Mecanica Cardiovascular

I. MODELS OF THE PERIPHERAL CIRCULATION
A. Introduction

Our objective in this section is to develop a simple conceptual and analytical model for the vasculature which will be valid for bothsteady and pulsatile flows.

There are three major functional components in the systemic vascular bed: the elastic arteries, the microcirculation (including arterioles, capillaries, and venules), and thevenous system.

We will assume that the major resistive component in the systemic circulation is located at the level of the microcirculation and that the large arteries and veins contributeprimarily capacitance. The venous capacitance is much larger than that of the arteries and provides the major reservoir for blood volume.

B. Vascular Resistance

Laminar viscous flow in rigid tubes(Poiseuille flow) results in a parabolic distribution of velocities across the tube, and a linear relationship exists between the pressure drop, P, and the flow rate, Q, through the tube.

∆P RQThe constant of proportionality is the resistance to flow, R. It is dependent upon the geometry of the tube and the viscosity, μ, of the fluid.

Where l is the length of the tube over which P ismeasured, and r is the radius of the tube. If the flow is measured in cc/sec, and P in dynes/cm2, then the units of resistance are dyne-sec/cm5. If pressure is measured in mmHg and flow in cc/sec.,resistance is expressed in “peripheral resistance units,” or PRU.

The resistance of the tube is directly proportional to length and viscosity and inversely proportional to the fourth power of theradius. Thus, one would expect that the major contribution to vascular resistance would be made by the smallest vessels.

Although Poiseuille’s law has many engineering applications, and although itgives considerable insight into flow in the circulation; nevertheless, it cannot be rigorously applied to the circulation. It requires the following assumptions:

i) The fluid is homogeneous and...