Necessity of Quantitative EEG for Daily Clinical Practice

The two main problems in the daily clinical practice of EEG are i) its under-use dedicated mainly to epilepsy and ii) subjectivity in de visu analysis. However, both problems can be overcome by using numerical tools in clinical practice that broaden the scope and introduce real objectivity to bioelectrical measurements. We have developed a method for quantitative EEG (qEEG) for daily use based on the homeostatic foundation of EEG. This method is robust, easy, and not time consum-ing and is arranged in two branches: the analysis of the spectral composition in each channel and synchronization. Notably, channels are arranged in differential mode. Since 2016, we have used this method for more than 4100 EEGs from scalp recordings in outpatients, epilepsy evaluation, and evaluation and monitoring in the intensive care unit (ICU). We have been able to identify numerical properties that are not visually evident in several pathologies, including COVID-19 in patients suffering encephalopathy, and have performed diagnosis in ICU patients and differentiation between epileptic and non-epileptic spells or minimum cognitive states. The use of numerical variables across successive recordings in the same patient has proven to be of great utility. We propose that qEEG use should be expanded globally for daily clinical practice.


Introduction
Electroencephalography (EEG) is one of the oldest diagnostic methods currently used in medicine. It was described one century ago by the German psychiatrist Hans Berger [1]. Since then, its use has rapidly spread, and practically every hospital in the world has an EEG device. However, although EEG is probably the fastest, cheapest, and most straightforward method to obtain neurophysiological information from the human brain in a non-invasive way [2], its use is sometimes excessively restricted to the diagnosis of epilepsy, even in patients in whom the level of consciousness should be carefully evaluated [3]. Nevertheless, it should be always remembered that the primary function of the cerebral cortex is to exchange information by generating bioelectrical signals, not only in epilepsy.
In addition to this excessive restriction to epilepsy, EEG is sometimes reported as a subjective method, depending strongly on the interpreter [4][5][6][7][8]. There has been an attempt to reduce inter-rater variability among interpreters by the introduction of a consensus for EEG interpretation [9][10][11][12][13]. Although these consensus and classifications introduce some objectivity in EEG analysis, the variables are mostly qualitative or binary (present/absent), and specificity is therefore not very high.
In the past few decades, clinicians, neuroscientists, mathematicians, physicists, and engineers (among other experts) have sought a way to overcome these flaws to increase the true field of EEG application and reduce subjectivity in diagnosis. Some research has been devoted to combining EEGs and imaging techniques, mainly magnetic resonance imaging [14][15][16]. Another direction has been to develop mathematical tools to increase the reliability and deepen the information extracted from neurophysiological recordings. Collectively, this approach is called quantitative EEG (qEEG [17]). A canonical formulation toolbox is not needed to define qEEG. Instead, we can say that every EEG recording that uses any kind of post hoc numerical method to obtain a result about frequency spectrum, synchronization, network dynamics, or anything else of bioelectrical magnitude can be considered qEEG. This approach has been increasing in popularity since the introduction of digitalization in electroencephalography. As an example, in the past few decades, the number of papers referenced in PubMed with the word "qEEG" in the title/ abstract rose from two in 1979, to 31 in 1999, and 76 in 2019 (a factor of x38!). However, the use of qEEG in clinical practice is far from being generalized, with the exception of ICUs where long-term monitoring (continuous EEG, cEEG) and qEEG are slowly increasing [18][19][20][21][22][23][24][25].
The time required for a cEEG review is one of the most commonly given reasons for the use of qEEG in the ICU and other diagnostic fields. However, we have taken a different approach to qEEG during cEEG or standard EEG for ambulatory/hospitalized patients: instead of just simplifying seizure detection (another manifestation of the excessive focus on epilepsy), our aim is to obtain a comprehensive and efficient view of the bioelectrical brain physiology/physiopathology in the most objective way. To do this, we have developed qEEG using classical mathematical methods, but in a neurophysiologically and clinically oriented fashion [26].
In this chapter, we want to describe in detail the physiological basis of qEEGs, the method implemented for its quantification, and provide some examples of its use.

