The blood flow patterns in the region around the aortic valve depend on the geometry of the aorta and on the complex flow–structure interaction between the pulsatile flow and the valve leaflets. Consequently, the flow depends strongly on the constitutive properties of the tissue, which can be expected to vary between healthy and diseased heart valves or native and prosthetic valves. The main goal of this work is to qualitatively demonstrate that the choice of the constitutive model of the aortic valve is critical in analysis of heart hemodynamics. To accomplish that two different constitutive models were used in curvilinear immersed boundary–finite element–fluid–structure interaction (CURVIB-FE-FSI) method developed by Gilmanov et al. (2015, “A Numerical Approach for Simulating Fluid Structure Interaction of Flexible Thin Shells Undergoing Arbitrarily Large Deformations in Complex Domains,” J. Comput. Phys., 300, pp. 814–843.) to simulate an aortic valve in an anatomic aorta at physiologic conditions. The two constitutive models are: (1) the Saint-Venant (StV) model and (2) the modified May-Newman&Yin (MNY) model. The MNY model is more general and includes nonlinear, anisotropic effects. It is appropriate to model the behavior of both prosthetic and biological tissue including native valves. Both models are employed to carry out FSI simulations of the same valve in the same aorta anatomy. The computed results reveal dramatic differences in both the vorticity dynamics in the aortic sinus and the wall shear-stress patterns on the aortic valve leaflets and underscore the importance of tissue constitutive models for clinically relevant simulations of aortic valves.

References

References
1.
Gilmanov
,
A.
,
Le
,
T.
, and
Sotiropoulos
,
F.
,
2015
, “
A Numerical Approach for Simulating Fluid Structure Interaction of Flexible Thin Shells Undergoing Arbitrarily Large Deformations in Complex Domains
,”
J. Comput. Phys.
,
300
, pp.
814
843
.
2.
Sotiropoulos
,
F.
,
Le
,
T.
, and
Gilmanov
,
A.
,
2016
, “
Fluid Mechanics of Heart Valves and Their Replacements
,”
Annu. Rev.
,
48
, pp.
259
283
.
3.
Back
,
M.
,
Gasser
,
T. C.
,
Miche
,
J.-B.
, and
Caligiuri
,
G.
,
2013
, “
Biomechanical Factors in the Biology of Aortic Wall and Aortic Valve Diseases
,”
Cardiovasc. Res.
,
99
(2), pp.
232
241
.
4.
Weinberg
,
E. J.
, and
Mofrad
,
M. R. K.
,
2005
, “
On the Constitutive Models for Heart Valve Leaflet Mechanics
,”
Cardiovasc. Eng.
,
5
(1), pp.
37
43
.
5.
Fan
,
R.
, and
Sacks
,
M.
,
2014
, “
Simulation of Planar Soft Tissues Using a Structural Constitutive Model: Finite Element Implementation and Validation
,”
J. Biomech.
,
47
(9), pp.
2043
2054
.
6.
Ge
,
L.
, and
Sotiropoulos
,
F.
,
2010
, “
Direction and Magnitude of Blood Flow Shear Stresses on the Leaflets of Aortic Valves: Is There a Link With Valve Calcification?
,”
ASME J. Biomech. Eng.
,
132
(1), p. 014505.
7.
Sotiropoulos
,
F.
,
Aidun
,
C.
,
Borazjani
,
I.
, and
MacMeccan
,
R.
,
2011
, “
Computational Techniques for Biological Fluids: From Blood Vessel Scale to Blood Cells
,”
Image-Based Computational Modeling of the Human Circulatory and Pulmonary. Methods and Applications
,
K. B.
Chandran
,
H. S.
Udaykumar
, and
J. M.
Reinhardt
, eds.,
Springer
,
Boston, MA
, pp.
105
156
.
8.
Claiborne
,
T. E.
,
Xenos
,
M.
,
Sheriff
,
J.
,
Chiu
,
W.-C.
,
Soares
,
J.
,
Alemu
,
Y.
,
Gupta
,
S.
,
Judex
,
S.
,
Slepian
,
M. J.
, and
Bluestein
,
D.
,
2013
, “
Towards Optimization of a Novel Trileaflet Polymeric Prosthetic Heart Valve Via Device Thrombogenicity Emulation (DTE)
,”
ASAIO J.
,
59
(3), pp.
275
283
.
9.
Votta
,
E.
,
Le
,
T.
,
Stevanella
,
M.
,
Fusini
,
L.
,
Caiani
,
E.
,
Redaelli
,
A.
, and
Sotiropoulos
,
F.
,
2013
, “
Toward Patient-Specific Simulations of Cardiac Valves: State-of-the-Art and Future Directions
,”
J. Biomech.
,
46
(
2
), pp.
217
228
.
