Research Papers

Modeling the Effect of Red Blood Cells Deformability on Blood Flow Conditions in Human Carotid Artery Bifurcation

[+] Author and Article Information
Janez Urevc

Laboratory for Numerical Modelling and Simulations,
Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia
e-mail: janez.urevc@fs.uni-lj.si

Iztok Žun

Laboratory for Fluid Dynamics and Thermodynamics,
Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia

Milan Brumen

Chair of Biophysics,
Faculty of Medicine,
University of Maribor,
Maribor 2000, Slovenia

Boris Štok

Laboratory for Numerical Modelling and Simulations,
Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia

1Corresponding author.

Manuscript received June 3, 2016; final manuscript received September 29, 2016; published online November 30, 2016. Assoc. Editor: Ender A. Finol.

J Biomech Eng 139(1), 011011 (Nov 30, 2016) (11 pages) Paper No: BIO-16-1235; doi: 10.1115/1.4035122 History: Received June 03, 2016; Revised September 29, 2016

The purpose of this work is to predict the effect of impaired red blood cells (RBCs) deformability on blood flow conditions in human carotid artery bifurcation. First, a blood viscosity model is developed that predicts the steady-state blood viscosity as a function of shear rate, plasma viscosity, and mechanical (and geometrical) properties of RBC's. Viscosity model is developed by modifying the well-known Krieger and Dougherty equation for monodisperse suspensions by using the dimensional analysis approach. With the approach, we manage to account for the microscopic properties of RBC's, such as their deformability, in the macroscopic behavior of blood via blood viscosity. In the second part of the paper, the deduced viscosity model is used to numerically predict blood flow conditions in human carotid artery bifurcation. Simulations are performed for different values of RBC's deformability and analyzed by investigating parameters, such as the temporal mean wall shear stress (WSS), oscillatory shear index (OSI), and mean temporal gradient of WSS. The analyses show that the decrease of RBC's deformability decrease the regions of low WSS (i.e., sites known to be prevalent at atherosclerosis-prone regions); increase, in average, the value of WSS along the artery; and decrease the areas of high OSI. These observations provide an insight into the influence of blood's microscopic properties, such as the deformability of RBC's, on hemodynamics in larger arteries and their influence on parameters that are known to play a role in the initiation and progression of atherosclerosis.

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Grahic Jump Location
Fig. 1

Measured data of blood viscosity (for Ht = 45%, log.-log. scale) [15] and individual parts of the modeled relative steady-state blood viscosity Πfp (Eq. (2)).

Grahic Jump Location
Fig. 2

(a) Comparison between the measured blood viscosity (black broken curves) as a function of Ht (log. scale) for different values of shear rate (γ˙1  = 52 s−1, γ˙2  = 5.2 s−1, γ˙3  = 0.52 s−1, γ˙4  = 0.052 s−1) [16] and model predictions (gray dotted curves); (b) predicted viscosity as a function of Ht for different values of RBC deformability μ0 (Eq. (12)) at shear rate 52 s−1 and measured relative viscosity of blood containing rigid RBCs (black broken curve), taken from Chien et al. [26].

Grahic Jump Location
Fig. 3

(a) Predicted blood viscosity for differently hardened RBCs (corresponding values of μ0 are obtained using Eq. (12)) for Ht = 45% (dotted curves) along with measured data: HA and NP data (log.–log. scale) [15], (b) cross-plot of Fig. 3(a) at shear rates 0.01 s−1 and 200 s−1.

Grahic Jump Location
Fig. 4

(a) Geometrical model of the CCA and (b) flow rate waveforms applied on the ICA and ECA (obtained from Ref. [36])

Grahic Jump Location
Fig. 5

Axial velocity profile (a), mean WSSTG (b), and mean WSS (c) at location S of the model (Fig. 4(a)) along with the estimated range of the converged numerical solution (with the range [ϕ1 (1-GCI21), ϕ1 (1+GCI21)])

Grahic Jump Location
Fig. 6

Plots of time-averaged WSS: (a) results for constant blood viscosity, ηN = 3.6 mPa·s; and (b)–(d) by using the derived viscosity model for different RBC shear modulus μ0 (relation (12)): μ0_N, μ0_1, and μ0_2 (with the corresponding variation of blood viscosity presented in Fig. 3(a)). Plots are presented in logarithmic scale to highlight the regions of low (<0.4 Pa) WSS. Views 1 and 2 are presented in Fig. 4(a).

Grahic Jump Location
Fig. 7

Oscillatory shear index (OSI): (a) results for constant blood viscosity, ηN = 3.6 mPa·s; and (b)–(d) by using the derived viscosity model for different RBC shear modulus μ0 (relation (12)): μ0_N, μ0_1, and μ0_2. Views 1 and 2 are presented in Fig.4(a).

Grahic Jump Location
Fig. 8

Mean WSS temporal gradient (WSSTGavg): (a) results for constant blood viscosity, ηN = 3.6 mPa·s; and (b)–(d) by using the derived viscosity model for different RBC shear modulus μ0 (relation (12)): μ0_N, μ0_1, and μ0_2. Views 1 and 2 are presented in Fig. 4(a)



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