Physiological basis of qEEG
We have adopted the assumption that EEG is founded in a homeostatic system to obtain the main variables of our method [26][27][28]. This aspect is of extraordinary relevance because its specific application in different pathologies will lead to specific changes in the different numerical variables obtained. EEG consists of the multivariate spatio-temporal determination of the electrical potentials generated by the brain and recorded on the surface of the scalp. The oscillatory activity of the EEG, in clinical practice, is divided into four bands, depending on its oscillation frequency: delta (δ; 0-4 Hz), theta (θ; 4-8 Hz), alpha (α; 8-13 Hz), and beta (β; 13-30 Hz). Frequencies above 30 Hz, although very important in cognitive research, are not customarily used in clinical practice.
Briefly, the regulation of different bands is given by the following systems [29]: • Delta. The hyperpolarization of the thalamic-cortical (TC) interstitial pacemaker cells by the nucleus reticularis, together with a lower excitatory effect of the ascending activating reticular system (AARS), releases the spontaneous activity of cortical cells, oscillating at <4 Hz. This oscillation throughout the putamen/globus pallidus inhibits the brainstem nuclei responsible for AARS.
• Theta. There are two theta-generating systems: i) activation of the nucleus reticularis (activated by the AARS) and inhibiting TC neurons and ii) through the mesolimbic system, which includes multiple afferents from the entorhinal cortex, hippocampus, amygdala, septum and anterior cingulate cortex; activating the intralaminar thalamic nuclei, and projecting to layer I of the cerebral cortex.
• Alpha. TC neurons spontaneously oscillate at 6-12 Hz and regulate the excitation of large cortical areas through thalamic-cortico-thalamic re-entry loops. The membrane potential of these cells determines the frequency of oscillation and is regulated by synaptic inputs from the AARS (which includes the intralaminar nuclei of the thalamus), mainly from the brainstem and cortical inputs. Within the cortex, this activity is propagated from some nodes of special importance through interneuronal connections.
• Beta. Originates primarily from cortico-cortical interactions and is facilitated by diffuse activation of the AARS and depolarization of TC cells, allowing the free transfer of information from the sensory systems through the thalamus to the cerebral cortex.
This complex neuroanatomical homeostatic system is probably genetically determined and regulates basal levels of local synchronization, global interactions between different regions, spectral composition, and periodic signal space sampling [30][31][32][33].
One of the main limits in our approach is to maintain a close relationship between numerical magnitude variation and the underlying anatomo-functional system. For example, an increase in cortical activity (e.g., a seizure) must always be associated with an increase in β and probably α bands. Obviously, it does not preclude an increase in slower bands, but rising activity in faster bands is mandatory [26].

Quantified EEG
There are two branches of analysis: power spectra and synchronization. For both of them, dynamic (i.e., varying along the time) and mean measurements (i.e., mean spectra or mean graph of synchronization) are obtained. The process is summarized in Figure 1.
The process used for qEEG followed these steps: Different length raw records are exported from the EEG device (EEG32, NeuroWorks, XLTEK®, Oakville, ON, Canada) to an ASCII file. Usually, artifacts are excluded by the export of several artifact-free chunks, which are later combined for analysis. We have shown that this process does not changes the main properties analyzed (see below). This process (exportation to an ASCII file) would probably be different for other EEG suppliers, but we have not assessed this possibility. We have computed the export time (t export ) as a function of the ASCII file size (S) and obtained a linear expression by means of least-square fitting (r = 0.9947): Although the raw recordings were digitized at 512 or 1024 Hz, we down-sampled to 128 or 256 Hz.
Exported files are digitally are filtered by a sixth-order Butterworth digital filter between 0.5 and 30 Hz.
A differential EEG montage is then reconstructed. Topographic placement of channels is defined on the scalp as the midpoint between the electrode pairs defining the channel; e.g., the Fp1-F3 channel would be placed at the midpoint of the geodesic between the Fp1 and F3 electrodes.
All recording can be divided into different lengths of moving windows (1-5 s each) with different overlaps (between 0 to 50%, but usually 10%). The total length used during the fast Fourier transform (FFT) is directly related to frequency precision in the power spectrum (PS). Overlap is used to minimize the border effect produced by windowing [35].
For each window (n) and frequency (k), we computed the fast Fourier transform (FFT) of the voltage (V m n ð Þ) obtained from each channel (m) to obtain the power spectrum (S m n,k , in μV 2 /Hz). We used the expression: We also computed Shannon's spectral entropy (SSE) according to: where F is the maximum frequency computed and p k is the probability density of S, obtained from the expression:

