Appendix 1Descriptive Statistics of the Experiment

The following table provides an overview of the main characteristics of the conducted experiments. It includes the identification number of each pig (Pig), the episode number (Ep.), the inflation rate of saline solution (Infusion rate), the time span for the infusion rate (Ramp.), and the maintenance of intracranial hypertension period (Mnt.).

Appendix 2A Brief Explanation About PSD Calculation

The Welch method, based on the Fourier transform, was applied to estimate PSD from the EEG signal. To calculate the PSD, the EEG was divided into L segments of M samples overlapping D samples. The periodogram from each windowed segment \(}_\) was calculated as follows:

$$S_ \left( f \right) = \frac}}}\left| ^ }_ \left[ n \right]w\left[ n \right]e^ } \right|^$$

(2)

where \(}_ \left[ n \right]\) with \(n = 0,1, \ldots ,M - 1\), \(i = 0,1, \ldots ,L - 1\), and E is a normalization factor for the power or the window function used, defined as follows:

$$E = \frac\mathop \sum \limits_^ \left| \right|^$$

(3)

Then the PSD is estimated from the average of K periodograms:

$$S\left( f \right) = \frac\mathop \sum \limits_^ S_ \left( f \right)$$

(4)

Choice of Data Windows

The Welch method allows us to reduce the variance in the estimation of the PSD with respect to the periodogram technique. If we average over L segments, we obtain a reduction of the variance of approximately \(1/L\) if it does not have overlapping segments. Therefore, if the length of the series N is sufficiently large, we can select \(D = 0\), i.e., there is no overlap between successive data segments.

If N is not sufficiently large, to obtain a minimum variance, overlapping segments can be taken. Normally, they overlap by one half their length, i.e., \(D = M/2\), which is 50% overlap between successive data segments.

Given a compromise relationship between the computational cost and the reduction of the variance using this method, in the present work, \(L = 8\) and \(D = M/2\), which represented a 50% overlap. M was established by L and D (Table 2).

Table 2 Main characteristics of the experiments conductedAppendix 3Evolution of Power in EEG Bands with Intracranial Hypertension

Table 3 displays the power in each EEG band during the periods represented in Fig. 2. Figure 2a represents the baseline period, Fig. 2b represents a period of intracranial hypertension (ICH) with a CPP value around 100 mm Hg (the hypertension period where the CPP value decreases to approximately 80 mm Hg), and Fig. 2c represents the period of CCA with a CPP value of approximately 3 mm Hg.

Table 3 Power in each EEG band during the experiment

Regarding the reduction in power among the different periods shown in Fig. 1, the main reduction between the baseline and ICH states occurs in the alpha band, followed by theta, beta, and delta bands, in that order. When comparing the ICH period to the CCA period, the maximum reduction is observed in the power of the delta band. This pattern indicates the typical process of ischemia, with the loss of higher frequencies followed by the lower frequencies.

An interesting detail worth noting is that the power of higher frequencies (alpha and beta) increases in the CCA period compared to the ICH period. We hypothesize that this increase may be due to the higher presence of noise during the CCA period, although an accurate determination of the nature of this noise, whether it is residual electrical activity, noise generated by the surrounding environment, etc., is beyond the scope of this article. This reduction is marked with an (*) in Table 3.

Appendix 4Spatial Evolution of the Φ Angle and the ADR

In this appendix, we present the temporal evolution of the angle and the ADR for all electrodes in all pigs as well as the correlation between the angle calculated for each electrode and separately calculated ADR.

Appendix 5A Brief Comparison Between Φ Angle and ADR

The ADR is one of the main features used in the detection of ischemia in subarachnoid hemorrhage [15], showing promising results in prospective and retrospective studies. It is defined as follows:

$$} \equiv \frac }} }}$$

(5)

where \(E_\) and \(E_\) are the energy of alpha and delta bands, respectively, defined as follows:

$$EEG_ = \mathop \sum \limits_^ \left| \right)}} \left( n \right)} \right|^$$

(6)

where r stands as one of the subbands and n refers to the n-th point of the w-th window where N is the window length. A comparison with Φ angle is presented in the following paragraph.

To compare the Φ angle with the ADR, the EEG signal was decomposed in five subbands using a band-pass Butterworth filter according to their frequency (alpha [8–13 Hz], beta [14–30 Hz], delta [< 4 Hz], gamma [> 30 Hz], and theta [4–7 Hz]), and the ratio between the alpha and delta powers was calculated for the same windows as the Φ angle for all electrodes in all pigs.

In Appendix 4 (Figs. 6, 7 and 8 for pig 1, 2, and 3, respectively) (visually) and in Fig. 9 (through the correlation of the ADR calculated between all electrodes), we find differences between the ADR evolution and electrodes within each animal. The median correlations (IQR) between the ADR calculated between pairs of electrodes are 0.7 (0.35), 0.75 (0.28), and 0.86 (0.12) for pigs 1, 2, and 3, respectively. That is because when comparing the Φ angle with the ADR, we compare across all electrodes of all pigs. This approach allows us to obtain 88 correlations (11 episodes and 8 electrodes) for both measures, thereby enabling us to use Wilcoxon’s test with greater statistical power than if we used an average of electrodes or other alternative strategies.

In Table 4 we reproduce the values of ICP and CPP correlation with Φ angle together with the values of ADR correlation with the same signals. In Fig. 6, we can observe the superiority of the correlation when slope is taken into account instead of ADR for tracking the two signals. Given the difference between the medians of the two groups, the power of the Wilcoxon test for the difference between groups is 0.73 and 0.99, with a type I error of 0.05, for ICP and CPP, respectively, so we could conclude that to follow the two signals, the slope is more accurate than the ADR.

Table 4 Comparison of the correlation between (Φ angle, ICP) column 2 (ADR, ICP), column 3 (Φ angle, CPP), column 4 and (ADR, CPP), column 5