Frequency Independent Stable Cross-Correlation Pattern in the Peri-Ictal Transition of Focal Onset Seizures

Abstract

Objective:

Here we aim to search for stable intra- and inter-band cross-correlations during the peri-ictal transition of focal onset seizures. Furthermore, we search for dynamic features by analyzing relative eigenvalues of the cross-correlation matrix.

Methods:

In this study, we analyze 50 extracranial electroencephalographic recordings from 24 patients with different types of focal epilepsy, separating the data into different frequency bands. Thereby we construct a multiband cross-correlation matrix, evaluate stability of the correlation structures and the time evolution of relative eigenvalues using a running window approach.

Results:

We find a consistent, pronounced average cross-correlation pattern that is independent of the physiological state, is subject-independent, and is highly similar across different frequency bands. In contrast, dynamic features of brain activity are encoded in deviations from this baseline pattern, expressed by relative eigenvalues along the whole spectrum.

Conclusion:

We associate the stable background pattern as the dynamics upon (or close to) the attractor dynamics, necessary to maintain the brain in an efficient operational mode. Transient dynamical features are expressed by temporal deviations from this pattern. Our results are congruent with the hypothesis that the brain is a complex system operating close to a critical point of a phase transition.

Impact Statement

We found a distinct average cross-correlation pattern, which is independent of the physiological state, is subject-independent, and is very similar in different frequency bands. This is surprising, as it is well known that different brain activities are associated with different frequency bands. We relate this counterintuitive result to the hypothesis that the brain operates near a critical point of a phase transition, which explains the presence of permanently active, pronounced large-scale cross-correlations. Our research opens new avenues of linear correlation analysis of brain activity, which can help in understanding sleep architecture, cognitive processes, and learning of brain activity during epileptic events.

Keywords

critical brain hypothesis electroencephalography focal epilepsy multivariate analysis stable cross-correlation pattern

Introduction

Epilepsy is a neurological disorder of the brain characterized by a persistent predisposition to generate epileptic seizures, along with the associated neurological, cognitive, psychological, and social consequences. It is one of the most prevalent neurological diseases, affecting approximately 1 in 200 people (West et al., 2019). A seizure is defined as “a transient occurrence of signs and/or symptoms due to abnormal excessive or synchronous neuronal activity in the brain” (Fisher et al., 2005). The clinical manifestations of an epileptic seizure depend on various factors and may vary drastically, a fact that led Jean Gotman to the conclusion “that some seizures are totally unambiguous, some are very uncertain, and there is continuity between the two extremes” (Gotman, 2011).

The scalp electroencephalogram (EEG) is most commonly used in practice because it is noninvasive, relatively inexpensive, easily accessible, and quick to prepare. However, besides the large variety of different manifestations of epileptic seizures, there is also the high non-stationary nature of EEG recordings and the contamination by various noisy sources and muscle artifacts (Hughes, 1994). In addition, extracranial EEGs may have a significant amount of volume conduction, and the signals depend on the reference scheme used to measure the electrical potential (Chella et al., 2016; Fein et al., 1988; Nunez, 2010; Rummel et al., 2007), which might crucially affect the quantitative analyses like, for example, the construction and characterization of the functional network (Ríos-Herrera et al., 2019; Rummel et al., 2007). We will come back to this point later on.

Since the individual dynamic unit of a brain component, a neuron, behaves nonlinearly, it can be assumed that the entire brain also exhibits nonlinear, possibly chaotic dynamics (Grassberger et al., 2000; Sarbadhikari and Chakrabarty, 2001), which suggests the usage of nonlinear techniques of analysis (Stam, 2005). However, evidence for nonlinear dynamics in EEG recordings is not or only rarely found (Casdagli, 1992; Palus, 1996; Pijn et al., 1997; Stepien, 2002; Theiler and Rapp, 1996), and often of tiny magnitude in comparison with linear components (Müller et al., 2020). Besides, using nonlinear numerical models in the chaotic regime, it turned out that linear cross-correlations perform equally well or even better than selected nonlinear techniques of analysis (Kreuz et al., 2007), and also, in real EEG recordings, linear approaches are highly competitive in terms of seizure prediction or the identification of pre-seizure periods (Jerger et al., 2003; Mormann et al., 2005). The authors of Ansari-Asl et al. (2006) explicitly recommend linear cross-correlations as a first attempt for the construction of the functional network. Thus, we focus in the present study on linear zero-lag cross-correlations.

Given the non-stationary nature of EEG recordings, one might assume that an index such as the Pearson coefficient, whose numerical estimates range between ± 1, is equally likely to take on positive and negative values when estimated using a running window approach over longer data segments. This might be particularly true for recordings of the highly non-stationary peri-ictal transition of focal onset seizures. The average values of these correlation estimates should quickly tend toward zero.

However, opposite results have been reported (Müller et al., 2014). Although a focal epileptic seizure implies drastic mental and behavioral changes, as well as notable alterations in physiological parameters, such as blood flow or oxygen consumption, and significant morphological changes of EEG signals, on average, the mean linear interrelations between different scalp regions are, surprisingly, pronounced. For broadband EEGs, numerical estimates of average cross-correlation matrices yield considerably large positive as well as negative values. Even more surprisingly, average cross-correlation matrices computed over pre-ictal, ictal, or post-ictal intervals are practically indistinguishable. This is true for extra- as well as intracranial recordings (Müller et al., 2014, 2020). In addition, this pronounced pattern seems to be universal in the sense that these matrices are highly similar across subjects. The authors of Olguín-Rodríguez et al. (2018) showed that the same structure appears in healthy subjects during the night, regardless of the sleep phase, or in awake subjects with eyes open or eyes closed; viz., this stable pattern is not an expression of the pathology. Thus, given that this pronounced correlation structure is, according to previous findings, independent of the physiological (and pathological) brain state and subject-independent, it seems to be a universal phenomenon, which is referred to as the “stationary correlation pattern” in the sequel.

In Apablaza-Yevenes et al. (2024), Arzate-Mena et al. (2022), Müller et al. (2014), and Olguín-Rodríguez et al. (2018), this pattern was interpreted as a “basal dynamic state,” necessary to maintain the minimum required functions and convenient for coordinating the interaction between distant brain circuits, that is, to keep the brain in an efficient mode for information processing. In other words, the basal state of brain dynamics is not a fixed point of zero activity but rather has a more complex attractor. The existence of this correlation pattern that covers the entire scalp may act favorably to moderate rapid and efficient communication between even distant regions of the brain (“top-down” process) and may also promote the spread or transmission of local activity across the scalp (“bottom-up” process). In this way, this constant correlation structure not only maintains the necessary minimal activity but also likely plays an important role in information processing in terms of the segregation and integration of information (Tononi, 2004; Tononi and Edelman, 1998).

