A novel mathematical model of blood flow

Abstract

The interface between mathematics and biology has initiated and fostered new mathematical areas, where the ideas from mathematics and biology 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 cardiovascular physics. However, models have been developed so far are very complex with three dimensional analysis. This project presents a novel and simple mathematical model of blood flow. The main fluid component of the cardiovascular system is the body. 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 Cardiovascular System equation is derived. Then by applying the logical assumptions on this model, the general mathematical model of the normal blood flow rate is developed. Using Poisuelli’s equation, the Cardiovascular System equation is also used to develope a model for blood pressure. These two models are then analyzed against surface, pressure gradient and the vessel’s length using MAPLE 13. Our results are in agreement those obtained by Sanjeev, Chandel and Harjeet (2011) in A Mathematical Model for Blood Flow and Cross Sectional Area of an Artery.