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Research Papers

Flow–Structure Interaction Simulations of the Aortic Heart Valve at Physiologic Conditions: The Role of Tissue Constitutive Model

[+] Author and Article Information
Anvar Gilmanov

Saint Anthony Falls Laboratory,
University of Minnesota,
Minneapolis, MN 55414
e-mail: gilmanov.anvar@gmail.com

Henryk Stolarski

Department of Civil, Environmental,
and Geo-Engineering,
University of Minnesota,
Minneapolis, MN 55414
e-mail: stola001@umn.edu

Fotis Sotiropoulos

College of Engineering and Applied Sciences,
Stony Brook University,
Stony Brook, NY 11794-2200
e-mail: fotis.sotiropoulos@stonybrook.edu

1Corresponding author.

Manuscript received December 20, 2016; final manuscript received December 28, 2017; published online January 23, 2018. Assoc. Editor: Keefe B. Manning.

J Biomech Eng 140(4), 041003 (Jan 23, 2018) (9 pages) Paper No: BIO-16-1530; doi: 10.1115/1.4038885 History: Received December 20, 2016; Revised December 28, 2017

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.

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Figures

Grahic Jump Location
Fig. 3

Calculated time history of geometric orifice area GOA(t) (a) and mean velocity Vm(t) through the orifice area (b) for tri-leaflet aortic valve with different constitutive relationship for StV (dashed-dot-dot) and MNY (solid line) models. Dashed line is the prescribed inflow flux.

Grahic Jump Location
Fig. 4

Time history of dissipation energy Ediss(t) (a) and kinetic energy Ek(t) (b) for the StV (dash-dot-dot line) and MNY (solid line) models. Dashed line is the prescribed inflow flux.

Grahic Jump Location
Fig. 2

Temporal variation of prescribed at the inlet flux (dashed line, left axis) and calculated (dash-dot-dot line for the StV model and solid line for the MNY model) transvalvular pressure gradient (right axis) at the centerline of the aorta

Grahic Jump Location
Fig. 1

(a) Computational domain for the FSI simulations of a trileaflet aortic valve in an anatomic aorta. (b) Straight line is Saint-Venant and curved solid line is MNY (S11(E11)) and curved dashed line is MNY (S22(E22)). (Online version of this figure is in color).

Grahic Jump Location
Fig. 5

Time history of average magnitude of vorticity Ωa(t) (a) and impulse |Ia(t)| (b) for the StV (dash-dot-dot line) and MNY (solid line) models. Dashed line is the prescribed inflow flux.

Grahic Jump Location
Fig. 6

Comparison of instantaneous contours of vorticity on a plane through the aorta during systolic phase showing the opening process of the StV aortic valve (first column) and MNY aortic valve (second column). The third and fourth columns are the instantaneous iso-surfaces of the Q-criterion [52] for StV and MNY models, respectively. The dot in the inset of each figure identifies the corresponding instant during the cardiac cycle: (a) ta = 0.128 s, (b) tb = 0.16 s, and (c) tc = 0.192 s. (Online version of this figure is in color).

Grahic Jump Location
Fig. 7

Contours of wall shear stresses (WSS, in Pa) and limiting streamlines (LSL, white lines with arrows, indicating direction of a blood flow) on the StV aortic valve (left column) and MNY aortic valve (right column) leaflet surfaces from the ventricular side (bottom row) and aortic side (top row) at the peak systole (t = 0.23 s.) (Online version of this figure is in color).

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