In the previously mentioned studies on the pronounced stationary correlation pattern, only broadband signals were considered, all within the same frequency range of approximately 0.5 and 40 Hz. But it is amply accepted that activity in different frequency bands is responsible for different brain functions like attention, cognitive acts, different sleep stages, or degrees of consciousness (Ashtiani et al., 2021; Fell et al., 2010; Krishnan and Athavale, 2018; Mann et al., 1993; Von Stein and Sarnthein, 2000). At this point, the question arises whether an analysis separated by frequency bands yields different results and—if stationary structures are found—whether these differ across frequency ranges. To answer this question, we analyze 50 EEG recordings of patients with focal epilepsy divided into three groups: (1) temporal lobe (TL), (2) frontal lobe (FL), and (3) left posterior quadrant (LPQ) epilepsy.

Materials and Methods

Patient selection and data acquisition

EEGs were recorded from 24 patients (19 male, age range $21 - 57$ ; and 5 female, age range $34 - 63$ ) suffering from focal epilepsy. For 20 patients, temporal lobe epilepsy (TLE); for 3 patients, frontal lobe epilepsy (FLE); and for 1, posterior quadrant epilepsy (PQE) have been diagnosed. All EEGs were recorded in the Neurological Institute of Antioquia, Colombia, in accordance with its presurgical protocol for each patient. All participants gave written informed consent, and the protocol was approved by the Ethics Committee of the Clinical Research Neurological Institute of Colombia.

All patients were continuously recorded for 5 days, while awake as well as during natural sleep. During this period, patients were hyperventilated, stimulated by light stimuli, sleep deprived (during the first night), and gradually weaned off the medication in percentages of 25% per day until they were off medication on the fourth day and back to usual doses on the fifth day.

In the present study, we only included recordings that contain sufficiently long pre- and post-ictal periods of at least 1,200 sec, excluding EEGs contaminated by muscle artifacts and those with seizure durations below 40 sec. This procedure resulted in 50 recordings with sufficiently long ictal periods. Detailed information about the patients is displayed in Table 1. In addition, for each seizure, an interictal interval of at least 1200 sec was selected, either 1 h before or after the seizure.

Table 1.

Information about Patients, Seizure Duration, Lateralization

Patient	Age	Sex	Seizures	Day	Time(s)	Laterality
Temporal lobe epilepsy
1	35	M	1	3	229	RTL
1	35	M	2	3	132	RTL
2	26	M	3	1	232	LTL
			4	1	140	LTL
			5	2	122	LTL
			6	2	85	LTL
			7	2	72	LTL
			8	3	78	LTL
3	33	M	9	2	50	RTL
4	50	M	10	3	86	LTL
4	50	M	11	3	96	LTL
5	47	M	12	5	110	RTL
5	47	M	13	5	88	RTL
6	52	M	14	2	49	RTL
6	52	M	15	2	63	RTL
7	31	M	16	4	46	RTL
7	31	M	17	4	93	RTL
8	37	M	18	4	99	LTL
9	48	M	19	3	85	LTL
10	35	M	20	3	70	LTL
11	57	M	21	4	121	LTL
			22	4	55	LTL
			23	5	80	LTL
12	40	F	24	4	111	RTL
13	34	F	25	4	110	LTL
14	32	M	26	2	83	LTL
			27	3	52	RTL
			28	3	47	RTL
15	51	F	29	2	130	LTL
			30	3	127	LTL
			31	3	91	LTL
16	21	M	32	2	122	RTL
17	56	F	33	2	76	LTL
18	39	M	34	2	59	RTL
19	63	F	35	4	87	RTL
			36	4	79	RTL
			37	4	52	RTL
20	35	M	38	3	84	LTL
			39	3	86	LTL

Frontal lobe epilepsy
21	30	M	40	2	117	LFL
22	22	M	41	4	69	RFL
22	22	M	42	4	71	RFL
23	29	M	43	4	78	RFL
			44	4	83	RFL
			45	5	78	RFL

Posterior quadrant epilepsy
24	49	M	46	2	54	LPQ
			47	2	54	LPQ
			48	2	54	LPQ
			49	2	54	LPQ
			50	2	55	LPQ

RTL, right temporal lobe; LTL, left temporal lobe; RFL, right frontal lobe; LFL, left frontal lobe; LPQ, left posterior quadrant.

The recordings were obtained by using the Easy III software by Cadwell Inc., Washington, USA, with 32 channels using the settings of the international $10 / 20$ system. Here, we restrict the analysis to the standard 19 channels using the following electrodes: Fp1, F3, F7, C3, T1, T3, T5, P3, O1, Fz, Cz, Pz, Fp2, F4, F8, C4, T2, T4, T6, P4, and O2, referenced to the left earlobe A1. The sampling frequency was fixed at 250 Hz. The impedance of all electrodes was kept below $10 k Ω$ during the whole recording period. The signals were band-pass filtered between 0.1 and 70 Hz, in addition to a Notch filter at 60 Hz. Ten-second segments were evaluated by an experienced clinical neurophysiologist (J.F.Z-B.). Segments strongly contaminated by muscle artifacts were excluded from the analysis. As signals recorded at Fp1 and Fp2 are occasionally contaminated by blink and movement artifacts, we excluded them from the present study. We used only 19 standard electrodes for the present analysis.

In Figure 1, we display the distribution of seizure durations of the 50 seizures considered in this study. The first group includes 39 seizures from patients with TLE; the remaining seizures correspond to FLE and PQE. The average duration of the whole group is 89 ± 19 sec.

FIG. 1.

Duration in seconds of the 50 focal onset seizures. The vertical black lines differentiate between temporal lobe seizures (TLE), frontal lobe seizures (FLE), and posterior quadrant epilepsy seizures (PQE).

The number of seizures that occurred during the 5 days of continuous monitoring was distributed as follows: 2 seizures on the first day, 17 on the second day, 13 on the third day, 14 on the fourth day, and 4 on the fifth day.

