The Mechanics of the Circulation

by C.G. Caro, T.J. Pedley,
R.C. Schroter and W.A. Seed

 

Oxford University Press, 1978

 

ISBN 0-19-263323-6

ISBN 0-19-261171-2 Pbk

 

 

 

 

 

 

Contents

Preface

Part I : Background mechanics

1. PARTICLES AND CONTINUOUS MATERIALS

2. PARTICLE MECHANICS

3. UNITS

4. BASIC IDEAS IN FLUID MECHANICS

5. FLOW IN PIPES AND AROUND OBJECTS

6. DIMENSIONAL ANALYSIS

7. SOLID MECHANICS AND THE PROPERTIES OF BLOOD VESSEL WALLS

8. OSCILLATIONS AND WAVES

9. AN INTRODUCTION TO MASS TRANSFER

Part II : Mechanics of the circulation

10. BLOOD

11. THE HEART

12. THE SYSTEMIC ARTERIES

13. THE SYSTEMIC MICROCIRCULATION

14. THE SYSTEMIC VEINS

15. THE PULMONARY CIRCULATION

INDEX

 

Part I : Background mechanics

1 PARTICLES AND CONTINUOUS MATERIALS

2 PARTICLE MECHANICS

2.1 Position
2.2 Velocity
2.3 Acceleration
2.4 Newton's laws of motion: mass and force
2.5 Momentum
2.6 Work and energy
 

3 UNITS

3.1 The difference between units and dimensions
3.2 Mass, length, and time as fundamental units
3.3 The inconvenience of force as a fundamental unit
3.4 Energy and heat
3.5 The concept of substance
3.6 Dimensional homogeneity and consistency of units
3.7 The use of volume and flow-rate in physiology
3.8 Systeme International (SI)
 

4 BASIC IDEAS IN FLUID MECHANICS

4.1 Stress
4.2 Hydrostatic pressure
4.3 Stress in a moving fluid: viscosity
4.4 The equation of motion of a fluid
4.5 Convective and local acceleration
4.6 Conservation of mass
4.7 Bernoulli's theorem
 

5 FLOW IN PIPES AND AROUND OBJECTS

5.1 Poiseuille flow in a tube
5.2 Flow in the entrance region
5.3 The idea of the boundary layer
5.4 Reynolds number
5.5 Turbulence in pipe flow
5.6 Unsteady flow in a very long pipe
5.7 Effects of constrictions on pipe flow characteristics
5.8 Flow in curved pipes
5.9 Flow past bodies
 

6 DIMENSIONAL ANALYSIS

6.1 Similarity and the idea of scale models
6.2 Some examples of scaling in biological systems
6.3 A method of obtaining homogeneous relationships between variables
 

7 SOLID MECHANICS AND THE PROPERTIES OF BLOOD VESSEL WALLS

7.1 Definitions of elastic properties
7.2 The properties of blood vessel walls
7.3 Statics of an elastic tube
 

8 OSCILLATIONS AND WAVES

8.1 Simple harmonic motion
8.2 Simple waves
8.3 Damping
8.4 Wave reflections and resonance
8.5 Linearity
8.6 Fourier analysis
 

9 AN INTRODUCTION TO MASS TRANSFER

9.1 Diffusion
9.2 The colloidal state
9.3 Mass transfer coefficients
9.4 Diffusion through pores and membranes
    9.4.1 Restricted diffusion
    9.4.2 Active transport
9.5 Permeability
9.6 Filtration through membranes
9.7 Osmosis
9.8 A simple mass transfer model
9.9 The interaction of bulk flow and diffusion
    9.9.1 The Schmidt number

 

