Abstract

Blood-flow downstream of stenotic and healthy aortic valves exhibits intermittent random fluctuations in the velocity field which are associated with turbulence. Such flows warrant the use of computationally demanding scale-resolving models. The aim of this work was to compute and quantify this turbulent flow in healthy and stenotic heart valves for steady and pulsatile flow conditions. Large eddy simulations (LESs) and Reynolds-averaged Navier–Stokes (RANS) simulations were used to compute the flow field at inlet Reynolds numbers of 2700 and 5400 for valves with an opening area of 70 mm2 and 175 mm2 and their projected orifice-plate type counterparts. Power spectra and turbulent kinetic energy were quantified on the centerline. Projected geometries exhibited an increased pressure-drop (>90%) and elevated turbulent kinetic energy levels (>147%). Turbulence production was an order of magnitude higher in stenotic heart valves compared to healthy valves. Pulsatile flow stabilizes flow in the acceleration phase, whereas onset of deceleration triggered (healthy valve) or amplified (stenotic valve) turbulence. Simplification of the aortic valve by projecting the orifice area should be avoided in computational fluid dynamics (CFD). RANS simulations may be used to predict the transvalvular pressure-drop, but scale-resolving models are recommended when detailed information of the flow field is required.

References

1.
Nkomo
,
V. T.
,
Gardin
,
J. M.
,
Skelton
,
T. N.
,
Gottdiener
,
J. S.
,
Scott
,
C. G.
, and
Enriquez-Sarano
,
M.
,
2006
, “
Burden of Valvular Heart Diseases: A Population-Based Study
,”
Lancet
,
368
(
9540
), pp.
1005
1011
.10.1016/S0140-6736(06)69208-8
2.
Baumgartner
,
H.
,
Hung
,
J.
,
Bermejo
,
J.
,
Chambers
,
J. B.
,
Edvardsen
,
T.
,
Goldstein
,
S.
,
Lancellotti
,
P.
,
LeFevre
,
M.
,
Miller
,
F.
, and
Otto
,
C. M.
,
2017
, “
Recommendations on the Echocardiographic Assessment of Aortic Valve Stenosis: A Focused Update From the European Association of Cardiovascular Imaging and the American Society of Echocardiography
,”
Eur. Heart J. Cardiovasc. Imaging
,
18
(
3
), pp.
254
275
.10.1093/ehjci/jew335
3.
Niederberger
,
J.
,
Schima
,
H.
,
Maurer
,
G.
, and
Baumgartner
,
H.
,
1996
, “
Importance of Pressure Recovery for the Assessment of Aortic Stenosis by Doppler Ultrasound. Role of Aortic Size, Aortic Valve Area, and Direction of the Stenotic Jet In Vitro
,”
Circulation
,
94
(
8
), pp.
1934
1940
.10.1161/01.CIR.94.8.1934
4.
Baumgartner
,
H.
,
Stefenelli
,
T.
,
Niederberger
,
J.
,
Schima
,
H.
, and
Maurer
,
G.
,
1999
, “
‘Overestimation’ of Catheter Gradients by Doppler Ultrasound in Patients With Aortic Stenosis: A Predictable Manifestation of Pressure Recovery
,”
J. Am. Coll. Cardiol.
,
33
(
6
), pp.
1655
1661
.10.1016/S0735-1097(99)00066-2
5.
Bahlmann
,
E.
,
Cramariuc
,
D.
,
Gerdts
,
E.
,
Gohlke-Baerwolf
,
C.
,
Nienaber
,
C. A.
,
Eriksen
,
E.
,
Wachtell
,
K.
,
Chambers
,
J.
,
Kuck
,
K. H.
, and
Ray
,
S.
,
2010
, “
Impact of Pressure Recovery on Echocardiographic Assessment of Asymptomatic Aortic Stenosis: A SEAS Substudy
,”
JACC Cardiovasc. Imaging
,
3
(
6
), pp.
555
562
.10.1016/j.jcmg.2009.11.019
6.
