Artificial Neural Network modelling for the System of blood flow through tapered artery with mild stenosis

ANN model was designed to study the effect of blood flow and cross sectional area through tapered artery with mild stenosis , considering blood flow as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. Different ANN architecture were tested by varying network topology, resulting into an excellent agreement between the experimental data and the analytical values. Various experimental parameters i.e. stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index were used for ANN modelling and their effect on the velocity, wall shear stress, flow rate and the longitudinal impedance are analysed. It is reported that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of effected arterial system. The findings indicate that the ANN provides reasonable predictive performance in resemblance to the analytical values. The Levenberg– Marquardt algorithm (LMA) was found best of BP algorithms with a minimum mean squared error (MSE) for training and cross validation. Keywords— Artificial Neural Network; Wall shear stress; tapered artery; mild stenosis. Introduction Many cardiovascular diseases, particularly atherosclerosis, blockage of arteries are the main cause for deaths in developing countries. The factors which influence the development of this type of disease are not yet exactly answered. An abnormal growth, formed due to deposits of atherosclerotic plaques in the lumen of an artery is usually called stenosis (atherosclerosis) and, its subsequent and severe growth on the artery wall results in serious circulatory disorders [1,2]. Stenoses developed in the arteries pertaining to brain can cause cerebral strokes and the once developed in the coronary arteries can cause myocardial infarction which leads to heart failure [3]. It has been reported that the fluid dynamical properties of blood flow through non uniform cross-section of the arteries play a major role in the fundamental understanding and treatment of many cardiovascular diseases [4]. The Rheology of circulation was deeply discussed by Whitmore [5]. The analysis of blood flow through a symmetrically stenosed artery has been studied by Singh et al. [6]. Sanyal and Maji [7] investigated the unsteady blood flow through an indented tube in presence of stenosis. Young [8] observed the effect of time-dependent stenosis on flow of a Newtonian fluid through a tube. Chakravarty and Datta [9] performed rheological study on the effect of mild stenoses on the flow behaviour of blood in a stenosed arterial segment. Chaturani and Ponnalagar Samy [10] and Sankar and Hemalatha [11] have mentioned that, for tube diameter 0.095mm, blood behaves like H-B fluid rather than power law and Bingham fluids. Iida [12] says, “The velocity profile in the arterioles having diameter less than 0.1mm are generally explained fairly by the Casson and H-B fluid models. However, the velocity profile in the arterioles whose diameters less than 0.065mm does not conform to the Casson fluid model, but, can still be explained by the H-B model.” Furthermore, the H-B fluid model can be reduced to the Newtonian fluid model, power-law fluid model, and Bingham fluid model for appropriate values of the powerlaw index and yield index . Since the H-B fluid model’s constitutive equation has one more parameter than the Casson fluid model, one can get more detailed information about the flow characteristics by using the H-B fluid model. Moreover, the H-B fluid model can also be used to study the blood flow through larger arteries, since the Newtonian fluid model can be obtained as a particular case of this model. Hence, it is appropriate to represent the fluid in the core region of the two-fluid model by the H-B fluid model rather than the Casson fluid model. Thus, in this paper, we study a two-fluid model for blood flow through narrow tapered arteries with mild stenosis at low shear rates, treating the fluid in the core region as H-B fluid and the plasma in the peripheral region as Newtonian fluid (Fig. 1). Fig. 1: Geometry of tapered arteries with mild stenosis The finite-element method is employed to solve the resulting nonlinear system of partial differential equations with the appropriate boundary conditions. Neural networks are useful when a mathematical relationship is not available to describe a phenomenon to be modelled. If the property in question can be modelled by very complex and highly demanding computational techniques, neural networks provide an alternative approach to obtain accurate numerical values in a computationally less intensive fashion. Because of reliable, robust and salient characteristics in capturing the non-linear relationships of variables in complex systems, application of Artificial Neural Network (ANN) has been successfully employed in environmental engineering [13-15] and The study of blood flow through a stenotic artery is important due to nature of blood movement and behaviour of vessel walls International Journal of Mathematics Trends and TechnologyJuly to Aug 2011 ISSN: 2231-5373 http://www.internationaljournalssrg.org Page 2 are causes of many cardiovascular diseases. [16] bioprocesses [17-20]. Keeping these views in mind, an attempt has been made to find the effect of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index parameters on the velocity, wall shear stress, flow rate and the longitudinal impedance for Newtonian fluid flow through the tapered artery with mild stenosis are analysed. Materials and Methods