UC San Diego

The membrane electric potential of the human heart depends on numerous of ionic channels and concentrations. Spikes in the membrane potential are responsible for the contracting of the heart, but disruptions to the membrane potential are also responsible for disorders. A cardiac arrhythmia is an irregular heartbeat that is caused by an abnormal activation pattern in the membrane potential. This dissertation focuses on the development of computational models that describe the membrane potential, and examines the conditions for when an arrhythmia can occur. We begin by comparing the efficacy of a highly detailed model, and a very simple one, to describe patient specific quantities of the membrane potential. From this we conclude that increased complexity does not improve the model's ability to describe the data. Next, we use a unique approach of reducing a detailed model in order to develop our own simplified model. In this way we remove the variables and equations that are not necessary, while still preserving physical relevance for the parameters that are most essential to describing the voltage. Finally, we examine the spiral wave dynamics typically seen in cardiac systems, and look to understand when these spirals can become chaotic. Surprisingly, a single spiral can become chaotic without breaking up into multiple waves. Together these results offer new insights into the physics of cardiac dynamics, and present new possibilities for future treatment of cardiac arrhythmias.