Stein
,
P. D.
, and
Sabbah
,
H. N.
,
1976
, “
Turbulent Blood Flow in the Ascending Aorta of Humans With Normal and Diseased Aortic Valves
,”
Circ. Res.
,
39
(
1
), pp.
58
65
.10.1161/01.RES.39.1.58
7.
Walburn
,
F. J.
,
Sabbah
,
H. N.
, and
Stein
,
P. D.
,
1983
, “
An Experimental Evaluation of the Use of an Ensemble Average for the Calculation of Turbulence in Pulsatile Flow
,”
Ann. Biomed. Eng.
,
11
(
5
), pp.
385
399
.10.1007/BF02584215
8.
Yamaguchi
,
T.
,
Kikkawa
,
S.
,
Yoshikawa
,
T.
,
Tanishita
,
K.
, and
Sugawara
,
M.
,
1983
, “
Measurement of Turbulence Intensity in the Center of the Canine Ascending Aorta With a Hot-Film Anemometer
,”
ASME J. Biomech. Eng.
,
105
(
2
), pp.
177
187
.10.1115/1.3138403
9.
Bluestein
,
D.
, and
Einav
,
S.
,
1995
, “
The Effect of Varying Degrees of Stenosis on the Characteristics of Turbulent Pulsatile Flow Through Heart Valves
,”
J. Biomech.
,
28
(
8
), pp.
915
924
.10.1016/0021-9290(94)00154-V
10.
Yoganathan
,
A. P.
,
Corcoran
,
W. H.
, and
Harrison
,
E. C.
,
1979
, “
In Vitro Velocity Measurements in the Vicinity of Aortic Prostheses
,”
J. Biomech.
,
12
(
2
), pp.
135
152
.10.1016/0021-9290(79)90153-2
11.
Clark
,
C.
,
1976
, “
Turbulent Velocity Measurements in a Model of Aortic Stenosis
,”
J. Biomech.
,
9
(
11
), pp.
677
687
.10.1016/0021-9290(76)90169-X
12.
Sallam
,
A. M.
, and
Hwang
,
N. H. C.
,
1984
, “
Human Red Blood Cell Hemolysis in a Turbulent Shear Flow: Contribution of Reynolds Shear Stresses
,”
Biorheology
,
21
(
6
), pp.
783
797
.10.3233/BIR-1984-21605
13.
Kameneva
,
M. V.
,
Burgreen
,
G. W.
,
Kono
,
K.
,
Repko
,
B.
,
Antaki
,
J. F.
, and
Umezu
,
M.
,
2004
, “
Effects of Turbulent Stresses Upon Mechanical Hemolysis: Experimental and Computational Analysis
,”
ASAIO J.
,
50
(
5
), pp.
418
423
.10.1097/01.MAT.0000136512.36370.B5
14.
Stein
,
P. D.
, and
Sabbah
,
H. N.
,
1974
, “
Measured Turbulence and Its Effect on Thrombus Formation
,”
Circ. Res.
,
35
(
4
), pp.
608
614
.10.1161/01.RES.35.4.608
15.
Dangas
,
G. D.
,
Weitz
,
J. I.
,
Giustino
,
G.
,
Makkar
,
R.
, and
Mehran
,
R.
,
2016
, “
Prosthetic Heart Valve Thrombosis
,”
J. Am. Coll. Cardiol.
,
68
(
24
), pp.
2670
2689
.10.1016/j.jacc.2016.09.958
16.
Nygaard
,
H.
,
Paulsen
,
P.
,
Hasenkam
,
J.
,
Kromannhansen
,
O.
,
Pedersen
,
E.
, and
Rovsing
,
P.
,
1992
, “
Quantitation of the Turbulent Stress Distribution Downstream of Normal, Diseased and Artificial Aortic Valves in Humans
,”
Eur. J. Cardiothorac. Surg.
,
6
(
11
), pp.
609
617
.10.1016/1010-7940(92)90135-K
17.
Nygaard
,
H.
