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  • Hemodynamic Model of the

    Cardiovascular System during

    Valsalva Maneuver and

    Orthostatic Changes

    Niklas Moberg

    November 23, 2011

    Master’s Thesis in Engineering Physics, 30 credits Supervisors at Med-Uni Wien: Univ.-Prof. Dr. techn. H. Schima, Dipl.-Ing.

    Dr. techn F. Moscato Supervisors at TU Wien: Univ.-Prof. Dr. techn. A. Kugi, Dr.-Ing. W.

    Kemmetmüller, K. Speicher Examiner: Urban Wiklund

    Umeå University

    Department of Engineering Physics

    SE-901 87 UMEÅ SWEDEN

  • Abstract

    The goal of the Master’s Thesis was to extend an existing cardiovascular model to include the mechanics of the lungs, thus allowing to simulate breathing maneuvers such as the Valsalva maneuver and the Forced Vital Capacity maneuver. This included a remodeling of the pulmonary capillaries and of the existing interactions of the model with the intrathoracic pressure. The existing description of the vascular compartments was found to be insufficient to describe the hemodynamic response to orthostatic changes and was extended to include a compartment representing the upper body. Stress relaxation was included into all the larger vascular compartments. The results showed an improved accuracy of the extended model when subjected to large intrathoracic pressure changes and during orthostatic stress. The internal responses of the newly modeled pulmonary capillaries were studied and verified against literature with satisfying results.

    Sammanfattning

    Målet med detta examensarbete var att utvidga en existerande kardiovaskulär modell till att inkludera lungmekanik, för att därigenom möjliggöra simulering av andningsmanövrar som Valsalva-manövern och Forced Vital Capacity-manövern. Detta inkluderade en omformning av de pulmonära kapillärerna samt hur modellen som helhet påverkades av det intratho- rakala trycket. Den existerande vaskulära modellen ansågs vara otillräcklig för beskriva de hemodynamiska responsen under ortostatisk stress och utökades därför till att inkludera ett fack som representerade överkroppen. Stress relaxation inkluderas in i all större vaskulära kärlrum. Resultatet visade på en förbättrad noggrannhet hos den utökade modellen vid större intrathorakala tryckändringar och även vid ortostatisk stress. De interna svaren hos den utökade pulmonära kapillära modellen studerades och verifierades gentemot litteratur med positiva resultat.

  • Contents

    1 Problem Description 2

    1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    2 The Human Cardiovascular System 4

    2.1 Basic Structure of the Cardiovascular System . . . . . . . . . . . . . . . . . . 4

    2.2 Physiology of the Heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    2.3 The Circulatory System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.3.1 Arteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.3.2 Arterioles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.3.3 Capillaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.3.4 Venules and Veins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.3.5 Systemic Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.3.6 Pulmonary Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.4 Regulatory Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    2.4.1 Arterial Baroreflex Controller . . . . . . . . . . . . . . . . . . . . . . . 13

    2.5 Pathology of the Heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.5.1 Hypertension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.5.2 Systolic Dysfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.5.3 Cardiac Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.6 Mechanical Circulatory Assist Devices . . . . . . . . . . . . . . . . . . . . . . 16

    2.6.1 Pulsatile Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.6.2 Continuous Blood Pumps . . . . . . . . . . . . . . . . . . . . . . . . . 17

    3 Model Theory 19

    3.1 Conservation of Mass/Volume . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    3.2 Modeling of Blood Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    3.3 Heart Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    3.3.1 Active and Passive Pressure Functions . . . . . . . . . . . . . . . . . . 22

    i

  • CONTENTS ii

    3.3.2 Contractility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    3.3.3 Atria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.3.4 Ventricles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.3.5 Intraventricular Septum . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    3.3.6 Heart Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    3.4 Baroreflex Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    3.4.1 Systemic Arterial Resistance Controller . . . . . . . . . . . . . . . . . 29

    3.4.2 Heart Rate Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    3.4.3 Unstressed Volume Controller . . . . . . . . . . . . . . . . . . . . . . . 31

    3.5 Systemic Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    3.5.1 Arterial Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    3.5.2 Venous Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    3.6 Lungs and Airways Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    3.7 Pulmonary Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    3.7.1 Pulmonary Arteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    3.7.2 Pulmonary Capillary Model . . . . . . . . . . . . . . . . . . . . . . . . 46

    3.7.3 Pulmonary Veins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    3.8 LVAD Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    3.9 Valsalva Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    3.10 FVC Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

    4 Matlab Simulink Implementation 55

    4.1 Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    4.2 Matlab-code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    4.3 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    5 Results and Conclusions 57

    5.1 Normal Physiological Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 57

    5.1.1 Breathing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    5.2 Left Heart Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    5.3 Orthostatic Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    5.4 Valsava Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

    5.4.1 Pathological Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 66

    5.5 FVC-Maneuver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

    6 Review 73

    6.1 Achieved Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    6.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    6.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    7 Acknowledgements 76

  • CONTENTS iii

    A Parameters and Variables 80

    B Full Model Schematic 81

  • Introduction

    This Master’s Thesis is divided into six main parts: a problem description, a basic intro- duction to the human cardiovascular system, the theory behind the model development, the model implementation, the results achieved and a discussion reviewing the results.

    The first chapter describes the aims of this Master’s Thesis and the methods used to accomplish them. The second chapter describes the working physiology of the human heart, the vessels, the body’s own control mechanisms and gives some basic information on the pathology of the heart. The third chapter describes the equations ruling the physical system, how they were derived and their physiological meaning. The fourth chapter explains how the model was implemented in Matlab-Simulink and the basic function calls within the code. The simulated results of the model are then presented and compared to experimental results from articles and books. The thesis then reviews the results including limitations, future work and includes a summary of the whole project.

    The main goal of this work is to build a comprehensive mathematical model that gives an accurate representation of the flows, pressures and blood volumes in the human car- diovascular system and its interaction with a Left Ventricular Assistant Device (LVAD)

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