When excitable cardiac tissue is electrically paced at a sufficientlyhigh rate, the duration of excitation can alternate from beat to beatdespite a constant stimulation period. This rhythm, known as alternans,has been identified as an early stage in a sequence of increasingly complexinstabilities leading to the lethal arrhythmia ventricular fibrillation (VF).This connection served as as a motivation for research into the control ofalternans as a strategy to prevent VF. Control methods that do not use a modelof the dynamics have been used for the suppression of alternans. However, thesemethodspossess limitations.In this thesis we study theoretically model-based control techniques with the goalof developing protocols that would overcome the shortcomings of non model-basedapproaches. 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 forlinear time invariant systems to a stroboscopic map of the linearized dynamics aroundthe normal rhythm. We found that, in the ring geometry, model-based control is able tosuppress 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 tosuppress alternans for longer fibers and higher pacing frequencies in comparisonwith non-model-based control. The methodology presented here can be extended totwo- and three-dimensional tissue, and could eventually lead to the suppressionof alternans on the entire ventricles.
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Model-based control of cardiac alternans on one dimensional tissue