Method of electroencephalogram (EEG) quantification in two branches: Power spectra (b-d) and synchronization (e,f). (a) Raw
We computed the area under the S m n,k according to the classical segmentation of EEG bands. We used the expression: The expression sup refers to the upper limit of each EEG band. The absolute value of Pearson's correlation coefficient (ρ) is computed for each pair of channels (i,j) according to the expression: where N window is the number of points included in a window (usually 128) and x i , x j represents the mean of both channels.
The mean value of all windows is then computed, obtaining the mean correlation matrix.
Areas of the same band are grouped by cerebral lobes. In the case of the left hemisphere (shown as an example), we grouped the frontal F ¼ . Channels from the right hemisphere were grouped accordingly. These areas, for both bands (j) and lobes (r), A r j t ð Þ; r ¼ F, PO, T, are plotted as time functions and compared between the hemispheres. The same groups were used to compute SSe.
The total time of analysis (t analysis ) is obtained from this linear expression, which was obtained from least-square fitting: From expressions 1 and 7, for a typical 88 MB file (10 min record), we can estimate the time spent in export + analysis as less than 2 min.
We can optionally introduce two time-markers to define different states (e.g., pre-ictal, ictal, and post-ictal periods) in order to statistically compare the changes.
We can optionally export the numerical results to an Excel® file (e.g., mean AE SEM of power, synchronization; and SSe for channels, lobes, and hemispheres). This last step is the most time-consuming (up to 3 min for a custom-length file).
Numerical analysis of EEG recordings was performed with custom-made MATLAB® software (MathWorks, Natick, MA, USA).
For power spectra as well as for synchronization, we can represent measurements either as dynamic time-dependent variables (Figure 1d), or as the mean values, averaged over the file (Figure 1b,f). Therefore, although complementary, information obtained from both kinds of computations must be interpreted differently. In other words, average measurements are only useful if the stationarity of the record is evident (e.g., basal recordings, well-defined phases of sleep, etc.).

Robustness of the method
A very important aspect of any numerical method is its robustness, e.g., the evaluation of the method wherein the results obtained are found to be reliable, even when performed under slightly varied conditions. It is the ability of a method to remain unaffected when slight variations are applied. It is extremely important to check trials of the numerical method within the same group of EEG records under the different conditions of i) down sampling, ii) windowing, or iii) overlapping. Moreover, it is important to check whether synchronization measures are affected by the global analysis of different, non-consecutive chunks.
For this purpose, we selected EEG recordings of five minutes in length, from six control individuals (without any neurological or psychiatric pathology, between 20 and 30 years old, and with no pharmacological treatment). We analyzed each EEG under different conditions, namely: • Down-sampling at 128 and 512 Hz, (f is for frequency).
Overall, we had 18 combinations for frequency/windows/overlapping (f,w,o). The structure of EEG for each patient (p i , i = 1,2, … 6) can be described by a 10-element vector as: Obviously, every structure can be described as p i f , w, o ð Þ. A robust method should not affect the structure of EEG for the same patient, irrespective of changes in absolute values. For each patient, we have plotted along the x-axis (coordinates of EEG structure) the normalized band values and correlations for all of the 18 combinations (Figure 2).
From Figure 2, we can observe that different combinations cannot affect the structure of EEG.
The effect of multiple compositions of the analyzed file on synchronicity was assessed as follows: an EEG record of 3 min was analyzed. Then, the same record was exported in three different chunks, and a new analysis was performed on a recombined file with the parts randomly ordered (1,3,2/2,1,3/2,3,1/3,1,2 or 3,2,1). We did not observed any difference in synchronization between the whole record and a recombined one (not shown).
In summary, these results demonstrate that the method is highly robust, at least for the limits addressed.

Some examples of the utility of qEEG
It is out of the scope of this chapter to illustrate the objective and quantified difference between the classical, de visu, analysis of EEG and qEEG. Instead, we will provide some examples of qEEG application to real clinical problems and the results. In these examples it will be shown that information obtained by qEEG clearly exceeds the possibility of de visu analysis.

