In the Preface to the first edition, we commented on the benefits and drawbacks of interdisciplinary research; the contributions of specialists to advance our understanding and the difficulty for the non-specialist in understanding these advances. We were thinking particularly about the mechanics of the circulation and the contributions that had been made by engineers, physicists and mathematicians working in collaboration with physiologists and medical doctors. Our goal in writing the book was to alleviate the problem of understanding these advances by providing an introductory text on the mechanics of the circulation that was accessible to physiologists and medical practitioners.

The three decades since the book was published have seen an explosive growth in research on the cardiovascular system. In 1978, bioengineering did not exist as a separate academic discipline and the field of cardiovascular mechanics was relatively small, although it had a long and distinguished history extending over more than three centuries. Today, bioengineering is widely recognized as an academic discipline and interdisciplinary research is generally accepted as essential to progress.

Our understanding of the circulation is immeasurably greater today than it was in 1978, but many problems remain unsolved and cardiovascular disease is still the largest single cause of death world-wide. Again, however, these advances have brought increased difficulty in understanding. We believe that the need for an introductory text on the mechanics of the circulation that is accessible to the non-specialist is even greater now than it was when the book was first published.

We saw in the last chapter that in the large arteries blood may be treated as a homogeneous fluid and its particulate structure ignored. Furthermore, fluid inertia is a dominant feature of the flow in the larger vessels since the Reynolds numbers are large. The fluid mechanical reasons for treating the circulation in two separate parts, with a division at vessels of 100μm diameter, were also given in that chapter. In the microcirculation, which comprises the smallest arteries and veins and the capillaries, conditions are very different from those in large arteries and it is appropriate to consider the flow properties within them separately.

First, it is no longer possible to think of the blood as a homogeneous fluid; it is essential to treat it as a suspension of red cells and other formed elements in plasma. As will be seen later in the chapter, this comes about because even the largest vessels of the microcirculation are only approximately 15 red cells in diameter. Second, in all vessels, viscous rather than inertial effects dominate and the Reynolds numbers are very low; typical Reynolds numbers in 100μm arteries are about 0.5 and in a 10μm capillary they fall to less than 0.005 (see Table I).

In larger arteries, the Womersley parameter α (p. 60) is always considerably greater than unity. In the microcirculation, however, α is very small; in the dog (assuming a heart rate of 2Hz) it is approximately 0.08 in 100μm vessels and falls to approximately 0.005 in capillaries. This means that everywhere in these small vessels the flow is in phase with the local pressure gradient and conditions are quasi-steady.

Simple harmonic motion

When blood is ejected from the heart during systole, the pressure in the aorta and other large arteries rises, and then during diastole it falls again. The pressure rise is associated with outward motions of the walls, and they subsequently return because they are elastic. This process occurs during every cardiac cycle, and it can be seen that elements of the vessel walls oscillate cyclically, with a frequency of oscillation equal to that of the heartbeat. The blood, too, flows in a pulsatile manner, in response to the pulsatile pressure. In fact, as we shall see in Chapter 12, a pressure wave is propagated down the arterial tree. It is therefore appropriate in this chapter to consider the mechanics of pulsatile phenomena in general, and the propagation of waves in particular.

Let us examine first the oscillatory motion of a single particle. Suppose that the particle can be in equilibrium at a certain point, say P, but when it is disturbed from this position, it experiences a restoring force, tending to return it to P. There are many examples of this situation, as when a particle is hanging from a string and is displaced sideways (a simple pendulum) or when the string is elastic and the particle is pulled down below its equilibrium position. In cases like these, the restoring force increases as the distance by which the particle is displaced from P increases. In fact, for sufficiently small displacements, the restoring force is approximately proportional to the distance from P (see p. 124). If the particle is displaced and then released, it will return towards P, but will overshoot because of its inertia.

It soon becomes clear to any student of physiology that there are many systems of units and forms of terminology. For example, respiratory physiologists measure pressures in centimetres of water and cardiovascular physiologists use millimetres of mercury. As the study of any single branch of physiology becomes increasingly sophisticated, more and more use is made of other disciplines in science. As a result, the range of units has increased to such an extent that conversion between systems takes time and can easily cause confusion and mistakes.

We see also frequent misuse of terminology which can only confuse; for example, the partial pressure of oxygen in blood is often referred to as the ‘oxygen tension’, when in reality tension means a tensile force and is hardly the appropriate word to use.

