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Abstract
Atrial fibrillation (AF) is a complex, multifaceted arrhythmia. Pathogenesis of AF is associated with multiple aetiologies and the mechanisms by which it is sustained and perpetuated are similarly diverse. In particular, regional heterogeneity in the electrophysiological properties of normal and pathological tissue plays a critical role in the occurrence of AF. Understanding AF in the context of electrophysiological heterogeneity requires cell-specific ionic models of electrical activity which can then be incorporated into models on larger temporal and spatial scales.
Biophysically-based models have typically dominated the study of cellular excitability providing detailed and precise descriptions in the form of complex mathematical formulations. However, such models have limited applicability in multidimensional simulations as the computational expense is too prohibitive. Simplified mathematical models of cardiac cell electrical activity are an alternative approach to these traditional biophysically-detailed models. Utilizing this approach enables the embodiment of cellular excitation characteristics at minimal computational cost such that simulations of arrhythmogensis in atrial tissue are conceivable.
In this thesis, a simplified, generic mathematical model is proposed that characterizes and reproduces the action potential waveforms of individual cardiac myocytes. It incorporates three time-dependent ionic currents and an additional time-independent leakage current. The formulation of the three time-dependent ionic currents is based on 4-state Markov schemes with state transition rates expressed as nonlinear sigmoidal functions of the membrane potential. Parameters of the generic model were optimized to fit the action potential waveforms of the Beeler-Reuter model, and, experimental recordings from atrial and sinoatrial cells of rabbits. A nonlinear least-squares optimization routine was employed for the parameter fits.
The model was successfully fitted to the Beeler-Reuter waveform (RMS error: 1.4999 mV) and action potentials recorded from atrial tissue (RMS error: 1.3398 mV) and cells of the peripheral (RMS error: 2.4821 mV) and central (RMS error: 2.3126 mV) sinoatrial node. Thus, the model presented here is a mathematical framework by which a wide variety of cell-specific AP morphologies can be reproduced. Such a model offers the potential for insights into possible mechanisms that contribute to heterogeneity and/or arrhythmia.