Chapter 2: Vascular Hemodynamics

OVERVIEW AND HISTORICAL BACKGROUND

Vascular Hemodynamics is the study of the flow of blood and physiology of the cardiovascular system.¹

The understanding of hemodynamics started in the late 1950s, with William Harvey’s quantitative reasoning leading to the idea that blood continuously circulates in our body.¹ This was followed in the late 1960s and mid-1970s by experimental studies run by philosophers and scientists on animal models that led to a clearer understanding of the circulatory pathways and to the direct measurement of arterial pressure.² Principles of physics were then integrated in the study of hemodynamics and, with the contribution of Thomas Young and J.L.M Poiseuille, led to an understanding of the elastic properties of the vessels, the pulse speed, and establishing the relationship between flow rate and diameter for a long cylindrical tube subject to a fixed pressure gradient along its length.^3,4 Pierre Laplace then described the forces regulating the circulation of blood explaining aneurysm development.⁵ The standard reference used nowadays in the field of hemodynamics is inspired by the work of Donald A. McDonald in the mid-1990s, where he analyzed the motion of blood in arteries in a time-dependent manner with a fluctuating pressure gradient.^6,7

PHYSICS

Velocity of Blood Flow

The velocity of blood flow is the rate of displacement of blood at a given time interval.⁸ Its basic equation is as follows:

where

v = velocity of blood flow (cm/sec)

Q = Flow (mL/sec)

A = Cross-sectional area (cm²)

Flow (Q) is the volume of blood displaced per unit time. In our circulatory system, blood flow is the same and equal to the cardiac output. This is for the simple reason that in a normal state, the volume of blood that is pumped out of the heart is approximately the same as the one returning to the heart.⁸ The area is calculated as A = πr², where π is a constant and r is the radius of a single blood vessel or group of vessels. The cross-sectional area is determined by the area of interest through which the blood flows, that is, if we are interested in the blood flow through the aorta, we would use the cross-sectional area of the aorta. However, if we are interested in the blood flow at the level of a capillary bed, we would need to use the total cross-sectional area of all the capillaries within this bed.⁸

A simple illustration of the inverse relationship between velocity and cross-sectional area is illustrated in Figure 2-1. Assuming the flow is the same throughout the cylinder, as the area of the cylinder decreases, the velocity of blood flow increases, and vice-versa. The aorta ...