Minimal models in cardiac dynamics
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Cardiac Arrhythmia is a leading cause of death in the western industrialized world. To date, multiple pathways to examine and treat this disease exist. In this thesis, I focus on computational modeling and nonlinear analysis of cardiac dynamics. While a variety of cardiac models exist, I examine minimal models that produce phenomenological properties of cardiac dynamics. The usefulness of such models is that they are intuitively easy to understand and manipulated. From our results, I first demonstrate the usefulness of minimal models by using a two variable model to produce a novel technique to predict the onset of instability. By reducing current models to a minimal version, I show through graphical and nonlinear methods that action potential amplitude alternans is of equal importance to action potential duration alternans. By further reduction of the two-variable model through fitting to simple equations, I show that phenomenological models can reproduce results that better fit experimental data. Moreover, not only can my constructed minimal produce common phenomena, they can also demonstrate novel dynamics with the adjustment of a small group of parameters. To further expand the usefulness of minimal models, in the last chapter, I construct a minimal model of not only voltage but also the calcium cycling system. Overall, while mathematically complex models are useful and necessary, in this thesis, we present an alternative perspective to study arrhythmia.