Proper heart function results from the periodic execution of a series of coordinated interdependent mechanical, chemical, and electrical processes within the cardiac tissue. Central to these processes is the action potential---the electrochemical event that initiates contraction of the individual cardiac myocytes. Many models of the cardiac action potential exist with varying levels of complexity, but none account for the electrophysiological role played by caveolae---small invaginations of the cardiac cell plasma membrane. Recent electrophysiological studies regarding these microdomains reveal that cardiac caveolae function as reservoirs of 'recruitable' sodium ion channels. As such, caveolar channels constitute a substantial and previously unrecognized source of sodium current that can significantly influence action potential morphology. In this thesis, I formulate and analyze new models of cardiac action potential which account for these caveolar sodium currents and provide computational venues in which to develop and test new hypotheses. My results provide insight into the role played by caveolar sodium currents in regulating the electrodynamics of cardiac myocytes and suggest that in certain pathological cases, caveolae may play an arrhythmogenic role.
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