Atrial fibrillation (Afib) is the most common cardiac arrhythmia affecting millions of people around the world. Mapping and analysis of electrical activation patterns such as electric rotors during Afib is crucial in understanding arrhythmic mechanisms and assessment of diagnostic measures. To this end, there exists various mapping studies where textit{'quantitative'} features such as local activation time, dominant frequency, wave direction, and conduction velocity are extracted from recorded intracardiac electrograms (EGMs). However, obtaining quantitative features further adds to multiplicity of the data and henceforth does not help interpretation of measured signals as opposed to using a more compressed diagnostic terms such as linking the measurements to reentry mechanisms. Through some techniques it is possible to construct isopotential and phase mappings by the help of monophasic action potential recordings in higher spatial resolution. In those cases, however, both expensive mapping tools performing multi-site simultaneous recordings which are not available to most of electrophysiologists are required. On the other hand, the most commonly used catheters which provide high resolution but local measurements remain rather rudimentary in mapping a spatially more global arrhythmic behaviors in a simultaneous fashion. Spiral waves are tissue level phenomena observed in both clinical and experimental settings. They are the product of electrical rotors which are associated with reentry mechanisms during Afib. They can be reproduced using computer models of cardiac electrical activity. Current computer models vary in complexity, accuracy, and efficiency. One particular type is called biophysical models which are based on detailed ion channel interactions. Besides being computationally demanding, they are exceedingly complex and intractable preventing their use in a systems approach where multilevel events are generally considered together. Phenomenological models, on the other hand, include summarized details of ionic events yet preserve fundamental biophysical accuracy. A particular one of them, a minimal resistor model (MRM), was shown to reproduce relevant basic electrophysiological behaviors such as (action potential) AP and electrical restitution properties for human ventricular tissue. The objective in present thesis is to 'qualitatively' characterize fibrillatory wavefront propagation dynamics in cardiac tissue using simulated intracardiac EGMs obtained from most commonly used and lower cost catheter types providing high resolution but localized readings. Another purpose connected to the previous is to show adequacy of a phenomenological model, MRM, in reproducing biophysically related behaviors for human atria. In this respect, two category of problems are handled throughout the thesis: (1) parameter estimation of MRM and (2) discrimination of spiral wave behaviors through intracardiac EGMs simulated using MRM. In the first part, representativeness of MRM for human atrial electrophysiology is established through adaptation of it to a biophysically detailed model originated from experimental data. Specifically, a method is proposed for parameter estimation of the simple model, MRM, to match a targeted behavior such as AP and electrical restitutions first generated from a complex model, by using extended Kalman filter (EKF). In the second part, a method that receives intracardiac EGMs and returns corresponding wavefront propagation patterns classified in terms of electric rotor dynamics is introduced. The method incorporates an information theoretical distance which is called normalized compression distance (NCD) used for assessment of distance measure between simulated behaviors. Achieving outstanding performance together with robustness in discrimination through usage of simulated data enables a theoretical validation of the method. Proposed frameworks collectively yield (1) potential usability of a computationally efficient and easier in analysis model for tissue level cardiac events and (2) simplicity and practicality in clinics through a mapping from a multiple, complex EGM signals to electric rotor behaviors, symptoms more relevant to the diagnosis.Ph.D., Electrical Engineering -- Drexel University, 201
