Back to the Future of Quantitative EEG: Normative Biomarkers from Spectral Ratios and Functional Indices for Diagnosis and Therapeutic Monitoring

Back to the Future of Quantitative EEG: Normative Biomarkers from Spectral Ratios and Functional Indices for Diagnosis and Therapeutic Monitoring | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Back to the Future of Quantitative EEG: Normative Biomarkers from Spectral Ratios and Functional Indices for Diagnosis and Therapeutic Monitoring Jorge F. Bosch-Bayard, Judith Guerrero-Sauzameda, Rodolfo Bosch-Bayard, and 13 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9333312/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract Background Quantitative EEG (qEEG) provides objective, millisecond-resolution measures of brain dynamics. Despite decades of methodological advances, clinically relevant derived indices—spectral power ratios, cognitive-emotional state markers, and physiological parameters—are typically reported as raw values without the normative context required for individualized clinical inference. Objective To develop the first systematic age-dependent normative models for this family of derived qEEG indices using a multinational database, enabling probabilistic Z-score interpretation at the individual level and objective therapeutic monitoring. Methods Normative modeling was applied to the HarMNqEEG database (n = 1,564 neurologically healthy participants, ages 5–97, 9 countries, eyes-closed resting state). Electrode-level Spectral Normalization (ESN) removed inter-individual and inter-device amplitude variability while preserving the neurophysiological interpretability of each index. Age-dependent normative trajectories were estimated using Generalized Additive Models for Location, Scale, and Shape (GAMLSS) with P-splines on log(age), allowing conditional mean and variance to vary non-linearly across the lifespan. Results GAMLSS modeling revealed significant non-linear age-dependent trajectories for all indices. Slow-wave-dominated ratios showed steep decreases from childhood to early adulthood, consistent with cortical maturation; alpha-dominated indices increased during adolescence before stabilizing. ESN normalization yielded well-calibrated normative residuals across the full age range and across all nine recording devices. Conclusions These normative models enable principled, age-adjusted probabilistic inference at the individual level, bridging the historical gap between advanced qEEG methodology and routine clinical practice. The ESN strategy requires no knowledge of recording equipment, ensuring broad applicability. The framework provides an objective tool for monitoring neurophysiological change during therapeutic interventions. quantitative EEG normative models GAMLSS spectral ratios (theta/beta arousal) electrode-level spectral normalization therapeutic monitoring Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction The electroencephalogram (EEG) occupies a singular position among clinical neurophysiological tools. Unlike functional magnetic resonance imaging (fMRI) or positron emission tomography (PET), which measure hemodynamic and metabolic correlates of neural activity with temporal resolution on the order of seconds, EEG directly records the electrical potentials generated by the postsynaptic currents of cortical neuronal populations with millisecond temporal resolution (Michel et al. 2019 ; Rajkumar et al. 2021 ). This direct access to neuronal dynamics, combined with its relatively low cost, portability, and bedside applicability, preserves the EEG's irreplaceable position in clinical neurology, cognitive neuroscience, and neurorehabilitation. The history of EEG analysis has followed a pendular trajectory. Following Hans Berger's seminal recordings in 1929, EEG established itself over several decades as the primary tool for evaluating brain function in clinical practice. During the 1970s and 1980s, the development of quantitative EEG (qEEG) introduced a fundamental conceptual shift: rather than relying solely on expert visual inspection of waveforms, EEG features could be extracted mathematically, characterized statistically, and interpreted against population norms. The pioneering work of Matoušek and Petersen (Matoušek and Petersen 1973 ) on age-related EEG frequency analysis and the foundational contributions of E. Roy John and colleagues to the development of neurometrics (John 1977 ; John et al. 1988 ) established the conceptual and methodological foundations for this approach. Neurometrics, as operationalized by John, constitutes a framework for quantitative EEG analysis that provides a precise and reproducible estimate of the deviation of an individual record from normality through statistical comparison with normative databases derived from large samples of healthy subjects (John et al. 1988 ), statistically, and interpreted against population norms. The 1990s witnessed a marked decline in the clinical prominence of qEEG. The rapid expansion of structural and functional neuroimaging—MRI, PET, and functional MRI—shifted scientific and clinical attention toward modalities offering superior spatial localization. This transition generated a partly unfounded belief that EEG was a diagnostic tool of relatively lower informative value compared to these emerging technologies (Turner 2021 ). Beginning in the early 2000s, however, a sustained renaissance of quantitative EEG started to consolidate, driven by the maturation of distributed electromagnetic source imaging methods, such as VARETA (Bosch-Bayard et al. 2001 ) and sLORETA (Pascual-Marqui 2002 ), and the increasing availability of large-scale normative databases (Li et al. 2022 ; Valdes-Sosa et al., 2021; Bosch-Bayard et al., 2020 ; Thatcher and Lubar 2009; Thatcher et al. 2003 ; Valdes-Sosa et al., 1990; Szava et al., 1994 ) (Fig. 1 A). Alongside these spectral and source imaging advances, a complementary tradition within quantitative EEG developed independently: the analysis of the global spatial configuration of the scalp potential field and its dynamics over time. Lehmann and colleagues established that the momentary electric field of the brain can be described by a small number of quasi-stable topographic configurations—now termed EEG microstates—whose spatial patterns, durations, and transition probabilities constitute fundamental descriptors of spontaneous brain dynamics (Lehmann et al. 1987 ). Koenig, Michel, and collaborators subsequently demonstrated that the four canonical microstate classes follow systematic age-dependent normative trajectories across the human lifespan, with childhood-to-adulthood transitions in microstate duration and occurrence rates that parallel the maturational changes observed in spectral indices (Koenig et al. 2002 ). The recent resurgence of interest in microstates—driven by their robust correlation with large-scale resting-state fMRI networks (Rajkumar et al. 2021 ) and their sensitivity to neurological and psychiatric conditions—has established them as a complementary normative framework operating at the level of global field dynamics rather than frequency-domain features (Michel and Koenig 2018 ). The present work occupies a parallel and complementary niche: while microstate analysis characterizes the spatiotemporal architecture of brain electric fields, the spectral ratio and functional indices addressed here capture the frequency-domain composition of those same fields, providing clinically actionable biomarkers with direct electrode-level interpretability. Despite this methodological progress, routine clinical practice remains predominantly qualitative. EEG reports continue to rely primarily on expert visual descriptions, and, at best, on raw topographic maps of spectral power. The quantitative potential of normative maps, Z-scores, and derived functional indices is frequently underused. As a consequence, valuable information regarding how an individual's brain activity deviates from an age-typical population rarely enters formal clinical decision-making (Ko et al. 2021 ). A critical limitation of current clinical workflows is the reliance on raw pre and post–treatment comparisons. Without reference to a normative framework, any observed change in an EEG index remains ambiguous: it is impossible to determine whether the observed shift represents movement toward neurotypical function, persistence within an abnormal range, or merely state-dependent fluctuation. Normative Z-score frameworks directly address this limitation by anchoring individual measurements to age-dependent population norms, enabling the clinician to quantify both the magnitude of initial deviation and the direction and significance of longitudinal change. An additional gap concerns the limited exploitation of multiple physiological states within qEEG protocols. Parameters assessed during eyes-open recording—such as alpha rhythm reactivity to eye opening—as well as responses to activation procedures (hyperventilation, photic stimulation) and EEG dynamics under cognitive load, provide complementary windows onto neurophysiological integrity absent from resting eyes-closed recordings alone. The individual alpha frequency (IAF) and its age-related developmental trajectory constitute particularly sensitive markers of neurophysiological maturation and thalamocortical integrity (Klimesch 1999 ; Pfurtscheller and Lopes da Silva 1999 ), yet they are seldom quantified within normative frameworks in routine clinical reports. This limitation is clinically relevant because some electrophysiological abnormalities may remain subtle at rest but become evident during cognitive activation. In clinical practice, Swingle has explicitly recommended complementing