Differentiation between periodic patterns and seizures
Patients in the ICU usually undergo a limited clinical neurological examination because of either structurally or functionally altered conditions of the central nervous system (CNS) or due to the effects of drugs used for sedoanalgesia [36]. Therefore, we can evaluate brain function in these conditions by EEG. However, a dynamic evolution of injury is frequently observed in critically ill patients due to the occurrence of epileptic seizures (ES), status epilepticus (SE), or other brain insults [37,38]. In this sense, cEEG allows the functional assessment of the cerebral cortex in real time for prolonged periods. It has been proven to be an extraordinarily useful tool for detecting electrographic seizures and non-convulsive epileptic status (NCES), modifying treatment and assessing the functional prognosis [10, 11, [39][40][41][42].
The particularity of cEEG records of patients in the ICU comprises a high frequency of artifacts and frequently observed rhythmic and periodic patterns, which are easily confused with seizures. Both can be difficult to interpret not only in a raw EEG but also with the qEEG tools currently used [43,44]. As indicated above, the use of multiple drugs acting on the CNS and primary and secondary injuries profoundly affect the bioelectrical brain dynamics. Therefore, it can be quite difficult to differentiate between bursts of periodic activity (BPA) and true ES/SE. The main problem is that EEG patterns analyzed de visu do not always exhibit the sharp morphology of ES/SE of not-ICU patients.
According to the ILAE, an ES is a transient occurrence of signs and/or symptoms due to abnormal excessive or synchronous neuronal activity in the cortex of the brain [45]. Signs/symptoms are usually excluded in critically ill patients, but the excessive activity of the cortex is mandatory for a positive identification. We have used this pathophysiological feature for the numerical definition of ES. Therefore, we can use this method to exclude epilepsy in those cases where α/β activity does not change (or even decreases) during the event (see below). The limits of change for the different bands ( Table 1) can be used to distinguish PBA from ES.
From this table we can observe that the superposition is very high for δ bands (i.e., this band is not discriminative), low for θ and Se, and practically null for α and β bands. Therefore, the intervals for increments of normalized activity defining an ES in these types of patients are as follows (excluding superposition and rounding): We have defined the numerical features of ES and BPA in critically ill patients using the pathophysiological definition of epilepsy. This will facilitate its identification in clinical practice, allowing a precocious and more adequate treatment.

Specific characterization of encephalopathy in SARS-CoV-2 patients
Neurological complications in COVID-19-infected patients have been reported. The CNS effects reported include encephalitis, toxic encephalopathy, ageusia and anosmia, headaches, or acute cerebrovascular disease [46][47][48][49][50][51][52]. The mechanisms of CNS infection in the pathophysiology of COVID-19 are still debated, and it has been proposed to result from direct invasion through the blood-brain barrier, a neuronal pathway, hypoxia damage, immune-response mediated injury, or angiotensinconverter enzyme 2 activity, among other possibilities [47,53,54]. Encephalopathy refers clinically to state of impaired cognition, generally acute or subacute [55]. Descriptions de visu of EEG are based on classical analysis by visual inspection and not on specific features [56][57][58].
We applied our method of qEEG to patients discharged from the ICU after COVID-19 infection [34]. We used two control groups from patients previously studied in our hospital: (i) patients with infectious toxic encephalopathy (ENC) and (ii) patients after cardiorespiratory arrest (CRA), as an example of severe hypoxic insult to the CNS.
Visually, in COVID-19, EEG records the apparent absence of delta/theta activity conferred a near-physiological aspect to the recordings. Despite the different visual aspects appearing between ENC and COVID-19, the mean spectra by channel were quite similar. Examples of typical recordings are shown in Figure 3.
We assessed the specific differences for each band in ENC, COVID-19, and CRA patients. Subsequently, we performed one-way ANOVA (ANOVA on ranks when normality failed) for each lobe and band, and for SSe and synchronization (Figure 4).
The pattern of ENC and CRA was clearly different for all bands. However, the COVID-19 group was not completely different from the ENC and CRA groups, although it was evidently observed that the distribution is between the two extreme groups. Nonetheless, the behavior of temporal lobes clearly differs for the ENC and COVID-19 groups for the δ, α, and β bands. Contrary to EEG bands, SSe was higher for the COVID-19 group and lower for the ENC group. In fact, SSe was different for all groups at all lobes. This result may be surprising considering the kind of spectra shown in Figure 3c, where the distribution was apparently more complex. However, the presence of α and β bands (scarcely present in the CRA group) increased the SSe for COVID-19 patients.
Finally, although ρ was not as different between groups as SSe, a clear difference was seen in the hemispheric synchronization and frontal lobes of ENC and COVID-19 patients, with lower synchronization for the latter group.
In summary, we have demonstrated that qEEG can differentiate between encephalopathy types, and we have described the numerical features of each. In this context, we show that COVID-19 patients display EEG structures that are truly distinguishable from those of both infectious toxic encephalopathy and encephalopathies of patients who experience severe hypoxic conditions. Significantly, the EEG pattern of COVID-19 patients was between those of the ENC and CRA groups. Therefore, it can be speculated that hypoxia may show some participation in this electroclinical entity. However, the EEG structures of the CRA and COVID-19 groups were different enough to consider that other factors besides hypoxia must be responsible for the bioelectrical pattern.
It is extremely relevant to bear in mind that COVID-19 patients showed mild to severe cognitive symptoms despite de visu quasi-normal recordings. However, the severe numerical alterations of temporal lobes spectra, structure of SSe and  Table 1. [26].

