Modeling the temporal fluctuations of the cerebral blood flow velocity waveforms using surrogate data testing

The objective of this study is to find out which mathematical model best explains the temporal fluctuations of the axial blood flow velocity waveforms in the basal arteries of the brain. Blood flow velocity time series were sampled by transcranial Doppler (TCD) examination of the middle cerebral arteries in 10 healthy volunteers. A recently developed mathematical test (surrogate data analysis) was used to examine whether the spectral Doppler maximum waveform consistent with some prespecified model (null hypothesis). We tested four different null hypothesis. 1. Uncorrelated white noise. 2. Linearly filtered noise. 3. Linearly filtered noise with a static nonlinear amplitude transformation. 4. Noisy nonlinear limit cycle. All null hypotheses except the last one could be rejected. We conclude that the TCD waveforms are best described as nonlinear limit cycle with some percentage of noise, either dynamical and/or observational, which is uncorrelated from one single oscillation to the next. These results are a strong argument to perform nonlinear analysis in future TCD studies in order to obtain a better understanding of the cerebral hemodynamics.