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Mathematical modeling of unsteady blood flow through elastic tapered artery with overlapping stenosis

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Abstract

A nonlinear two-dimensional pulsatile blood flow through a stenosed artery is investigated by treating the deformable vascular wall as an elastic cylindrical tube containing the Newtonian fluid. In order to establish a resemblance to the in vivo conditions, the mathematical model of an improved shape of the time-variant overlapping stenosis is considered in the tapered arterial lumen. By applying a suitable coordinate transformation, the tapered cosine-shaped artery becames a non-tapered rectangular and rigid artery. The continuity and the nonlinear momentum equations are numerically solved under the appropriate physically realistic prescribed boundary conditions. In order to solve the resulting simultaneous equation system, the finite difference approximation code is developed and utilized. The effects of the taper angle, wall deformation, and severity of the stenosis within its fixed length on velocity profiles, volumetric flow rate, and resistive impedance are studied considering their dependencies with time. The present results are found in agreement with similar data from the literature.

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Acknowledgments

The computation was carried out at Math. Computing Center of IPM (http://math.ipm.ac.ir/mcc).

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Authors and Affiliations

  1. Department of Mathematics, Urmia University of Technology, Urmia, Iran

    Ahmad Reza Haghighi & Mohammad Shahbazi Asl

  2. Faculty of Engineering, CFD Research Center, Urmia University, Urmia, Iran

    Mehdi Kiyasatfar

Authors
  1. Ahmad Reza Haghighi
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  2. Mohammad Shahbazi Asl
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  3. Mehdi Kiyasatfar
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Correspondence to Ahmad Reza Haghighi.

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Technical Editor: Marcos Pinotti.

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Haghighi, A.R., Asl, M.S. & Kiyasatfar, M. Mathematical modeling of unsteady blood flow through elastic tapered artery with overlapping stenosis. J Braz. Soc. Mech. Sci. Eng. 37, 571–578 (2015). https://doi.org/10.1007/s40430-014-0206-3

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  • DOI: https://doi.org/10.1007/s40430-014-0206-3

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