Estimation of the correlation dimension of heart rate using surrogate data techniques

Researchers have recently applied nonlinear dynamical systems theory to physiological time series data. However, the direct implementation of the deterministic equations used to estimate the correlation dimension is problematic for physiological data. Importantly, the distinction between a nonlinear process and noise is particularly difficult for experimental data. One technique that has been developed to help with this distinction is the use of surrogate data. These data preserve many of the properties of the original time series but in fact are a randomization of the original data. Whereas in a sufficiently high embedding space the estimates of the correlation dimension of a nonlinear process will plateau, such estimates for a noise process will continue to rise with increases in the embedding dimension. In the present experiment two data sets were examined. Heart period time series were collected from a female subject during spontaneous breathing and breathing paced at 15 breaths per minute. Both data sets consisted of approximately 3000 interbeat intervals and embedding dimensions of m = 2 through m = 6 were examined. Results indicate that the correlation dimension estimate for the spontaneous breathing data reached a plateau around 4, whereas the surrogate data for this series showed no such plateau. For the paced breathing data, both the original and the surrogate data failed to show evidence of a plateau in the estimates of the correlation dimension. These results suggest that caution must be used in interpreting finite values of correlation dimension as evidence of a chaotic attractor in experimental data if no test for determinism is performed.