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Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models

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Abstract

To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow in large arteries is carried out using the two widely used models, McDonald’s and Burton’s models, for the pressure gradient. For both models, the blood velocity in the lumen is obtained analytically. Elaborate investigations on the wall shear stress (WSS) and oscillatory shear index (OSI) are carried out. The results are in good agreement with the available data in the literature. The superiority of McDonald’s model in capturing the pulsatile nature of blood flow, especially the OSI, is highlighted. The present investigation supports the hypothesis that not only WSS but also OSI are the essential features determining the pathogenesis of atherosclerosis. Finally, by reviewing the limitations of the present investigation, the possibility of improvement is explored.

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Abbreviations

x :

horizontal coordinate axis (m)

y :

vertical coordinate axis (m)

u :

x-component of velocity (m · s−1)

v :

y-component of velocity (m · s−1)

t :

time(s)

h :

half width of channel (m)

ρ :

density of blood (kg · m−3)

μ :

viscosity of blood (kg · m−1 · s−1)

p :

pressure (Pa)

∇ p :

pressure gradient (Pa · m−1)

a 0 :

steady part of pressure gradient (Pa · m−1)

a n :

unsteady part of pressure gradient (Pa · m−1)

α n :

phase angle

k :

permeability of wall (m2)

\(\bar \alpha \) :

Beavers and Joseph (BJ) slip coefficient

\(\bar Q\) :

steady part of Darcy velocity (m · s−1)

\(\tilde Q_n \) :

unsteady part of Darcy velocity (m · s−1)

u B :

slip-velocity at interface (m · s−1)

f :

heart frequency (Hz)

ω :

angular frequency 2πf (rad · s−1)

α :

Womersely number \(\sqrt {\tfrac{{\omega \rho h^2 }} {\mu }} \)

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Ettimadai, 641112, Coimbatore, Tamilnadu, India

    K. Gayathri & K. Shailendhra

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  1. K. Gayathri
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Correspondence to K. Shailendhra.

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Gayathri, K., Shailendhra, K. Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models. Appl. Math. Mech.-Engl. Ed. 35, 575–590 (2014). https://doi.org/10.1007/s10483-014-1814-7

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  • DOI: https://doi.org/10.1007/s10483-014-1814-7

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