REJECTION OF THE FILTERED NOISE HYPOTHESIS TO EXPLAIN THE VARIABILITYOF TRANSCRANIAL DOPPLER SIGNALS - A COMPARISON OF ORIGINAL TCD DATA WITH GAUSSIAN-SCALED PHASE RANDOMIZED SURROGATE DATA SETS

Until the last few years the correlation dimension (D-2) Or the Lyapun ow exponent were the two dominant mathematical methods which were appl ied to identify possible chaotic behavior in biological systems. Detec tion of deterministic chaos is important, because it suggests that a r elatively simple nonlinear model might explain the data. It was howeve r discovered that these methods could give rise to an erroneous detect ion of chaos. For this reason a new method was proposed in which the o riginally measured data set was directly compared with a computer gene rated 'surrogate' data set with exactly the same linear correlations a s the original. The basic idea is then to compute a nonlinear statisti c for the original data and for each of the surrogate data sets. In pr inciple any statistic can be used. We used the correlation dimension ( D-2), 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 sur rogate data sets the D-2 was measured. The D-2 values of the original TCD waveforms differed significantly from the mean D-2 Of the surrogat e data sets. Therefore the null hypothesis, which stated that the orig inal TCD time series arise from filtered noise, is rejected and nonlin earity is detected. The clinical significance and implications are dis cussed.