In order to combat a situation which is deteriorating, considerable effort is being made to reorganize and unify the systems of nomenclature and units as employed in physiology. For any agreed procedure to be of value, it must be self-consistent and widely applicable. Therefore, it has to be based upon a proper understanding of mathematical principles and the laws of physics.

The system of units which has been adopted throughout the world and is now in use in most branches of science is known as the Système International or SI (see p. 28).

The study of the mechanics of blood flow in veins has been far less extensive than that of blood flow in arteries. However, virtually all the blood ejected by the left ventricle must return to the right atrium through the veins; they normally contain almost 80% of the total volume of blood in the systemic vascular system and have an important controlling influence on cardiac output. It is therefore important to understand their mechanics.

The venous system resembles the arterial system, in that it consists of a tree-like network of branching vessels; the main trunks are the venae cavae, which come together and lead into the heart. However, it is fundamentally different from the arterial system in several respects:

1. (1) As can be seen from Fig. 12.11, p. 257, the pressure in a vein is normally much lower than that in an artery at the same level, and may be less than atmospheric (for example in veins above the level of the heart).

2. (2) The vessels have thinner walls and their distensibility varies over a much wider range than that of arteries at physiological pressures.

3. (3) The blood flows from the periphery towards the heart, and the flow rate into a vein is determined by the arterio-venous pressure difference and the resistance of the intervening microcirculation.

4. (4) Many veins contain valves which prevent backflow.

The mammalian heart consists of two pumps, connected to each other in series, so that the output from each is eventually applied as the input to the other. Since they are developed, embryologically, by differentiation of a single structure, it is not surprising that the pumps are intimately connected anatomically, and that they share a number of features. These include a single excitation mechanism, so that they act almost synchronously; a unique type of muscle, cardiac muscle, which has an anatomical structure similar to skeletal muscle, but some important functional differences; and a similar arrangement of chambers and one-way valves. Not surprisingly, the assumption has often been made that the function of the two pumps will also be similar. Thus it has become common practice to examine the properties of one pump, usually the left, and to assume that the results apply to the other also. This may often be unjustified, particularly in studies of cardiac mechanics, with the result that our knowledge of the mechanics of the right heart and the pulmonary circulation remains very incomplete. It must also be remembered that the scope for experiments on the human heart is very limited, and we must rely heavily on experimental information from animal studies. Thus the descriptions which follow apply primarily to the dog heart.

Many factors which affect the performance of the heart are not our concern in this chapter, among the most important being the wide range of reflexes which act on the heart. For example, nerve endings in the aortic wall and carotid sinus are sensitive to stretch, and thus to changes in arterial pressure.

In 1808 Thomas Young introduced his Croonian lecture to the Royal Society on the function of the heart and arteries with the words:

For Young this was a natural approach to physiology; like many other scientists in the nineteenth century, he paid scant attention to the distinction between biological and physical science. Indeed, during his lifetime he was both a practising physician and a professor of physics; and, although he is remembered today mainly for his work on the wave theory of light and because the elastic modulus of materials is named after him, he also wrote authoritatively about optic mechanisms, colour vision, and the blood circulation, including wave propagation in arteries.

This polymath tradition seems to have been particularly strong among the early students of the circulation, as names like Borelli, Hales, Bernoulli, Euler, Poiseuille, Helmholtz, Fick, and Frank testify; but, as science developed, so did specialization and the study of the cardiovascular system became separated from physical science.

This chapter deals with the mechanisms of flow in the larger systemic arteries. The pulmonary arteries are specifically excluded, because they have special properties and are dealt with separately; thus, we are concerned here with the aorta and its branches, which supply oxygenated blood to the organs of the body. As in other parts of the book, we take the vascular system of the dog as our primary example because it has been so widely studied experimentally; but we will refer to the situation in the human wherever specific differences of function or structure appear important. Again, we do not deal with active physiological processes, such as reflexes or mechanisms of vasoconstriction which may alter the flow or distribution of blood, but concentrate upon the physical properties of the system which are changed when such processes act.

This book deals with the arterial part of the systemic circulation in two parts: the arteries in this chapter and the microcirculation in Chapter 13. First, therefore, we must describe how and why this subdivision is made, and then we shall provide a brief description of the anatomy and structure of systemic arteries, and of pressures and flows which occur within them. Thereafter we shall introduce the fundamental mechanics which govern events and then successively add the complicating or modifying features which bring us nearer to a complete description of the pressure and flow in the arteries; in doing this, we shall repeatedly refer to the mechanics described earlier in the book.