Part II : Mechanics of the circulation

10 BLOOD

10.1 Viscosity of fluids and suspensions
    10.1.1 Spherical particles
    10.1.2 Asymmetric particles
    10.1.3 Viscosity of plasma
10.2 Osmotic pressure of plasma
10.3 The suspended elements
    10.3.1 The blood cells
    10.3.2 Red cells
    10.3.3 White cells
    10.3.4 Platelets
10.4 Blood coagulation
10.5 Thrombosis
10.6 Mechanical properties of whole blood
    10.6.1 Sedimentation of red cells
    10.6.2 Principles of measurement of blood viscosity
    10.6.3 Viscous properties of blood
 

11 THE HEART

11.1 Anatomy of the heart
11.2 The cardiac cycle
    11.2.1 Electrical events
    11.2.2 Mechanical events
11.3 Properties of cardiac muscle
    11.3.1 Structure
    11.3.2 Static mechanical properties of cardiac muscle
    11.3.3 Dynamic mechanical properties of cardiac muscle
    11.3.4 Summary
11.4 Mechanical behaviour of the intact heart
    11.4.1 Left ventricular shape and wall-stresses
    11.4.2 Right ventricular shape
    11.4.3 The mechanics of the entire ventricle
    11.4.4 Summary
11.5 Fluid mechanical aspects of cardiac function
    11.5.1 Right heart
    11.5.2 Left heart
    11.5.3 Sounds and murmurs in the heart
 

12 THE SYSTEMIC ARTERIES

12.1 Anatomy and structure
    12.1.1 The anatomy of large blood vessels
    12.1.2 Branching ratios and angles
    12.1.3 The structure of the arterial wall
    12.1.4 Arterial wall thickness
    12.1.5 Changes in the arterial wall with age
12.2 Blood pressure and flow in systemic arteries
    12.2.1 Transmural pressures
    12.2.2 Unsteady pressure in large arteries
    12.2.3 Flow
    12.2.4 Terminology
    12.2.5 Fourier analysis
12.3 Wave propagation in arteries
    12.3.1 The Windkessel model
    12.3.2 The propagation of the pressure wave
    12.3.3 Determination of the wave-speed
    12.3.4 Comparison of theory with experiment
    12.3.5 Further limitations of the simple elastic model
12.4 Reflection and transmission of the wave at junctions
    12.4.1 Reflection at a single junction
    12.4.2 The matching of impedances
    12.4.3 Positive and negative reflection
    12.4.4 Physiological evidence of wave reflections
    12.4.5 Multiple reflections
    12.4.6 Interpretation of observed pressure wave-forms in large arteries
    12.4.7 The effect of taper
12.5 The influence of non-linearities
12.6 Viscous effects
    12.6.1 Effect of blood viscosity on flow-rate wave-form
    12.6.2 Effect of viscosity on wave propagation
    12.6.3 Effect of wall visco-elasticity
12.7 Other types of wave
12.8 Flow patterns in arteries
    12.8.1 Velocity profiles in large arteries
    12.8.2 Physical mechanisms underlying the velocity profiles
    12.8.3 Stability and turbulence
12.9 Mixing and mass transport in arteries
    12.9.1 Mixing in the heart and large blood vessels
    12.9.2 Mass transport across artery walls
12.10 Appendix: Impedance
 
