Symbolic coupling traces for causality analysis of cardiovascular control

Directional coupling analysis of time series is an important subject of current research. In this paper, a method based on symbolic dynamics for the detection of time-delayed coupling in biosignals is presented. The symbolic coupling traces, defined as the symmetric and diametric traces of the bivariate word distribution, allow for a more reliable quantification of coupling and are compared with established methods like mutual information and cross recurrence analysis. The symbolic coupling traces method is applied to appropriate model systems and cardiological data which demonstrate its advantages especially for nonstationary and noisy data. Moreover, the method of symbolic coupling traces is used to analyze and quantify time-delayed coupling of cardiovascular measurements during different sleep stages. Significant different regulatory mechanisms are detected not only between the deep sleep and the other sleep stages but also between healthy subjects and patients. The proposed method may help to indicate pathological changes in cardiovascular regulation and also effects of continuous positive airway pressure therapy on the cardiovascular system.