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The impact of the aortic valve impairment on the distant coronary arteries hemodynamics: a fluid–structure interaction study

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Abstract

Atherosclerosis is still the leading cause of death in the developed world. Although its initiation and progression is a complex multifactorial process, it is well known that blood flow-induced wall shear stress (WSS) is an important factor involved in early atherosclerotic plaque initiation. In recent clinical studies, it was established that the regional pathologies of the aortic valve can be involved in the formation of atherosclerotic plaques. However, the impact of hemodynamic effects is not yet fully elucidated for disease initiation and progression. In this study, our developed 3D global fluid–structure interaction model of the aortic root incorporating coronary arteries is used to investigate the possible interaction between coronary arteries and aortic valve pathologies. The coronary hemodynamics was examined and quantified for different degrees of aortic stenosis varying from nonexistent to severe. For the simulated healthy model, the calculated WSS varied between 0.41 and 1.34 Pa which is in the atheroprotective range. However, for moderate and severe aortic stenoses, wide regions of the coronary structures, especially the proximal sections around the first bifurcation, were exposed to lower values of WSS and therefore they were prone to atherosclerosis even in the case of healthy coronary arteries.

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Abbreviations

\({\mathbf{F}}\) :

Material deformation tensor at the current configuration

\({\mathbf{f}}_{f}\) :

Body force applied on the fluid domain, \({\text{dyne}}\)

\({\mathbf{f}}_{s}\) :

Body force applied on the solid domain, \({\text{dyne}}\)

\({\mathbf{n}}_{s}\) :

Outward pointing normal unit vector to solid domain, dimensionless

\({\mathbf{n}}_{f}\) :

Outward pointing normal unit vector to fluid domain, dimensionless

\(p_{f}\) :

Hydrostatic pressure in the fluid domain, \({\text{Barye}}\)

\(p_{s}\) :

Hydrostatic pressure in the solid domain, \({\text{Barye}}\)

\({\mathbf{q}}_{f}\) :

Appropriate weight function for the continuity equation in fluid domain, arbitrary

\({\mathbf{q}}_{s}\) :

Appropriate weight function for the continuity equation in fluid domain, arbitrary

\(t\) :

Time, s

\({\mathbf{v}}_{f}\) :

Fluid domain velocity vector, cm/s

\({\mathbf{v}}_{s}\) :

Solid domain velocity vector, cm/s

\(v_{\text{grid}}\) :

Velocity of the moving fluid grid, cm/s

\({\mathbf{w}}_{f}\) :

Appropriate weight function for the momentum equation in fluid domain, arbitrary

\({\mathbf{w}}_{s}\) :

Appropriate weight function for the momentum equation in solid domain, arbitrary

\(\rho_{f}\) :

Fluid domain density, g/cm3

\(\rho_{s}\) :

Solid domain density, g/cm3

\({\varvec{\upsigma}}_{f}\) :

Cauchy stress tensor in fluid domain, \({\text{Barye}}\)

\({\varvec{\upsigma}}_{s}\) :

Cauchy stress tensor in solid domain, \({\text{Barye}}\)

\(\varOmega_{f}\) :

Fluid domain, cm3

\(\varOmega_{s}\) :

Solid domain, cm3

\(\varOmega\) :

Entire computational domain, cm3

\(\partial \varOmega_{s}\) :

Fluid–structure interface, cm2

\(\nabla\) :

Gradient operator with respect to the current configuration, cm−1

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Acknowledgements

This research was supported by McGill Engineering Doctoral Award (MEDA), NSERC and Montreal Heart institute (MHI). This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada.

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  1. Mechanical Engineering Department, McGill University, Montreal, QC, H3A 0C3, Canada

    Hossein Mohammadi & Rosaire Mongrain

  2. Department of Cardiovascular Surgery, Montreal Heart Institute, Montreal, QC, H1T 1C8, Canada

    Raymond Cartier & Rosaire Mongrain

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Correspondence to Rosaire Mongrain.

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Mohammadi, H., Cartier, R. & Mongrain, R. The impact of the aortic valve impairment on the distant coronary arteries hemodynamics: a fluid–structure interaction study. Med Biol Eng Comput 55, 1859–1872 (2017). https://doi.org/10.1007/s11517-017-1636-8

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