This monograph provides a mathematical analysis of electrical wave propagation in cardiac tissue. Models of the cardiac action potential are similar to the Nobel Prize-winning Hogdkin-Huxley model of the nerve action potential. In Chapter 2, we carefully construct a simple, two-variable model of the cardiac action potential, modeling the cell membrane as an electrical circuit. Unlike nerve cells, cardiac tissue exhibits a feature known as electrical restitution, which can be exploited to predict the onset of certain arrhythmias. Chapters 3 and 4 illustrate how to derive restitution relationships for both the duration and velocity of action potential, using the model from Chapter 2 as a starting point. Finally, in Chapter 5 we use these restitution relationships to analyze how cardiac fibers respond to a sudden change in the pacing rate. Our mathematical analysis provides some rather surprising predictions regarding how abnormal rhythms may originate.

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