eyes-closed and eyes-open conditions with a brief cognitive challenge such as reading or counting backwards, noting that certain patterns emerge only when the patient is cognitively challenged (Swingle 2015 ). From a physiological perspective, the transition from eyes-closed to eyes-open already constitutes a shift toward higher EEG arousal (Barry and De Blasio 2017 ; Barry et al. 2007 ). Beyond this basic manipulation, mental arithmetic and serial subtraction paradigms offer a practical and well-supported way to induce graded cognitive load without additional materials (Fairclough et al. 2024 ), while backward digit span provides a brief probe of working-memory manipulation (Onton et al. 2005 ). Although normative lifespan references for these activation conditions remain largely unavailable, their integration into future normative protocols would substantially enrich the clinical interpretability of qEEG-derived biomarkers. Although several normative qEEG databases have been developed for spectral power and related Z-score inference, and harmonized multinational norms are now available for cross-spectral EEG measures, the literature remains comparatively sparse regarding clinically standardized normative references for derived frequency ratios and composite functional metrics. Indices such as theta/beta, delta/beta, frontal alpha asymmetry-related measures, arousal-related EEG markers, and engagement metrics have been widely studied, but mostly as research variables, group discriminators, or task-sensitive markers rather than as integrated age-referenced biomarkers for individualized clinical inference. The present study aims to fill this gap by providing the first systematic normative models for this family of indices derived from the HarMNqEEG project database (Li et al. 2022 ), comprising 1,564 neurologically healthy subjects from 9 countries spanning the full human lifespan (ages 5 to 97). We derive age-dependent normative trajectories and individualized Z-scores and define a unified normative framework with electrode-level spectral normalization (ESN) to ensure applicability across the full range of clinical recording contexts. 2. Materials and Methods 2.1. The HarMNqEEG Multinational Database The normative data used in this study were derived from the Harmonized-Multinational qEEG Norms (HarMNqEEG) project, an international collaborative initiative coordinated by the Global Brain Consortium (GBC) (Li et al. 2022 ). The database comprises resting-state EEG recordings from 1,564 neurologically healthy subjects, spanning the full human lifespan from 5 to 97 years of age, collected across 9 countries: Cuba, China, Malaysia, Russia, Germany, Switzerland, Canada, Colombia, and the United States. Data were obtained from 14 independent studies conducted with 12 different EEG acquisition systems, reflecting the diversity of equipment and protocols encountered in international multicenter research. 2.1.1. Inclusion and Exclusion Criteria Participants were selected according to strict clinical criteria designed to constitute a representative healthy population rather than a highly selected "super-normal" sample. Exclusion criteria included: history of neurological or psychiatric disorders; current or recent use of psychoactive medications or substances with known effects on the central nervous system; significant head trauma or loss of consciousness; systemic diseases with documented neurological impact (e.g., uncontrolled diabetes mellitus, severe arterial hypertension); and abnormalities identified on neurological examination. Where available, structural MRI and cognitive screening results were also used to confirm neurological health. 2.2. Data Preprocessing A central challenge in aggregating EEG data across multiple recording sites and device types is the presence of systematic inter-site variability—commonly referred to as "batch effects"—that can introduce spurious differences unrelated to neurophysiology. The pipeline used here addressed this through the following procedure: Artifact Rejection : Visual inspection and automated quality-control procedures were applied to select a minimum of 60 seconds of stationary, artifact-free EEG activity per participant. Spectral Estimation : Cross-spectral matrices were computed for the standard 19-electrode array of the International 10–20 system using the Fast Fourier Transform (FFT) with a frequency resolution of 0.39 Hz. Electrode-level Spectral Normalization (ESN) : For each subject i and electrode ch, the Electrode-level Spectral Normalization factor is defined as ESN(ch, i) = mean_f[S(ch, f, i)] for f ∈ [0.39, 19.11] Hz, where S(ch, f, i) is the spectral power density at electrode ch and frequency f, and the average is taken over all frequency bins used in index computation. Each spectral value is then normalized by division: S_norm(ch, f, i) = S(ch, f, i) / ESN(ch, i) (5). On a log scale, this is an additive correction — equivalent to a multiplicative factor on a linear scale. The ESN simultaneously accounts for individual-level variability in scalp and skull conductivity and other multiplicative amplitude offsets that are flat across the analysis band. This universality is a key advantage over device-covariate approaches: ESN normalization is always applicable, including when the acquisition system is unknown, which is common in clinical practice. Residual variability : after ESN normalization, residual inter-site amplitude variability is absorbed within the normative dispersion term of the GAMLSS model, since the per-electrode ESN correction removes both individual-level and external-level multiplicative scale differences before index computation. The complete computational pipeline proposed in this work is summarized in Fig. 2 . It includes Eyes Open (EO) and Cognitive Load (CL), although at present, normative databases are available only for the Eyes Closed (EC) condition. It is our purpose to standardize some Cognitive Load tasks in the future (as proposed in section 4.5.1 ) and gather databases recorded under these parameters to calculate norms for these physiological tasks, which can provide useful information for the clinical use of qEEG. 2.3. Calculation of Quantitative Indices For each participant in the database, 18 quantitative indices were calculated from the spectral power densities obtained after preprocessing. Four canonical frequency bands were defined: Delta (δ: 1.5–3.5 Hz), Theta (θ: 3.9–7.5 Hz), Alpha (α: 7.9–12.5 Hz), and Beta (β: 12.9–19.14 Hz). Spectral power at a given electrode ch and band is denoted P_band(ch). Where an index is computed over a set of electrodes, the mean power across that set is used. All ratio-based indices are computed on log-transformed band powers, so that a ratio becomes a difference of logarithms: ln(P₁) − ln(P₂) ≡ ln(P₁/P₂). This log-ratio formulation is symmetric, improves distributional properties, and is standard in qEEG normative modeling (Bosch-Bayard et al. 2001 ; Arns et al. 2013 ). 2.3.1. Electrode-Level Spectral Ratios The following three ratios are computed separately for each of the 19 electrodes of the 10–20 system, yielding 19 values per ratio. Each electrode–ratio combination receives its own age-dependent normative model. Theta/Beta Ratio (TBR, per electrode) : TBR(ch) = ln[θ(ch)] − ln[β(ch)]. Widely used as a marker of attentional regulation and cortical arousal (Arns et al. 2013 ; Ogrim et al. 2012 ). Theta/Alpha Ratio (TAR, per electrode) : TAR(ch) = ln[θ(ch)] − ln[α(ch)]. Reflects the relative dominance of theta over alpha; sensitive to vigilance level and cognitive fatigue (Klimesch 1999 ). Alpha/Beta Ratio (ABR, per electrode) : ABR(ch) = ln[α(ch)] − ln[β(ch)]. Indexes the balance between idling alpha states and active beta processing; elevated values are associated with reduced cortical arousal and drowsiness. Delta/Beta Ratio (DBR, per electrode) : DBR(ch) = ln[δ(ch)] − ln[β(ch)]. Captures the balance between slow delta oscillations and fast beta activity; elevated DBR has been associated with cortical hypoactivation and is sensitive to disorders of consciousness and severe attentional dysregulation (Thatcher et al. 1989 ). Delta/Alpha Ratio (DAR, per electrode) : DAR(ch) = ln[δ(ch)] − ln[α(ch)]. Widely used as an indicator of cerebral ischemia, diffuse encephalopathy, and cognitive impairment, elevated DAR reflects pathological slow-wave dominance (Claassen et al. 2024 ). Delta/Theta Ratio (DTR, per electrode) : DTR(ch) = ln[δ(ch)] − ln[θ(ch)]. Reflects the relative contribution of infra-slow delta versus theta activity; sensitive to depth of sleep and severe cortical depression, and useful for distinguishing delta-dominant from theta-dominant slow-wave profiles. 2.3.2. Global Functional State Indices These four indices characterize broad functional brain states and are computed from spatially averaged power across all 19 electrodes (denoted β̅, α̅, θ̅, δ̅), except where noted. Engagement Index (EI) : EI = β̅ / (α̅ + θ̅), following Pope et al., 1995 ). Computed over all 19 electrodes. Captures the relative suppression of slow-wave activity during sustained cognitive engagement. Arousal Index (AI) : AI = β_F̅ / (δ_F̅ + θ_F̅), where the overbar denotes the mean over the frontal cluster F3, F4, Cz. Quantifies the balance between frontal fast and slow oscillations as a measure of CNS activation level (Bonnet and Arand 2007 ). Valence Index (Frontal Alpha Asymmetry, FAA) : FAA = α(F3)]/β(F3) − α(F4)/β(F4), computed from the alpha power at electrodes F3 and F4 individually. Operationalizes the frontal EEG asymmetry framework linking hemispheric alpha lateralization to emotional valence (Allen et al. 2018 ; Davidson 1998 ). Cognitive-Affective Index (CAI) : CAI = FC-TBR × FAA, where FC-TBR is the frontocentral theta/beta ratio defined in section 2.3.3 , and FAA is the frontal alpha asymmetry defined above. This compound index captures the simultaneous contribution of frontocentral cognitive load and hemispheric emotional lateralization. 