R

13 THE SYSTEMIC MICROCIRCULATION

13.1 The organization of a microvascular bed
    13.1.1 The arteriolar system
    13.1.2 The capillary system
    13.1.3 The venular system
    13.1.4 The lymphatic system
13.2 The structure of the vessels of the microcirculation
    13.2.1 The arterioles
    13.2.2 The capillaries
    13.2.3 The venules
    13.2.4 The lymphatics
    13.2.5 The junctions between vascular endothelial cells
    13.2.6 The pinocytic vesicles
    13.2.7 The interstitial space
13.3 Static mechanical properties of the microcirculatory vessels
    13.3.1 Elastic properties of the arterioles
    13.3.2 Mechanical properties of the capillaries
    13.3.3 Elastic properties of the venules
13.4 Pressure in the microcirculation
    13.4.1 The distribution of pressure
    13.4.2 The propagation of cardiac pressure oscillations
    13.4.3 Pressure in the interstitial space
13.5 Flow in models and in the large vessels of the microcirculation
    13.5.1 The motion of single particles at very low flow-rates
    13.5.2 The motion of single particles at high flow-rates
    13.5.3 The motion of single red blood cells in Poiseuille flow
    13.5.4 The flow of concentrated suspensions of particles and red cells
    13.5.5 The viscosity of whole blood
    13.5.6 Radial dispersion of red cells
    13.5.7 The cell free layer
    13.5.8 Velocity profiles in vessels
13.6 Blood flow in capillaries
    13.6.1 Positive clearance
    13.6.2 Negative clearance
13.7 Mass transport in the microcirculation
    13.7.1 Filtration and re-absorption of water within single capillaries
    13.7.2 Capillary pressure and filtration of water in whole organ preparations
    13.7.3 The dependence of plasma oncotic pressure on protein concentration
    13.7.4 Evidence for the existence of filtration pores in the capillary wall
    13.7.5 Diffusion across the capillary wall
    13.7.6 Methods of measuring permeability coefficients
    13.7.7 The diffusion pathway across the capillary wall
    13.7.8 The Pappenheimer equivalent pore theory
    13.7.9 The pathway for water transport across the capillary wall
    13.7.10 The transport of large molecules
 

14 THE SYSTEMIC VEINS

14.1 Anatomy
14.2 Transmural pressure and static elastic properties
    14.2.1 The resistance to bending of a tube wall
14.3 Dynamics of blood flow in large veins
    14.3.1 Observed pressure and flow-rate wave-forms
    14.3.2 Wave propagation in veins
    14.3.3 Flow patterns and velocity profiles in veins
14.4 Flow in collapsible tubes
    14.4.1 Model experiments
    14.4.2 Mechanisms
    14.4.3 Physiological evidence: Korotkoff sounds
14.5 Mechanics of venous beds
    14.5.1 Elevation of a venous bed above the level of the heart
    14.5.2 Contraction of skeletal muscle
    14.5.3 Respiratory manoeuvres
 

15 THE PULMONARY CIRCULATION

15.1 Anatomy
    15.1.1 Pulmonary circulation
    15.1.2 Bronchial circulation
15.2 Transmural pressure and static elastic properties of vessels
    15.2.1 Intravascular pressure
    15.2.2 Perivascular pressure
    15.2.3 Elastic properties
    15.2.4 Pulmonary blood volume
15.3 Dynamics of blood flow in large pulmonary vessels
    15.3.1 Wave-forms
    15.3.2 Wave propagation
    15.3.3 Flow patterns
15.4 Pulmonary vascular resistance
    15.4.1 Flow in the alveolar sheet
    15.4.2 Zonal distribution of blood flow
    15.4.3 Effect of lung mechanics

 

Preface

In 1808 Thomas Young introduced his Croonian lecture to the Royal Society on the function of the heart and arteries with the words: The mechanical motions, which take place in an animal body, are regulated by the same general laws as the motions of inanimate bodies ... and it is obvious that the inquiry, in what manner and in what degree, the circulation of the blood depends on the muscular and elastic powers of the heart and of the arteries, supposing the nature of those powers to be known, must become simply a question belonging to the most refined departments of the theory of hydraulics.

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 process was not, of course, complete because collaborative work between scientists from different disciplines has always gone on. However, its scale was quite limited, and many medical and physiological workers found it difficult to comprehend because of their inadequate background in mathematics and mechanics, just as physical scientists found the complexity and empiricism of physiological studies, as well as the terminology, forbidding.

The separation caused by specialization has now assumed new importance. Over about the last twenty years physical scientists and engineers have made considerable contributions to the understanding of the mechanics of the circulation. These have strongly stimulated collaborative research, but at the same time have made the field increasingly difficult for those with a limited training in physics and mathematics. Several recent reviews and monographs bear witness to the importance of this interdisciplinary work, but do little to help the medical reader, since they invariably assume an understanding of mechanics and are often quite mathematical in format.

