## Abstract

Until 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) waveforms is the result of nonlinearity or not. From 10 healthy volunteers, left middle cerebral artery (MCA) blood flow velocities were measured by TCD examinations. An artifact free epoch of each TCD was used for analysis. From each original data set 50 surrogate data sets were constructed using the Gaussian-scaled phase-randomized Fourier transform. For both the original and the surrogate data sets the D2 was measured. The D2 values of the original TCD waveforms differed significantly from the mean D2 of the surrogate data sets. Therefore the null hypothesis, which stated that the original TCD time series arise from filtered noise, is rejected and nonlinearity is detected. The clinical significance and implications are discussed.

Original language | English |
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Pages (from-to) | 19-24 |

Number of pages | 6 |

Journal | Neurological Research |

Volume | 18 |

Issue number | 1 |

Publication status | Published - Feb 1996 |

## Keywords

- Adult
- Cerebral Arteries/diagnostic imaging
- Female
- Humans
- Male
- Models, Neurological
- Models, Statistical
- Nonlinear Dynamics
- Random Allocation
- Reference Values
- Regional Blood Flow
- Ultrasonography, Doppler, Color
- Ultrasonography, Doppler, Transcranial