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Hemodynamic Model of the Cardiovascular System During Valsalva Maneuver and Orthostatic Changes

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Hemodynamic Model of the Cardiovascular System During Valsalva Maneuver and Orthostatic Changes 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 ProblemStatement................................ 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 PhysiologyoftheHeart ............................. 4 2.3 TheCirculatorySystem . 8 2.3.1 Arteries ................................... 8 2.3.2 Arterioles .................................. 9 2.3.3 Capillaries.................................. 9 2.3.4 VenulesandVeins ............................. 9 2.3.5 SystemicCirculation . 10 2.3.6 Pulmonary Circulation . 10 2.4 RegulatoryMechanisms . 13 2.4.1 Arterial Baroreflex Controller . 13 2.5 PathologyoftheHeart.............................. 15 2.5.1 Hypertension ................................ 15 2.5.2 SystolicDysfunction . 16 2.5.3 Cardiac Arrhythmia . 16 2.6 Mechanical Circulatory Assist Devices . ....... 16 2.6.1 PulsatileDevices .............................. 17 2.6.2 ContinuousBloodPumps . 17 3 Model Theory 19 3.1 Conservation of Mass/Volume . 19 3.2 ModelingofBloodVessels . 19 3.3 HeartModel..................................... 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 IntraventricularSeptum . 26 3.3.6 HeartValves ................................ 28 3.4 BaroreflexController. 28 3.4.1 Systemic Arterial Resistance Controller . ...... 29 3.4.2 HeartRateController ........................... 30 3.4.3 Unstressed Volume Controller . 31 3.5 SystemicCirculation . 33 3.5.1 Arterial Circulation . 33 3.5.2 VenousCirculation. 34 3.6 LungsandAirwaysModel ............................. 41 3.7 PulmonaryCirculation. 46 3.7.1 PulmonaryArteries ............................ 46 3.7.2 Pulmonary Capillary Model . 46 3.7.3 PulmonaryVeins .............................. 49 3.8 LVADModeling................................... 50 3.9 ValsalvaManeuver ................................ 51 3.10FVCManeuver ................................... 52 4 Matlab Simulink Implementation 55 4.1 Simulink....................................... 55 4.2 Matlab-code..................................... 55 4.3 SystemRequirements .............................. 56 5 Results and Conclusions 57 5.1 Normal Physiological Conditions . ..... 57 5.1.1 Breathing .................................. 59 5.2 LeftHeartFailure ................................. 61 5.3 OrthostaticStress ............................... 62 5.4 ValsavaManeuver ................................. 64 5.4.1 Pathological Conditions . 66 5.5 FVC-Maneuver ................................... 68 6 Review 73 6.1 AchievedResults ................................. 73 6.2 Limitations ..................................... 74 6.3 Futurework..................................... 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). This model shall include the cardiopulmonary interaction with the lung mechanics and the response to orthostatic position changes. It is important that the hemodynamic responses of orthostatic position changes and breathing maneuvers, such as the Valsalva maneuver, are modeled correctly. This since the hemodynamic responses can be used to diagnose left heart failure in patients and also test reflex controller reactions. The Master’s Thesis is based on the Master’s Thesis done by Michael Baumann in cooperation with the Research Group in Cardiovascular Dynamics and Artificial Organs at the Medical University of Vienna situated at the General Hospital of Vienna and the Automation and Control Institute (ACIN) at Vienna University of Technology [1]. 1 Chapter 1 Problem Description 1.1 Problem Statement As mentioned in the introduction, this is a continuation from another Master’s Thesis done by Michael Baumann [1]. He modified and extended an existing mathematical model of the human cardiovascular system and its interactions with a cardiac support system developed by the Medical University of Vienna [30]. The goal of this project is to extend the model making it a more accurate representation of the human cardiovascular system. 1.2 Goals I. Extend the existing mathematical model, found in [1], by including the interactions of the lungs and pulmonary capillaries. II. Evaluate the new interactions by simulating changes in lung volume and pressure, and verifying the results against literature. III. Extend the existing systemic venous model to better reproduce the hemodynamic responses associated with orthostatic stress. 1.3 Purpose The purpose of including the cardiopulmonary interactions of the lungs is to be able to accurately simulate the influence of breathing maneuvers such as the Valsalva maneuver. Breathing maneuvers are non-invasive to the patients, the expected cardiovascular response is known and can therefore be used for diagnosis. 1.4 Methods The Master’s Thesis starts with an introductory study of the human cardiovascular system and heart mechanics. This is needed to get a basic understanding of the hemodynamics of the body. The study is followed by a review of the equations describing the mathematical cardiovascular model and their physiological meaning as described in Baumann [1]. 2 1.4. Methods 3 In order to extend the existing model to include the interactions of the lungs, a math- ematical description needs to be created. This is done by searching for already existing models describing the cardiopulmonary interactions of the lungs and choosing a suitable one to implement. When a model is found, an in-depth study needs to be made to de- termine the important parts of the model, which simplifications can be made and how to include the new cardiopulmonary model into the entire cardiovascular system model. The Master’s Thesis
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