This book is an attempt to alleviate the problem. It is intended as an introductory text on the mechanics of the circulation which, so far as is practicable, avoids mathematical formulations and presents mechanics in readily comprehensible terms. Our experience in teaching students of physiology and medicine, and cardiological physicians and surgeons, suggests that this approach is helpful, and it is to such a readership that the book is primarily directed. In addition, we think that the book will prove useful to physical scientists, mathematicians, and engineers interested in the field, since it provides the relevant anatomical and physiological background to the mechanics, and gives definitions of terms and numerical data wherever possible.

The book is divided into two parts. The first part, 'Background mechanics', provides a non-mathematical outline of the physical processes and mechanisms which have general importance in the circulation. Thus it forms a physical introduction to the later material, though since it is self-contained and deals in a general rather than a specific way with solid and fluid mechanics and mass transport, it may also prove useful as a background to the study of systems other than the circulation.

The second part, 'The mechanics of the circulation', examines in some detail the physiological events that occur in the circulation and the physical mechanisms that underlie them. It deals first with the relevant properties of blood and then considers the circulation systematically, starting with the heart and moving forward chapter by chapter through the circulation. No attempt is made to deal in detail with active physiological mechanisms such as reflexes, but the resulting changes in the physical properties of the system are studied. In each chapter the relevant anatomical and physiological background is presented first, followed by a discussion of the mechanics. There is extensive cross-referencing to physical processes already examined earlier in the book; more specialized physical processes, relevant to the mechanics of a part of the circulation, are introduced as they arise.

We have attempted to cover all the mechanical features of the circulation which are currently considered important. However, the book is not intended as a research review, and we have therefore largely avoided citing original research references in the text. Instead, we have provided a reading list for each chapter in the second part of the book, chosen to guide readers unfamiliar with the literature to suitable reviews and sources. In addition, we have, wherever possible, taken our illustrations from important sources, in many cases the original research literature, so that the references given in the Figure captions supplement the reading list.

A temptation in writing an interdisciplinary book of this kind is to oversimplify, usually at the expense of one of the disciplines; we have tried hard to avoid doing this. We have also tried, wherever possible, to supply numerical data; for convenience the more important measured and derived values, which'are referred to repeatedly throughout the book, are collected together in a table reproduced on the end-pages. The units used are those of the Systeme Internationale, though with quantities such as pressure, where confusion might arise, we have added the traditional units. Since physical scale is important to so much of mechanics, and the dog is the only species for which anything like a comprehensive range of reliable measurements is available, we have given values from this animal throughout the book. Even so, we have had to turn to other species in describing the microcirculation, though this is a region where inter-species differences in scale appear to be relatively slight. Finally we have referred specifically to the human circulation wherever the mechanics appears to be different, or where we believe that it has relevance to a circulatory disease process.

July 1977

C.G.C.

T.J.P.

R.C.S.

W.A.S.

Acknowledgments

We owe debts of gratitude to many colleagues for their advice and help. In particular we would like to thank Dr Laurence Smaje, who contributed a major part of the physiological material contained in the chapter on the microcirculation, and without whose guidance we could not have surveyed that topic.

Mr Paul Minton of Imperial College, Dr Giorgio Gabella of University College, and Drs Graham Miller and Derek Gibson of the Brompton Hospital all made available to us original data or material for figures. Dr Michael Sudlow contributed greatly to early discussions on the scope and form of the book, and provided material for the chapter on veins; and Prof. Ilsley Ingram and Drs Julien Hoffmann and Michael Hughes made valuable comments and suggestions about the chapters on the blood, heart, and pulmonary circulation respectively. In addition, we owe our thanks to all the authors and journals cited in the Figure captions for permission to reproduce Figures.

Finally, we give our special thanks to Miss Evelyn Edwards, whose editorial precision helped (and chastened) us throughout the preparation of the book.