| Περίληψη: | Mathematical models and simulation studies of the electrical function of the heart contribute significantly to better understanding and treatment of cardiac arrhythmias. Although great progress has been made in this area, particularly in single cell models, many problems related to macroscopic electrical behavior of the heart remain unsolved or require reevaluation as new experimental data appear. The scope of this thesis is the development of mathematical models of effects of heterogeneity and loss of channel function on electrocardiographic (ECG) signal and cardiac vulnerability. Our studies contribute to better arrhythmia understanding, prediction and prevention. In the first study theoretical body-surface potentials were computed from single, branching and tortuous strands of the Luo-Rudy model cells, representing different areas of an infarct scar. When action potential (AP) propagation either in longitudinal or transverse direction was slow (3-12 cm/s), the depolarization signals contained high-frequency (100- 300 Hz) oscillations. The frequencies were related to macroscopic propagation velocity and strand architecture by simple formulas. Next, we proposed a mathematical model of the QRS-complex that simulates unstable activation wavefront. It combines signals from different strands with small timing fluctuations relative to a large repetitive QRS-like waveform and can account for dynamic changes of real arrhythmogenic micropotentials. Variance spectrum of wavelet coefficients calculated from the composite QRS-complex contained the high frequencies of the individual abnormal signals. We concluded that slow AP propagation through fibrotic regions after myocardial infarction is a source of high-frequency arrhythmogenic components that increase beat-to-beat variability of the QRS, and wavelet variance parameters can be used for ventricular tachycardia risk assessment. xv In the second study we quantify the vulnerable period (VP) in heterogeneous models of ventricular wall and its modulation by loss of cardiac sodium channel function (NaLOF). According to several articles, NaLOF prolongs the VP and, therefore, increases risk of reentrant arrhythmias, but the studies used uniform models neglecting spatial variation of action potential duration (APD). Here, we introduce physiological transmural heterogeneity into one-dimensional cables of the Luo-Rudy model cells. We propose a generalized formula for the VP and describe new phenomena pertaining to the VP that are not present in homogeneous excitable media. We conclude that realistic models of cardiac vulnerability should take into account spatial variations of cellular refractoriness. It reveals several new qualitative and quantitative aspects of the VP and the modulation of the VP by NaLOF differs significantly in heterogeneous and homogeneous models. Finally we examine proarrhythmic potential of E-4031, a class III antiarrhythmic agent that blocks selectively rapid potassium current (IKr), during ischemia. Effective refractory periods (ERP) and action potential durations of the Luo-Rudy dynamic model cell were measured for normal and ischemic conditions, after IKr block and at different basic cycle lengths (BCL). Acute ischemia is introduced into the model by hyperkalemia, acidosis and anoxia. The IKr block caused reverse use-dependent prolongation of APD and ERP for normal and the ischemic conditions. Differences in APD and ERP between normal and acutely ischemic cells increased after the IKr block for all BCLs. We conclude that E-4031 has the potential to amplify electrophysiologic heterogeneity between normal and ischemic cardiac tissue that underlies some serious ventricular arrhythmias. This increased dispersion can cancel out the poor antiarrhythmic effect of AP and ERP prolongation at fast heart rates.
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