2.3.3. Frontocentral Regional Ratios These two indices restrict the spectral ratio computation to the frontocentral cluster comprising electrodes F3, F4, and Cz, yielding a single value per index, the mean ratio across those three electrodes. FrontoCentral Theta/Beta (FC-TBR) : FC-TBR = ln[θ_FC̅] − ln[β_FC̅], where the overbar denotes the mean over F3, F4, Cz. The regional counterpart of the per-electrode TBR, focusing on the frontocentral region relevant to executive control and attentional regulation (Arns et al. 2013 ). FrontoCentral Delta/Beta (FC-DBR) : FC-DBR = ln[δ_FC̅] − ln[β_FC̅], computed over the same cluster F3, F4, Cz. Captures the balance between frontocentral delta and beta activity. 2.3.4. Hemispheric Asymmetry Indices Two families of asymmetry indices are computed, both using the log-difference formulation: Asymmetry = ln[M(left electrode)] − ln[M(right electrode)] (A) where M is either absolute band power or a spectral ratio. A positive value indicates left-hemisphere dominance; a negative value indicates right-hemisphere dominance. 2.3.4a. Asymmetry Index (per band, per homologous pair) The Asymmetry Index is computed as the log-difference of absolute band power between homologous electrode pairs, separately for each of the four canonical frequency bands: AI(band, pair) = ln[P_band(left)] − ln[P_band(right)] (B) This yields a matrix of values indexed by band (δ, θ, α, β) and homologous pair. The pairs used are: Fp1/Fp2, F3/F4, F7/F8, C3/C4, T3/T4, T5/T6, P3/P4, and O1/O2. Each band–pair combination receives its own age-dependent normative model. 2.3.4b. Ratio-Based Asymmetry Indices Eight indices combine spectral ratios with hemispheric asymmetry, computed at four clinically selected pairs of homologous electrodes using two ratios (δ/β and θ/β): Asym(ratio, pair) = ln[ratio(left)] − ln[ratio(right)] (C) The eight indices are: δ/β Asymmetry F3 − F4 : ln[δ(F3)/β(F3)] − ln[δ(F4)/β(F4)]. θ/β Asymmetry F3 − F4 : ln[θ(F3)/β(F3)] − ln[θ(F4)/β(F4)]. δ/β Asymmetry F7 − F8 : ln[δ(F7)/β(F7)] − ln[δ(F8)/β(F8)]. θ/β Asymmetry F7 − F8 : ln[θ(F7)/β(F7)] − ln[θ(F8)/β(F8)]. δ/β Asymmetry T3 − T4 : ln[δ(T3)/β(T3)] − ln[δ(T4)/β(T4)]. θ/β Asymmetry T3 − T4 : ln[θ(T3)/β(T3)] − ln[θ(T4)/β(T4)]. δ/β Asymmetry T5 − T6 : ln[δ(T5)/β(T5)] − ln[δ(T6)/β(T6)]. θ/β Asymmetry T5 − T6 : ln[θ(T5)/β(T5)] − ln[θ(T6)/β(T6)]. 2.4. Normative Modeling and Z-Score Derivation 2.4.1. Distributional Transformation The indices computed in this study are expressed as log-ratios or log-differences of band powers and therefore span negative and positive values with approximately symmetric distributions. No additional distributional transformation was applied before model fitting. This is consistent with the log-ratio formulation described in section 2.3 , which ensures that ratio-based indices are already on an approximately linear scale suitable for Gaussian normative modeling. 2.4.2. GAMLSS Normative Framework Age-dependent normative trajectories were estimated using a heteroscedastic regression framework consistent with the two-parameter GAMLSS family [Rigby & Stasinopoulos, 2005 ], with both the conditional mean (µ) and the log-standard deviation (log σ) modeled as smooth functions of age via penalized B-splines (P-splines). The conditional distribution family was selected adaptively for each index using a three-criterion procedure evaluated on the raw (pre-transformation) data. Three diagnostic statistics were computed: excess kurtosis (kurt − 3), skewness, and the p-value of a Shapiro–Wilk test on a subsample of up to 2,000 observations. When at least two of the three criteria indicated non-normality (excess kurtosis > 1, |skewness| > 0.5, or Shapiro–Wilk p < 0.05), a non-Normal family was attempted. For indices with strictly positive values, the Box–Cox t (BCT) family was fitted on the raw data — absorbing asymmetry and heavy tails through its shape parameters ν and τ, making a preliminary log-transformation redundant — with fallback to BCPE and then Normal (NO) if BCT failed to converge (see Supplementary Table 3 for more details). For indices with values spanning the real line (e.g., Valence/FAA), the Normal family was retained regardless of the diagnostic criteria, as empirical testing confirmed that alternative families (JSU, SHASHo) did not improve centile calibration for the spike-and-slab marginal distribution (see Supplementary Fig. 8, Valence panel) characteristic of frontal alpha asymmetry in healthy populations. When fewer than two criteria indicated non-normality, the Normal family was used directly, with any requested pre-transformation (e.g., log for Arousal) applied before fitting. Let Y i denote the (transformed) value of a given EEG-derived index for subject i. The conditional distribution of Y i is assumed to follow a parametric family: Y i ~ D(µ i , σ i , ν i , τ i ) (1) where µ i is the conditional mean, σ i is the conditional standard deviation, and ν i and τ i are optional shape parameters governing skewness and kurtosis, respectively. For most EEG indices, modeling of µ i and σ i was sufficient; higher-order parameters were included only when residual diagnostics indicated significant departure from distributional assumptions. The conditional mean and dispersion were modeled as: µ i = f(age i ) (2) log(σ i ) = g(age i ) (3) where f(·) and g(·) are smooth functions of log(age) estimated as penalized B-splines (P-splines) using the pb() smoother of the gamlss R package (Rigby & Stasinopoulos, 2005 ). The degree of smoothing is selected automatically by minimizing a generalized Akaike information criterion (GAIC), avoiding the need to prespecify the number or location of knots. Both location and dispersion submodels are fitted jointly by alternating IRLS cycles (maximum 50 outer iterations). When residual diagnostics—specifically, worm plots and Q–Q plots of normalized quantile residuals—indicated significant departure from normality, operationalized as excess kurtosis greater than 5, the Box–Cox t (BCT) family was substituted for the Normal family to accommodate heavy-tailed distributions. For all remaining indices, the Normal (NO) conditional family was used. This adaptive family selection ensures distributional adequacy across the full set of indices, which differ substantially in tail behavior. 2.4.3. Electrode-level Spectral Normalization (ESN) A key preprocessing step before normative modeling is the removal of multiplicative amplitude variability that reflects physiological and technical sources unrelated to the neurophysiological indices of interest. These sources include individual differences in scalp and skull conductivity—which scale all electrode amplitudes by a subject-specific factor—and other externally related differences in electrode impedance, which introduce electrode-specific scale offsets that vary across acquisition systems. Critically, these two sources of variability are confounded and cannot be separated without detailed knowledge of the recording hardware. To address this, an Electrode-level Spectral Normalization factor (ESN) is computed for each subject i and electrode ch as: ESN(ch, i) = mean_f [ S(ch, f, i) ], f ∈ [0.39, 19.11] Hz (4) where S(ch, f, i) is the spectral power density at electrode ch, frequency bin f, and subject i, and the mean is taken over all frequency bins used in the computation of normative indices. The frequency range [0.39, 19.11] Hz is fixed and identical for all subjects and studies, ensuring that the ESN factor is strictly comparable across individuals and recording systems. Each spectral value is then normalized by division: S_norm(ch, f, i) = S(ch, f, i) / ESN(ch, i) (5) In log-scale, this corresponds to a subtraction: ln[Sₙₒ℠ₘ] = ln[S] − ln[ESN], making the ESN correction additive on the scale on which normative models are fitted. Equivalently, on the original power scale, the correction is multiplicative. This distinction is methodologically important: multiplicative normalization preserves the relative spectral structure within each subject while removing between-subject and between other recording-conditions-related scale differences. ESN corrects multiplicative amplitude differences per electrode within the analysis band but does not account for frequency-dependent transfer function differences across devices (e.g., differential roll-off slopes or filter characteristics). Studies combining equipment with substantially different spectral response characteristics should verify residual device effects in GAMLSS model residuals. A fundamental advantage of ESN normalization over device-covariate approaches is that it requires no knowledge of the recording equipment. It is therefore universally applicable: it can be applied to any EEG recording, including archival data, referral recordings, and recordings from systems not represented in the normative database—contexts in which a device covariate cannot be specified. This universality ensures that the normative framework developed here can be applied in the full range of clinical and research settings encountered in practice. Following ESN normalization, the conditional mean of the GAMLSS model contains only the age-dependent smooth term: µ i = f(age i ) (6) log(σ i ) = g(age i ) (7) where f(·) and g(·) are P-spline smoothers on log(age). The individualized Z-score for subject i with index value Y i is: Z i = [Y i − µ̂ i ] / σ̂ i (8) where µ̂ i and σ̂ i are the age-adjusted normative mean and standard deviation derived from the GAMLSS model. 