CARDIAC ARRHYTHMIA AFTER MYOCARDIAL INFARCTION: INSIGHTS FROM A DYNAMIC CANINE VENTRICULAR MYOCYTE MODEL by Thomas J. Hund Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Thesis Advisor: Dr. Yoram Rudy Department of Biomedical Engineering CASE WESTERN RESERVE UNIVERSITY May 2004 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. For Keila iii TABLE OF CONTENTS List of Tables ...................................................................................................................... 3 List of Figures..................................................................................................................... 4 Acknowledgments............................................................................................................... 6 List of Abbreviations .......................................................................................................... 7 Glossary .............................................................................................................................. 9 Chapter 1 - Introduction.................................................................................................... 13 Objective....................................................................................................................... 14 Mathematical Modeling of Excitable Cells - A Brief History...................................... 14 Electrophysiological Remodeling................................................................................. 16 Ca2+/calmodulin-dependent protein kinase II ............................................................... 19 Works Cited .................................................................................................................. 24 Chapter 2 - A mathematical model of the canine ventricular myocyte ............................ 30 Introduction................................................................................................................... 31 Ca2+-Calmodulin-dependent Protein Kinase II............................................................. 32 Subspace Compartment ................................................................................................ 33 Ryanodine Receptor Ca2+ Release Channel.................................................................. 34 SR Ca2+-ATPase and phospholamban .......................................................................... 35 L-type Ca2+ Channel ..................................................................................................... 36 Two components of the delayed rectifier K+ current................................................... 38 Transient outward K+ current........................................................................................ 39 Ca2+-dependent transient outward Cl - current.............................................................. 39 Chloride Homeostasis ................................................................................................... 39 Na+-Ca2+ Exchanger...................................................................................................... 40 + The late Na current, INa,L ............................................................................................. 40 Works Cited .................................................................................................................. 41 Chapter 3 - Rate dependence of action potential duration and calcium transient............. 47 Ionic mechanism of APD rate dependence (adaptation)............................................... 49 The CaTamp-Frequency Relationship ............................................................................ 52 Discussion..................................................................................................................... 55 Works Cited .................................................................................................................. 60 Chapter 4 - Electrical remodeling in the epicardial border zone ...................................... 63 Introduction................................................................................................................... 64 Model Formulation ....................................................................................................... 65 Results........................................................................................................................... 68 Discussion..................................................................................................................... 76 Works Cited .................................................................................................................. 80 1 Chapter 5 - Discussion...................................................................................................... 83 Summary of Findings.................................................................................................... 84 Cell Modeling ............................................................................................................... 84 Myocardial Infarction ................................................................................................... 86 CaMKII......................................................................................................................... 86 Works Cited .................................................................................................................. 88 Appendix A - Conservation .............................................................................................. 92 Introduction................................................................................................................... 94 Differential method....................................................................................................... 95 Algebraic method.......................................................................................................... 96 Pacing protocols............................................................................................................ 97 Results........................................................................................................................... 99 Discussion................................................................................................................... 105 Works Cited ................................................................................................................ 111 Appendix B - Model Equations ...................................................................................... 113 Appendix C - Diseased Model Equations....................................................................... 136 Bibliography ................................................................................................................... 144 2 List of Tables Table 1. Control and BZ electrophysiological properties................................................ 71 Table 2. Model calcium transient properties.................................................................... 71 Table 3. Abbreviations for conservation study................................................................ 93 Table 4. Conservation initial conditions .......................................................................... 97 Table 5. Model abbreviations ........................................................................................ 114 Table 6. Control ion concentrations at rest .................................................................... 117 Table 7. BZ ion concentrations at rest ........................................................................... 137 3 List of Figures Figure 1 The chain of events following a myocardial insult that creates a pro- arrhythmic substrate..................................................................................17 Figure 2 Schematic illustrating the structure and functional states of Ca2+/calmodulin-dependent protein kinase II...........................................20 Figure 3 Canine ventricular cell model schematic..................................................32 Figure 4 Ratio of peak SR Ca2+ release flux to peak L-type Ca2+ channel flux vs. test potential..............................................................................................34 Figure 5 Validation of model ICa(L)..........................................................................36 Figure 6 ICa(L) fast and slow voltage-dependent inactivation time constants fitted to canine ventricular data..............................................................................37 Figure 7 Peak IKs and IKr tail currents compared to canine epicardial data.............38 Figure 8 Ito1 I-V relationship compared to canine epicardial data...........................39 Figure 9 Steady-state action potentials and adaptation curve in the model and a canine epicardial myocyte.........................................................................48