
, and
Humphrey
,
J. D.
, 1994, “
Regional Mechanical Properties of Passive Myocardium
,”
J. Biomech.
,
27
(
4
), pp.
403
412
.
23.
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.
,
20
(
6
), pp.
577
589
.
24.
Demer
,
L. L.
, and
Yin
,
F. C.
, 1983, “
Passive Biaxial Mechanical Properties of Isolated Canine Myocardium
,”
J. Physiol.
,
339
, pp.
615
630
.
25.
Dokos
,
S.
,
Smaill
,
B. H.
,
Young
,
A. A.
, and
LeGrice
,
I. J.
, 2002, “
Shear Properties of Passive Ventricular Myocardium
,”
Am. J. Physiol. Heart. Circ. Physiol.
,
283
(
6
), pp.
H2650
H2659
.
26.
Dokos
,
S.
,
LeGrice
,
I. J.
,
Smaill
,
B. H.
,
Kar
,
J.
, and
Young
,
A. A.
, 2000, “
A Triaxial-Measurement Shear-Test Device for Soft Biological Tissues
,”
J. Biomech. Eng.
,
122
(
5
), pp.
471
478
.
27.
Young
,
A. A.
,
LeGrice
,
I. J.
,
Young
,
M. A.
, and
Smaill
,
B. H.
, 1998, “
Extended Confocal Microscopy of Myocardial Laminae and Collagen Network
,”
J. Microsc.
,
192
(Pt 2), pp.
139
150
.
28.
Sands
,
G. B.
,
Gerneke
,
D. A.
,
Hooks
,
D. A.
,
Green
,
C. R.
,
Smaill
,
B. H.
, and
Legrice
,
I. J.
, 2005, “
Automated Imaging of Extended Tissue Volumes Using Confocal Microscopy
,”
Microsc. Res. Tech.
,
67
(
5
), pp.
227
239
.
29.
LeGrice
,
I. J.
,
Hunter
,
P. J.
, and
Smaill
,
B. H.
, 1997, “
Laminar Structure of the Heart: A Mathematical Model
,”
Am. J. Physiol.
,
272
(
5
, Pt 2), pp.
H2466
H2476
.
30.
LeGrice
,
I. J.
,
Smaill
,
B. H.
,
Chai
,
L. Z.
,
Edgar
,
S. G.
,
Gavin
,
J. B.
, and
Hunter
,
P. J.
, 1995, “
Laminar Structure of the Heart: Ventricular Myocyte Arrangement and Connective Tissue Architecture in the Dog
,”
Am. J. Physiol.
,
269
(
2
, Pt 2), pp.
H571
H582
.
31.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
, 2009, “
Constitutive Modelling of Passive Myocardium: A Structurally Based Framework for Material Characterization
,”
Philos. Trans. R. Soc. London
,
367
(
1902
), pp.
3445
3475
.
32.
Ho
,
S. Y.
,
Sanchez-Quintana
,
D.
,
Cabrera
,
J. A.
, and
Anderson
,
R. H.
, 1999, “
Anatomy of the Left Atrium: Implications for Radiofrequency Ablation of Atrial Fibrillation
,”
J. Cardiovasc. Electrophysiol.
,
10
(
11
), pp.
1525
1533
.
33.
Papez
,
J. W.
, 1920, “
Heart Musculature of the Atria
,”
Am. J. Anat.
,
27
(
3
), pp.
255
285
.
34.
Jernigan
,
S. R.
,
Buckner
,
G. D.
,
Eischen
,
J. W.
, and
Cormier
,
D. R.
, 2007, “
Finite Element Modeling of the Left Atrium to Facilitate the Design of an Endoscopic Atrial Retractor
,”
J. Biomech. Eng.
,
129
(
6
), pp.
825
837
.
35.
Humphrey
,
J. D.
, and
Yin
,
F. C.
, 1988, “
Biaxial Mechanical Behavior of Excised Epicardium
,”
J. Biomech. Eng.
,
110
(
4
), pp.
349
351
.
36.
Oldenbourg
,
R.
, 1996, “
A New View on Polarization Microscopy
,”
Nature
,
381
(
6585
), pp.
811
812
.
37.
Xia
,
Y.
,
Moody
,
J. B.
,
Burton-Wurster
,
N.
, and
Lust
,
G.
