When excitable cardiac tissue is electrically paced at a sufficiently high rate, the duration of excitation can alternate from beat to beat despite a constant stimulation period. This rhythm, known as alternans, has been identified as an early stage in a sequence of increasingly complex instabilities leading to the lethal arrhythmia ventricular fibrillation (VF). This connection served as as a motivation for research into the control of alternans as a strategy to prevent VF. Control methods that do not use a model of the dynamics have been used for the suppression of alternans. However, these methods possess limitations.

In this thesis we study theoretically model-based control techniques with the goal of developing protocols that would overcome the shortcomings of non model-based approaches. We consider one dimensional tissue in two different geometrical configurations: a ring and a fiber with free ends (open fiber). We apply standard control methods for linear time invariant systems to a stroboscopic map of the linearized dynamics around the normal rhythm. We found that, in the ring geometry, model-based control is able to suppress alternans faster and with lower current, thereby reducing the risk of tissue damage, compared with non-model-based control. In the open fiber, model-based control is able to suppress alternans for longer fibers and higher pacing frequencies in comparison with non-model-based control. The methodology presented here can be extended to two- and three-dimensional tissue, and could eventually lead to the suppression of alternans on the entire ventricles.