Rejection of the ‘filtered noise’ hypothesis to explain the variability of transcranial Doppler signals: A comparison of original TCD data with Gaussian-scaled phase randomized surrogate data sets

AbstractUntil the last few years the correlation dimension (D2) or the Lyapunow exponent were the two dominant mathematical methods which were applied to identify possible chaotic behavior in biological systems. Detection of deterministic chaos is important, because it suggests that a relatively simple nonlinear model might explain the data. It was however discovered that these methods could give rise to an erroneous detection of chaos. For this reason a new method was proposed in which the originally measured data set was directly compared with a computer generated ‘surrogate’ data set with exactly the same linear correlations as the original. The basic idea is then to compute a nonlinear statistic for the original data and for each of the surrogate data sets. In principle any statistic can be used. We used the correlation dimension (D2), which measures the complexity of a time series. In this study we applied this surrogate method to estimate whether the variability of the transcranial Doppler (TCD) wav...