Immersed boundary-finite element model of fluid–structure interaction in the aortic root

Vittoria Flamini, Abelardo DeAnda, Boyce E. Griffith

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid–structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.

Original languageEnglish (US)
Pages (from-to)139-164
Number of pages26
JournalTheoretical and Computational Fluid Dynamics
Volume30
Issue number1-2
DOIs
StatePublished - Apr 1 2016

Fingerprint

Insulator Elements
interactions
grids
sinuses
Elasticity
elastic properties
closures
cardiac output
diastole
aorta
annuli
high Reynolds number
fluid dynamics
Fluid dynamics
Mechanics
Kinematics

Keywords

  • Aortic valve
  • Finite difference method
  • Finite element method
  • Fluid–structure interaction
  • Hyperelasticity
  • Immersed boundary method
  • Incompressible flow

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Fluid Flow and Transfer Processes
  • Engineering(all)
  • Computational Mechanics

Cite this

Immersed boundary-finite element model of fluid–structure interaction in the aortic root. / Flamini, Vittoria; DeAnda, Abelardo; Griffith, Boyce E.

In: Theoretical and Computational Fluid Dynamics, Vol. 30, No. 1-2, 01.04.2016, p. 139-164.

Research output: Contribution to journalArticle

@article{fcea789033a048d5a596415d99cc8b89,
title = "Immersed boundary-finite element model of fluid–structure interaction in the aortic root",
abstract = "It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid–structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.",
keywords = "Aortic valve, Finite difference method, Finite element method, Fluid–structure interaction, Hyperelasticity, Immersed boundary method, Incompressible flow",
author = "Vittoria Flamini and Abelardo DeAnda and Griffith, {Boyce E.}",
year = "2016",
month = "4",
day = "1",
doi = "10.1007/s00162-015-0374-5",
language = "English (US)",
volume = "30",
pages = "139--164",
journal = "Theoretical and Computational Fluid Dynamics",
issn = "0935-4964",
publisher = "Springer New York",
number = "1-2",

}

TY - JOUR

T1 - Immersed boundary-finite element model of fluid–structure interaction in the aortic root

AU - Flamini, Vittoria

AU - DeAnda, Abelardo

AU - Griffith, Boyce E.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid–structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.

AB - It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid–structure interaction model of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configuration of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left-ventricular fluid dynamics.

KW - Aortic valve

KW - Finite difference method

KW - Finite element method

KW - Fluid–structure interaction

KW - Hyperelasticity

KW - Immersed boundary method

KW - Incompressible flow

UR - http://www.scopus.com/inward/record.url?scp=84958908439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958908439&partnerID=8YFLogxK

U2 - 10.1007/s00162-015-0374-5

DO - 10.1007/s00162-015-0374-5

M3 - Article

VL - 30

SP - 139

EP - 164

JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

SN - 0935-4964

IS - 1-2

ER -