, 2001, “
Quantitative In Situ Correlation Between Microscopic MRI and Polarized Light Microscopy Studies of Articular Cartilage
,”
Osteoarthritis Cartilage
,
9
(
5
), pp.
393
406
.
38.
Shurcliff
,
W. A.
, 1966,
Polarized Light: Production and Use
,
Harvard University Press
,
Cambridge
.
39.
Sacks
,
M. S.
, 2000, “
Biaxial Mechanical Evaluation of Planar Biological Materials
,”
J. Elast.
,
61
, pp.
199
246
.
40.
Simulia, Dessault Systèmes, Inc., 2009, Abaqus version 6.9 documentation, Providence, RI.
41.
Prot
,
V.
,
Skallerud
,
B.
, and
Holzapfel
,
G. A.
, 2007, “
Transversely Isotropic Membrane Shells with Application to Mitral Valve Mechanics. Constitutive Modelling and Finite Element Implementation
,”
Int. J. Numer. Methods Eng.
,
71
(
8
), pp.
987
1008
.
42.
Simo
,
J. C.
, and
Hughes
,
T. J. R.
, 1998,
Computational Inelasticity
,
Springer
,
New York
.
43.
Belytschko
,
T.
,
Liu
,
W. K.
, and
Moran
,
B.
, 2000,
Nonlinear Finite Elements for Continua and Structures
,
John Wiley & Sons
,
Chichester
.
44.
Wells
,
S. M.
, and
Sacks
,
M. S.
, 2002, “
Effects of Fixation Pressure on the Biaxial Mechanical Behavior of Porcine Bioprosthetic Heart Valves With Long-Term Cyclic Loading
,”
Biomaterials
,
23
(
11
), pp.
2389
2399
.
45.
Holzapfel
,
G. A.
, and
Weizsacker
,
H. W.
, 1998, “
Biomechanical Behavior of the Arterial Wall and Its Numerical Characterization
,”
Comput. Biol. Med.
,
28
(
4
), pp.
377
392
.
46.
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.
,
61
, pp.
1
48
.
47.
Fung
,
Y. C.
Fronek
,
K.
, and
Patitucci
,
P.
, 1979, “
Pseudoelasticity of Arteries and the Choice of Its Mathematical Expression
,”
Am. J. Physiol.
,
237
(
5
), pp.
H620
H631
.
48.
Federico
,
S.
,
Grillo
,
A.
,
Giaquinta
,
G.
, and
Herzog
,
W.
, 2008, “
Convex Fung-Type for Biological Tissues
,”
Meccanica
,
43
, pp.
279
288
.
49.
Sun
,
W.
, and
Sacks
,
M. S.
, 2005, “
Finite Element Implementation of a Generalized Fung-Elastic Constitutive Model for Planar Soft Tissues
,”
Biomech. Model. Mechanobiol.
,
4
(
2–3
), pp.
190
199
.
50.
Humphrey
,
J.
, 2003, “
Continuum Biomechanics of Soft Biological Tissues
,”
Proc. R. Soc. London, Ser. A
,
459
(
2029
), pp.
3
46
.
51.
VandeGeest
,
J. P.
,
Schmidt
,
D. E.
,
Sacks
,
M. S.
, and
Vorp
,
D. A.
, 2008, “
The Effects of Anisotropy on the Stress Analyses of Patient-Specific Abdominal Aortic Aneurysms
,”
Ann. Biomed. Eng.
,
36
(
6
), pp.
921
932
.
52.
Di Martino
,
E. S.
,
Bellini
,
C.
, and
Schwartzman
,
D.
, 2011, “
In Vivo Porcine Left Atrial Wall Stress: Effect of Ventricular Tachypacing on Spatial and Temporal Stress Distribution
,”
J. Biomech.
,
44
, pp.
2755
2760
.
53.
Hitch
,
D. C.
, and
Nolan
,
S. P.
, 1981, “
Descriptive Analysis of Instantaneous Left Atrial Volume-With Special Reference to Left Atrial Function
,”
J. Surg. Res.
,
30
(
2
), pp.
110
120
.
54.
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
,
3
(
6
), pp.
15
35
.
55.
Sacks
,
M. S.
, and
Sun
,
W.
, 2003, “
Multiaxial Mechanical Behavior of Biological Materials
,”
Annu. Rev. Biomed. Eng.
,
5
, pp.
251
284
.
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