Generation of the mathematical model to analyze the dynamical behaviour of the blood flow

Abstract

This paper focuses on the mathematical model based on the input output realization with a view to analyzing the time-invariant dynamical behaviour of the blood flow through carotid artery. The entire system’s characteristic is governed by the Navier-Stokes equation which is represented in this paper as differential-algebraic matrix representation. This mathematical representation is commonly known as state space model that is extracted from the Taylor-hood finite element discretization of the physical model. Later, for computational convenient, this model is divided into different sub-blocks studying the sparsity patterns of the matrices each of which contains the system’s parameters responsible for any dynamical changes. This form is well-known as index-II descriptor data model representing the relationship between the input external force applying to the artery’s boundary and the output measuring the changes in the blood velocity and the pressure. Based on the input-output realization, MATLAB interface is used to carry out numerical experiments and the results illustrate the numerical behaviour of the generated state space model for analyzing the blood flow nature through carotid artery.

Subject Classification:

• Primary 93A30
• Secondary 03C65

Keywords:

• State space model
• Navier-stokes equation
• Finite element discretization
• Blood flow
• Index-II descriptor system