2.4.4. Computation of Individualized Deviation Scores For any individual subject i with index value Y i measured at age t, the individualized Z-score under either normalization mode is interpreted as the number of age-adjusted standard deviations by which the observed measurement deviates from the normative expectation: Under conventional probabilistic thresholds: |Z| > 2.0 corresponds to approximately the 2.5th or 97.5th percentile of the normative population, indicating a borderline deviation. |Z| > 3.0 indicates a strong deviation, expected in fewer than 0.15% of neurotypical individuals of the same age. In addition to Z-scores, smooth age-dependent centile curves (5th, 10th, 25th, 50th, 75th, 90th, and 95th centiles) were generated for each index and electrode region, providing a reference for clinical and research use ( see Supplementary Table 2 ). 2.4.5. Model Validation The stability and predictive performance of the normative models were evaluated using several complementary procedures: k-fold cross-validation : Models were fitted on training subsets and evaluated on held-out data, with prediction error assessed separately within each age stratum. Residual diagnostics : Worm plots and Q-Q plots of normalized quantile residuals were inspected to verify distributional adequacy of the fitted models. Centile calibration : Empirical coverage of predicted centile intervals was compared against theoretical expectations across the full age range. Assessment of ESN normalization and model calibration : Assessment of ESN normalization: The reduction in inter-subject spectral amplitude variability following per-electrode ESN correction was quantified, and centile calibration was verified after normalization ( see Supplementary Fig. 10 ). Model calibration was assessed through two complementary procedures reported in Supplementary Tables 1 and 2: (1) the percentage of normative subjects with normalized quantile residuals |Z| > 1.96, computed using R's internal quantile residual diagnostics and expected to approximate 5.0% under a well-calibrated model; and (2) empirical centile coverage, evaluated by comparing each subject's observed value against the age-interpolated centile curve across seven thresholds (p2.5 through p97.5). 2.5. Software and Implementation Spectral analysis and preprocessing were implemented in MATLAB (R2015a). Normative modeling was performed in R (v4.3) using the gamlss package (Rigby & Stasinopoulos, 2005 ; Stasinopoulos & Rigby, 2007 (Stasinopoulos and Rigby 2007 )). For each index, a two-parameter GAMLSS model with P-spline smoothers on log(age) was fitted using the pb() function, with automatic smoothing parameter selection via GAIC. Inter-site and inter-individual amplitude variability was addressed through Electrode-level Spectral Normalization (ESN) applied at the electrode level before index computation (see Section 2.4.3 ) rather than as a separate preprocessing step. Topographic Z-score interpolation for electrode-level surfaces was performed using spherical spline interpolation of order 4 [Perrin et al., 1989 ]. 3. Results 3.1. Distribution of EEG Spectral Indices and Transformation Assessment The distribution of each spectral index was first examined across the full normative sample. Most indices displayed moderate skewness, typical of ratio-based measures derived from spectral power. Log-transformations were applied when appropriate to stabilize variance and improve model fit. Gaussian models for all major indices satisfactorily approximated post-transformation residual distributions. 3.2. Age-Dependent Normative Trajectories Normative trajectories estimated via GAMLSS revealed significant nonlinear developmental patterns for several indices (see Fig. 4 ). The theta/beta ratio decreased markedly from childhood to early adulthood, consistent with the maturation of attentional networks and the progressive reduction in slow oscillatory activity. The delta/beta ratio showed a similar decreasing trajectory. In contrast, the alpha/delta ratio and IAF exhibited progressive increases during adolescence followed by stabilization in adulthood, consistent with well-known developmental strengthening of alpha oscillations and thalamocortical maturation. Complete normative centile trajectories for all 19 electrode-level indices are provided as Supplementary Figures. Each supplementary figure displays, for a given index, the age-dependent normative mean and ± 1.96σ interval estimated by the GAMLSS model alongside individual observations from the HarMNqEEG normative database, arranged by electrode according to the standard 10–20 spatial layout. 3.3. Normative Centile Curves and Z-score Distributions Formal calibration diagnostics confirmed adequate model performance for all indices. In Supplementary Tables 1 and 2, we show the results for three of the most popular and used indices: Arousal, Valence, and TBR (Theta/Beta Ratio). TBR and Arousal Index models showed excellent calibration across all centile thresholds (max |Δ| < 1.4 pp and < 1.0 pp, respectively; residual rates within 0.1 pp of the nominal 5.0%). The Valence Index showed adequate global calibration (5.11% residuals outside ± 1.96σ) but systematic underdispersion in the central quantiles (p25: −10 pp; p75: +10 pp), reflecting the spike-and-slab character of the FAA distribution in healthy populations (see Supplementary Fig. 10 for the Valence Index individual distribution along the age). This limits normative precision in the intermediate range (|Z| 2). Device-stratified residual diagnostics confirmed the absence of clinically meaningful equipment-related bias across all indices (see Supplementary Fig. 10, panel A). 3.4. Clinical Case Illustrations To illustrate the clinical utility of the normative framework developed in this study, we present a representative pre–post intervention case from a neurorehabilitation program. This case demonstrates several key measurement dimensions covered by the normative models: broadband spectral amplitudes, functional state indices (arousal, emotional valence), and spectral ratios across multiple recording conditions (eyes-closed, eyes-open, and cognitive load). 3.4.1. Case Description The participant is an 8-year-old male (initials B.M., data used with institutional consent) from Mexico, presenting with a clinical diagnosis of dysexecutive syndrome—characterized by deficits in working memory, cognitive flexibility, inhibitory control, and goal-directed behavior. He received 21 sessions of transcranial direct current stimulation (tDCS) combined with cognitive-motor neurorehabilitation using the Kinestesia therapeutic video-game platform, targeting frontal executive networks. Quantitative EEG (qEEG) was recorded under standardized eyes-closed (EC), eyes-open (EO), and cognitive load (CL) conditions before and after the intervention. Broadband spectral power (absolute power, relative power, mean frequency), spectral ratios, and functional state indices were computed following the pipeline described in Section 2.3 . For the EC condition, normative Z-scores were derived using the age-matched models developed in this study. 3.4.2. Spectral Changes Pre-intervention qEEG showed a global mean EEG frequency between 5.86 and 7.81 Hz — below the age-expected range for an 8-year-old — with slow-frequency dominance consistent with the attentional and executive profile. Following intervention, mean EEG frequency increased to 5.86–8.3 Hz overall, reaching 8.3 Hz in posterior regions, indicating a shift toward a more mature, faster-dominant spectral composition. This change was accompanied by a well-defined anterior-to-posterior frequency gradient, which was less organized pre-intervention. No deviations from normative references were detected post-intervention in broadband or narrowband spectral analyses, except for a mild and circumscribed increase in spectral energy in the 10.16–10.55 Hz sub-band. Figures 5 A and 5 B illustrate electrode-level spectral ratios (delta/beta, theta/alpha, theta/beta, delta/alpha) and absolute spectral amplitudes in the eyes-open condition. Consistent reductions in slow-to-fast ratios were observed post-intervention across frontal and central sites, with the largest changes in theta/beta and delta/beta. Absolute spectral amplitudes confirmed this pattern: marked reductions in delta and theta were observed at nearly all electrode sites, particularly prominent at Cz and frontal locations (delta: Cz pre ≈ 95 µV, post ≈ 25 µV; theta: Cz pre ≈ 85 µV, post ≈ 40 µV). Beta amplitude showed selective increases at Cz and F4, consistent with enhanced frontocentral activation. The Z-score theta/beta ratio at F3 decreased from 0.48 to 0.03 (− 93.7%) and at F4 from 0.47 to 0.30 (− 36.2%), representing near-complete normalization of frontal attentional regulation indices (Arns et al. 2013 ; Ogrim et al. 2012 ). The individual alpha peak frequency increased from 9.38 to 9.77 Hz (+ 4.1%), consistent with accelerated thalamocortical maturation. 