Mathematical modeling of axial flow between two eccentric cylinders: Application on the injection of eccentric catheter through stenotic arteries

Abstract

This study is concerned with the surgical technique for the injection of catheter through stenotic arteries. The present theoretical model may be considered as mathematical representation to the movement of physiological fluid representing blood in the gap between two eccentric tubes (eccentric-annulus flows) where the inner tube is uniform rigid representing moving catheter while the other is a tapered cylindrical tube representing artery with overlapping stenosis. The nature of blood is analyzed mathematically by considering it as a Newtonian fluid. The analysis is carried out for an artery with a mild stenosis. The problem is formulated using a perturbation expansion in terms of a variant of the eccentricity parameter (the parameter that controls the eccentricity of the catheter position) to obtain explicit forms for the axial velocity, the stream function, the resistance impedance and the wall shear stress distribution also the results were studied for various values of the physical parameters, such as the eccentricity parameter ϵ, the radius of catheter σ, the velocity of catheter Vo, the angle of circumferential direction θ (azimuthal coordinate), the taper angle ϕ and the maximum height of stenosis δ⁎. The obtained results show that there is a significant deference between eccentric and concentric annulus flows through catheterized stenosed arteries.