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 the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland 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