Abstract
Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.
Highlights
Many vital physiological processes are characterized by rhythmic activity, ranging from the circadian clock regulating the daily sleep-wake cycle to temporal patterns of respiration that occur over a scale of seconds (Glass, 2001)
To identify the statistical signatures characterizing dynamical transitions to different types of arrhythmia, we systematically explore the spatiotemporal dynamics of the model systems in different parameter regimes
We have studied biophysically detailed models of ventricular activity to infer signatures of dynamical transitions characterizing the onset of different kinds of arrhythmia
Summary
Many vital physiological processes are characterized by rhythmic activity, ranging from the circadian clock regulating the daily sleep-wake cycle to temporal patterns of respiration that occur over a scale of seconds (Glass, 2001). Certain types of disturbances in the cardiac rhythmicity, referred to as arrhythmia, can severely impair the normal functioning of the heart and in the most critical instances, can result in sudden cardiac death (Winfree, 1980). Such “dynamical diseases” (Mackey and Glass, 1977; Belair et al, 1995), i.e., diseases resulting from abnormal activity in an otherwise intact physiological system, are a significant public health burden in developed countries. In recent times heart disease has overtaken other causes of death, e.g., sudden cardiac deaths contributed to about 10% of overall mortality in certain regions in India, accounting for upto half of all cardiovascular-related deaths (Madhavan et al, 2011; Rao et al, 2012)
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