To compare our results with a qualitatively different dataset, we also consider magnetoencephalographic (MEG) recordings from 48 subjects of the Human Connectome Project (Elam et al., 2021; Larson-Prior et al., 2013). The 3-h recordings include different physiological states: resting state, two working memory tasks (0-back and 2-back), as well as two motor tasks. This dataset was previously used for the comparison with results obtained for EEG data from healthy subjects during sleep (Marín–García et al., 2024). To this end, the 126 magnetometer channels are reduced to 19 signals simulating the international 10–20 EEG system, using three different reduction schemes (Marín–García et al., 2024). Here, we restrict ourselves to one of these schemes, namely selecting the magnetometers located closest to the positions of the 10–20 system. Furthermore, we use band-pass filtered MEG data between 1 and 40 Hz. Note that if we obtain a high similarity between the results obtained from EEG and MEG data, we can rule out volume conduction effects as a possible source of our findings.

EEG preprocessing and parameters settings

After registration, the data were band-pass filtered between 1 and 25 Hz, referred to as “broadband” signals in the following. In addition, the recordings were filtered in the classical EEG frequency bands: δ = 1–3.5 Hz, θ = 3.5–7.5 Hz, α = 7.5–12.5 Hz, β₁ = 13.5–17.5 Hz, and β₂ = 17.5–25.5 Hz. For this purpose, a fourth-order Butterworth filter was applied in both forward and backward directions to minimize potential phase shifts in the signal (Rios-Herrera et al., 2016). In a final step, the recordings were transformed to the median reference of the selected channels to minimize the induction of spurious correlations and thus a potential deformation of the functional network by the reference scheme. Previous studies using data derived from well-controlled numerical models showed that this reference causes minor distortions in the functional network compared to other prominent schemes (Ríos-Herrera et al., 2019). Furthermore, when comparing the average matrices derived from MEG and EEG recordings, the signals transformed to the median reference showed the highest similarity to the matrices derived for MEG signals (Marín–García et al., 2024).

We define a running time window of $T = 2500$ sampling points (corresponding to 10 sec), which is moved with a step width of $S = 250$ sampling points over the recording. EEG segments containing the peri-ictal transition of an epileptic seizure are divided into three intervals: a 20-min pre-seizure interval just before seizure onset, the seizure interval itself, and a 20-min post-seizure period starting at seizure offset. These recordings were used to estimate the stationary correlation pattern (Arzate-Mena et al., 2022; Müller et al., 2014; Olguín-Rodríguez et al., 2018). We calculated the temporal, zero-lag cross-correlation matrix C of the preprocessed EEG signals using the running time-window approach. Then, we estimated average cross-correlation matrices separately for each interval (pre-seizure, seizure, and post-seizure) as well as the average over the whole peri-ictal transition. We followed the same process for the interictal intervals.

Statistical analysis

As argued above, to measure linear relations between data channels, we focus on the cross-correlation coefficient in the present study. For a proper computation of the cross-correlation coefficients within a data window of T recordings, the N time series $X_{i} (t_{k})$ ( $i = 1, \dots, N$ and $k = 1, \dots, T$ ) are first normalized to zero mean and unit variance:

{\tilde{X}}_{i} (t_{k}) = \frac{X_{i} (t_{k}) - {⟨ X_{i} ⟩}_{T}}{σ_{i}},

(1)

where brackets

〈 X_{i} 〉

denote time average and

σ_{i}

the standard deviation estimated over the same time window of length T. Then, the

N \times N

zero-lag cross-correlation matrix C is computed:

C_{i j} = \frac{1}{T} \sum_{k = 1}^{T} {\tilde{X}}_{i} (t_{k}) {\tilde{X}}_{j} (t_{k}) = {⟨ {\tilde{X}}_{i} (t_{k}) {\tilde{X}}_{j} (t_{k}) ⟩}_{T} .

(2)

The matrix defined in Eq. (2) is real symmetric and, being a quadratic form, is positive semi-definite.

The normalization (Eq. 1) removes amplitude information and a possible offset from each of the $X_{i} (t_{k})$ , such that the measured cross-correlations exclusively reflect shape-phase correlations of the signals. In addition, the normalization provides a well-defined scale; that is, the matrix elements of C vary between $+ 1$ (completely correlated series) and $- 1$ (completely anti-correlated series), passing through zero (completely independent series).

We are interested in correlation structures stable in time. Therefore, we estimated average correlation matrices $〈 C 〉$ for each interval and for each frequency band of the 50 focal seizures.

To quantify the statistical similarity between two average matrices, we sort the non-diagonal elements of each average matrix into a vector, which was subsequently normalized to zero mean and unit variance. The scalar product of such two vectors, denoted by $\hat{C}$ in the sequel, serves as a measure of topological similarity. In fact:

{\hat{C}}_{l, k} = \frac{2}{N (N - 1)} \sum_{i > j}^{N} C_{i j}^{l} C_{i j}^{k},

(3)

where l, k denote matrix estimates for different intervals and/or different frequency bands. We frequently display probability densities

ρ (x)

as a cumulative distribution.

A C (x) = \int_{- \infty}^{x} ρ (x') d x',

(4)

instead of using the traditional representation using histograms. This has the advantage that a cumulative distribution does not require any externally imposed discretization of the abscissa (Apablaza-Yevenes et al., 2024).

Given that C is real and symmetric, it has real eigenvalues $λ_{i}$ and eigenvectors $\vec{υ_{i}}$ such that:

C \vec{υ_{i}} = λ_{i} \vec{υ_{i}},

(5)

where the eigenvalues

λ_{i}

should be ordered in ascending order:

λ_{1} \leq λ_{2} \leq \dots \leq λ_{N}

. The distribution of the eigenvalues is directly related to the correlation structure of the multivariate dataset (Müller et al., 2005, 2006). Furthermore, given that the trace of a matrix is invariant to orthogonal transformations, it holds that.

T r (C) = \sum_{i} C_{i i} = \sum_{i} λ_{i} = N .

(6)

Therefore, if one of the eigenvalues alters, its change has to be compensated by some others such that the condition (Eq. 6) is still fulfilled.