,
Paulsen
,
P. K.
,
Hasenkam
,
J. M.
,
Pedersen
,
E. M.
, and
Rovsing
,
P. E.
,
1994
, “
Turbulent Stresses Downstream of Three Mechanical Aortic Valve Prostheses in Human Beings
,”
J. Thorac. Cardiovasc. Surg.
,
107
(
2
), pp.
438
446
.10.1016/S0022-5223(94)70088-5
18.
Binter
,
C.
,
Gülan
,
U.
,
Holzner
,
M.
, and
Kozerke
,
S.
,
2016
, “
On the Accuracy of Viscous and Turbulent Loss Quantification in Stenotic Aortic Flow Using Phase-Contrast MRI
,”
Magn. Reson. Med.
,
76
(
1
), pp.
191
196
.10.1002/mrm.25862
19.
Ha
,
H.
,
Kvitting
,
J. P.
,
Dyverfeldt
,
P.
, and
Ebbers
,
T.
,
2019
, “
Validation of Pressure Drop Assessment Using 4D Flow MRI-Based Turbulence Production in Various Shapes of Aortic Stenoses
,”
Magn. Reson. Med.
,
81
(
2
), pp.
893
906
.10.1002/mrm.27437
20.
Ha
,
H.
,
Kim
,
G. B.
,
Kweon
,
J.
,
Huh
,
H. K.
,
Lee
,
S. J.
,
Koo
,
H. J.
,
Kang
,
J.-W.
,
2016
, “
Turbulent Kinetic Energy Measurement Using Phase Contrast MRI for Estimating the Post-Stenotic Pressure Drop: In Vitro Validation and Clinical Application
,”
PLoS One
,
11
(
3
), p.
e0151540
.10.1371/journal.pone.0151540
21.
Ha
,
H.
,
Ziegler
,
M.
,
Welander
,
M.
,
Bjarnegård
,
N.
,
Carlhäll
,
C.-J.
,
Lindenberger
,
M.
,
Länne
,
T.
,
Ebbers
,
T.
, and
Dyverfeldt
,
P.
,
2018
, “
Age-Related Vascular Changes Affect Turbulence in Aortic Blood Flow
,”
Front. Physiol.
,
9
, p.
36
.10.3389/fphys.2018.00036
22.
Andersson
,
M.
,
Lantz
,
J.
,
Ebbers
,
T.
, and
Karlsson
,
M.
,
2017
, “
Multidirectional WSS Disturbances in Stenotic Turbulent Flows: A Pre- and Post-Intervention Study in an Aortic Coarctation
,”
J. Biomech.
,
51
, pp.
8
16
.10.1016/j.jbiomech.2016.11.064
23.
Arzani
,
A.
,
Dyverfeldt
,
P.
,
Ebbers
,
T.
, and
Shadden
,
S. C.
,
2012
, “
In Vivo Validation of Numerical Prediction for Turbulence Intensity in an Aortic Coarctation
,”
Ann. Biomed. Eng.
,
40
(
4
), pp.
860
870
.10.1007/s10439-011-0447-6
24.
Goubergrits
,
L.
,
Mevert
,
R.
,
Yevtushenko
,
P.
,
Schaller
,
J.
,
Kertzscher
,
U.
,
Meier
,
S.
,
Schubert
,
S.
,
Riesenkampff
,
E.
, and
Kuehne
,
T.
,
2013
, “
The Impact of MRI-Based Inflow for the Hemodynamic Evaluation of Aortic Coarctation
,”
Ann. Biomed. Eng.
,
41
(
12
), pp.
2575
2587
.10.1007/s10439-013-0879-2
25.
Lantz
,
J.
,
Ebbers
,
T.
,
Engvall
,
J.
, and
Karlsson
,
M.
,
2013
, “
Numerical and Experimental Assessment of Turbulent Kinetic Energy in an Aortic Coarctation
,”
J. Biomech.
,
46
(
11
), pp.
1851
1858
.10.1016/j.jbiomech.2013.04.028
26.
Hoeijmakers
,
M. J. M. M.
,
Soto
,
D. A. S.
,
Wächter-Stehle
,
I.
