Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education

306 Pages·2019·7.95 MB·English

by  Nicolaas Westerhof

Snapshots of
Hemodynamics
An Aid for Clinical Research
and Graduate Education
Nicolaas Westerhof
Nikolaos Stergiopulos
Mark I. M. Noble
Berend E. Westerhof
Third Edition
123
Snapshots of Hemodynamics
Nicolaas Westerhof • Nikolaos Stergiopulos
Mark I.M. Noble • Berend E. Westerhof
Snapshots of Hemodynamics
An Aid for Clinical Research
and Graduate Education
Third Edition
Nicolaas Westerhof Nikolaos Stergiopulos
Department of Pulmonary Diseases Laboratory of Hemodynamics
Amsterdam Cardiovascular Sciences and Cardiovascular Technology
VU University Medical Center Ecole Polytechnique Fédérale
Amsterdam de Lausanne (EPFL)
The Netherlands Institute of Bioengineering
Lausanne
Mark I.M. Noble Switzerland
Cardiovascular Medicine
Department of Medicine and Therapeutics Berend E. Westerhof
University of Aberdeen Department of Pulmonary Diseases
Aberdeen Amsterdam Cardiovascular Sciences
United Kingdom VU University Medical Center
Amsterdam
The Netherlands
ISBN 978-3-319-91931-7 ISBN 978-3-319-91932-4 (eBook)
https://doi.org/10.1007/978-3-319-91932-4
Library of Congress Control Number: 2018952091
© Springer International Publishing AG, part of Springer Nature 2019
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
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Preface
This book is written in a quick reference style to help clinical and basic researchers,
as well as graduate students, in the understanding of hemodynamics. Hemodynamics
makes it possible to characterize, in a quantitative way, and presently more and
more with noninvasive techniques, the function of the heart and the arterial system,
separately and in combination.
We have made the layout of this book such that it gives an overview of individual
topics, in short chapters. Every chapter starts with a “Box” containing a figure and
caption, describing the main aspects of the subject. It is often sufficient to study the
contents of this Box alone to obtain the essential information on the subject, and it
is then not necessary to read the whole chapter.
Each chapter is further written in such a way that one is able to grasp the basic
and applied principles of the hemodynamic topic. The part called “Description”
can be used to get more detailed information. The chapters end with a section
“Physiological and Clinical Relevance” to place the information into perspective. If
more details or broader perspectives are desired, one can go to the other, related,
chapters to which the text refers or to the limited number of references given in
each chapter.
More comprehensive information on the subjects discussed can be found in text-
books on physiology and cardiology, as well as in special books on hemodynamics.
A number of these books are listed in the section “Reference Books” (Appendix 5).
Amsterdam, The Netherlands Nicolaas Westerhof
Lausanne, Switzerland Nikolaos Stergiopulos
Aberdeen, United Kingdom Mark I. M. Noble
Amsterdam, The Netherlands Berend E. Westerhof
v
How to Use Snapshots of Hemodynamics
Chapter 2 Law of Poiseuille Chapter number and title
∆P/l The ‘Box’ contains a figure and a
short text that illustrates the main
Parabolic velocity message of the chapter.
ri r profile Q = (∆P/l)·(π·ri4)/8h·
v
max v(r)= (∆P/l)·(ri2–r2)/4h
τ= 4h·Q/(π·ri3)
The law of Poiseuille describes the relation between pressure drop, ∆P/l,
and blood flow, Q, in a stiff tube under steady flow conditions. This figure
shows a tube with circular cross-section where the blood flows in a laminar
fashion, i.e., each fluid layer stays at the same constant distance from the
center. The flow depends strongly on the radius of the tube (fourth power),
and also on the pressure drop over the tube length (∆P/l) and viscosity of
blood (h). The velocity profile, ν(r), is parabolic (second formula).
Resistance can be calculated as R = ∆P/Q = 8h·l /π·ri4.
The wall shear stress, t, (third formula) acting on the intimal layer
(endothelium) equals t = 4h·Q/(π·r3) = (DP/l)·(ri/2).
Description The ‘Description’ section gives the
With laminar flow through a uniform essential background and discusses
tube the velocity profile over the the different aspects of the subject.
cross-section is a parabola.
Physiological and clinical relevance The ‘Physiological and clinical
The more general form of Poiseuille’s relevance’ section places the subject
law given above, i.e., Q = ∆P/R allows in a broader pathophysiological
the derivation of resistance, R, from context and shows clinical
measurements of mean pressure and applications.
mean flow.
References A limited number of ‘References’
1. Murgo JP, Westerhof N, Giolma JP, is given. Major reference books are
Altobelli SA. Aortic input impedance given in Appendix 5.
in normal man: relationship to pressure
wave forms. Circulation. 1980;62:101–16.
vii
Contents
Part I B asics of Hemodynamics
1 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Viscosity of Blood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Anomalous Viscosity or Non-Newtonian Behavior
of Blood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 How to Measure Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Law of Poiseuille . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Calculation of Wall Shear Stress . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 E xample of the Use of Poiseuille’s Law to Obtain Viscosity . . . 12
2.1.3 Murray’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Bernoulli’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 Applying Bernoulli’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 Calculation of Aortic Valvular Area . . . . . . . . . . . . . . . . . . . . 19
3.2.3 Jets and Vena Contracta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.5 The Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 24
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
ix
x Contents
5 Arterial Stenosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1 Post Stenotic Dilatation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2.1 Flow Reserve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2.2 Fractional Flow Reserve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.1.1 Addition of Resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.1.2 Physical Reason Why the Systemic Resistance Is Mainly
Located in the Arterioles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.1.3 Resistance of Capillaries and Veins . . . . . . . . . . . . . . . . . . . . 36
