Evidence of phase transitions in heart period dynamics

Abstract.

Complexity measures of non-linear dynamics are a useful tool for quantifying observed stretching, folding, scaling and mixing processes in the Takens-reconstructed state space of heart period dynamics. Although such measures are not suited to provide evidence of deterministic chaos or to estimate true fractal dimensions and Lyapunov spectra in heart period time series, they allow the classification of RR dynamics and the identification of changes in RR complexity (RRC). The aim of this study was to develop appropriate measures and examine their utility in identifying the physiological effect of changes between the sleeping and waking state. Twenty-four hour electrocardiography (ECG) recordings and diaries noting their waking/sleeping period were obtained from 78 healthy subjects, aged 20 to 55 years. The approximate information dimension (ApD1) and the approximate Kolmogorov entropy (ApEn), introduced by Pincus, Kaplan and others, were modified in order to allow the calculation of strictly local values. That is, the local or pointwise dimensions and entropies were calculated for each reference vector with respect to its symmetric neighbourhood in time. For each subject the values for the local measures were averaged for 10-min periods, resulting in 144 global values over 24 h. Similarly, low- and high-frequency spectral parameters were calculated. All measures were examined and compared for the waking and the sleeping periods. All complexity measures as well as to a lesser degree high-frequency power showed a linear dependency on mean RR interval with a large individual variation. For the RRC measures this linear correlation was separated into two different clusters corresponding to the sleeping and waking periods. In almost all cases the correlation was greater in the waking period. In particular, in many cases no correlation was observed in the sleeping period. However, the $r$ values for LF were appreciably lower and indicated solely a weak relationship to the RR interval in the waking period. Analysis of variance combining mean RR interval with RRC or spectral parameters singly and in couples revealed that the best separation with respect to physiological state could be achieved with the complexity measures, in particular with ApEn. The results show evidence of at least two dynamical regimes (phases) of heart period dynamics and a close but different functional relationship within the phases between RR interval and RR complexity. The separation between these regimes and the relatively sudden shift from one regime to the other suggest the existence of a phase transition with respect to waking and sleeping periods in terms of synergetics.