Computer simulation of a nonlinear blood flow model

Abstract

The following equations are proposed in identifying a portion of the vascular system of a human. The derivation of the equations is similar to the approach used for a waterhammer analysis and is based on those of Dr. Victor Streeter, who has written extensively on the problem of waterhammer. The approach that is followed here is similar to that used for elastic waterhammer, which considers the flow of a fluid in an elastic pipe. In the human vascular system there is also the flow of a fluid in an elastic pipe. With the proper parameters and boundary conditions it is reasonable to assume that these derivations will lead to a set of equations which can be used to describe the dynamical properties of the vascular system. In order to apply these equations to the flow of blood it is necessary to make the following assumptions: 1. The blood vessel and elastic tube have a constant modulus of elasticity and a constant wave velocity. 2. The blood vessel is not permeable and is cylindrical with a constant internal diameter at rest. 3. Blood flow is laminar after leaving the upper portion of the aorta. 4. The loss of energy due to friction between the fluid and the walls of the blood vessel is proportional to the square of the velocity. 5. There are no discontinuities. This is to say that there is no branching along the section of blood vessel under consideration.