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

Haghighi, Ahmad Reza; Asl, Mohammad Shahbazi; Kiyasatfar, Mehdi

doi:10.1007/s40430-014-0206-3

Cited by 31 publications

(14 citation statements)

References 28 publications

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“…1) [6,7,17,25]: where R(z, t) is the radius of the arterial segment in the constricted region, R 0 is the constant radius of the normal artery outside the stenotic region, 3l0 2 is the length of the stenosis, L is the finite length of arterial segment, d is the upstream length of the artery, ψ is the angle of tapering, m = tan(ψ) is the slope of the tapered vessel and τ m is the critical height of the overlapping stenosis. The time-variant parameter a 1 (t) is given by a 1 (t) = 1 + k r cos(ωt − φ) [14,16,32], in which k r represents the amplitude parameter and φ the phase angle.…”

Section: Geometry Of the Stenosismentioning

confidence: 99%

“…The two-dimensional unsteady flow of blood through a tapered flexible artery in the presence of stenosis under a pulsatile pressure gradient have been satisfactorily investigated by Chakravarty and Mandal [7] and Haghighi et al [14] who treated flowing blood as a Newtonian fluid. In the case of flow through large arteries, shear rate is high and the assumption of Newtonian behavior of blood is acceptable, whereas, blood behave as a non-Newtonian fluid at low shear rates and in small diameter arteries, also under diseased conditions blood flow has non-Newtonian behavior [15,22,29].…”

Section: Introductionmentioning

confidence: 99%

“…Most of the blood vessels could be considered as long and narrow tapered cones that have varying cross-section, moreover assuming blood vessel as a rigid tube is not suitable and it must be considered as a flexible artery [7,14,21]. Vessel tapering is a significant aspect of mammalian arterial system and the effects of vessel tapering and the shape of stenosis on blood flow characteristics together with the non-Newtonian behavior of the blood flow are important and deserve special attention [7,22,29].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

Haghighi

Asl

2015

Int. J. Biomath.

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In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics considering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrotational velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.

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Section: Geometry Of the Stenosismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

Haghighi

Asl

2015

Int. J. Biomath.

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“…The Navier-Stokes equations for Newtonian flow together with the equation of continuity, may be written in nondimensional forms [4,6,9,12,15] as:…”

Section: The Mathematical Formulationmentioning

confidence: 99%

Numerical Investigation of Pulsatile Blood Flow in Stenosed Artery

Haghighi

Kabdool

Asl

et al. 2015

Int. J. Appl. Comput. Math

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In the present study, a two-layered model of pulsatile flow of blood through a stenosed elastic artery is numerically examined. The two-fluid model consists of a core layer of a suspension of erythrocytes and peripheral plasma layer. It is assumed that the core and peripheral plasma layer behave as micropolar and Newtonian fluids respectively. The resulting system of nonlinear partial differential equations is numerically solved using the finite difference scheme by exploiting the suitably prescribed conditions. Effects of the tapering angle, wall deformation and severity of the stenosis on flow characteristics are discussed. The present results are compared with literature and found to be in good agreement.

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“…In most of the recent works, the stenotic geometry has been considered as time independent, which is suitable for blood flow through a rigid artery . But for flow through a deformable artery, the consideration of time variant geometry of constriction is to be considered.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of pulsatile flow of blood in a stenosed tapered artery

Mukhopadhyay¹,

Mandal

Mukhopadhyay

2018

Math Methods in App Sciences

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The aim of this paper is to throw some light on the rheological study of pulsatile blood flow in a stenosed tapered arterial segment. Arterial wall is considered to be rigid and flexible separately for improving the similarity to the in vivo situation. The streaming blood is considered to be Newtonian. The governing nonlinear equations of motion are sought using the well-known stream function-vorticity method and are solved numerically by finite difference technique. Important rheological parameters, such as axial velocity component, wall shear stress, and flow separation region are estimated in the neighborhood of the stenosis. Effects of stenosis height, vessel tapering, and wall flexibility on the blood flow are investigated properly and are explained in detail through their graphical representations.

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

Cited by 31 publications

References 28 publications

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

Numerical Investigation of Pulsatile Blood Flow in Stenosed Artery

Dynamic response of pulsatile flow of blood in a stenosed tapered artery

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