Finally, we estimated the global correlation strength of a multivariate dataset by the width of the eigenvalue spectrum. If no genuine correlations are present, eigenvalues are randomly distributed around unity according to the Marchenko–Pastur distribution (Laloux et al., 1999; Plerou et al., 2002, 1999). Genuine correlation structures, on the other hand, provoke specific repulsion schemes of the eigenvalues, which may occur along the whole spectrum (Müller et al., 2005, 2006, 2011). However, as a rough estimate, it suffices to consider the width of the eigenvalue distribution, and in fact, the time evolution of the largest eigenvalue already provides a fair estimate for this quantity (Plerou et al., 2002; Schindler et al., 2007). Here, we consider relative eigenvalues, normalized by their mean and standard deviation estimated over the whole recording containing the peri-ictal transition:

λ_{rel} (t) = \frac{λ_{largest} (t) - {〈 λ_{largest} 〉}_{t}}{σ_{λ_{largest}}} .

(7)

Results

In this section, we first present the results obtained for a focal onset seizure from patient 23 (seizure 43 listed in Table 1). Then, we merge the results obtained for all recordings, looking for certain similarities of average cross-correlation matrices, comparing different intervals (pre-seizure, seizure, and post-seizure periods) as well as frequency bands. Our analysis provides evidence for the existence of a pronounced and stable scaffold of linear interrelations that seem to be independent of the subject, the phase of the peri-ictal transition, and the frequency band. Finally, we examine dynamic features of the epileptic seizure through the time evolution of the largest relative eigenvalues.

Stationary correlation pattern in focal epilepsy

Exemplarily, we show in Figure 2 average correlation matrices of one recording of FLE (number 43 for patient 23), where averages have been taken separately for each interval Pre-ictal, Ictal, Post-ictal, and Peri-ictal as well as for each frequency band, respectively.

FIG. 2.

Average correlation matrices of seizure 43 of patient 23, who suffers from frontal lobe epilepsy (Table 1). Each average is taken separately for the pre-seizure (Pre-ictal), seizure (Ictal), post-seizure (Post-ictal), and Peri-ictal intervals, as well as for the frequency bands δ, θ, α, β₁, and β₂. The diagonal elements of all matrices are drawn in gray in order to improve visibility.

Upon visual inspection, we note an intriguing similarity across all matrices shown in Figure 2, although the average taken over the seizure interval deviates somewhat in all frequency bands. However, as previously reported for the broadband case (Apablaza-Yevenes et al., 2024; Arzate-Mena et al., 2022; Müller et al., 2014; Olguín-Rodríguez et al., 2018), we find a pronounced cross-correlation pattern, with dominant positive intra-hemispheric and negative inter-hemispheric correlation coefficients across all frequency bands. In view of the high noise level of scalp EEGs and the non-stationarity of brain activity, the occurrence of high average cross-correlations and the independence of the correlation pattern from the frequency ranges is at first glance a counterintuitive result.

To quantify similarity between average matrix estimates for different intervals and frequency bands, we estimated Pearson correlations. Figure 3 summarizes the results for all recordings considered in the present study.

FIG. 3.

Stability of average cross-correlations: Pearson coefficients of the three possible pairs of correlation matrices averaged separately over the intervals Pre-ictal, Ictal, and Post-ictal, for the 50 focal epilepsies considered in this study. The vertical blue lines separate the three groups (temporal lobe epilepsy [TLE], frontal lobe epilepsy [FLE], and posterior quadrant epilepsy [PQE]); the color palette white–red indicates the degree of similarity of the average cross-correlation matrices estimated over different intervals. Note: The color scale initiates at 0.5.

We note that the similarity between average cross-correlation matrices, estimated separately over the Pre-ictal, Ictal, and Post-ictal intervals for each focal epilepsy, is extraordinarily high for all frequency bands. We observe that the Pearson coefficients take values between 0.5 and 1, with the vast majority taking values above 0.8. The highest similarity values are observed for slower frequency bands and the largest variations for the $β_{2}$ -band. However, considering that a focal epileptic seizure is an extraordinarily drastic event accompanied by severe physiological, mental, and behavioral changes, and that the EEG recordings also show strong changes in magnitude and morphology, we consider similarity values above 0.5 to be remarkably high. Figure 4 provides a more quantitative picture of these findings.

FIG. 4.

Cumulative probability distributions of the Pearson coefficients comparing structural similarity between cross-correlation matrices derived for temporal lobe seizures, averaged separately for each interval (Pre-ictal, Ictal, and Post-ictal). Different panels display the results for the different frequency bands. Probability distributions for the comparison Pre–Pos are drawn in blue; the comparisons Pre-Ict and Ict-Post are shown in green and red, respectively.

Figure 4 shows the cumulative probability distribution of Pearson correlations comparing average correlation matrices estimated separately for each interval and for each of the six frequency bands for all 39 TLE.

We observe the highest similarity between the pre- and post-seizure intervals. The probability distribution is centered well above 0.9 for all frequency bands. Given this extraordinary similarity, it is not surprising that the comparison between the seizure interval and the two others is statistically almost identical. Probability distributions are centered at about 0.9. Only for the high-frequency bands $β_{1}$ and $β_{2}$ they are somewhat shifted to lower values (about 0.8) and show a larger tail toward smaller values. However, the results document the presence of a distinct framework of linear cross-correlations that remains stable even during the peri-ictal transition of a temporal lobe seizure.

The high similarity between the average cross-correlation matrices, which were estimated separately for the three intervals, justifies averaging over the entire peri-ictal interval. Consequently, we evaluated in the next step the similarity of the peri-ictal average (1) within a certain frequency band as well as (2) its similarity between different frequency bands. Figure 5 displays the cumulative probability distributions for these intra- and inter-frequency band comparisons for all 39 TLE.

FIG. 5.

Cumulative probability distribution of the Pearson coefficients obtained for the intra-frequency band comparison of the peri-ictal average of the cross-correlation matrices (left panel) of all 39 TLE. The panel on the right side shows the comparison between the six frequency bands of the peri-ictal averaged correlation matrices. TLE, temporal lobe epilepsy.

We observe a high similarity for both the intra- and inter-band comparisons. For both cases the probability distributions are centered at about 0.95, an extraordinarily high value, which implies that cross-correlation matrices averaged over the whole peri-ictal interval of different seizures and patients are practically indistinguishable. Considering that brain activity in different frequency ranges is associated with quite different tasks, we find that the high similarity between bands is surprising. Furthermore, the quantitative comparison between recordings of different patients emphasizes the universality of this pronounced interrelation structure.

