This project concerns the combined study of two signals: EEG power variability (EEG-PV) and middle cerebral artery blood flow velocity (BFV). A first phase of the study was conducted in subjects under anaesthesia, so in a non-physiological situation where heartbeat and breathing oscillations are limited. The results were published in (Zanatta et al., The human brain pacemaker, Neuroimage 2013). The study is now extended to subjects studied under normal conditions. The dataset used was provided in the Biological Signals Processing course, held by Professor Toffolo, Bioengineering, Department of Information Engineering, University of Padua, academic year 2014/2015.
The code is contained in the scripit main.m.
The two signals provided in the data folder are:
BFV2 : blood flow rate (cm/sec) measured with ecodoppler at the right
cerebral artery with sampling frequency Fs BFV = 0.5 Hz.
F4C4 : EEG (mV) measured from a frontal derivation located on the right
side of the scalp with sampling frequency Fs EEG = 512 Hz.
To extract the delta component (DELTA2: 0-4Hz) from F4C4 a lowpass filter was used, the optimum order of 5 was found with
the ellipord function while the b and a parameters were obtained thanks to the ellip function. To eliminate phase distortion,
Forward-Backward filtering was used using the filtfilt function.
The Difference equation of the 5th order filter is:
y(n) = 4.9382y(n-1)-9.7584y(n-2) + 9.6455y(n-3)-4.7689y(n-4) + 0.9435y(n-5) + 0.0044x(n)-0.0131x(n-1) + 0.0087x(n-2) + 0.0087x(n-3)-0.0131x(n-4) + 0.0044x(n-5)
Gain and Phase of the Frequency Response of the filter are shown in Fig. 1:
Figure 1: Frequency Response of the lowpass filter
The result of the filtering process is DELTA2, shown in Fig 2.:
Figure 2: Signals F4C4 and DELTA2 with mean and SD intervals
Once the delta component (DELTA2 signal) had been obtained through filtering, it was segmented into 150 segments
by 1024 samples at 2-second intervals. To construct the Power Variability signal (DELTA2_PV), the spectrum of each segment
was calculated using the Periodogram method, having first removed the average for each segment. Then each spectrum was
integrated, with trapz, to obtain the power relative to the delta band. DELTA2_PV was formed by combining the values for
each segment.
The obtained signal DELTA2_PV is shown in Fig. 3:
Figure 3: Power Variability in the delta band
The spectrum of DELTA2_PV signal, obtained by the Periodogram method is shown in Fig 4:
Figure 4: Spectrum of DELTA2_PV
Subsequently the AR model of optimal order was identified on the DELTA2_PV signal.
To find the optimal, three indicators were evaluated for every order between [1:20]: MSE, Akaike's Final Prediction
Error (FPE), Akaike Information Criterion (AIC). AIC and FPE returned 1 as optimal order while MSE returned 3.
The results for MSE, AIC and FPE are shown in Fig. 5, Fig. 6, Fig. 7:
Figure 5: MSE for 20 model orders
Figure 6: AIC for 20 model orders
Figure 7: FPE for 20 model orders
Anderson–Darling test was carried out to verify the whiteness of the prediction error and the level of significance was set at α = 5%.
The results of Anderson test are show in Fig. 8:
Figure 8: Anderson–Darling test, with α = 5%
Accordingly, by adopting order 1, the difference equation of the AR model is:
y(n)= -0.0664*y(n-1) + x(n)
Then, the optimal order AR model is used to estimate the spectrum of DELTA2 PV signal. The model cannot explain the data properly and seems to do oversmoothing. The Power Spectral Density obtained in this way is shown in Fig. 9:
Figure 9: Power Spectral Density obtained from the AR model
As a consequence of what has just been said, the Spectral Coherence is calculated between
DELTA2_PV obtained by the Periodogram's method and BFV2.
The mscohere function was used to calculate the Coherence function between DELTA2_PV and BFV2.
After a tuning phase, a window containing 30 samples (L/5) was used, where L = 150 is the number of DELTA2_PV
and BFV2 samples. As overlap a number of samples equal to 50% of the window was used.
The Spectral Coherence has a maximum of max = 0.5911 at a frequency of 0.095 Hz indicating the presence of a
possible casuality link between DELTA2_PV and BFV2.
Coherence function is shown in Fig. 10:
Figure 10: Spectral Coherence between DELTA2_PV and BFV2