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A Balance Point Approach to Modeling Hemodynamics In A BALANCE POINT APPROACH TO MODELING HEMODYNAMICS IN CHRONIC HEART FAILURE A Dissertation by SARAH FUSAYO COQUIS-KNEZEK Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of Committee, Christopher Quick Committee Members, Randolph Stewart Ranjeet Dongaonkar John Criscione Head of Department, Larry Suva December 2016 Major Subject: Biomedical Sciences Copyright 2016 Sarah Fusayo Coquis-Knezek ABSTRACT Chronic heart failure is a complex disease state that can yield reduced cardiac output, pulmonary edema, and increased peripheral resistance. Pressures, flows, and volumes in these conditions emerge from the complex interaction of multiple mechanical properties of the cardiovascular system. The shear complexity of emergent behavior poses a challenge to both basic scientists, who use reductionist approaches to study subsystems in isolation, and clinical researchers, who use inductive approaches to infer the causes of observed changes in clinical variables. This dissertation instead takes a deductive approach using mathematical models to relate three critical cardiovascular variables impacted by heart failure (cardiac output, pulmonary interstitial pressure, and microvascular resistance) to mechanical properties of three subsystems of the cardiovascular system. In contrast to common modeling approaches, three strategies are employed to reduce the complexity and generalize results. First, systems are strategically lumped into descriptions that can be characterized empirically. Second, algebraic formulas are derived to generalize results. Third, the critical interaction of physiological subsystems is represented with opposing processes in the form of “balance points.” The use of all three strategies allows us to: 1) quantify Guyton’s classic cardiac output-venous return graph, 2) predict pulmonary interstitial pressure from interaction of the heart, vascular, and lymphatic systems, and 3) characterize adaptation of the microvasculature to changes in pulsatile blood flow. Cardiac output and venous return curves can now be predicted from parameters characterizing the mechanical properties ii of the closed-loop system with chronic heart failure. The primary determinants of pulmonary interstitial pressure can now be identified for different phenotypes of heart failure. Finally, increased peripheral resistance, capillary rarefaction, and the formation of arteriovenous malformations are predicted with a decrease in the pulsatility of blood flow. Taken together, applying a physiological balance point approach to integrate subsystems clarifies how changes in the mechanical properties of the cardiovascular system impacts blood and interstitial pressures, volumes, and flows. iii ACKNOWLEDGEMENTS I would like to thank my committee chair, Dr. Quick, and my committee members, Dr. Criscione, Dr. Dongaonkar, and Dr. Stewart for their guidance and support throughout the course of this research. Finally, thanks to my mother and father for their encouragement and to my husband for his patience and love. iv CONTRIBUTORS AND FUNDING SOURCES Contributors This work was supervised by a dissertation committee consisting of Dr. Christopher Quick (advisor), Dr. Randolph Stewart, and Dr. Ranjeet Dongaonkar of the Department of Veterinary Physiology and Pharmacology and Dr. John Criscione of the Department of Biomedical Engineering. All work conducted for the dissertation was completed by the student independently. Funding Sources This work was made possible in part by American Heart Association under Grant Number 10GRNT4320043 and the National Science Foundation under Grant Number CMMI-1063954. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the American Heart Association or the National Science Foundation. v TABLE OF CONTENTS Page ABSTRACT ....................................................................................................................... ii ACKNOWLEDGEMENTS .............................................................................................. iv CONTRIBUTORS AND FUNDING SOURCES ............................................................. v TABLE OF CONTENTS .................................................................................................. vi LIST OF FIGURES ........................................................................................................ viii LIST OF TABLES ............................................................................................................. x 1. INTRODUCTION ......................................................................................................... 1 2. CHRONIC CARDIAC OUTPUT-VENOUS RETURN BALANCE POINT ............ 10 2.1 Background .................................................................................................... 10 2.2 Methods.......................................................................................................... 13 2.3 Results ............................................................................................................ 20 2.4 Discussion ...................................................................................................... 26 3. COUPLING VASCULAR AND INTERSTITIAL COMPARTMENTS ................... 37 3.1 Background .................................................................................................... 37 3.2 Methods.......................................................................................................... 40 3.3 Results ............................................................................................................ 49 3.4 Discussion ...................................................................................................... 62 4. ARTERIOLAR ADAPTATION TO PULSATILITY ................................................. 77 4.1 Background .................................................................................................... 77 4.2 Methods.......................................................................................................... 81 4.3 Results ............................................................................................................ 94 4.4 Discussion .................................................................................................... 107 5. CONCLUSIONS ....................................................................................................... 122 REFERENCES .............................................................................................................. 124 vi APPENDIX A ................................................................................................................ 155 APPENDIX B ................................................................................................................ 157 APPENDIX C ................................................................................................................ 159 APPENDIX D ................................................................................................................ 160 APPENDIX E ................................................................................................................ 164 APPENDIX F ................................................................................................................ 168 vii LIST OF FIGURES Page Figure 1. Description of the three components of the minimal closed-loop model ..... 14 Figure 2. Illustration of standard minimal closed-loop system is composed of four vascular compartments: systemic arteries (SA), systemic veins (SV), pulmonary arteries (PA), and pulmonary veins (PV); two peripheral resistances: pulmonary resistance (Rp) and systemic resistance (Rs); and the left ventricle (LV) and the right ventricle (RV) ....................................... 15 Figure 3. Representation of the chronic cardiac function-venous return balance point in terms of parameters for the minimal closed-loop model ................. 23 Figure 4. Graphical representations of compensation to heart failure ......................... 25 Figure 5. Effect of characterizing the nonlinear end-diastolic pressure-volume relationship by two linear relationships ........................................................ 29 Figure 6. Components of the closed-loop and interstitial system ................................ 41 Figure 7. Lumped description of the coupled vascular and pulmonary interstitial compartments ................................................................................................ 44 Figure 8. Equilibrium pulmonary capillary pressure (Pcp) and systemic venous pressure (Psv) both arise from the balance of input and output flows ........... 50 Figure 9. Pulmonary interstitial pressure (Pip) arises from the balance of flow into the interstitium characterized by the Starling-Landis equation (Eq. 13) and flow out of the interstitium characterized by the Drake-Laine equation (Eq. 14), with the vascular space influencing interstitial pressure through systemic venous pressure (Psv) and pulmonary capillary pressure (Pcp) ............................................................................................................... 52 Figure 10. Sensitivity analysis of pulmonary interstitial pressure (Pip) for normal human parameters ......................................................................................... 54 Figure 11. Non-dimensional
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