10.
Sotiropoulos
,
F.
, and
Yang
,
X.
,
2014
, “
Immersed Boundary Methods for Simulating Fluid–Structure Interaction
,”
Prog. Aerosp. Sci.
,
65
, pp.
1
21
.
11.
Gilmanov
,
A.
, and
Sotiropoulos
,
F.
,
2015
, “
Comparative Hemodynamics in an Aorta With Bicuspid and Trileaflet Valves
,”
Theor. Comput. Fluid Dyn.
,
30
(1–2), pp.
67
85
.
12.
Tezduyar
,
T.
,
Takizawa
,
K.
,
Brummer
,
T.
, and
Chen
,
P. R.
,
2011
, “
Space-Time Fluid-Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms
,”
Numer. Methods Biol. Eng.
,
27
(11), pp.
1665
1710
.
13.
Hsu
,
M.-C.
,
Kamensky
,
D.
,
Xu
,
F.
,
Kiendl
,
J.
,
Wang
,
C.
,
Wu
,
M. C. H.
,
Mineroff
,
J.
,
Reali
,
A.
,
Bazilevs
,
Y.
, and
Sacks
,
M. S.
,
2015
, “
Dynamic and Fluid-Structure Interaction Simulations of Bioprosthetic Heart Valves Using Parametric Design With T-Splines and Fung-Type Material Models
,”
Comput. Mech.
,
55
(6), pp.
1211
1225
.
14.
Fedele
,
M.
,
Dede
,
E. F. L.
, and
Quarteroni
,
A.
,
2016
, “A Patient-Specific Aortic valve Model Based on Moving Resistive Immersed Implicit Surfaces,”
Ph.D. dissertation
, Politecnico di Milano, Milano, Italy.https://www.ncbi.nlm.nih.gov/pubmed/28593469
15.
Nobari
,
S.
,
Mongrain
,
R.
,
Leask
,
R.
, and
Cartier
,
R.
,
2013
, “
The Effect of Aortic Wall and Aortic Leaflet Stiffening on Coronary Hemodynamic: A Fluid-Structure Interaction Study
,”
Med. Biol. Eng. Comput.
,
51
(8), pp.
923
936
.
16.
Bavo
,
A. M.
,
Rocatello
,
G.
,
Iannaccone
,
F.
,
Degroote
,
J.
,
Vierendeels
,
J.
, and
Segers
,
P.
,
2015
, “
Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison Between Immersed Boundary and Arbitrary Lagrangian-Eulerian Techniques for the Mesh Representation
,”
PLoS One
,
11
(
4
), p.
e0154517
.
17.
Kamensky
,
D.
,
Hsu
,
M.-C.
,
Schillinger
,
D.
,
Evans
,
J. A.
,
Aggarwal
,
A.
,
Bazilevs
,
Y.
,
Sacks
,
M. S.
, and
Hughes
,
T. J. R.
,
2015
, “
An Immersogeometric Variational Framework for Fluid-Structure Interaction: Application to Bioprosthetic Heart Valves
,”
Comput. Methods Appl. Mech. Eng.
,
284
, pp.
1005
1053
.
18.
Flamini
,
V.
,
De Anda
,
A.
, and
Griffith
,
B. E.
,
2016
, “
Immersed Boundary-Finite Element Model of Fluid-Structure Interaction in the Aortic Root
,”
Theor. Comput. Fluid Dyn.
,
30
(1–2), pp.
139
164
.
19.
Sturla
,
F.
,
Votta
,
E.
,
Stevanella
,
M.
,
Conti
,
C. A.
, and
Redaelli
,
A.
,
2016
, “
Impact of Modeling Fluid-Structure Interaction in the Computational Analysis of Aortic Root Biomechanics
,”
Med. Eng. Phys.
,
35
(12), pp.
1721
1730
.
20.
Wu
,
W.
,
Pott
,
D.
,
Mazza
,
B.
,
Sironi
,
T.
,
Dordoni
,
E.
,
Chiastra
,
C.
,
Petrini
,
L.
,
Pennati
,
G.
,
Dubini
,
G.
,
Steinseifer
,
U.
,
Sonntag
,
S.
,
Kuetting
,
M.
, and
Migliavacca
,
F.
,
2016
, “
Fluid-Structure Interaction Model of a Percutaneous Aortic Valve: Comparison With an In Vitro Test and Feasibility Study in a Patient-Specific Case
,”
Ann. Biomed. Eng.
,
44
(2), pp.
590
603
.
21.
Hsu
,
M.-C.
,
Kamensky
,
D.
,
Bazilevs
,
Y.
,
Sacks
,
M. S.
, and
Hughes
,
T. J. R.
,
2014
, “
Fluid-Structure Interaction Analysis of Bioprosthetic Heart Valves: Significance of Arterial Wall Deformation
,”
Comput. Mech.
