No evidence of chaos in the heart rate variability of normal and cardiac transplant human subjects.

INTRODUCTION: The variability observed in the heart rate may reflect fundamental aspects of cardiac activity. It has been under discussion whether heart rate variability (HRV) is due to noise or chaos, which is irregular behavior occurring in deterministic nonlinear systems. METHODS AND RESULTS: Using chaos analysis techniques, we analyzed HRV of five normal and five human cardiac transplant subjects at rest. HRV is studied using the beat-to-beat RR interval time series extracted from the ECG. The cardiac transplant subjects exhibited a much smaller HRV than the normal subjects because of heart denervation. We present the map and correlation dimension estimation for the RR time series. To test for nonlinear correlations in the dynamics, we built surrogate time series that have the same power spectra as the experimental time series, but also have randomized phases. The experimental and the surrogate data were compared using the correlation integral. No correlation dimension was found for the RR time series of either the normal or the cardiac transplant subjects. Nevertheless, nonlinear correlations were detected in the HRV of the normal subjects but not in HRV of the cardiac transplant subjects. For the latter, no significant changes were observed in the correlation integral as a function of time after transplantation. CONCLUSION: We found no evidence of low-dimensional chaos in the HRV of normal and cardiac transplant subjects. However, some nonlinear correlations were detected in the HRV of the normal subjects, which may be associated with autonomic nervous system influence.

Correlation dimension maps of EEG from epileptic absences.

PURPOSE: The understanding of brain activity, and in particular events such as epileptic seizures, lies on the characterisation of the dynamics of the neural networks. The theory of non-linear dynamics provides signal analysis techniques which may give new information on the behaviour of such networks. METHODS: We calculated correlation dimension maps for 19-channel EEG data from 3 patients with a total of 7 absence seizures. The signals were analysed before, during and after the seizures. Phase randomised surrogate data was used to test chaos. RESULTS: In the seizures of two patients we could distinguish two dynamical regions on the cerebral cortex, one that seemed to exhibit chaos whereas the other seemed to exhibit noise. The pattern shown is essentially the same for seizures triggered by hyperventilation, but differ for seizures triggered by light flashes. The chaotic dynamics that one seems to observe is determined by a small number of variables and has low complexity. On the other hand, in the seizures of another patient no chaotic region was found. Before and during the seizures no chaos was found either, in all cases. CONCLUSIONS: The application of non-linear signal analysis revealed the existence of differences in the spatial dynamics associated to absence seizures. This may contribute to the understanding of those seizures and be of assistance in clinical diagnosis.

Modelling a parasystolic rhythm in a heart-transplant patient.

A parasystole from a heart-transplant patient is analysed using a beat-to-beat RR interval time series obtained from an electrocardiogram (ECG). The dysrhythmia, resulting from the co-existence of two pacemakers, the sinus node and an ectopic focus, presents distinctive regular patterns, with transitions from one pattern to another occurring abruptly. It is shown that the parasystolic rhythm can be simulated by a model involving two oscillators firing at fixed rates, under the restriction that neither is allowed to fire during the other's refractory period. It is found that the structure of the generated RR time series is essentially determined by the ratio of the periods of the two oscillators. In the case of a heart-transplant patient with a small heart-rate variability as a result of heart denervation, the model predicts the RR intervals with an error of less than 6% for an 80-beat sequence. From a physiological point of view, the results imply that the interaction between the two pacemakers in the heart is fairly weak, and hence the parasystole observed in the heart-transplant patient can be modelled as pure parasystole.