A Mathematical Model of Blood Flow in a Catheterized artery with multiple stenoses

A mathematical model is developed in this investigation for studying the axi-symmetric flow of blood through a catheterized artery with multiple stenoses. Consideration of Newtonian character of blood is described following the report of Young (1968) and Srivastava (2009) with the appropriate constitutive equation governing the flow. The boundary conditions appropriate to the problem under study are the standard no slip conditions at the artery and the catheter wall. Analytical expressions for impedance (flow resistance), the wall stress distribution in the stenotic region and the shear stress at the stenosis throat in their non dimensional form are derived by using the model. The derived expressions are computed numerically and the results are presented graphically for different values of the rheological and other parameters. The study provides an insight into the effects of catheter radius and stenosis height on impedance, wall stress distribution in the stenotic region and the shear stress at the stenotic throat.

ON IMPROVEMENT OF THE IMPEDANCE EDUCATION ACCURACE BY ACCOUNT OF IMPEDANCE VARIABILITY ALONG THE ACOUSTIC LINER

An impedance eduction method considering impedance variability along the acoustic liner is proposed. Impedance eduction is based on minimization of the residual functional, which is the discrepancy between the experimental and computed values of acoustic pressure at the interferometer microphones. The computed values are obtained by solving the Helmholtz equation, convected Helmholtz equation and linearized Navier-Stokes equations for a two-dimensional duct with an impedance wall and flow based on finite-element method. The cases of constant and variable impedance along the liner sample are considered. It is established that when taking into account the variable impedance, the residual functional decreases more than twofold against the case of constant impedance.

Viscous effects on the acoustics and stability of a shear layer over an impedance wall

The effect of viscosity and thermal conduction on the acoustics in a shear layer above an impedance wall is investigated numerically and asymptotically by solving the linearised compressible Navier–Stokes equations (LNSE). It is found that viscothermal effects can be as important as shear, and therefore including shear while neglecting viscothermal effects by solving the linearised Euler equations (LEE) is questionable. In particular, the damping rate of upstream-propagating waves is found to be under-predicted by the LEE, and dramatically so in certain instances. The effects of viscosity on stability are also found to be important. Short wavelength disturbances are stabilised by viscosity, greatly altering the characteristic wavelength and maximum growth rate of instability. For the parameters considered here (chosen to be typical of aeroacoustic situations), the Reynolds number below which the flow stabilises ranges from$10^{5}$to$10^{7}$. By assuming a thin but non-zero-thickness boundary layer, asymptotic analysis leads to a system of boundary layer governing equations for the acoustics. This system may be solved numerically to produce an effective impedance boundary condition, applicable at the wall of a uniform inviscid flow, that accounts for both the shear and viscosity within the boundary layer. An alternative asymptotic analysis in the high-frequency limit yields a different set of boundary layer equations, which are solved to yield analytic solutions. The acoustic mode shapes and axial wavenumbers from both asymptotic analyses compare well with numerical solutions of the full LNSE. A closed-form effective impedance boundary condition is derived from the high-frequency asymptotics, suitable for application in frequency domain numerical simulations. Finally, surface waves are considered, and it is shown that a viscous flow over an impedance lining supports a greater number of surface wave modes than an inviscid flow.

Metallic nanoparticles analysis for the blood flow in tapered stenosed arteries: Application in nanomedicines

Blood flow model is recycled to study the influence of magnetic field and nanoparticles in tapered stenosed arteries. The metallic nanoparticles for the blood flow with water as base fluid are not explored so far. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest for pure water and Copper water ( Cu -water).

Mathematical analysis of Phan-Thien–Tanner fluid model for blood in arteries

In the present paper, we have studied the blood flow through tapered artery with a stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Phan-Thien–Tanner fluid. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

Mixed convection analysis for blood flow through arteries on Williamson fluid model

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. The effects of mixed convection heat and mass transfer are also carried out. Perturbation solutions have been calculated for velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Streamlines have been plotted at the end of the paper.

Blood flow of Carreau fluid in a tapered artery with mixed convection

This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equation of Carreau fluid has been invoked in the mathematical formulation. The representation of blood flow is considered through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is given due attention. Solutions have been obtained for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Graphical illustrations associated with the tapered arteries namely converging, diverging and non-tapered arteries are examined for different parameters of interest. Streamlines have been plotted and discussed.

Blood flow analysis in tapered stenosed arteries with pseudoplastic characteristics

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. Perturbation solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.