,
Kasztelnik
,
M.
,
Weese
,
J.
,
Hose
,
D. R.
, and
de Vosse
,
F. N.
,
2019
, “
Estimation of Valvular Resistance of Segmented Aortic Valves Using Computational Fluid Dynamics
,”
J. Biomech.
,
94
, pp.
49
58
.10.1016/j.jbiomech.2019.07.010
27.
Gilmanov
,
A.
,
Barker
,
A.
,
Stolarski
,
H.
, and
Sotiropoulos
,
F.
,
2019
, “
Image-Guided Fluid-Structure Interaction Simulation of Transvalvular Hemodynamics: Quantifying the Effects of Varying Aortic Valve Leaflet Thickness
,”
Fluids
,
4
(
3
), p.
119
.10.3390/fluids4030119
28.
Wendell
,
D. C.
,
Samyn
,
M. M.
,
Cava
,
J. R.
,
Ellwein
,
L. M.
,
Krolikowski
,
M. M.
,
Gandy
,
K. L.
,
Pelech
,
A. N.
,
Shadden
,
S. C.
, and
LaDisa
,
J. F.
,
2013
, “
Including Aortic Valve Morphology in Computational Fluid Dynamics Simulations: Initial Findings and Application to Aortic Coarctation
,”
Med. Eng. Phys.
,
35
(
6
), pp.
723
735
.10.1016/j.medengphy.2012.07.015
29.
Luraghi
,
G.
,
Migliavacca
,
F.
,
Garcia-Gonzalez
,
A.
,
Chiastra
,
C.
,
Rossi
,
A.
,
Cao
,
D.
,
Stefanini
,
G.
, and
Matas
,
J. F. R.
,
2019
, “
On the Modeling of Patient-Specific Transcatheter Aortic Valve Replacement: A Fluid-Structure Interaction Approach
,”
Cardiovasc. Eng. Technol.
,
10
(
3
), pp.
437
455
.10.1007/s13239-019-00427-0
30.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1974
, “
The Numerical Computation of Turbulent Flows
,”
Comput. Methods Appl. Mech. Eng.
,
3
(
2
), pp.
269
289
.10.1016/0045-7825(74)90029-2
31.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
32.
Yoganathan
,
A. P.
,
Chandran
,
K. B.
, and
Sotiropoulos
,
F.
,
2005
, “
Flow in Prosthetic Heart Valves: State-of-the-Art and Future Directions
,”
Ann. Biomed. Eng.
,
33
(
12
), pp.
1689
1694
.10.1007/s10439-005-8759-z
33.
Varghese
,
S. S.
, and
Frankel
,
S. H.
,
2003
, “
Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels
,”
ASME J. Biomech. Eng.
,
125
(
4
), pp.
445
460
.10.1115/1.1589774
34.
Weese
,
J.
,
Lungu
,
A.
,
Peters
,
J.
,
Weber
,
F. M.
,
Waechter-Stehle
,
I.
, and
Hose
,
D. R.
,
2017
, “
CFD- and Bernoulli-Based Pressure Drop Estimates: A Comparison Using Patient Anatomies From Heart and Aortic Valve Segmentation of CT Images
,”
Med. Phys.
,
44
(
6
), pp.
2281
2292
.10.1002/mp.12203
35.
Ecabert
,
O.
,
Peters
,
J.
,
Walker
,
M. J.
,
Ivanc
,
T.
,
Lorenz
,
C.
,
von Berg
,
J.
,
Lessick
,
J.
,
Vembar
,
M.
, and
Weese
,
J.
,
2011
, “
Segmentation of the Heart and Great Vessels in CT Images Using a Model-Based Adaptation Framework
,”
Med. Image Anal.
,
15
(
6
), pp.
863
876
.10.1016/j.media.2011.06.004
36.
Okura
,
H.
,
Yoshida
,
K.
,
Hozumi
,
T.
,
Akasaka
,
T.
, and
Yoshikawa
,
J.