3.4.3. Functional State Indices and Z-Score Normalization Figure 5 . Pre–post neurorehabilitation EEG changes in a representative clinical case (B.M., 8 years, dysexecutive syndrome). Quantitative EEG was recorded before and after the therapeutic intervention under eyes-open (OA) and cognitive load (UT) conditions. Blue: pre-intervention; orange: post-intervention. (A) Spectral ratios — eyes open. Pre–post trajectories of four log-ratio indices (delta/beta, theta/alpha, theta/beta, delta/alpha) across eight electrodes (Fz, Cz, F3, F4, T5, T6, O1, O2). Green shading indicates post > pre (increase); red shading indicates post < pre (reduction). Consistent reductions in slow-to-fast ratios are observed across frontal and central sites, with the largest changes in theta/beta and delta/beta, reflecting reduced slow-wave dominance and improved cortical activation. (B) Spectral amplitudes — eyes open. Absolute spectral power (µV) pre and post for delta, theta, alpha, and beta bands across the same electrode set. Arrows indicate the direction of change at each electrode; orange arrows indicate reduction (post pre). Marked reductions in delta and theta amplitude are observed at frontal and central sites (notably Cz and F3), alongside selective beta increases at Cz and F4, consistent with enhanced frontocentral activation. (C) Functional state indices. Pre–post bar comparison of the Arousal and Valence (frontal alpha asymmetry) indices under OA and UT conditions. Arrows indicate the magnitude and direction of change (Δ). Post-intervention increases in Arousal and Valence under OA reflect enhanced cortical activation; the reduction in Valence under UT suggests a shift toward right-hemisphere dominance under cognitive demand, consistent with reduced frontal cognitive load. (D) Emotional regulation Z-scores (eyes-closed condition). Pre–post comparison of Valence and Arousal expressed as normative Z-scores derived from the age-matched models developed in this study. The shaded band indicates the ± 1 SD normative range (Z = ± 1). Pre-intervention Valence deviated markedly from the norm (Z = + 2.20), returning to within the normative range post-intervention (Z = − 0.50). Arousal showed a smaller but consistent shift toward normalization. The dashed line marks Z = 0 (population mean). Figure 5 D shows the pre–post Z-score comparison of Valence and Arousal in the eyes-closed condition, anchored to the age-matched normative models developed in this study. The Valence index (frontal alpha asymmetry, FAA) shifted from Z = + 2.20 pre-intervention to Z = − 0.50 post-intervention — a reduction of more than 2.7 standard deviations into the normative range — consistent with normalization of pathological left-hemisphere alpha dominance. The Arousal index showed a parallel shift from Z = − 0.62 to Z = − 0.50, remaining within the normative band throughout but moving toward the population mean. These shifts in the eyes-closed condition are complemented by the broader pattern of functional index changes observed across states: in the eyes-closed condition, the Valence index had shown a marked deviation of Z = − 2.82 pre-intervention, returning to Z = − 0.61 post-intervention, while the Arousal index decreased by 0.10, together reflecting a generalized normalization of the neurophysiological state at rest. These results are clinically corroborated by the expert neurologist's assessment, which noted improved organization of the resting EEG, a stable and well-organized posterior alpha rhythm, and only mild intermittent disturbance of frontal-temporal activity — a substantially improved profile relative to the pre-intervention recording. The quantitative indices provide an objective, reproducible complement to visual inspection, anchoring the observed changes within a normative probabilistic framework and enabling their direct comparison against age-expected population distributions. 3.4.4. The Need for Multi-State Normative References This case also highlights a methodological gap that the present framework only partially addresses. The most clinically informative changes were observed not only in the eyes-closed resting condition—for which normative models are available—but in the EO and CL conditions (Figs. 5 A– 5 B). The reduction in theta/beta ratio under cognitive load, the increase in beta amplitude at frontal sites during EO, and the modulation of Arousal and Valence indices across conditions all constitute evidence of improved neurophysiological function that cannot currently be anchored to age-expected norms, because lifespan normative references for EO and cognitive activation conditions remain unavailable. This observation reinforces the call for future normative databases incorporating multi-state recording protocols (see Section 4.5.1 ) and underscores that the clinical interpretability of qEEG as a therapeutic monitoring tool depends critically on the availability of condition-specific normative references. 4. Discussion The present study contributes to the ongoing revival of quantitative EEG by embedding a clinically relevant family of derived spectral indices within age-dependent probabilistic normative frameworks. The resulting models enable individualized inference—answering not merely whether brain activity is atypical, but by how much and in which direction relative to the population norm for a given age. In doing so, this work revisits the original vision of neurometrics while integrating the computational and data-harmonization advances of modern neuroscience. 4.1. From Qualitative Heuristics to Normative Precision For decades, clinical EEG practice has relied on expert visual inspection to identify paroxysmal activity, focal slowing, or diffuse abnormalities. While this remains essential for the detection of unambiguous pathology, it systematically discards the wealth of information encoded in quantitative spectral features. The neurometrics framework proposed by John et al. (John 1977 ; John et al. 1988 ) articulated a compelling alternative: brain function follows predictable statistical trajectories across the lifespan that can be modeled, and departures from these trajectories can be expressed as probabilistic scores amenable to clinical interpretation. The present results demonstrate that this principle extends naturally to derived spectral ratios and composite functional indices. A theta/beta ratio reported as a raw value has no intrinsic clinical meaning; the same value expressed as a Z-score of + 2.5 relative to an age-matched normative distribution immediately communicates a meaningful deviation, with a probability of occurrence below 1.2% in a neurotypical population of that age. This translation from measurement to inference is what distinguishes a normative biomarker from a descriptive metric, and it is precisely the translation that routine clinical reports currently fail to provide (Ko et al. 2021 ; Prichep 2005 ). 4.2. Functional Indices as Evidence of Therapeutic Efficacy One of the most clinically significant contributions of this framework lies in the extension of normative modeling beyond simple spectral power to functional indices of arousal, emotional valence, and cognitive engagement. These composite metrics have been repeatedly linked to neuropsychiatric conditions and to the outcomes of therapeutic interventions: theta/beta elevation in attentional dysregulation (Arns et al. 2013 ; Ogrim et al. 2012 ), frontal alpha asymmetry in mood disorders and affective valence (Davidson 1998 ; Smith et al. 2017 ), engagement index reduction in fatigue and inattention (Pope et al. 1995 ), and arousal index perturbations in vigilance disorders (Hegerl et al. 2012 ; Olbrich et al. 2015 ). However, the clinical utility of these indices has been severely constrained by the absence of normative reference values. Without such references, pre–post comparisons in therapeutic monitoring yield only directional information—the index increased or decreased—without any indication of whether the change represents movement toward, arrival at, or departure from normotypical function. A patient whose frontal alpha asymmetry shifts from Z = − 2.8 to Z = − 1.2 following treatment has improved substantially in neurophysiological terms, even if the absolute index value remains in a range that appears clinically abnormal without normative context. Conversely, a patient who moves from Z = − 0.4 to Z = − 0.8 may show a numerically similar absolute change that is actually a mild deterioration within the normative range. The normative Z-score framework resolves this ambiguity by providing a principled measure of the direction and magnitude of neurophysiological change relative to the population distribution. This constitutes a qualitative upgrade in the evidential value of longitudinal qEEG monitoring—from a descriptive record of change to a quantitative index of normalization—that is directly relevant to evidence-based neurorehabilitation (Kropotov 2009 ; Kropotov 2016 ; Collura et al. 2010 ). 4.3. Electrode-level Spectral Normalization: A Universal and Principled Preprocessing Step A distinctive methodological contribution of this work is the adoption of Electrode-level Spectral Normalization (ESN) as a universal preprocessing step applied to each electrode’s spectral values before index computation. Technical variability between EEG acquisition systems—arising from differences in amplifier characteristics, electrode impedance standards, reference schemes, and digital filtering—constitutes a well-documented source of systematic variance in spectral estimates that is unrelated to neurophysiology (Li et al. 2022 ). At the same time, individual differences in scalp and skull conductivity introduce subject-specific multiplicative scale factors that affect all electrodes simultaneously. Both sources of variability are multiplicative on the power scale and therefore appear as additive offsets in log-transformed spectral values—precisely the scale on which normative indices are computed. 