Stationary correlation pattern in frontal lobe and posterior quadrant seizures

Here, we test the similarity of the cross-correlation matrices averaged separately for the three intervals (pre-ictal, ictal, and post-ictal) of the FLE and the PQE group. Figure 6 displays the results as cumulative probability distributions estimated separately for different frequency bands.

FIG. 6.

Cumulative probability distributions of the Pearson coefficients comparing structural similarity for each frequency band between cross-correlation matrices of FLE (upper row) and PQE (bottom row), averaged separately over each of the three intervals (Pre-ictal, Ictal, and Post-ictal). The results for the comparison of the different frequency bands are color-coded. Different panels display the results for the comparison of different intervals: Pre-Ict (left panel), Pre–Pos (middle panel), and Ict-Pos (right panel). FLE, frontal lobe epilepsy; PQE, posterior quadrant epilepsy.

Again, the similarity of the average cross-correlation matrices is greatest when comparing the period before and after the seizure. The minimum values of the Pearson coefficients are all above 0.9, and the centers of the distributions are close to 0.95, which implies an almost perfect similarity. When comparing the average correlation matrices of the seizure period with those determined before and after the seizure, the similarity values are somewhat lower, especially for higher frequency bands. While the distributions for the $δ$ -, $θ$ -, and broadband are centered at about 0.9 or higher, the center values for the $β_{2}$ -band are around 0.6 for both seizure types, and minimum values are about 0.5. Considering the supposed highly non-stationary nature of a peri-ictal transition, this indicates a notably high similarity between the mean correlation structures for all cases.

These results imply that, also for frontal lobe and posterior quadrant seizures, we find a pronounced, stable correlation structure in all frequency bands, which is also present during the apparently drastic changes of a peri-ictal transition. This finding justifies an average over the whole peri-ictal period. Then, we might compare these peri-ictal averages obtained for different seizures and patients. Results are summarized in Figure 7.

FIG. 7.

Cumulative probability distribution of Pearson coefficients for the comparison of cross-correlation matrices averaged over the whole peri-ictal transition of FLE (upper row) and PQE seizures (bottom row). The left panel displays results for the comparison of matrices obtained for the same frequency band (intra-band); the right panel shows the outcome for the comparisons between frequency bands (inter-band). FLE, frontal lobe epilepsy; PQE, posterior quadrant epilepsy.

With the exception of the $β_{2}$ -band, all probability distributions are centered at values above 0.9, and in all cases, the minimum values are above 0.6. For the slow-frequency bands, minimum values are even above 0.8. In the case of PQE, all matrices were derived from seizures of the same patient, leading to much narrower distributions. For the intra-band comparisons, even minimum values are above 0.9, while the Pearson coefficients obtained for the inter-band comparisons are still centered at values notably above 0.9. As in the case of temporal lobe seizures, both the comparison of different seizures/patients within a frequency band and the comparison between frequency bands lead to notably high values. Note that for the comparisons between the frequency bands for both TLE and FLE, recordings from different patients were also used, which causes much broader asymmetrical distributions with a tail toward smaller similarity values.

Similarity of the stationary correlation pattern between temporal, frontal lobe, and left posterior quadrant seizures

The high similarity values already indicate the generic character of the stable background pattern. However, FLE, PQE, and TLE seizures not only have different seizure onset zone locations but also show qualitatively different physiological profiles (Doldan et al., 2013). Therefore, one might expect that the average cross-correlation pattern could also be qualitatively different for the two groups. We performed a quantitative comparison, again employing Pearson coefficients as a similarity index between average cross-correlation matrices. Corresponding results are displayed as cumulative probability distributions in Figure 8.

FIG. 8.

Cumulative probability distributions for the comparison of cross-correlation matrices averaged over the whole peri-ictal transition. Drawn are accumulated probability densities of Pearson coefficients for the comparisons between TLE, FLE, and PQE separately for different frequency bands. Color codes are indicated by the insets. FLE, frontal lobe epilepsy; PQE, posterior quadrant epilepsy; TLE, temporal lobe epilepsy.

With the exception of the fast $β_{2}$ -band, all probability distributions are centered at 0.9 or higher, with minimum values of at least 0.8. However, the central values for the $β_{2}$ -band are also considerably high, at least 0.85 (for the comparison of TLE and PQE, it is even above 0.9). As in the previous figures, heterogeneity increases for fast frequency bands. Furthermore, we observe that peri-ictal averages of the correlation matrices derived from FLE recordings deviate somewhat more from the TLE and PQE cases. Nevertheless, Figure 8 clearly documents the universal character of the stationary cross-correlation pattern, which is almost independent of the seizure type, is almost subject-independent, and shows high similarity across the classical EEG frequency bands.

However, EEG recordings can be strongly contaminated by volume conduction effects, which may drastically affect the numerical analysis when zero-lag cross-correlations are considered, as in the present study. Such phenomena might have a strong influence, particularly during an extreme event like a focal onset seizure. In a previous study, we also applied maximum lag correlations, where each coefficient of the correlation matrix was maximized within a maximal range of time lags. In addition, the weighted phase delay index (Vinck et al., 2011), which is based on the imaginary part of the Fourier coefficients and is not influenced by volume conduction, was also taken into account. The numerical results are very similar to those of the correlation matrix without delay (Müller et al., 2014).

Finally, in Marín–García et al. (2024), we demonstrated the high similarity between average correlation matrices obtained from MEG data of subjects during rest and four different task conditions and those matrices constructed from EEG recordings of healthy subjects during sleep. Since MEG recordings are much less influenced by volume conduction and do not require a reference scheme like the electric potential, this comparison provides convincing arguments for the genuine nature of the stationary interrelation pattern. To illustrate this comparison with the actual dataset of different focal onset seizures, we have summarized it in Figure 9.

FIG. 9.

Upper row, left panel: Average cross-correlation matrix obtained from MEG recordings of subject 25 (see Marín–García et al., 2024). The average was taken over the resting state and four different task conditions. The reduction of MEG detectors was achieved by selecting detectors closest to the positions of the International 10–20 System. Right panel: Cumulative probability distributions of Pearson coefficients for the comparison of MEG data of 48 clinically healthy subjects performing cognitive tasks and the EEG recordings of the focal onset seizures considered so far. Lower row: Comparison of the pre-ictal, ictal, post-ictal, and peri-ictal averages of the TLE (left), FLE (center), and PQE (right) with a corresponding interictal interval with at least a 1-h distance to epileptic events. FLE, frontal lobe epilepsy; PQE, posterior quadrant epilepsy; TLE, temporal lobe epilepsy.

