Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.
REFERENCES
1.
L.
Rouleau
, M.
Farcas
, J.
Tardif
, R.
Mongrain
, and R.
Leask
, “Endothelial cell morphologic response to asymmetric stenosis hemodynamics: Effects of spatial wall shear stress gradients
,” J. Biomech. Eng.
132
(8
), 081013
(2010
).2.
Z.
Xu
, N.
Chen
, M.
Kamocka
, E.
Rosen
, and M.
Alber
, “A multiscale model of thrombus development
,” J. R. Soc., Interface
5
(24
), 705
–722
(2008
).3.
H.
Meng
, Z.
Wang
, Y.
Hoi
, L.
Gao
, E.
Metaxa
, D.
Swartz
, and J.
Kolega
, “Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation
,” Stroke
38
(6
), 1924
–1931
(2007
).4.
V.
Turitto
and C.
Hall
, “Mechanical factors affecting hemostasis and thrombosis
,” Thromb. Res.
92
(6, Supplement 2
), S25
–S31
(1998
).5.
P.
Holme
, U.
Orvim
, M.
Hamers
, N.
Solum
, F.
Brosstad
, R.
Barstad
, and K.
Sakariassen
, “Shear-induced platelet activation and platelet microparticle formation at blood flow conditions as in arteries with a severe stenosis
,” Arterioscler., Thromb., Vasc. Biol.
17
(4
), 646
–653
(1997
).6.
W.
Yin
, S.
Shanmugavelayudam
, and D.
Rubenstein
, “The effect of physiologically relevant dynamic shear stress on platelet and endothelial cell activation
,” Thromb. Res.
127
(3
), 235
–241
(2011
).7.
D.
Bluestein
, L.
Niu
, R.
Schoephoerster
, and M.
Dewanjee
, “Fluid mechanics of arterial stenosis: Relationship to the development of mural thrombus
,” Ann. Biomed. Eng.
25
, 344
–356
(1997
).8.
A.
Reininger
, C.
Reininger
, U.
Heinzmann
, and L.
Wurzinger
, “Residence time in niches of stagnant flow determines fibrin clot formation in an arterial branching model–detailed flow analysis and experimental results
,” Thromb. Haemostasis
74
, 916
–922
(1995
).9.
W.
Yang
, A.
Jeffrey
, and A.
Marsden
, “Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise
,” Comput. Methods Appl. Mech. Eng.
199
(33–36
), 2135
–2149
(2010
).10.
A.
Marsden
, J.
Feinstein
, and C.
Taylor
, “A computational framework for derivative-free optimization of cardiovascular geometries
,” Comput. Methods Appl. Mech. Eng.
197
(21–24
), 1890
–1905
(2008
).11.
C.
Taylor
and C.
Figueroa
, “Patient-specific modeling of cardiovascular mechanics
,” Annu. Rev. Biomed. Eng.
11
, 109
–134
(2009
).12.
S.
Sankaran
, M.
Esmaily-Moghadam
, A.
Kahn
, E.
Tseng
, J.
Guccione
, and A.
Marsden
, “Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery
,” Ann. Biomed. Eng.
40
, 2228
–2242
(2012
).13.
M.
Kunov
, D.
Steinman
, and C.
Ethier
, “Particle volumetric residence time calculations in arterial geometries
,” J. Biomech. Eng.
118
, 158
–164
(1996
).14.
G.
Suh
, A.
Les
, A.
Tenforde
, S.
Shadden
, R.
Spilker
, J.
Yeung
, C.
Cheng
, R.
Herfkens
, R.
Dalman
, and C.
Taylor
, “Quantification of particle residence time in abdominal aortic aneurysms using magnetic resonance imaging and computational fluid dynamics
,” Ann. Biomed. Eng.
39
, 864
–883
(2011
).15.
D.
Sengupta
, A.
Kahn
, J.
Burns
, S.
Sankaran
, S.
Shadden
, and A.
Marsden
, “Image-based modeling of hemodynamics in coronary artery aneurysms caused by kawasaki disease
,” Biomech. Model. Mechanobiol.
11
, 915
–932
(2012
).16.
A.
Lonyai
, A.
Dubin
, J.
Feinstein
, C.
Taylor
, and S.
Shadden
, “New insights into pacemaker lead-induced venous occlusion: Simulation-based investigation of alterations in venous biomechanics
,” Cardiovasc. Eng.
10
, 84
–90
(2010
).17.
T.