4.4. Relation to the Normative Modeling Tradition in Neuroscience The present work aligns with a broader movement in computational neuroscience toward normative modeling as a framework for understanding individual variability in brain measurements (Marquand et al. 2016 ). Marquand et al. ( 2016 ) articulated the key insight that heterogeneous clinical populations cannot be understood through group-mean comparisons alone but require individual-level deviation scores relative to a well-characterized healthy distribution. Subsequent applications of this paradigm to structural MRI—including the large-scale lifespan brain charts of Bethlehem et al. (Bethlehem et al. 2022 )—have demonstrated its value for identifying individuals whose brain measurements deviate from typical developmental trajectories, independently of diagnostic category. Quantitative EEG is particularly well-suited for this approach. Its low cost, temporal resolution, and widespread clinical availability make it a practical complement to MRI-based normative atlases, extending the reach of normative modeling to settings where structural or functional neuroimaging is unavailable. The HarMNqEEG database (Li et al. 2022 ), with its multinational harmonized design and lifespan coverage, provides a foundation for qEEG normative modeling that is broadly comparable in scope—if not yet in spatial resolution—to the large neuroimaging datasets underlying MRI brain charts. 4.5. Limitations and Future Directions Complementarity with EEG Microstate Normative Frameworks. The spectral normative framework developed here is complementary to the microstate-based normative tradition pioneered by Koenig, Michel, and colleagues (Koenig et al. 2002 ; Michel and Koenig 2018 ). The two frameworks address orthogonal dimensions of spontaneous brain dynamics: momentary global field topography (microstates) versus frequency-domain composition (spectral ratios). Both have converged on the same normative imperative: individual measurements acquire clinical meaning only when anchored to age-expected population distributions (Koenig et al. 2002 ; Marquand et al. 2016 ; Bethlehem et al. 2022 ). Future work integrating both frameworks within a unified lifespan reference would provide a substantially richer normative atlas of human brain electrophysiology. Several limitations of the present work merit explicit acknowledgment. First, the HarMNqEEG database is exclusively restricted to eyes-closed resting-state recordings. While this condition provides the most stable and reproducible baseline for normative reference, it necessarily leaves uncharacterized a clinically important dimension of EEG dynamics: the brain's response to external stimulation and cognitive demand. Alpha reactivity upon eye opening—a robust index of thalamocortical integrity (Pfurtscheller and Lopes da Silva 1999 ; Fonseca et al. 2011 )—and electrophysiological changes during mental arithmetic, working-memory tasks, or hyperventilation may reveal abnormalities that are invisible at rest. Future normative databases should prioritize the harmonized collection of eyes-open and cognitive activation recordings to enable "functional neurometrics" that capture the full dynamic repertoire of the human brain. Second, inter-site technical variability is addressed through ESN rather than Riemannian harmonization of the cross-spectral matrices (Li et al. 2022 ). This choice is deliberate: Riemannian harmonization operates on the full cross-spectral tensor and efficiently removes site-level biases in the covariance geometry, but it introduces cross-electrode mixing that removes the direct neurophysiological interpretation of per-electrode spectral ratios and asymmetry indices. ESN corrects for multiplicative amplitude offsets while preserving the electrode-level meaning of each index, without requiring knowledge of the acquisition system. Riemannian harmonization remains a valuable approach for applications where the full covariance structure is the object of interest, such as source imaging and functional connectivity analysis. Third, the present normative models were derived exclusively from resting-state spectral features and do not incorporate source-level information. The integration of electromagnetic source imaging methods such as VARETA (Bosch-Bayard et al. 2001 ) and sLORETA (Pascual-Marqui 2002 ) within a normative framework would allow the localization of deviating generators, adding a spatial dimension to the probabilistic biomarker approach. This extension is technically feasible within the HarMNqEEG infrastructure and constitutes a natural next step toward a comprehensive normative atlas of human brain electrophysiology. Finally, the clinical validation of these normative indices as diagnostic or prognostic biomarkers in specific neurological and psychiatric conditions—ADHD, mood disorders, mild cognitive impairment, epilepsy—requires prospective studies comparing Z-score profiles against gold-standard clinical diagnoses and longitudinal outcomes. The normative models presented here provide the infrastructure for such studies; their clinical sensitivity and specificity remain to be established across patient populations. 4.5.1. Toward Cognitive Activation Norms: A Proposed Protocol To our knowledge, normative qEEG frameworks have focused predominantly on eyes-closed resting conditions. However, the inclusion of brief cognitive challenge blocks may substantially enrich clinical interpretation by revealing how EEG-derived biomarkers change under increasing mental demand. Existing literature supports the use of such tasks as practical probes of arousal, workload, and executive function (Fairclough et al. 2024 ; Onton et al. 2005 ; Borghini et al. 2014 ), although normative lifespan references for these activation conditions remain largely unavailable. From a practical standpoint, the most clinically defensible approach is a short sequential protocol that establishes a graded continuum from baseline resting state to executive load, using only verbal instructions and no additional materials. Based on the available EEG literature on cognitive workload (Fairclough et al. 2024 ; Onton et al. 2005 ; Borghini et al. 2014 ) and clinical practice guidelines (Swingle 2015 ), the following six-block protocol is proposed as a future standard for normative expansion (see Table 1 ): Block 1 — Eyes closed (EC) : 2–3 min. Thalamocortical baseline; standard HarMNqEEG reference condition. Block 2 — Eyes open (EO) : 1–2 min. Physiological activation; alpha reactivity and EC→EO modulation. Block 3 — Backward counting (easy) : 30–60 s. Count backward from 100 by 1s. Sustained attention and executive control. Block 4 — Serial subtraction (hard) : 30–90 s. Subtract 7s from 100 mentally. Cognitive load, working memory, and inhibitory control. Block 5 — Backward digit span : 1–2 min. Repeat digit sequences in reverse. Working-memory manipulation. Block 6 — Covert verbal fluency : 30–60 s. Generate as many animal names as possible mentally. Lexical retrieval and executive search. This gradient ranges from simple physiological activation (EC→EO) to genuine executive and working-memory demands. Swingle explicitly recommends including an eyes-open condition and a cognitive challenge, such as reading or counting backwards, noting that certain EEG patterns emerge only under cognitive demand and are invisible at rest (Swingle 2015 ). Tasks involving overt speech should be avoided due to electromyographic contamination; covert or minimal-response variants are strongly preferred. Table 2 summarizes the key properties of the proposed tasks. Table 1 Brief cognitive challenge tasks that can be integrated into a resting-state qEEG protocol, ordered by increasing cognitive demand. Tasks are proposed as a future extension of eyes-closed normative protocols to capture EEG dynamics under graded activation conditions. Task Domain probed Typical instruction Duration Main advantages Limitations / artifacts Clinical utility in qEEG Eyes open (EO) Arousal/alpha reactivity "Eyes open, look straight ahead." 1–3 min No materials; standardized Eye blinks, saccades Alpha reactivity; EC→EO modulation (Barry et al., 2017) Backward counting Sustained attention, executive control "Count backward from 100 to 1." 30–60 s Easy; scalable; no materials Overt speech adds EMG; use covert Practical challenge; recommended by Swingle/ClinicalQ (Swingle 2015 ) Serial subtraction Cognitive load, working memory, inhibitory control "Subtract 7s from 100 mentally." 30–90 s Strong EEG workload literature; adjustable difficulty Overt response contaminates the EEG; arithmetic skill confound Best no-equipment workload task for brief EEG blocks (Fairclough et al. 2024 ) Backward digit span Working memory manipulation "Repeat these digits backwards." 1–2 min Well-defined executive demand; adaptable Examiner timing required; overt artifacts Frontal-executive probe; sensitive to WM capacity (Onton et al. 2005 ) Covert verbal fluency Lexical retrieval, executive search "Think of as many animals as possible." 