6.1.4 Calculation of Vascular Resistance . . . . . . . . . . . . . . . . . . . . 37
6.1.5 The Zero Flow Intercept Pressure, Starling Resistor
and the Waterfall Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 38
6.2.1 Low Resistance of an Arterio-Venous Fistula . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7 Inertance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7.1.1 Addition of Series and Parallel Inertances . . . . . . . . . . . . . . . 44
7.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 44
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
8 Oscillatory Flow Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
8.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
9 Law of Laplace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
9.1.1 Applicability of the Law of Laplace . . . . . . . . . . . . . . . . . . . 52
9.1.2 Relation to the Youngs Modulus . . . . . . . . . . . . . . . . . . . . . . 53
9.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10.1.1 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
10.1.2 Viscoelastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
10.1.3 Residual Stresses and Stress Distribution
at Physiological Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Contents xi
10.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . 62
10.2.1 The Elasticity of Cardiovascular Tissue . . . . . . . . . . . . . . 63
10.2.2 Determination of the Youngs Modulus . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
11 Compliance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
11.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
11.1.1 Measurement of Elastance and Compliance . . . . . . . . . . . 67
11.1.2 Distensibility and Bulk Modulus . . . . . . . . . . . . . . . . . . . . 68
11.1.3 The Pressure-Strain Elastic Modulus . . . . . . . . . . . . . . . . . 68
11.1.4 The Stiffness Index β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
11.1.5 Describing the Pressure-Area or Pressure-Diameter
Relation of Blood Vessels . . . . . . . . . . . . . . . . . . . . . . . . . 68
11.1.6 Addition of Compliances and Elastances . . . . . . . . . . . . . 69
11.1.7 Relating Compliance to Youngs Modulus . . . . . . . . . . . . . 71
11.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . 72
11.2.1 Buffering Function of Arterial Compliance . . . . . . . . . . . . 73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
12 Wave Travel and Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
12.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
12.1.1 Reflection of Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
12.1.2 Transmission of Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
12.1.3 Derivation of Characteristic Impedance . . . . . . . . . . . . . . 81
12.1.4 Forward and Reflected Waves . . . . . . . . . . . . . . . . . . . . . . 82
12.1.5 Amplification of Pressure, and Form Factor . . . . . . . . . . . 84
12.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . 85
12.2.1 Wave Speed and Reflection . . . . . . . . . . . . . . . . . . . . . . . . 86
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Part II C ardiac Hemodynamics
13 Cardiac Muscle Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
13.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
13.1.1 Calcium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
13.1.2 The Force-length Relation . . . . . . . . . . . . . . . . . . . . . . . . . 94
13.1.3 The Force-Velocity Relation . . . . . . . . . . . . . . . . . . . . . . . 94
13.1.4 The F-v Relation and Pump Function . . . . . . . . . . . . . . . . 95
13.1.5 Experimental Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
13.1.6 Nomenclature Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
13.1.7 Limitations of the Sliding Filament Model . . . . . . . . . . . . 97
13.1.8 Diastolic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
xii Contents
14 The Pressure-Volume Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
14.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
14.1.1 The Varying Elastance Model . . . . . . . . . . . . . . . . . . . . . 103
14.1.2 Determination of End Systolic Elastance . . . . . . . . . . . . 104
14.1.3 Determination of End Diastolic Elastance . . . . . . . . . . . . 106
14.1.4 Derivation of End Systolic Elastance and End
Diastolic Elastance from Single Beats . . . . . . . . . . . . . . . 106
14.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . 107
14.2.1 The Frank-Starling Law . . . . . . . . . . . . . . . . . . . . . . . . . . 108
14.2.2 Systolic and Diastolic Dysfunction . . . . . . . . . . . . . . . . . 108
14.2.3 Concentric and Eccentric Hypertrophy . . . . . . . . . . . . . . 109
14.2.4 Modeling on the Basis of the Varying Elastance
Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
14.2.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15 The Pump Function Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
15.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
15.1.1 Determination of the Pump Function Graph
from Single Beats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
15.1.2 Relation Between the Pump Function Graph
and the End-Systolic Pressure-Volume Relation . . . . . . . 119
15.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . 120
15.2.1 The Frank-Starling Law . . . . . . . . . . . . . . . . . . . . . . . . . . 120
15.2.2 Concentric Hypertrophy and Heart Failure . . . . . . . . . . . 121
15.2.3 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
15.2.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
16 Cardiac Work, Energy and Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
16.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
16.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . 127
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
17 Cardiac Oxygen Consumption and Hemodynamics . . . . . . . . . . . . . . 129
17.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
17.1.1 Rate Pressure Product and Tension Time Index . . . . . . . 130
17.1.2 Cardiac Oxygen Consumption and the Pressure
Volume Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
17.1.3 Heterogeneity of Metabolism . . . . . . . . . . . . . . . . . . . . . 133
17.2 Physiological and Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . 133
17.2.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
18 Cardiac Power and Ventriculo-Arterial Coupling . . . . . . . . . . . . . . . . 135
18.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
18.1.1 Power and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136