Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation

University of Minnesota M.S. thesis. June 2013. Major: Electrical Engineering. Advisor: Dr. Alena Talkachova. 1 computer file (PDF); viii, 50 pages, appendix p. 42-50.Ventricular fibrillation, a leading cause of death in the US, is an instability observed at the whole heart level which may result from the alternation of action potential viz. alternans at the cellular level. Previous approaches to predict alternans formation are based on the slope of the restitution curve which is the relation between the action potential duration (APD) and the duration of the preceding diastolic interval (DI). These approaches propose that alternans exists when the slope of this curve is greater than one and ceases to exist otherwise. However restitution based approaches have not been successful in all cases. One of the shortcomings of restitution approach is the non-uniqueness of the restitution curve which results from the variety of pacing protocols used to construct it. This has lead to observations in which alternans existed when the slope was less than one and vice a versa. Moreover restitution approaches use just one measurement from each action potential(AP). Another shortcoming of these approaches is periodic pacing, which is employed to attain the responses (APD and DI) at different basic cycle lengths (BCL) to construct the restitution curve. Upon analysis of electrocardiograms, it is evident that natural pacing is not periodic and exhibits rate variability which can be seen from measurement of RR intervals (which are analogous to BCL) over time. It would be beneficial to develop a method which is not very related to the restitution approach to predict alternans formation and which would not necessitate the generation of a curve and thus reduce errors introduced due to slope calculation. Such a method could also use multiple measurements from each AP to characterize it. Also, it would be beneficial to study the effects of introducing variability in pacing, on alternans formation. Analysis of such data would give us some valuable insight into the complex phenomenon of alternans. With these two shortcomings in sight two studies were conducted with specific aims as follows:Aim1: Apply a dominant eigenvalue method to predict alternans formation in the rabbit heart. A dominant eigenvalue based alternans prediction was recently developed and tested on data obtained from single cell numerical simulation data. I applied this technique at whole heart level to test whether alternans formation could be predicted using a eigenvalue calculated at each BCL from AP response data. I found that the eigenvalue showed decreasing trend towards the value of -1 as BCL was decreased and approached alternans onset. Aim2: Study the effect of introducing rate variability in pacing on a ionic model of a single cell. Ionic model of a single cell was paced using two protocols which introduced variability in the pacing rate by either varying the BCL or DI to test the effects on alternans formation. It was found that introducing variability using first method (varying BCL) lead to alternans formation over wider range of BCL than without variability. The second method (varying DI) however did not give rise to alternans in the model with or without variability