Assessment of time irreversibility in a time series using visibility graphs

From physiological complexity to data interactions-A case study of recordings from exercise monitoring

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.