,
54
, pp. 1055–1071.
22.
Piatti
,
F.
,
Sturla
,
F.
,
Marom
,
G.
,
Sheriff
,
J.
,
Claiborne
,
T. E.
,
Slepian
,
M. J.
,
Redaelli
,
A.
, and
Bluestein
,
D.
,
2015
, “
Hemodynamic and Thrombogenic Analysis of a Trileaflet Polymeric Valve Using a Fluid-Structure Interaction Approach
,”
J. Biomech.
,
48
(13), pp.
3650
3658
.
23.
Morganti
,
S.
,
Auricchio
,
F.
,
Benson
,
D.
,
Gambarin
,
F.
,
Hartmann
,
S.
,
Hughes
,
T.
, and
Reali
,
A.
,
2015
, “
Patient-Specific Isogeometric Structural Analysis of Aortic Valve Closure
,”
Comput. Methods Appl. Mech. Eng.
,
284
, pp.
508
520
.
24.
Borazjani
,
I.
,
Ge
,
L.
, and
Sotiropoulos
,
F.
,
2010
, “
High-Resolution Fluid-Structure Interaction Simulations of Flow Through a Bi-Leaflet Mechanical Heart Valve in an Anatomic Aorta
,”
Ann. Biomed. Eng.
,
38
(2), pp.
326
344
.
25.
Le
,
T. B.
, and
Sotiropoulos
,
F.
,
2013
, “
Fluid-Structure Interaction of an Aortic Heart Valve Prosthesis Driven by an Animated Anatomic Left Ventricle
,”
J. Comput. Phys.
,
244
, pp.
41
62
.
26.
Stolarski
,
H.
,
Gilmanov
,
A.
, and
Sotiropoulos
,
F.
,
2013
, “
Non-Linear Rotation-Free 3-Node Shell Finite-Element Formulation
,”
Int. J. Numer. Methods Eng.
,
95
(9), pp.
740
770
.
27.
Tepole
,
A. B.
,
Kabari
,
H.
,
Bletzinger
,
K.-U.
, and
Kuhl
,
E.
,
2015
, “
Isogeometric Kirchhoff-Love Shell Formulations for Biological Membranes
,”
Comput. Methods Appl. Mech. Eng.
,
293
, pp.
328
347
.
28.
Gilmanov
,
A.
,
Stolarski
,
H.
, and
Sotiropoulos
,
F.
,
2016
, “
Non-Linear Rotation-Free Shell Finite-Element Models for Aortic Heart Valves
,”
J. Biomech.
,
50
, pp. 56–62.
29.
Ge
,
L.
, and
Sotiropoulos
,
F.
,
2007
, “
A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains With Complex Immersed Boundaries
,”
J. Comput. Phys.
,
225
(
2
), pp.
1782
1809
.
30.
Gilmanov
,
A.
, and
Sotiropoulos
,
F.
,
2005
, “
A Hybrid Cartesian/Immersed Boundary Method for Simulating Flows With 3D, Geometrically Complex, Moving Bodies
,”
J. Comput. Phys.
,
207
(
2
), p.
457
.
31.
Borazjani
,
I.
,
Ge
,
L.
, and
Sotiropoulos
,
F.
,
2008
, “
Curvilinear Immersed Boundary Method for Simulating Fluid-Structure Interaction With Complex 3D Rigid Bodies
,”
J. Comput. Phys.
,
227
(
16
), pp.
7587
7620
.
32.
Felippa
,
C. A.
,
Park
,
K. C.
, and
Farhat
,
C.
,
2001
, “
Partitioned Analysis of Coupled Mechanical Systems
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
24–25
), pp.
3247
3270
.
33.
Fernandez
,
M.
,
Gerbeau
,
J.-F.
, and
Grandmont
,
C.
,
2007
, “
A Projection Semi-Implicit Scheme for the Coupling of an Elastic Structure With an Incompressible Fluid
,”
Int. J. Numer. Methods Eng.
,
69
(4), pp.
794
821
.
34.
Bathe
,
K.
,
1996
,
Finite Element Procedures in Engineering Analysis
,
Prentice Hall
,
Englewood Cliffs, NJ
.
35.
May-Newman
,
K.
, and
Yin
,
F.
,
1998
, “
A Constitutive Law for Mitral Valve Tissue
,”
ASME J. Biomech. Eng.
,
120
(1), pp.
38
47
.
36.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2010
, “
Constitutive Modelling of Arteries
,”
Proc. R. Soc. A
,
466
(2118), pp.
1551
1597
.
37.
Gould
,
P. L.
,
Cataloglu
,
A.
, and
Clark
,
R. E.
,
1976
, “
Mathematical Modelling of Human Aortic Valve Leaflets
,”
Appl. Math. Modell.