Inter-percentile 25-75 intervals for bands and lobes in BPA and ES. Superposition is indicated with respect to the ES interval
synchronization were highly different and are probably explained by symptomatology with quasi-normal EEG traces.

Continuous EEG monitoring in ICU
Long-term EEG monitoring in the ICU (cEEG) has been one of the main developing fields of electroencephalography in recent years. There are several methods used for EEG monitoring, and most of them share a similar philosophy: to identify the presence of seizure/status epilepticus to make the information of monitoring easy and fast. As stated above, we think that this reductionist approach impoverishes the scope of electroencephalography.
We systematically used qEEG during cEEG for the below indications: • Monitoring the presence of ES/SE. More useful than identifying the presence of ES, qEEG is essential to discriminate between epileptic and non-epileptic patters, as we stated above. • Titration of sedation/anti-epileptic drugs (AEDs). Identifying changes in background from the variations in spectra or mean values of specific EEG bands is mandatory to increase/decrease the dose of sedation. Additionally, AEDs are adjusted with the help of qEEG, although de visu inspection of irritative activity is mandatory. • Long-term recordings in patients with alterations of consciousness without sedo-analgesia to evaluate brain physiology. Severe encephalopathy can induce a low-consciousness level. These recordings typically lack irritative activity, and changes in the background are slow. However, these changes correlate with the level of consciousness and predict the outcome. Therefore, it is important identify changes to adjust treatment as soon as possible, especially to avoid unnecessary therapeutic actions.
In this way, we have performed more than 250 cEEG + qEEG in the ICU in the last five years. This is a time-consuming task (especially considering that every cEEG takes 1.4-4.3 days (inter-percentile 25-75 range)), but the clinical utiliy is clear because the demand increased from 1.0 AE 0.2 cEEG/month in 2015 to 5.5 AE 0.8 cEEG/month in 2019.

Utility in dementia
There are numerous articles in the literature showing that the initial phases of dementia can be detected by qEEG [59][60][61][62][63]. We have used our numerical method in patients with either minimum cognitive impairment (MCI) or aphasia. Obviously, the de visu analysis of raw recordings shows only a nearly normal aspect or lowvoltage. However, numerical analysis can show very relevant facts that are not observable by eye (Figure 5).
At this time, we are conducting a study to identify specific properties of different pathologies (sub-types of primary aphasia, Alzheimer disease, vascular dementia, etc). Although we have not yet defined different groups of features specific to each pathology, what is clear from the above figure is that connectivity is a magnitude that is affected early and consistently in most cognitive alterations.

