A review of mathematical modelling of blood flow in human circulatory system

An interface between biology and mathematics has initiated and fostered new mathematical areas, where the ideas from biology and mathematics are synergistically applied. Study of fluid dynamics plays a significant role in fluid flow inside the human body, and modeling of blood flow is an important field in circulatory physics. However, models have been developed are very complex with three-dimensional analysis. This project presents a novel and simple mathematical model of blood flow. Assuming blood is a Newtonian fluid which is governed by the Navier-Stokes equations and continuity equation and with making use of the Navier-Stokes equation, a simple differential equation called as the circulatory system equation is derived. Then by applying the ogical assumptions on this model, the general mathematical model of the normal blood flow rate is developed. Using Poisuelli's equation, the sirculatory system equation is also used to develop a model for blood pressure. These two models are then analyzed against surface, pressure gradient and the vessel's length using MATLAB. (paper)