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TECHNICAL BRIEFS

# On the Relative Importance of Rheology for Image-Based CFD Models of the Carotid Bifurcation

[+] Author and Article Information
Sang-Wook Lee

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada M5S 3G8

David A. Steinman

Department of Mechanical and Industrial Engineering, Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Canada M5S 3G8steinman@mie.utoronto.ca

J Biomech Eng 129(2), 273-278 (Aug 26, 2006) (6 pages) doi:10.1115/1.2540836 History: Received May 19, 2006; Revised August 26, 2006

## Abstract

Background: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. Method of Approach: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. Results: Sensitivity of WSS to the various rheological assumptions was roughly $1.0dyn∕cm2$ or 8%, nearly seven times less than that due to geometric uncertainty ($6.7dyn∕cm2$ or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. Conclusions: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.

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## Figures

Figure 1

Blood viscosity as a function of shear rate for the different rheological models

Figure 2

Distribution of time-averaged WSS, based on the Week 1 geometry and assuming (a) constant viscosity of 3.5cP. (b) Carreau and (c) Ballyk viscosity models: Rescaled Newtonian viscosity derived from each subject’s characteristic inlet shear rate at (d) mean and (e) minimum flow. (f) Newtonian viscosity assuming Hct=0.35. Also shown are WSS patterns based on (g) Week 2 and (h) Week 3 models assuming a Newtonian viscosity of 3.5cP.

Figure 3

Distribution of oscillatory shear index (OSI). Refer to caption of Fig. 2 for details.

Figure 4

Comparisons of axial velocity profiles at the nominal midplane at peak systole and end diastole for the Newtonian model with μ=3.5cP (thick solid line), the Carreau model (thin solid line) and the rescaled Newtonian model based on characteristic viscosity at mean flow rate, μc,mean (thin dashed line). Note that velocities are normalized by bulk velocity at each location.

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