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

Abstract

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 (< or = 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.

Estimation of Coherence Between Blood Flow and Spontaneous EEG Activity in Neonates

“…In previous work [8], we had found that there is low, but statistically significant cross-correlation between mean CBFV and the power of the EEG signal during TA activity in the newborn. There are sound physiological reasons why such correlation might be expected, given our understanding of cerebral blood flow control [1].…”

“…The set of signals used are the same as in the previous work [8]. A group of nine normal newborns (gestational age 37-41 weeks, Apgar at 1 and 5 min) were studied within seven days of birth (six of them within the first three days), after written informed parental consent and with approval of the local ethics committee (Instituto Fernandes Figueira, Fiocruz, Rio de Janeiro, Brazil).…”

“…Thus, the surrogate signals should have the same power-spectrum as the recorded signals, and according to the null-hypothesis, they must of course also be uncorrelated. In previous work [8], we obtained these signals by using the amplitude spectra of the recorded data and by generating random phase spectra. In the present application, Table I).…”

“…However, this solution cannot be employed in the current problem, because the coherence estimates are not independent. Following our previous approach [8], we therefore developed a solution using the Monte Carlo method, which can deal with the twin problem of 1) testing the significance of our modified coherence estimator (i.e., with missing samples), and 2) assessing the significance of the maximum coherence within a given frequency range.…”

“…Blood flow to the brain changes, for example, with sleep [3], [4], during epileptic seizures [5], [6], and with sensory stimulation [7]. In previous work [8], we investigated the correlation between cerebral blood flow velocity (CBFV), as measured by transcranial Doppler ultrasound, and spontaneous electroencephalogram (EEG) activity during quiet sleep in newborn babies [Tracé Alternant (TA) EEG pattern]. We found low, but significant, correlation between the signals, with changes in CBFV lagging those in the EEG by about 5 s. In this paper, we extend that work by investigating the coherence between these signals.…”