,
1997
, “
Planimetry and Transthoracic Two-Dimensional Echocardiography in Noninvasive Assessment of Aortic Valve Area in Patients With Valvular Aortic Stenosis
,”
J. Am. Coll. Cardiol.
,
30
(
3
), pp.
753
759
.10.1016/S0735-1097(97)00200-3
37.
Shah
,
R. G.
,
Novaro
,
G. M.
,
Blandon
,
R. J.
,
Whiteman
,
M. S.
,
Asher
,
C. R.
, and
Kirsch
,
J.
,
2009
, “
Aortic Valve Area: Meta-Analysis of Diagnostic Performance of Multi-Detector Computed Tomography for Aortic Valve Area Measurements as Compared to Transthoracic Echocardiography
,”
Int. J. Cardiovasc. Imaging
,
25
(
6
), pp.
601
609
.10.1007/s10554-009-9464-z
38.
Hoeijmakers
,
M.
,
Waechter-Stehle
,
I.
,
Weese
,
J.
, and
de Vosse
,
F. V.
,
2020
, “
Combining Statistical Shape Modeling, CFD, and Meta-Modeling to Approximate the Patient-Specific Pressure-Drop Across the Aortic Valve in Real-Time
,”
Int. J. Numer. Methods Biomed. Eng.
,
36
(
10
), p.
e3387
.10.1002/cnm.3387
39.
Alfonsi
,
G.
,
2009
, “
Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling
,”
ASME Appl. Mech. Rev.
,
62
(
4
), p.
040802
.10.1115/1.3124648
40.
Chant
,
L. J. D.
,
2005
, “
The Venerable 1/7th Power Law Turbulent Velocity Profile: A Classical Nonlinear Boundary Value Problem Solution and Its Relationship to Stochastic Processes
,”
Appl. Math. Comput.
,
161
(
2
), pp.
463
474
.10.1016/j.amc.2003.12.109
41.
Armfield
,
S.
, and
Street
,
R.
,
1999
, “
The Fractional-Step Method for the Navier–Stokes Equations on Staggered Grids: The Accuracy of Three Variations
,”
J. Comput. Phys.
,
153
(
2
), pp.
660
665
.10.1006/jcph.1999.6275
42.
Olufsen
,
M. S.
,
Peskin
,
C. S.
,
Kim
,
W. Y.
,
Pedersen
,
E. M.
,
Nadim
,
A.
, and
Larsen
,
J.
,
2000
, “
Numerical Simulation and Experimental Validation of Blood Flow in Arteries With Structured-Tree Outflow Conditions
,”
Ann. Biomed. Eng.
,
28
(
11
), pp.
1281
1299
.10.1114/1.1326031
43.
Mittal
,
R.
,
Simmons
,
S. P.
, and
Najjar
,
F.
,
2003
, “
Numerical Study of Pulsatile Flow in a Constricted Channel
,”
J. Fluid Mech.
,
485
, pp.
337
378
.10.1017/S002211200300449X
44.
Scotti
,
A.
, and
Piomelli
,
U.
,
2001
, “
Numerical Simulation of Pulsating Turbulent Channel Flow
,”
Phys. Fluids
,
13
(
5
), pp.
1367
1384
.10.1063/1.1359766
45.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fischer
,
P. F.
,
2007
, “
Direct Numerical Simulation of Stenotic Flows. Part 2. Pulsatile Flow
,”
J. Fluid Mech.
,
582
, pp.
281
318
.10.1017/S0022112007005836
46.
Welch
,
P.
,
1967
, “
The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms
,”
IEEE Trans. Audio Electroacoust.
,
15
(
2
), pp.
70
73
.10.1109/TAU.1967.1161901
47.
Bergersen
,
A. W.
,
Mortensen
,
M.
, and
Valen-Sendstad
,
K.
,
2019
, “
The FDA Nozzle Benchmark: ‘In Theory There Is No Difference Between Theory and Practice, But in Practice There Is’
,”
Int. J. Numer. Methods Biomed. Eng.
,
35
(
1
), p.
e3150
.10.1002/cnm.3150
48.
