Scientific Modelling of Vascular Blood Circulation

Abstract

Blood flow is the study of measuring blood pressure and determining the flow through blood vessels. The problem of blood flow has been studied for centuries, one motivation being to understand the conditions that cause hypertension. This article presents a mathematical modelling of arterial blood flow derived from the Navier-Stokes equations and some assumptions. A system of nonlinear partial differential equations for blood flow and arterial cross-sectional area was obtained. Blood is non-Newtonian fluid and to model such fluid is very complicated. Even though this will make the problem much simpler, it still is valid since blood in a large vessel acting almost like a Newtonian fluid. The obtained result is very sensitive to the values of the initial state and it helps to explain the state of hypertension.