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Atrial fibrillation (AF) is a frequently encountered cardiac arrhythmia characterized by rapid and irregular atrial activity, which increases the risk of strokes, heart failure and other heart-related complications. The mechanisms of AF are complicated. Although various mechanisms were proposed in previous research, the precise mechanisms of AF are not clear yet and the optimal therapy for AF patients are still under debated. A higher success rate of AF treatments requires a deeper understanding of the problem of AF and potentially a better screening of the patients. In order to study AF, instead of using human body surface ECGs, we use the epicardial electrograms (EGMs) obtained directly from the epicardial sites of the human atria during open heart surgery. This data is measured using a high-resolution mapping array and exhibits irregular properties during AF. Although different studies have analyzed electrograms in time and frequency domain, there remain many open questions that require alternative and novel tools to investigate AF. Experience in signal processing suggests that incorporating the spatial dimension into the time-frequency analysis on the multi-electrode electrograms may provide improved insights on the atrial activity. However, the electrophysiologcial models for describing spatial propagation are relatively complex and non-linear such that conventional signal processing methods are less suitable for a joint space, time, and frequency domain analysis. It is also difficult to use very detailed electrophysiologcial models to extract tissue parameters related to AF from the high-dimensional data. In this dissertation, we wish to propose a radically different approach to study and analyze the EGMs from a higher abstraction level and from different perspectives to get more understanding of the characteristics of AF. We also aim to develop a simplified electrophysiological model that can capture the spatial structure of the data and propose an efficient method to estimate the tissue parameters, which are helpful to analyze the electropathology of the tissue, e.g., cell activation time or conductivity.In the first part of this study, we put forward a graph-time spectral analysis framework to analyze EGMs during normal heart rhythm and AF with a higher-level model. To capture the frequency content along both time domain and graph domain, we propose the joint graph and short-time Fourier transform, which allows us to evaluate the temporal and spatial variation of EGMs and capture the interaction between space and time. The spectral analysis of the EGMs helps us to recognize atrial fibrillation impact on the atrial activity and identify the differences between the atrial activity and the ventricular activity. We find that the difference in graph smoothness between the atrial and ventricular activities enables us to better extract the atrial activity from the noisy measurements.The second part of this study is to find a simplified but accurate enough electrophysiological model for the high dimensional EGMs and to make more efficient use of the data to detect the arrythmogenic substrate that causes abnormalities in atrial tissue. In this dissertation, we develop the cross power spectral density matrix (CPSDM) model of the multi-electrode EGMs and make use of an effective method called confirmatory factor analysis (CFA) to jointly estimate the model parameters. The conductivity, the activation time, and the anisotropy ratio are useful parameters to determine abnormalities in cardiac tissue and are therefore the target parameters to be estimated. With the reasonable assumptions that the conductivity parameters and the anisotropy parameters are constant across different frequencies and heart beats, and the activation time of cells are constant across different frequencies, we propose simultaneous CFA (SCFA) to jointly estimate these parameters using multiple frequencies and multiple heart beats. The identifiability conditions which need to be satisfied in the CFA problem are used to find the relationship between the desired resolution and the required amount of data. Evaluations on the simulated data and the clinical data demonstrate that the proposed method can localize the conduction blocks in the tissue and reconstruct the clinical EGMs well using the estimated parameters. |