Varghese
,
S. S.
,
Frankel
,
S. H.
, and
Fischer
,
P. F.
,
2007
, “
Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow
,”
J. Fluid Mech.
,
582
, pp.
253
280
.10.1017/S0022112007005848
49.
Khair
,
A.
,
Wang
,
B.-C.
, and
Kuhn
,
D. C. S.
,
2015
, “
Study of Laminar–Turbulent Flow Transition Under Pulsatile Conditions in a Constricted Channel
,”
Int. J. Comput. Fluid Dyn.
,
29
(
9–10
), pp.
447
463
.10.1080/10618562.2015.1130222
50.
Sherwin
,
S. J.
, and
Blackburn
,
H. M.
,
2005
, “
Three-Dimensional Instabilities and Transition of Steady and Pulsatile Axisymmetric Stenotic Flows
,”
J. Fluid Mech.
,
533
, pp.
297
327
.10.1017/S0022112005004271
51.
Garcia
,
D.
,
Pibarot
,
P.
,
Landry
,
C.
,
Allard
,
A.
,
Chayer
,
B.
,
Dumesnil
,
J. G.
, and
Durand
,
L.-G.
,
2004
, “
Estimation of Aortic Valve Effective Orifice Area by Doppler Echocardiography: Effects of Valve Inflow Shape and Flow Rate
,”
J. Am. Soc. Echocardiogr.
,
17
(
7
), pp.
756
765
.10.1016/j.echo.2004.03.030
52.
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://pubmed.ncbi.nlm.nih.gov/17044363/
53.
Stewart
,
S. F. C.
,
Paterson
,
E. G.
,
Burgreen
,
G. W.
,
Hariharan
,
P.
,
Giarra
,
M.
,
Reddy
,
V.
,
Day
,
S. W.
,
2012
, “
Assessment of CFD Performance in Simulations of an Idealized Medical Device: Results of FDA's First Computational Interlaboratory Study
,”
Cardiovasc. Eng. Technol.
,
3
(
2
), pp.
139
160
.10.1007/s13239-012-0087-5
54.
Abad
,
N. S.
,
Vinuesa
,
R.
,
Schlatter
,
P.
,
Andersson
,
M.
, and
Karlsson
,
M.
,
2020
, “
Simulation Strategies for the Food and Drug Administration Nozzle Using Nek5000
,”
AIP Adv.
,
10
(
2
), p.
025033
.10.1063/1.5142703
55.
Bohbot
,
Y.
,
Kowalski
,
C.
,
Rusinaru
,
D.
,
Ringle
,
A.
,
Marechaux
,
S.
, and
Tribouilloy
,
C.
,
2017
, “
Impact of Mean Transaortic Pressure Gradient on Long-Term Outcome in Patients With Severe Aortic Stenosis and Preserved Left Ventricular Ejection Fraction
,”
J. Am. Heart Assoc.
,
6
(
6
), p.
e005850
.10.1161/JAHA.117.005850
56.
Falk
,
V.
,
Baumgartner
,
H.
,
Bax
,
J. J.
,
Bonis
,
M. D.
,
Hamm
,
C.
,
Holm
,
P. J.
,
Iung
,
B.
,
2017
, “
2017 ESC/EACTS Guidelines for the Management of Valvular Heart Disease
,”
Eur. J. Cardiothorac. Surg.
,
52
(
4
), pp.
616
664
.10.1093/ejcts/ezx324
57.
Nishimura
,
R. A.
,
Otto
,
C. M.
,
Bonow
,
R. O.
,
Carabello
,
B. A.
,
Erwin
,
J. P.
,
Guyton
,
R. A.
,
O'Gara
,
P. T.
,
2014
, “
2014 AHA/ACC Guideline for the Management of Patients With Valvular Heart Disease
,”
J. Am. Coll. Cardiol.
,
63
(
22
), pp.
e57
e185
.10.1016/j.jacc.2014.02.536
58.
Yang
,
C.-S.
,
Marshall
,
E. S.
,
Fanari
,
Z.