Gundert
, S.
Shadden
, A.
Williams
, B.-K.
Koo
, J.
Feinstein
, and J.
LaDisa
, “A rapid and computationally inexpensive method to virtually implant current and next-generation stents into subject-specific computational fluid dynamics models
,” Ann. Biomed. Eng.
39
, 1423
–1437
(2011
).18.
J.
Jozsa
and T.
Kramer
, “Modelling residence time as advection-diffusion with zero-order reaction kinetics
,” in Proceedings of the Hydrodynamics 2000 Conference, International Association of Hydraulic Engineering and Research
, 2000
.19.
V.
Rayz
, L.
Boussel
, L.
Ge
, J.
Leach
, A.
Martin
, M.
Lawton
, C.
McCulloch
, and D.
Saloner
, “Flow residence time and regions of intraluminal thrombus deposition in intracranial aneurysms
,” Ann. Biomed. Eng.
38
(10
), 3058
–3069
(2010
).20.
A.
Narracott
, S.
Smith
, P.
Lawford
, H.
Liu
, R.
Himeno
, I.
Wilkinson
, P.
Griffiths
, and R.
Hose
, “Development and validation of models for the investigation of blood clotting in idealized stenoses and cerebral aneurysms
,” Int. J. Artif. Organs
8
, 56
–62
(2005
).21.
T.
Hughes
, M.
Mallet
, and M.
Akira
, “A new finite element formulation for computational fluid dynamics: II. beyond SUPG
,” Comput. Methods Appl. Mech. Eng.
54
(3
), 341
–355
(1986
).22.
T.
Hughes
, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
(Dover Publications
, 2000
).23.
Y.
Bazilevs
, V.
Calo
, T.
Tezduyar
, and T.
Hughes
, “Yzβ discontinuity capturing for advection-dominated processes with application to arterial drug delivery
,” Int. J. Numer. Methods Fluids
54
(6–8
), 593
–608
(2007
).24.
R.
Steen
, E.
Evers
, B. V.
Hattum
, W.
Cofino
, and U.
Brinkman
, “Net fluxes of pesticides from the scheldt estuary into the north sea: a model approach
,” Environ. Pollut.
116
(1
), 75
–84
(2002
).25.
E.
Delhez
, A.
Heemink
, and E.
Deleersnijder
, “Residence time in a semi-enclosed domain from the solution of an adjoint problem
,” Estuarine Coastal Shelf Sci.
61
(4
), 691
–702
(2004
).26.
Y.
Bazilevs
, V.
Calo
, T.
Hughes
, and Y.
Zhang
, “Isogeometric fluid-structure interaction: theory, algorithms, and computations
,” Comput. Mech.
43
, 3
–37
(2008
).27.
M.
Canfield
, M.
Honein
, N.
Yuskiv
, J.
Xing
, C.
Mai
, J.
Collins
, O.
Devine
, J.
Petrini
, T.
Ramadhani
, C.
Hobbs
, and R.
Kirby
, “National estimates and race/ethnic-specific variation of selected birth defects in the united states, 1999–2001
,” Birth Defects ResA
76
(11
), 747
–756
(2006
).28.
J.
Tikkanen
and O.
Heinonen
, “Risk factors for hypoplastic left heart syndrome
,” Teratology
50
(2
), 112
–117
(1994
).29.
J.
Schmidt
, S.
Delp
, M.
Sherman
, C.
Taylor
, V.
Pande
, and R.
Altman
, “The Simbios National Center: Systems biology in motion
,” Proc. IEEE
96
(8
), 1266
–1280
(2008
).30.
M.
Esmaily-Moghadam
, F.
Migliavacca
, I.
Vignon-Clementel
, T.
Hsia
, and A.
Marsden
, “Optimization of shunt placement for the Norwood surgery using multi-domain modeling
,” J. Biomech. Eng.
134
(5
), 051002
(2012
).31.
F.
Migliavacca
, G.
Pennati
, G.
Dubini
, R.
Fumero
, R.
Pietrabissa
, G.
Urcelay
, E.
Bove
, T.
Hsia
, and M.
de Leval
, “Modeling of the Norwood circulation: Effects of shunt size, vascular resistances, and heart rate
,” Am. J. Physiol. Heart Circ. Physiol.
280
, H2076
–H2086
(2001
).32.
K.
Lagana
, R.
Balossino
, F.
Migliavacca
, G.
Pennati
, E.
Bove
, M.
de Leval
, and G.