30–60 s No materials; language/executive load Compliance harder to verify if fully covert Frontal/language network assessment (Borghini et al. 2014 ) EC = eyes closed; EO = eyes open; EMG = electromyographic artifact; WM = working memory. Covert or minimal-response variants are preferred to minimize signal contamination. References in brackets correspond to citations in the main text. 5. Conclusions Reclaiming quantitative EEG as a primary diagnostic and monitoring instrument is not a nostalgic return to the past, but a scientifically grounded necessity for modern precision neurophysiology. The normative models presented here—for spectral power ratios, cognitive-emotional state indices, and physiological parameters—provide the statistical infrastructure required to transform descriptive EEG metrics into probabilistic clinical biomarkers. By anchoring individual measurements to age-adjusted population distributions and expressing deviations as Z-scores under the unified ESN-normalized framework, clinicians gain direct, interpretable answers to the questions that matter most in practice: Is this patient's brain activity typical for their age? Has treatment produced a neurophysiologically meaningful change toward normotypical function? The use of GAMLSS modeling captures the non-linear developmental trajectories of EEG indices across the lifespan and appropriately represents age-dependent changes in both expected values and inter-individual variability—properties that earlier normative approaches based on fixed-variance linear models could not accommodate. The ESN normalization strategy ensures that the framework remains applicable across the full spectrum of clinical recording contexts, from well-documented research-grade EEG to legacy or minimally documented clinical files, without sacrificing methodological transparency. To our knowledge, this represents the first systematic effort to construct harmonized, multinational normative models for this family of derived functional qEEG indices. The work establishes the foundational normative layer for eyes-closed resting-state conditions. Future extensions—incorporating eyes-open, cognitive activation, hyperventilation, and photic stimulation conditions, and integrating source-level normative mapping—will complete the transition from static to functional neurometrics and fulfill the original promise of quantitative EEG as an objective, individualized tool for evidence-based neurorehabilitation. Declarations Acknowledgements The authors thank the HarMNqEEG consortium for making the multinational normative database publicly available, and the participants of all contributing sites. The clinical case illustration was provided by CIMMCO (Querétaro, México). Competing Interests The authors have no relevant financial or non-financial interests to disclose. Funding JBB was partially funded by the German Research Foundation core facility, grant INST 184/216-1. Author Contributions Jorge Bosch-Bayard: Conceptualization, Methodology, Formal analysis, Software, Writing – original draft, Writing – review & editing, Data curation, Supervision. J. Guerrero-Sauzameda: Conceptualization, Formal analysis, Visualization, Writing – original draft, Writing – review & editing. R. Bosch-Bayard: Conceptualization; Writing – review & editing. R. Pérez-Elvira: Writing – review & editing. A. Bosch-Castro, J. Sánchez-Rodríguez, A. Flores, K. Flores, E. Resendiz-Flores: Visualization, Figures Design, testing, review & editing. A. Ferrando, P. Ferrando: Data curation, Writing – review & editing. L. Galán-García: Methodology, Data curation, Writing – review & editing. P. Valdes-Sosa: Methodology, Data curation, Writing – review & editing. G.A. Chiarenza: Conceptualization; Writing – review & editing. R.J. Biscay: Methodology, Conceptualization; Writing – review & editing. L. Morales-Chacón: Conceptualization, Methodology, Formal analysis, Data curation, Supervision, Writing – review & editing. Ethics Approval and Informed Consent The HarMNqEEG normative dataset was derived from retrospectively harmonized data collected under institutional ethics approvals at each contributing site (Li et al. 2022). The clinical case illustration (Section 3.4) was obtained with institutional approval and written informed consent from the participant’s legal guardian. All procedures comply with the Declaration of Helsinki. Data Availability The HarMNqEEG normative database is publicly available at https://github.com/CCC-members/HarMNqEEG. GAMLSS model parameters, centile curves, and Z-score computation scripts (MATLAB/R) will be released under an open-source license upon acceptance. 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Int J Psychophysiol 18(1):49–65 Perrin F, Pernier J, Bertrand O, Echallier JF (1989) Spherical splines for scalp potential and current density mapping. Electroencephalogr Clin Neurophysiol 72(2):184–187. https://doi.org/10.1016/0013-4694(89)90180-6 Pfurtscheller G, Lopes da Silva FH (1999) Event-related EEG/MEG synchronization and desynchronization: Basic principles. Clin Neurophysiol 110(11):1842–1857. https://doi.org/10.1016/S1388-2457(99)00141-8 Pope AT, Bogart EH, Bartolome DS (1995) Biocybernetic system evaluates indices of operator engagement in automated task. Biol Psychol 40(1–2):187–195. https://doi.org/10.1016/0301-0511(95)05116-3 Prichep LS (2005) Use of normative databases and statistical methods in demonstrating clinical utility of QEEG. Clin EEG Neurosci 36(2):82–87. https://doi.org/10.1177/155005940503600206 Rajkumar R, Ripp I, Kramer D, Bhatt D, Bali S, Bhatt A (2021) Comparison of EEG microstates with resting state fMRI and FDG-PET measures. 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Clin Electroencephalogr 31(1):45–55 Swingle PG (2015) Biofeedback for the Brain: How Neurotherapy Effectively Treats Depression, ADHD, Autism, and More. Rutgers University Press, New Brunswick Szava S, Valdés P, Biscay R, Galán L, Bosch J, Clark I, Jiménez JC (1994) High resolution quantitative EEG analysis. Brain Topogr 6(3):211–219. https://doi.org/10.1007/BF01187711 Thatcher RW, Lubar JF (2009) History of the scientific standards of QEEG normative databases. In: Budzynski TH et al (eds) Introduction to Quantitative EEG and Neurofeedback, 2nd edn. Academic Thatcher RW, Moore N, John ER, Duffy F, Hughes JR, Krieger M (2003) Quantitative EEG normative databases: Validation and clinical correlation. J Neurotherapy 7(3–4):87–121 Thatcher RW, Walker RA, Gerson I, Geisler FH (1989) EEG discriminant analyses of mild head trauma. Electroencephalogr Clin Neurophysiol 73(2):94–106 Turner RP (2021) Clinical application of combined EEG-qEEG functional neuroimaging. Clin EEG Neurosci 52(1):4–10. https://doi.org/10.1177/1550059420959232 Valdés-Sosa PA, Galán-García L, Bosch-Bayard J, Bringas-Vega ML, Aubert-Vazquez E, Rodriguez-Gil I et al (2021) The Cuban Human Brain Mapping Project, a young and middle age population-based EEG, MRI, and cognition dataset. Sci Data 8:45. https://doi.org/10.1038/s41597-021-00829-7 Valdés-Sosa et al (1990) Esta referencia corresponde a las developmental surfaces — las ecuaciones normativas de alta resolución espectral en. Springer, Brain Topography Valdés-Sosa PA, Biscay R, Galán L, Bosch J, Szava S, Virues T (1990) High resolution spectral EEG norms for topography. Brain Topogr 3:281–282. https://doi.org/10.1007/BF01187711 Additional Declarations No competing interests reported. Supplementary Files qeegbacktofuturebtopSupplementary.docx Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 15 May, 2026 Reviews received at journal 07 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviews received at journal 02 May, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers invited by journal 13 Apr, 2026 Editor assigned by journal 08 Apr, 2026 Submission checks completed at journal 08 Apr, 2026 First submitted to journal 06 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Chiarenza","email":"","orcid":"","institution":"Centro Internazionale Disturbi di Apprendimento, Attenzione, Iperattività, CIDAAI","correspondingAuthor":false,"prefix":"","firstName":"Giuseppe","middleName":"A.","lastName":"Chiarenza","suffix":""},{"id":622430516,"identity":"ef21c983-99cc-429a-b455-1e622e1fa5ee","order_by":14,"name":"Rolando J. Biscay","email":"","orcid":"","institution":"Centro de Investigaciones en Matemática (CIMAT)","correspondingAuthor":false,"prefix":"","firstName":"Rolando","middleName":"J.","lastName":"Biscay","suffix":""},{"id":622430518,"identity":"c1b4d01d-7a6a-4629-82b3-9df539c6268a","order_by":15,"name":"Lilia Morales-Chacón","email":"","orcid":"","institution":"Universidad Internacional De La Rioja","correspondingAuthor":false,"prefix":"","firstName":"Lilia","middleName":"","lastName":"Morales-Chacón","suffix":""}],"badges":[],"createdAt":"2026-04-06 11:23:52","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9333312/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9333312/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107378098,"identity":"ed11b5aa-346f-46cb-8883-ab087aa01085","added_by":"auto","created_at":"2026-04-21 01:33:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":347070,"visible":true,"origin":"","legend":"\u003cp\u003eBack to the Future of quantitative EEG: historical development, conceptual evolution, and clinical translation pipeline. (A) Historical timeline. Key milestones in EEG analysis from Berger's first recording (1929) to the present. The red band marks the relative decline of qEEG during the neuroimaging era (1990s), when MRI, fMRI, and PET shifted clinical and scientific attention toward hemodynamic modalities. The green band marks the ongoing renaissance, driven by three convergent lines of methodological progress: the development of distributed electromagnetic source imaging methods — including LORETA (Pascual-Marqui 2002) and qEEG VARETA (Bosch-Bayard et al. 2001), which extended quantitative EEG analysis to the cortical source level; the formalization of EEG microstate analysis as a normative framework for global spatiotemporal field dynamics (Lehmann et al. 1987; Koenig et al. 2002; Michel and Koenig 2018); and the availability of large multinational normative databases such as HarMNqEEG (Li et al. 2022). (B) Conceptual shift. The progressive transition from qualitative visual inspection to quantitative spectral analysis, normative modeling, and individualized probabilistic clinical biomarkers. The present study occupies the fourth stage, providing age-dependent normative references for derived spectral indices. (C) Clinical translation pipeline. The complete workflow from EEG acquisition (eyes-closed, eyes-open, and cognitive load conditions) through index computation, GAMLSS-based normative modeling, and individualized Z-score derivation, to pre–post therapeutic monitoring. The normative model is trained on the HarMNqEEG database (dashed input arrow). The dashed feedback loop illustrates longitudinal use for monitoring neurophysiological change across therapeutic interventions.