,
Kostal
,
M. J.
,
West
,
J. T.
,
Kolm
,
P.
,
Weintraub
,
W. S.
, and
Doorey
,
A. J.
,
2016
, “
Discrepancies Between Direct Catheter and Echocardiography-Based Values in Aortic Stenosis
,”
Catheter. Cardiovasc. Interventions
,
87
(
3
), pp.
488
497
.10.1002/ccd.26033
59.
Johnson
,
N. P.
,
Zelis
,
J. M.
,
Tonino
,
P. A. L.
,
Houthuizen
,
P.
,
Bouwman
,
R. A.
,
Brueren
,
G. R. G.
,
Johnson
,
D. T.
,
2018
, “
Pressure Gradient Vs. Flow Relationships to Characterize the Physiology of a Severely Stenotic Aortic Valve Before and After Transcatheter Valve Implantation
,”
Eur. Heart J.
,
39
(
28
), pp.
2646
2655
.10.1093/eurheartj/ehy126
60.
Takeda
,
S.
,
Rimington
,
H.
, and
Chambers
,
J.
,
2001
, “
Prediction of Symptom-Onset in Aortic Stenosis: A Comparison of Pressure Drop/Flow Slope and Haemodynamic Measures at Rest
,”
Int. J. Cardiol.
,
81
(
2–3
), pp.
131
137
.10.1016/S0167-5273(01)00544-7
61.
Blais
,
C.
,
Burwash
,
I. G.
,
Mundigler
,
G.
,
Dumesnil
,
J. G.
,
Loho
,
N.
,
Rader
,
F.
,
Baumgartner
,
H.
,
2006
, “
Projected Valve Area at Normal Flow Rate Improves the Assessment of Stenosis Severity in Patients With Low-Flow, Low-Gradient Aortic Stenosis
,”
Circulation
,
113
(
5
), pp.
711
721
.10.1161/CIRCULATIONAHA.105.557678
62.
Barannyk
,
O.
, and
Oshkai
,
P.
,
2015
, “
The Influence of the Aortic Root Geometry on Flow Characteristics of a Prosthetic Heart Valve
,”
ASME J. Biomech. Eng.
,
137
(
5
), p.
051005
.10.1115/1.4029747
63.
Zhu
,
C.
,
Seo
,
J.-H.
, and
Mittal
,
R.
,
2018
, “
Computational Modelling and Analysis of Haemodynamics in a Simple Model of Aortic Stenosis
,”
J. Fluid Mech.
,
851
, pp.
23
49
.10.1017/jfm.2018.463
64.
Long
,
J. A.
,
Undar
,
A.
,
Manning
,
K. B.
, and
Deutsch
,
S.
,
2005
, “
Viscoelasticity of Pediatric Blood and Its Implications for the Testing of a Pulsatile Pediatric Blood Pump
,”
ASAIO J.
,
51
(
5
), pp.
563
566
.10.1097/01.mat.0000180353.12963.f2
65.
Walker
,
A. M.
,
Johnston
,
C. R.
, and
Rival
,
D. E.
,
2014
, “
On the Characterization of a Non-Newtonian Blood Analog and Its Response to Pulsatile Flow Downstream of a Simplified Stenosis
,”
Ann. Biomed. Eng.
,
42
(
1
), pp.
97
109
.10.1007/s10439-013-0893-4
66.
Arzani
,
A.
,
2018
, “
Accounting for Residence-Time in Blood Rheology Models: Do We Really Need Non-Newtonian Blood Flow Modelling in Large Arteries?
,”
J. R. Soc. Interface
,
15
(
146
), p.
20180486
.10.1098/rsif.2018.0486
67.
Vita
,
F. D.
,
de Tullio
,
M. D.
, and
Verzicco
,
R.
,
2016
, “
Numerical Simulation of the Non-Newtonian Blood Flow Through a Mechanical Aortic Valve
,”
Theor. Comput. Fluid Dyn.
,
30
(
1–2
), pp.
129
138
.10.1007/s00162-015-0369-2
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