Estimation and significance testing of cross-correlation between cerebral blood flow velocity and background electro-encephalograph activity in signals with missing samples

Cross-correlation between cerebral blood flow (CBF) and background EEG activity can indicate the integrity of CBF control under changing metabolic demand. The difficulty of obtaining long, continuous recordings of good quality for both EEG and CBF signals in a clinical setting is overcome, in the present work, by an algorithm that allows the cross-correlation function (CCF) to be estimated when the signals are interrupted by segments of missing data. Methods are also presented to test the statistical significance of the CCF obtained in this way and to estimate the power of this test, both based on Monte Carlo simulations. The techniques are applied to the time-series given by the mean CBF velocity (recorded by transcranial Doppler) and the mean power of the EEG signal, obtained in 1 s intervals from nine sleeping neonates. The peak of the CCF is found to be low (≤0.35), but reached statistical significance (p<0.05) in five of the nine subjects. The CCF further indicates a delay of 4–6s between changes in EEG and CBF velocity. The proposed signal-analysis methods prove effective and convenient and can be of wide use in dealing with the common problem of missing samples in biological signals.