A visual inspection of the average correlation matrix obtained from the MEG data of subject 25 reveals a tendency toward positive intra-hemispheric correlations and negative inter-hemispheric correlations, similar to the patterns observed in Figure 2. A quantitative comparison confirms this visual impression. All Pearson coefficients are distributed between 0.4 and 0.7 and are centered around 0.55. If the matrices do not have a similar structure, these distributions should be closely distributed around zero.

As a second control, for each seizure type separately, we compared the correlation matrix generated from an interictal interval with those generated from the ictal, Pre-ictal, and Post-ictal episodes (lower row of Fig. 9). If the stationary pattern shown above is closely related to the ictal activity, the similarity with interictal activity should be low. However, our numerical results indicate the opposite direction. In all cases, we observe a high similarity between matrices constructed from the interictal interval and those generated around the seizures. Although the similarity between the average cross-correlation pattern of the $inter - ictal$ and ictal interval turns out to be somewhat reduced for all seizure types, Pearson coefficients are essentially above 0.6 for TLE and above 0.8 for FLE and PQE.

In summary, we can conclude that the pronounced stable cross-correlation structure reported above is certainly neither related to ictal activity nor generated by volume conduction or the influence of the EEG reference; instead, it is a real phenomenon. Thus, the question remains in which manner the drastic dynamical changes during a peri-ictal transition translate into cross-correlations, considering that the pronounced pattern of linear interrelations is always present as a kind of background pattern. Note that its presence in no way implies the absence of dynamic changes in brain activity but rather that the dynamics should be imprinted in continuous deformations of this structure. In the next section, we discuss some of those aspects when focusing on the time evolution of the largest relative eigenvalues.

Some dynamical aspects of the peri-ictal transition of focal epilepsy

In principle, all features of the cross-correlation structure are encoded in the spectrum of eigenvalues and eigenvectors of cross-correlation matrices (Rummel, 2008; Rummel et al., 2008). In particular, these objects have served to distinguish between random and genuine correlations (Laloux et al., 1999; Müller et al., 2005, 2006; Plerou et al., 2002, 1999). It turns out that the largest eigenvalue (and its corresponding eigenvector) represents the overall amount of correlations of the system (Müller et al., 2005, 2006; Plerou et al., 2002), thus serving as a global measure of the system dynamics.

To provide clear evidence of the dynamical nature of an epileptic seizure (Milton and Jung, 2003), we focus here on the time evolution of the largest relative eigenvalues (Eq. 7) extracted for each frequency band. We specifically focus on relative eigenvalues, normalized to zero mean and unit variance, such that only relative changes from the mean are considered. This is motivated by previous results showing that an almost similarly pronounced cross-correlation pattern is found in all cases. By focusing on the time evolution of the largest eigenvalue, only global deviations from the distinct background pattern are visualized.

To summarize the results obtained for all TLE and FLE recordings considered in the present study, we normalize the seizure duration as in Schindler et al. (2007). Specifically, we consider eigenvalues relative to an interictal interval. We may draw average values as well as standard deviations obtained for all recordings listed in Table 1. Figure 10 displays these results.

FIG. 10.

Temporal evolution of the largest relative eigenvalues λ_rel(t) for the 39 temporal lobe (left column) and the 11 frontal lobe (middle column) and 5 posterior quadrant seizures (right column). In each curve, the temporal evolution of the group mean and standard deviation is drawn. Seizure duration is normalized for all cases, as in Schindler et al. (2007). Seizure onset and offset are marked by vertical black lines.

For the pre-seizure interval, we do not observe any specific behavior in any of the considered frequency bands for the three seizure types. Largest relative eigenvalues show only small fluctuations centered close to zero.

The same is true for TLE in the $δ$ -band, both during and after the seizure. Only large error bars indicate notable heterogeneity across subjects, particularly during the seizure period. For the $θ$ -band, temporal lobe seizures show a pronounced increase during the first third of the seizure period, followed by a gradual decrease toward seizure offset. Then, during the post-seizure period, only slightly increased fluctuations around zero are observed, with a mean value slightly below zero. Similarly, for the $α$ -band, $λ_{rel}$ increases somewhat during the seizure period, showing a significant decrease during the post-seizure period, where values are notably below zero.

The fast frequency bands $β_{1}$ and $β_{2}$ behave similarly. They show a gradual increase up to the seizure offset, after which overall correlation strengths drop abruptly below zero. Thus, during seizure, overall cross-correlations increase and then show a notable decrease immediately after seizure offset. This scenario somewhat aligns with the results presented in Schindler et al. (2007), where similar results have been obtained. These authors interpreted the global increase in correlations at the end of the seizure as an active mechanism of the brain to terminate the crisis. For the broadband case, no specific behavior can be observed for the entire peri-ictal interval, apart from a clear increase in the standard deviation during the seizure as with the other frequency bands, which indicates greater heterogeneity between the subjects.

FLE seizures exhibit an almost abrupt, short-lasting increase in the overall correlation strength just after seizure onset, which is somewhat less pronounced for the $α$ -band. Then, during the seizure, for all but the $θ$ -band, the global correlation strength decreases and takes values below zero. The end of the seizure is well characterized by a sudden, short-lasting increase in $λ_{rel}$ for the $θ$ and $α$ bands. Here, the broadband case somewhat mimics the behavior of the $θ$ and $α$ bands. It shows a pronounced, narrow maximum of $λ_{rel}$ just after seizure onset, then takes negative values during the seizure and the post-seizure period, separated only by a local maximum at seizure offset.

For PQE, we generally observe much reduced standard deviations, likely due to the five seizures considered here stemming from the same patient. For the $δ$ -band, $λ_{rel}$ only fluctuates slightly above zero but then shows a sudden, quite pronounced increase just at seizure offset, which gradually decreases to zero in the time after the seizure. This abrupt increase of $λ_{rel}$ up to two and three standard deviations is also observed for the $θ$ and $α$ -bands. However, for these cases, $λ_{rel}$ already takes positive values during the second half of the seizure, also accompanied by large fluctuations. This increase at seizure offset can also be observed for the $β - 2$ -band, although it is much less pronounced. In general, for both $β$ -bands, $λ_{rel}$ stays close to zero during the seizure and then drops down toward negative values during the post-seizure period. For the PQE, the $λ_{rel}$ extracted for the broadband is somewhat similar to the behavior observed for the three slowest frequency bands.