Dubini
, “Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation
,” J. Biomech.
38
(5
), 1129
–1141
(2005
).33.
M.
Esmaily-Moghadam
, I.
Vignon-Clementel
, R.
Figliola
, and A.
Marsden
, “A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations
,” J. Comput. Phys.
244
, 63
–79
(2013
).34.
C.
Whiting
and K.
Jansen
, “A stabilized finite element method for the incompressible Navier-Stokes equations using a hierarchical basis
,” Int. J. Numer. Methods Fluids
35
(1
), 93
–116
(2001
).35.
L.
Franca
and S.
Frey
, “Stabilized finite element methods: II. the incompressible Navier-Stokes equations
,” Comput. Methods Appl. Mech. Eng.
99
(2–3
), 209
–233
(1992
).36.
A.
Brooks
and T.
Hughes
, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
,” Comput. Methods Appl. Mech. Eng.
32
(1–3
), 199
–259
(1982
).37.
Y.
Bazilevs
, V.
Calo
, J.
Cottrell
, T.
Hughes
, A.
Reali
, and G.
Scovazzi
, “Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
,” Comput. Methods Appl. Mech. Eng.
197
(1–4
), 173
–201
(2007
).38.
M.
Esmaily-Moghadam
, Y.
Bazilevs
, T.
Hsia
, I.
Vignon-Clementel
, and A.
Marsden
, “A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations
,” Comput. Mech.
48
(3
), 277
–291
(2011
).39.
Y.
Bazilevs
, J.
Gohean
, T.
Hughes
, R.
Moser
, and Y.
Zhang
, “Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device
,” Comput. Methods Appl. Mech. Eng.
198
(45–46
), 3534
–3550
(2009
).40.
M.
Esmaily-Moghadam
, Y.
Bazilevs
, and A. L.
Marsden
, “A new preconditioning technique for implicitly coupled multidomain simulations with applications to hemodynamics
,” Comput. Mech.
(published online).41.
J.
Newburger
, M.
Takahashi
, M.
Gerber
, M.
Gewitz
, L.
Tani
, J.
Burns
, S.
Shulman
, A.
Bolger
, P.
Ferrieri
, R.
Baltimore
et al., “Diagnosis, treatment, and long-term management of kawasaki disease
,” Circulation
110
(17
), 2747
–2771
(2004
).42.
J.
Gordon
, A.
Kahn
, and J.
Burns
, “When children with kawasaki disease grow up: Myocardial and vascular complications in adulthood
,” J. Am. Coll. Cardiol.
54
(21
), 1911
–1920
(2009
).43.
D.
Sengupta
, E.
Kung
, A.
Kahn
, J.
Burns
, and A.
Marsden
, “CFD-based thrombotic risk assessment in Kawasaki disease patients with coronary artery aneurysms
,” in Proceedings of 65th Annual Meeting of the APS Division of Fluid Dynamics
(APS
, 2012
), Vol. 57
.44.
H.
Kim
, I.
Vignon-Clementel
, J.
Coogan
, C.
Figueroa
, K.
Jansen
, and C.
Taylor
, “Patient-specific modeling of blood flow and pressure in human coronary arteries
,” Ann. Biomed. Eng.
38
, 3195
–3209
(2010
).45.
S. C.
Shadden
, F.
Lekien
, and J. E.
Marsden
, “Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
,” Physica D
212
(3
), 271
–304
(2005
).46.
F.
Lekien
, S. C.
Shadden
, and J. E.
Marsden
, “Lagrangian coherent structures in n-dimensional systems
,” J. Math. Phys.
48
, 065404
(2007
).47.
H. A.
Himburg
, D. M.
Grzybowski
, A. L.
Hazel
, J. A.
LaMack
, X.-M.
Li
, and M. H.
Friedman
, “Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability
,” Am. J. Physiol. Heart Circ. Physiol.
286
(5
), H1916
–H1922
(2004
).48.
D.
Kersh
and A.
Liberzon
, “Relations of pulsatility index and particle residence time to the wall-shear-stress properties in pulsating flows with reverse flow phase
,” eprint arXiv:1303.3727.49.
M.
Esmaily-Moghadam
, Y.
Bazilevs
, and A.
Marsden
, “Low entropy data mapping for sparse iterative linear solvers
,” in Proceedings of the Conference on Extreme Science and Engineering Discovery Environment: Gateway to Discovery
, p. 2
(ACM
, 2013
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.