Other examples of qEEG utility
Finally, we provide two more representative examples of diagnosis highly aided by the use of qEEG. Case 1. A 17-year-old male patient with severe cognitive and behavioral impairment, secondary to severe epileptic encephalopathy due to refractory epilepsy in childhood after a central nervous system infection. Daily seizure frequency, with countless seizures per day. In treatment with zonisamide (400 mg), valproic acid (1200 mg), oxcarbazepine (1400 mg), and clobazam (10 mg) daily. Rectal diazepam 10 mg if required. A video of EEG is performed in which it is observed that during sleep, the patient exhibits several episodes of lateral head movement and growls. De visu recordings (Figure 6a) can be described as global desynchronization. However, the dynamics of the EEG bands show a decrease (practically total) for all the bands (Figure 6b). As stated above, epilepsy is expected to be accompanied by an increase in cortical activity (α and β bands). Therefore, this event cannot be identified as epileptic.
Although the patient also presented true epileptic events, the number of these was substantially lowered and AED was adjusted according to the real number of ES. The final diagnosis for this event was a nonepileptic behavioral disorder, secondary to severe epileptic encephalopathy. Case 2. A 22-year-old female diagnosed with epilepsy at the age of 14 years and with anxious-depressive illness from the age of 20 years. The applied treatment was lamotrigine (100 mg/day) and clonazepam (0.5 mg/8 h). Seizures occurred every 2-3 days, described as the perception of black dots in the visual field, weakness, loss of consciousness and muscle tone, loss of balance and falling to the ground. During telemetry, we recorded one episode of black dot perception followed by a loss of consciousness while in bed. De visu EEG recordings showed no significant changes (Figure 7a). However, the dynamic variation of EEG bands indicated a generalized decrease, except for the occipital α band, which increased after the eyes closed (Figure 7b).
The final diagnosis was psychogenic non-epileptic seizure (PNES), and the AEDs were slowly removed.

Discussion
Numerous methods have been used for qEEG, although they are rarely used in daily clinical practice. There is, therefore, a huge gap between the promising (even spectacular) results obtained with qEEG and its practical usefulness. To the best of the knowledge of the authors, this issue has not been systematically addressed, although it has been said that electroencephalographers have poor trust in mathematical models [2,17].
The degree of mathematical complexity and abstraction is quite different among the methods proposed. Not all of the mathematical models can be included in the same category, and it is of extreme importance that mathematical solutions be robust with respect to physiological assumptions [2]. Then, some procedures require relatively simple and involve straightforward methods as FFT [26,34,[64][65][66] and synchronicity measurements [67,68], approaches that clinicians are familiar with. In contrast, other numerical methods are more complex, or the mathematical approach deviates from physiological assumptions [69][70][71][72][73][74], and this probably takes neurophysiologists out of their comfort zone.
We have developed a robust method that is physiologically founded and easy to use in daily clinical practice. The tools selected are neither unique nor are they necessarily the best. Other tools (e.g., coherence) can be implemented. A careful comparison between these methods will decide the fitted procedure for each pathology. From the beginning of 2016, we have performed more than 4100 analyses and used this toolbox in most patients, even those with EEG apparently evident. We did not use qEEG only when the record included so many artifacts (e.g., in agitated patients) that the results would not be reliable.
The method described can be implemented to automatically differentiate between paroxysmal events and ES during the long-term monitoring of ICU patients. This feature is very relevant for clinicians because it can shorten the review time, particularly during long cEEG, and can help apply adequate therapeutic measures, avoiding pharmacological blind trials that only delay correct treatment, increasing the inefficacy of treatment and diminishing the probability of recuperation. Therefore, considering that "time is brain", a fast and accurate treatment is mandatory to increase the probability of a good outcome.
Finally, it is extremely important to keep in mind that qEEG is only a tool to help better understand and diagnose brain pathophysiology; therefore, it should not be thought that numerical analysis (at least as we use it today) is enough, without evaluation by an expert, to make an automatic diagnosis. Not all brain pathologies are likely to benefit to the same degree from analysis. For example, the method described in this chapter is not well fitted to detect low-frequency transitory waves as medium/small focal epileptiform discharges, although visual inspection can identify them very well. However, patterns that are not readily visible in de visu analysis (e.g., asymmetries in power spectra compositions) are easily detected.

Conclusions
We can summarize the conclusions of this work as follows: • qEEG is a robust and non-time-consuming method that is able to produce numerical and objective values of several bioelectrical magnitudes with clinical significance.
• qEEG increases and facilitates diagnoses that are otherwise exceedingly difficult to obtain by de visu inspection. Therefore, the scope of the true applicability of EEG is expanded far beyond epilepsy.
• We propose that qEEG use should be expanded globally for daily clinical practice. Thus, clinical neurophysiologists should be informed of the methods of numerical analysis procedures.