Mathematical Modeling of the Arterial Blood Flow

Blood flow is a study of measuring the blood pressure and finding the flow through the blood vessel. Blood flow problem has been studied for centuries where one of the motivations was to understand the conditions that contribute to high blood pressure. This occurs when the blood vessel became narrowed from its normal size. This paper presents a mathematical modeling of the arterial blood flow which was derived from the Navier-Stokes equations and some assumptions. A system of nonlinear partial differential equations for blood flow and the cross-sectional area of the artery was obtained. Finite difference method was adopted to solve the equations numerically. The result obtained is very sensitive to the values of the initial conditions and this helps to explain the condition of hypertension