Contrary to the popular belief that the heart maintains a regular rhythm, healthy heartbeats fluctuate in a chaotic way. We now know that the fluctuations do not display uncorrelated randomness, but they contain long-range correlations and can be characterized by a fractal. This behavior supports the adaptability of the heart and may thus protect it from external stress. The fractal complexity is also found in the smallest parts of the heart: the cells. In the dawn of advanced pluripotent stem cell technology, producing independently beating cardiomyocytes in a laboratory, the beat-rate fluctuations of heart cells can be directly studied.
In this thesis, we investigate the complex fluctuations in the field potentials generated by clusters of human cardiomyocytes. We show that the heart cells exhibit similar correlation properties in the beat-to-beat intervals and field potential durations comparable to RR and QT intervals, i.e., time between consecutive R waves and time from Q wave to the end of T wave, respectively, in an electrocardiogram of a heart. The cells are studied under conditions resembling real-life situations such as cardiac disorders, application of cardioactive drugs, and injuries. The results show significant alteration of the scaling properties in the beat rates, reflecting the changes in the intrinsic mechanism at the cellular level.
By employing a set of nonlinear time series analysis tools, we explore their powerful applicability as well as their limitations. Our main method of choice throughout the work is detrended fluctuation analysis, which is designed to detect the degree of correlation in nonstationary time series. We demonstrate that detrended fluctuation analysis and its extensions are extremely useful in dealing with the field potential data of the heart cells despite the presence of abnormalities and irregular trends. The study of heartbeat dynamics at the cellular level using computational methods has important advantages. In particular, the methods provide non-invasive and versatile ways to improve our understanding of the intrinsic firing patterns of the heart cells, which play a crucial role in the future applications of in vitro human cardiomyocytes