,
1
(1), pp.
33
36
.
38.
May-Newman
,
K.
,
Lam
,
C.
, and
Yin
,
F. C. P.
,
2009
, “
A Hyperelastic Constitutive Law for Aortic Valve Tissue
,”
ASME J. Biomech. Eng.
,
131
(8), p. 081009.
39.
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
.
40.
Li
,
J.
,
Luob
,
X.
, and
Kuang
,
Z.
,
2001
, “
A Nonlinear Anisotropic Model for Porcine Aortic Heart Valves
,”
J. Biomech.
,
34
(10), pp.
1279
1289
.
41.
Balachandran
,
K.
,
Sucosky
,
P.
, and
Yoganathan
,
A. P.
,
2011
, “
Hemodynamics and Mechanobiology of Aortic Valve Inflammation and Calcification
,”
Int. J. Inflammation
,
2011
, p. 263870.
42.
Cataloglu
,
G. P. L.
, and
Clark
,
R. E.
,
2001
, “
Refined Stress Analysis of Human Aortic Heart Valves
,”
J. Eng. Mech. Div.
,
102
, pp.
135
150
.
43.
Liu
,
J. S.
,
Lu
,
P. C.
, and
Chu
,
S. H.
,
2000
, “
Turbulence Characteristics Downstream of Bileaflet Aortic Valve Prostheses
,”
ASME J. Biomech. Eng.
,
122
(2), pp.
118
124
.
44.
Carmody
,
C.
,
Burriesci
,
G.
,
Howard
,
I.
, and
Patterson
,
E.
,
2006
, “
An Approach to the Simulation of Fluid-Structure Interaction in the Aortic Valve
,”
J. Biomech.
,
39
(1), pp.
158
169
.
45.
Loudon
,
C.
, and
Tordesillas
,
A.
,
1998
, “
The Use of the Dimensionless Womersley Number to Characterize the Unsteady Nature of Internal Flow
,”
J. Theor. Biol.
,
191
(1), pp.
63
78
.
46.
Garcia
,
D.
, and
Kadem
,
L.
,
2006
, “
What Do You Mean by Aortic Valve Area: Geometric Orifice Area, Effective Orifice Area, or Gorlin Area?
,”
J. Heart Valve Dis.
,
15
(5), pp.
601
608
.https://www.icr-heart.com/?cid=1657
47.
Anderson
,
D.
,
Tennehill
,
J.
, and
Pletcher
,
R.
,
1984
,
Computational Fluid Mechanics and Head Transfer
,
Hemisphere
,
New York
.
48.
Kheradvar
,
A.
, and
Pedrizzetti
,
G.
,
2012
,
Vortex Formation in the Cardiovascular System
,
Springer-Verlag
,
London
.
49.
Falahatpisheh
,
A.
, and
Kheradvar
,
A.
,
2014
, “
A Measure of Axisymmetry for Vortex Rings
,”
Eur. J. Mech. B
,
49
(Part A), pp.
264
271
.
50.
Batchelor
,
G.
,
1973
,
An Introduction to Fluid Dynamics
,
Cambridge University Press
,
Cambridge, UK
.
51.
Aslam
,
A. K.
,
Aslam
,
A. F.
,
Vasavad
,
B. C.
, and
Khan
,
I. A.
,
2007
, “
Prosthetic Heart Valves: Types and Echocardiographic Evaluation
,”
Int. J. Cardiol.
,
122
(2), pp.
99
110
.
52.
Hunt
,
J.
,
Wray
,
A.
, and
Moin
,
P.
,
1988
, “
Eddies, Streams, and Convergence Zones in Turbulent Flows
,”
Summer Program
, pp.
193
208
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890015184.pdf
53.
Ku
,
D. N.
,
1997
, “
Blood Flow in Arteries
,”
Annu. Rev. Fluid Mech.
,
29
, pp.
399
434
.
54.
Entezari
,
P.
,
Schnell
,
S.
,
Mahadevia
,
R.
,
Malaisrie
,
C.
,
McCarthy
,
P.
,
Mendelson
,
M.
,
Collins
,
J.
,
Carr
,
J. C.
,
Markl
,
M.
, and
Barker
,
A. J.
,
2013
, “
From Unicuspid to Quadricuspid: Influence of Aortic Valve Morphology on Aortic Three-Dimensional Hemodynamics
,”
J. Magn. Reson. Imaging
,
40
(6), pp. 1342–1346.
55.
Malek
,
A.
,
Alper
,
S.
, and
Izumo
,
S.
,
1999
, “
Hemodynamic Shear Stress and Its Role in Atherosclerosis
,”
J. Am. Med. Assoc.
,
282
(21), pp.
2035
2042
.
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