Applying Lyapunov Exponents in heart rate time series to identify the Anaerobic Threshold in healthy men

During the last years a lot of papers have appeared dealing with the applications to physiological time series of some parameters originally found in Dynamical Systems. In this work, we looked for the Largest Lyapunov Exponents (LLE) in heart rate time series of healthy men in order to verify if it was possible to find the Anaerobic Threshold (AT) in a non-invasive way using just the time series and the LLE extracted from them. The work was undertaken in a group of 10 healthy individuals using a conventional electrocardiogram. The series of RR intervals, lasting for twelve minutes, were obtained in rest (supine and seated positions) and in a discontinuous protocol of dynamic exercise in seated position. The LLE were computed using the TISEAN system. The results were compared to those obtained by the measurement of AT using an autoregressive integrated moving-average model (ARIMA) and using the Kolmogorov-Sinai Entropy (KS). The Spearman test (rs) with α = 5% applied to these three methods gave: a) for KS × ARIMA: p <; 0.01, rs = 0.93; b) LLE × KS: p <; 0.01, rs = 0.94 and c) LLE × ARIMA: p <; 0.01, rs = 0.93. These results are very expressive concerning the use of LLE to find the AT.