Mass transfer to blood flowing through arterial stenosis

The present investigation deals with a mathematical model representing the mass transfer to blood streaming through the arteries under stenotic condition. The mass transport refers to the movement of atherogenic molecules, that is, blood-borne components, such as oxygen and low-density lipoproteins from flowing blood into the arterial walls or vice versa. The blood flowing through the artery is treated to be Newtonian and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The nonlinear unsteady pulsatile flow phenomenon unaffected by concentration-field of the macromolecules is governed by the Navier–Stokes equations together with the equation of continuity while that of mass transfer is controlled by the convection-diffusion equation. The governing equations of motion accompanied by appropriate choice of the boundary conditions are solved numerically by MAC(Marker and Cell) method and checked numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and concentration along with their distributions over the entire arterial segment as well. The key factors like the wall shear stress and Sherwood number are also examined for further qualitative insight into the flow and mass transport phenomena through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.     

Effect of surface irregularities on unsteady pulsatile flow in a compliant artery

Of concern in the paper is an analytical study of pulsatile blood flow in an irregular stenosed arterial segment through a mathematical model. The model is two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery [L. Back, Y. Cho, D. Crawford, R. Cuffel, Effect of mild atherosclerosis on flow resistance in a coronary artery casting of man, J. Biomech. Eng. 106 (1984) 48–53]. The combined influence of an asymmetric shape and surface irregularities of the constriction has been explored in a computational study of blood flow through arterial stenosis with 48% areal occlusion. The moving wall of the artery is included to be anisotropic, linear, viscoelastic, incompressible circular cylindrical membrane shell. The effect of the surrounding connective tissues on the motion of the arterial wall is also paid due attention. Results are also obtained for a smooth stenosis model and also for a stenosis model representative by the cosine curve. An extensive quantitative analysis has been performed in non-uniform non-staggered grids through numerical computations for the effect of surface irregularities on the flow velocity, the flux, the resistive impedance and on the wall shear stress through their graphical representations so as to validate the applicability of such an improved mathematical model.     

Numerical simulation of Casson fluid flow through differently shaped arterial stenoses

The present investigation deals with a mathematical model of blood flow through an asymmetric (about its narrowest point) arterial constriction obtained from casting of a mildly stenosed artery. The flowing blood is represented as the suspension of all red cells (erythrocytes) in plasma assumed to be Casson fluid, while the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell method in order to compute the physiologically significant quantities with desired degree of accuracy. The necessary checking for numerical stability has been incorporated in the algorithm for better precision of the results computed. The quantitative analyses have been carried out finally with the inclusion of the respective profiles of the flow field over the entire arterial segment as well. The key factors such as the wall shear stress, the pressure drop and the velocity profiles are exhibited graphically and examined thoroughly for qualitative insight into blood flow phenomena through arterial stenosis.     

Mass transfer to blood flowing through arterial stenosis

The present investigation deals with a mathematical model representing the mass transfer to blood streaming through the arteries under stenotic condition. The mass transport refers to the movement of atherogenic molecules, that is, blood-borne components, such as oxygen and low-density lipoproteins from flowing blood into the arterial walls or vice versa. The blood flowing through the artery is treated to be Newtonian and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The nonlinear unsteady pulsatile flow phenomenon unaffected by concentration-field of the macromolecules is governed by the Navier–Stokes equations together with the equation of continuity while that of mass transfer is controlled by the convection-diffusion equation. The governing equations of motion accompanied by appropriate choice of the boundary conditions are solved numerically by MAC(Marker and Cell) method and checked numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and concentration along with their distributions over the entire arterial segment as well. The key factors like the wall shear stress and Sherwood number are also examined for further qualitative insight into the flow and mass transport phenomena through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.      

Numerical simulation of mass transfer to micropolar fluid flow past a stenosed artery

A mathematical model of unsteady non‐Newtonian blood flow together with the mass transfer through constricted arteries has been developed. The mass transport refers to the movement of atherogenic molecules, i.e. blood‐borne components, such as low‐density lipoproteins from flowing blood into the arterial walls or vice versa. The flowing blood is represented as the suspension of all erythrocytes assumed to be Eringen's micropolar fluid and the arterial wall is considered to be rigid having cosine‐shaped stenosis in its lumen. The mass transfer to blood is controlled by the convection–diffusion equation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell method and the results obtained are checked for numerical stability with the desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow‐field and the mass concentration along with their distributions over the entire arterial segment as well. The key factors, such as the wall shear stress and Sherwood number, are also examined for further quantitative insight into the flow and the mass transport phenomena through arterial stenosis. The present results show consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration. Copyright © 2010 John Wiley & Sons, Ltd.