Control of abnormal heart rhythms

Abnormal heart rhythms are often associated with serious illness and sometimes cause death. A new strategy to control cardiac arrhythmias involves precisely-timed electrical stimulation of the heart in an attempt to restore normal dynamics. In the first part of this thesis, I demonstrate that a particular abnormal heart rhythm is caused by a period-doubling bifurcation. I describe a new control technique that suppresses the abnormal rhythm by directing the timing of electrical stimuli according to a simple feedback algorithm. Subsequent analysis of the feedback controller revealed a rich structure of stability zones that can be used for automatic adaptation of the previously fixed feedback gain parameter.While electrical stimulation of the heart guided by feedback control is a promising new treatment, the standard means of controlling an abnormal heart rhythm involves accurate diagnosis of the arrhythmia mechanism followed by appropriate medical or surgical intervention. Since different arrhythmia mechanism often have very different treatments, accurate diagnosis is crucial. In the second part of this thesis, I describe a new diagnostic technique that identifies the different spatio-temporal symmetry properties of electrical wave patterns underlying different mechanisms of cardiac arrhythmia. For one of the arrhythmia mechanisms, the surgical treatment involves locating and destroying an abnormal region of the heart that generates unwanted electrical oscillations. I present new techniques for locating these abnormal regions and I suggest a procedure to confirm when the correct location has been found