Although we measure the same distinct cross-correlation pattern covering the entire scalp region for the three seizure types, the time evolution of the overall cross-correlation strength is different. While a pronounced drop of $λ_{rel}$ at seizure offset is observed in TLE, we notice a short-lasting increase at seizure onset, at least for slower frequencies in FLE. Finally, for PQE $λ_{rel}$ at seizure onset and during the ictal period is completely nonspecific but shows a striking abrupt bump just at seizure offset. Thus, seizure dynamics, even when captured by the crude measure of global cross-correlation strength, differ for various seizure types and are likely heterogeneous between patients.

Discussion

Here, we present the analysis of extracranial recordings from the peri-ictal transition of 39 temporal lobe seizures from 20 patients, 6 frontal lobe seizures from 3 male patients, and 5 seizures from one patient with PQE. Motivated by previous studies, we focus on identifying a distinct spatial correlation pattern that is stable over time and thus becomes visible when averaging over longer time intervals. These average cross-correlation matrices should not change significantly across different physiological states.

The novelty of the present study is not only that we considered different seizure types but also that we conducted this analysis separately for different frequency bands associated with the performance of different brain functions (Bohbot et al., 2017; Daume et al., 2017; Kucewicz et al., 2024; Mann et al., 1993; Puentes-Mestril et al., 2019; Sadaghiani and Kleinschmidt, 2016; Von Stein and Sarnthein, 2000). Thus, one might suppose that the corresponding functional networks, obtained for signals filtered in different frequency bands, may also show qualitative differences. Earlier studies, which already reported a pronounced correlation pattern independent of the physiological state and almost subject-independent, were carried out exclusively in broadband frequency ranges up to 25 Hz or higher. However, due to the fact that the power spectrum of EEG recordings approximately follows a power law with a negative slope (Raichle and Mintun, 2006a), slow frequencies dominate, and results obtained for broadband signals are strongly biased by the activity of the $δ$ -band. Therefore, it is not known whether such a stable framework of spatial correlation also exists in higher frequency bands and, if so, whether a similar pattern can be found across all frequency bands. With the present contribution, we intend to fill this gap.

The answer is affirmative. We find a pronounced average cross-correlation pattern for all subjects, which is very similar during, as well as before and after, the seizure for the three types of epilepsy across all frequency bands considered. Different brain functions associated with different frequency bands are therefore not expressed by different pronounced background patterns of spatial correlations covering the whole scalp. The fact that the same pronounced long-range cross-correlations are found for slow and high-frequency bands is particularly surprising, as it is assumed that high-frequency oscillations are more spatially localized (von Stein and Sarnthein, 2000). These findings raise two main questions: (1) What role does this universal large-scale cross-correlation structure play, and what benefits does the brain derive from maintaining an averagely strong linear correlation even between distant brain regions? (2) How are the dynamics of specific brain functions associated with different frequency bands encoded in the functional network of linear connections?

A partial answer to the second question is provided by Figure 10, where the time evolution of the largest eigenvalue is drawn for the peri-ictal transition of TLE, FLE, and PQE. Apart from considerable large fluctuations, which reflect a notable heterogeneity across subjects, the average time evolution is qualitatively different for various frequency bands and also for different seizure types. Note, the largest eigenvalue represents the degree of overall correlations in the whole dataset and thus can be understood as a measure of the collectivity of the brain dynamics (Müller et al., 2005, 2006; Plerou et al., 2002). Therefore, it is not capable of detecting subtle changes or alterations possibly confined within a spatially localized brain region (Müller et al., 2006; Plerou et al., 2002). However, even though Figure 10 clearly documents that dynamical features are (a) imprinted in deviations from the average pattern (relative eigenvalues are drawn, that is, deviations from the mean value) and (b) dynamics are qualitatively different within various frequency bands and, of course, also for different seizure types.

Nevertheless, it remains evident that Figure 10 is by no means the ultimate answer to the question of the dynamic evolution expressed by the linear functional brain network. The study of focal onset seizures, as well as other pathologies and sleep dynamics, or the dynamics of cognitive processes, requires a detailed investigation of deviations from the stationary background pattern. The present results suggest that a worthwhile strategy might be to look at the differences or fluctuations around the stationary pattern (Apablaza-Yevenes et al., 2024). Another possibility involves variants of principal component analysis, where not the most dominant modes are considered but smaller ones, which may reflect local or more subtle changes in the network (Müller et al., 2005, 2005). In any case, the present findings open new avenues for the analysis of dynamical features of functional brain networks.

That leaves the discussion of the first question: the potential benefits of maintaining strong short- and long-range (anti-)correlations. This discussion is directly related to the critical brain hypothesis (Beggs, 2022; Beggs and Plenz, 2003, 2004; Beggs and Timme, 2012; Fraiman et al., 2009; Klaus et al., 2011; Linkenkaer-Hansen et al., 2001; Petermann et al., 2009; Tagliazucchi et al., 2012), where it is supposed that the brain operates in the vicinity of a critical point of a second-order phase transition. It has been explicitly shown that adaptation to the critical point places the brain in a favorable dynamic regime that is beneficial for information processing (Shew et al., 2009, 2011; Shew and Plenz, 2013), suggesting evolutionary optimization.

Given that the brain is permanently subject to external stimuli and continuously reacts to ever-changing internal conditions, its ongoing activity is highly non-stationary. However, even during the so-called “resting state,” the brain is constantly active. Certain populations of neurons fire spontaneously and synchronously. These groups can split into subgroups, which in turn can spread over larger regions, leading to further avalanches, or local activity can subside, providing space for the emergence of new space-time structures of synchronous activity. In fact, the brain permanently produces the largest possible variety of different space-time patterns of synchronized neural activity, expressed by power laws with exponents larger than one (Beggs, 2022; Beggs and Plenz, 2003; Beggs and Timme, 2012; Fosque et al., 2021). This means that these distributions have no first moment. Average values diverge, and thus there is no typical scale that describes a standard size of such patterns. This is true for both the spatial extensions as well as the lifetimes of spontaneously synchronized neural populations (Beggs, 2022; Beggs and Plenz, 2003; Beggs and Timme, 2012; Fosque et al., 2021).

