Cardiovascular Blood Flow Modeling

Abstract

It is common to regard the cardiovascular system as comprising a pump and a set of pipes carrying a fluid. The systems of blood vessels have different characteristics that help them to efficiently meet the needs of circulation. Under pathological conditions the vessels may become stiffer and less compliant; they may become smaller due to deposits on the inner surface, etc., all of which reduce the effectiveness of the cardiovascular system in transporting blood. An analogy can be drawn between fluid-carrying pipes and electrical circuits. The advantage of the electrical analogy is twofold; first a simple linear systems model can be developed for numerical simulation, and second an actual electrical circuit can be built to demonstrate the analogous flow of fluid in a complex network of pipes; even numerical simulation of electrical analogs is aided by the availability of sophisticated circuit simulation programs. Simulation of the vascular system using this model permits study of certain diseases like atherosclerosis and hypertension. A linear systems model of the systemic circulation and numerical solutions for it are discussed.

… wherever the motion of the blood through the arteries is impeded, whether it is by compression or infarction, or interception, there do the remote divisions of the artery beat less forcibly, seeing that the pulse of the arteries is nothing more than the impulse or shock of the blood in these vessels.

– William Harvey