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Technical Briefs

Accurate Prediction of Wall Shear Stress in a Stented Artery: Newtonian Versus Non-Newtonian Models

[+] Author and Article Information
Juan Mejia, Rosaire Mongrain, Olivier F. Bertrand

e-mail: Juan.Mejia2@mail.mcgill.ca e-mail: Rosaire.Mongrain@mcgill.ca Department of Mechanical Engineering,  McGill University, Montreal Heart Institute, Montreal, Quebec, CanadaFaculty of Medicine,  Laval University, Quebec Heart-Lung Institute, Quebec, Canada e-mail: Olivier.Bertrand@criucpq.ulaval.ca

J Biomech Eng 133(7), 074501 (Jul 22, 2011) (8 pages) doi:10.1115/1.4004408 History: Received May 27, 2010; Revised June 03, 2011; Posted June 13, 2011; Published July 22, 2011; Online July 22, 2011

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood’s lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Normalized cardiac waveform in a coronary artery

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Figure 2

Rheological behavior of the three types of fluids used in the numerical models

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Figure 3

Mesh used in all numerical simulations (1,357,000 nodes)

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Figure 4

Cross-stream contours of dynamic viscosity at instant A obtained using model III. Stream-wise distances correspond to 2.65 and 3 mm from the proximal edge of the stent. Viscosity is consistently highest close to the struts of the stent at all times. (a) 2.65 mm from the proximal stent edge at instant A and (b) 3 mm from the proximal stent edge at instant A.

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Figure 5

Stream-wise contour of viscosity measured at the end of the cardiac cycle, and along the x–y plane that cuts the vessel axially in half (z = 0)

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Figure 6

Comparison of velocity fields at end of second cardiac cycle, and obtained using model I (a), model II (b), and model III (c) (a) Model I, viscosity = 3.5 cP; (b) model II, viscosity = 4.7 cP; and (c) model III, viscosity is nonlinear and described by the Carreau-Yasuda model

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Figure 7

Contours of WSS for the three models at instants A, B, and C. Primary flow direction is axially upwards. (a) Model I, instant A; (b) model I, instant B; (c) model I, instant C; (d) model II, instant A; (e) model II, instant B; (f) model II, instant C; (g) model III, instant A; (h) model III, instant B; (i) model III, instant C; (j) legend.

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Figure 8

Wall shear stress measured along the wall and over the struts of the stented arterial segment. For comparison the wall shear stress at instants A, B, and C are presented for the three working fluids. (a) Instant A; (b) instant B; (c) instant C.

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