Such behavior is reminiscent of the dynamics in the vicinity of a second-order phase transition. Probably the best-known example is the transition of a ferromagnet to magnetization when the temperature drops. Then, at the critical point, the magnetic moment of the atoms starts to align such that a nonzero macroscopic magnetic field appears, whose magnitude linearly increases with decreasing temperature. Just at the critical point, the magnetization is still zero, but there is the greatest possible variety of mesoscopic regions with aligned magnetic moments obeying power laws, which describe the distribution of sizes as well as lifetimes of such structures. At the same time, the entire system is covered by strong correlations; that is, the correlation length diverges in an infinite system.

The origin of the phenomenon is the competition between two opposing interactions, namely the magnetic interaction that tries to align the dipoles and the thermal movement of the microscopic constituents that causes disorder. At the critical point, the strengths of the two forces are finely balanced in a certain equilibrium. Similarly, the dynamics of the brain are determined by two diametrically different interactions: excitatory and inhibitory communication between neurons. If the fine-tuned balance between excitation and inhibition is perturbed, the above-mentioned power law distributions also disappear, and the brain system apparently moves away from the critical point (Shew et al., 2009, 2011), which simultaneously diminishes optimized information processing (Shew and Plenz, 2013). An instructive example that nicely illustrates the analogy between the phase transition of a ferromagnet and the fluctuations of brain activity on the basis of functional magnetic resonance imaging can be found in Fraiman et al. (2009).

That implies that, for the brain dynamics, pronounced cross-correlations covering the entire system are necessary to control this enormous ongoing activity because task-related activities, such as motor or cognitive actions, are also reactions to synchronized space-time patterns of neuronal activity. To prevent ongoing activities from randomly generating a pattern that causes undesired reactions, the activity must be moderated, which explains the existence of this stationary background pattern. From the viewpoint of dynamical systems theory, these pronounced, permanent spatial interrelations can be interpreted as a shadow of the attractor in phase space, and this dynamics concerns all frequency bands equally. Non-stationary features should then be expressed by some kind of intermittent deviations from this stable structure. Consequently, task-related activity solely requires an appropriate deformation of already existent space-time patterns of synchronized neural activity.

This picture not only explains the extraordinary efficiency of brain dynamics but is also in accordance with the disproportionate energy consumption of the brain. Although it makes up only 2% of the total body weight, it permanently consumes around 20% of the total energy budget (Fox and Raichle, 2007; Llinás, 1988; Raichle, 2006, 2011) (attributable to the maintenance of the ongoing activity and the existence of the stationary pattern). In contrast, task-related activity leads only to a small increase in additional energy expenditure (small but well-coordinated deviations and fluctuations from the stable scaffold) (Raichle and Mintun, 2006). Note that the discussion above does not provide a proof of the criticality hypothesis, but the existence of spatial correlations covering the whole system is congruent with this hypothesis and explains its physical significance and physiological function. Furthermore, this pronounced, stable interrelation pattern has been identified solely for linear interrelations. It was shown that nonlinear networks turn out to be specific for the individual pathology and are strongly subject-dependent (Müller et al., 2020). Thus, it seems that linear and nonlinear networks play fundamentally different roles in the brain dynamics.

Conclusions

Epilepsy is a disorder of the brain characterized by an enduring predisposition to generate epileptic seizures and by the neurobiological, cognitive, psychological, and social consequences of this condition. A deeper understanding of the neuronal mechanisms that lead to a seizure would be appreciated and can certainly support therapeutic measures. The present study not only proves the general validity of the stationary pattern, which is independent of the physiological state, independent of the subject, and equally present across all frequency bands considered in the present study, but also, furthermore, new strategies for the analysis of electroencephalographic recordings are recommended. According to our results, task-related dynamics and the activity of different physiological states, such as sleep phases or pathological behavior, such as an epileptic event, are encoded in specific deviations from the average cross-correlation pattern.

Limitations and Future Perspectives

A major limitation of the present study consists in the fact that solely a linear interrelation measure has been used. Maybe nonlinear cross-correlations, as assessed by, for example, distance correlation or mutual information, show a qualitatively different behavior. A corresponding analysis could therefore provide further relevant insights into the phenomenon of epileptic seizures. The essential conclusion that dynamic features are imprinted in deviations (or fluctuations around) the stationary pattern also opens up new avenues for further studies. Such research can be carried out by just considering difference matrices (Apablaza-Yevenes et al., 2024; Olguín-Rodríguez et al., 2018) or, alternatively, one may focus, for example, on variants of the principal component analysis, where not only those components corresponding to the largest eigenvalues but also smaller ones that may reflect such deviations are considered. A recipe on how to encounter the adequate secondary components could be found in Müller et al. (2005, 2006).

Authors’ Contributions

A.C.: Conceptualization, data curation, formal analysis, and software (equal). J.F.Z.-B.: Funding acquisition, resources, and writing—review and editing (equal). D.S.-J.: Funding acquisition, resources, and writing—review and editing (equal). J.D.A.-M.: Formal analysis, methodology, validation, software, and writing—review and editing (equal). M.F.M.: Conceptualization (lead), formal analysis, funding acquisition, investigation (lead), methodology (lead), project administration, supervision, writing—original draft (lead), and writing—review and editing (lead). W.A.R.-H.: Conceptualization, data curation (lead), formal analysis (lead), funding acquisition (lead), methodology, project administration (lead), resources (lead), software (lead), supervision (lead), visualization (lead), writing—original draft, and writing—review and editing.

Footnotes

Author Disclosure Statement

The authors have no competing interests to declare.

Funding Information

This work was supported by Consejo Nacional de Ciencia y Tecnología (CONACyT) grants CF-263377 and Dirección General de Asuntos del Personal Académico Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica de la Universidad Nacional Autónoma de México (DGAPA-PAPIIT, UNAM): IA100522.

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Frontal lobe epilepsy
21	30	M	40	2	117	LFL
22	22	M	41	4	69	RFL
22	22	M	42	4	71	RFL
23	29	M	43	4	78	RFL
			44	4	83	RFL
			45	5	78	RFL

Frontal lobe epilepsy
21	30	M	40	2	117	LFL
22	22	M	41	4	69	RFL
22	22	M	42	4	71	RFL
23	29	M	43	4	78	RFL
			44	4	83	RFL
			45	5	78	RFL

Frontal lobe epilepsy
21	30	M	40	2	117	LFL
22	22	M	41	4	69	RFL
22	22	M	42	4	71	RFL
23	29	M	43	4	78	RFL
			44	4	83	RFL
			45	5	78	RFL