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/4f9d9f21605719cae78de132.png"},{"id":107489686,"identity":"defb7318-e734-48fb-b9e4-6030b9a9c50c","added_by":"auto","created_at":"2026-04-22 02:48:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":478619,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eComputational pipeline for normative qEEG index modeling.\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e Acquisition (gray): Resting-state EEG recordings from the HarMNqEEG database (n = 1,564; ages 5–97 years; 9 countries) under eyes-closed (EC), eyes-open (EO), and cognitive load (CL) conditions, 19-electrode 10–20 system. Preprocessing (gray): Three sequential steps — (1) artifact rejection retaining a minimum of 60 seconds of stationary, artifact-free signal; (2) re-referencing to the common average reference; and (3) Electrode-level Spectral Normalization (ESN), in which each electrode’s spectral values are divided by their mean power across the fixed frequency range [0.39–19.11 Hz]. This operation is multiplicative on the power scale and additive on the log scale, simultaneously removing individual-level variability in scalp and skull conductivity and other external-level variability in electrode impedance. Spectral decomposition (teal): Cross-spectral matrices computed via FFT at 0.39 Hz frequency resolution; power estimated in four canonical bands: delta (δ: 0.5–4 Hz), theta (θ: 4–8 Hz), alpha (α: 8–13 Hz), and beta (β: 13–30 Hz). Index computation (teal): Three families of derived indices — electrode-level spectral ratios (TBR, TAR, ABR, DBR, DAR; one normative model per electrode, 19 total); global functional state indices (EI, AI, FAA, CAI, FC-TBR, FC-DBR); and hemispheric asymmetry indices (δ/β and θ/β ratio asymmetries across 8 homologous electrode pairs). GAMLSS normative modeling (purple): A Generalized Additive Model for Location (μ), Scale (σ), and Shape (GAMLSS) was fitted per index and per electrode in R using P-spline smoothers on log(age) [pb(log(age))]; conditional distribution family selected adaptively — Normal (NO) for kurtosis ≤ 5, Box–Cox t (BCT) otherwise. Outputs (gray): Individualized Z-scores and smooth centile curves (p2.5, p10, p50, p90, p97.5) for each index and electrode across the full lifespan (ages 5–97 years).\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/6aa356c4c4cbd6b78cc5a29a.png"},{"id":107378100,"identity":"75e5fa26-4dea-42b7-b914-306db0eeddaa","added_by":"auto","created_at":"2026-04-21 01:33:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":164795,"visible":true,"origin":"","legend":"\u003cp\u003eAge-dependent normative centile curves for three representative qEEG indices across the human lifespan. Each panel displays individual observations from the HarMNqEEG normative database (n = 1,564; ages 5–97 years; grey dots) overlaid with smooth centile curves estimated by GAMLSS with P-spline smoothers on log(age). Shaded bands correspond to the 2.5–97.5th (lightest), 10–90th, and 25–75th (darkest) centile intervals; the solid line indicates the median (50th centile); dashed lines mark the 2.5th and 97.5th centiles. The x-axis is displayed on a logarithmic scale to compress the rapid developmental changes of childhood relative to the more gradual changes of adulthood. (A) Theta/Beta Ratio at Fz (TBR(Fz) = ln[θ(Fz)] − ln[β(Fz)]): a marker of attentional regulation and cortical arousal showing a pronounced age-dependent decrease from childhood to early adulthood, consistent with progressive cortical maturation and reduction of slow oscillatory dominance (Arns et al. 2013; Ogrim et al. 2012). (B) Arousal Index (AI = β̄_F / (δ̄_F + θ̄_F), frontal cluster F3–F4–Cz): an index of CNS activation level exhibiting a gradual increase across the lifespan, with greatest inter-individual variability in older age groups (Bonnet and Arand 2007). (C) Valence Index — Frontal Alpha Asymmetry (FAA = ln[α(F4)] − ln[α(F3)]): an index of hemispheric alpha lateralization linked to emotional valence, showing a near-zero median trajectory across the lifespan with wide normative dispersion, reflecting the high inter-individual variability of frontal asymmetry in a healthy population (Allen et al. 2018; Davidson 1998). Centile curves were derived following ESN normalization (see Section 2.4.3).\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/938f366b13813a770eb6051f.png"},{"id":107378102,"identity":"a03e9d8d-9de7-4f31-b379-88241e72f723","added_by":"auto","created_at":"2026-04-21 01:33:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":433872,"visible":true,"origin":"","legend":"\u003cp\u003eAge-dependent topographic distribution of normative median spectral ratio indices across five age groups. Each map displays the interpolated spatial distribution of the normative median (50th centile of the GAMLSS model) across the 19 electrodes of the standard 10–20 system, estimated at the representative age of each group. Color scale is centered at the median value of each index across all age groups, with red indicating higher values and blue indicating lower values; the scale is shared across age groups within each row to allow direct comparison of developmental change. Electrode positions follow the standard azimuthal projection (nose up). (Row 1) Theta/Beta Ratio (TBR): a pronounced fronto-central predominance is observed in childhood, with a systematic decrease in TBR values across all regions from childhood to adulthood, most marked in frontal and central sites, consistent with progressive cortical maturation and reduction of slow oscillatory dominance (Arns et al. 2013; Ogrim et al. 2012). (Row 2) Theta/Alpha Ratio (TAR): a broadly distributed slow-wave dominance pattern in childhood transitions toward a flatter, lower-amplitude distribution in adulthood, reflecting the developmental strengthening of alpha relative to theta activity. (Row 3) Delta/Beta Ratio (DBR): values are consistently higher in childhood and show a pronounced age-dependent decrease, particularly in frontal regions, consistent with the maturation of prefrontal inhibitory control and the progressive suppression of delta activity during wakefulness. DBR values at each age group represent the empirical median of subjects within the corresponding age window (5–10, 10–20, 20–40, 40–60, 60–80 years); remaining indices use the GAMLSS-estimated normative median interpolated at the representative age of each group (7.5, 15, 30, 50, 70 years). Spatial interpolation was performed using radial basis functions (thin-plate spline) on the electrode coordinates.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/f071fe78da8e571ff17c50dc.png"},{"id":107488553,"identity":"7d41058f-edd8-4783-92d1-e3412bb71252","added_by":"auto","created_at":"2026-04-22 02:45:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":224708,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003ePre–post neurorehabilitation EEG changes in a representative clinical case (B.M., 8 years, dysexecutive syndrome). Quantitative EEG was recorded before and after the therapeutic intervention under eyes-open (OA) and cognitive load (UT) conditions. Blue: pre-intervention; orange: post-intervention. (A) Spectral ratios — eyes open. Pre–post trajectories of four log-ratio indices (delta/beta, theta/alpha, theta/beta, delta/alpha) across eight electrodes (Fz, Cz, F3, F4, T5, T6, O1, O2). Green shading indicates post \u0026gt; pre (increase); red shading indicates post \u0026lt; pre (reduction). Consistent reductions in slow-to-fast ratios are observed across frontal and central sites, with the largest changes in theta/beta and delta/beta, reflecting reduced slow-wave dominance and improved cortical activation. (B) Spectral amplitudes — eyes open. Absolute spectral power (µV) pre and post for delta, theta, alpha, and beta bands across the same electrode set. Arrows indicate the direction of change at each electrode; orange arrows indicate reduction (post \u0026lt; pre), green arrows indicate increase (post \u0026gt; pre). Marked reductions in delta and theta amplitude are observed at frontal and central sites (notably Cz and F3), alongside selective beta increases at Cz and F4, consistent with enhanced frontocentral activation. (C) Functional state indices. Pre–post bar comparison of the Arousal and Valence (frontal alpha asymmetry) indices under OA and UT conditions. Arrows indicate the magnitude and direction of change (Δ). Post-intervention increases in Arousal and Valence under OA reflect enhanced cortical activation; the reduction in Valence under UT suggests a shift toward right-hemisphere dominance under cognitive demand, consistent with reduced frontal cognitive load. (D) Emotional regulation Z-scores (eyes-closed condition). Pre–post comparison of Valence and Arousal expressed as normative Z-scores derived from the age-matched models developed in this study. The shaded band indicates the ±1 SD normative range (Z = ±1). Pre-intervention Valence deviated markedly from the norm (Z = +2.20), returning to within the normative range post-intervention (Z = −0.50). Arousal showed a smaller but consistent shift toward normalization. The dashed line marks Z = 0 (population mean).\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/a452a671f3559ddd18830ad1.png"},{"id":107490166,"identity":"6b642e0f-5478-4740-b41c-7e0dd5111e2c","added_by":"auto","created_at":"2026-04-22 02:50:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2194447,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/9f34bc2d-039c-4dd8-93ff-fad979c7ad2b.pdf"},{"id":107378097,"identity":"53ba26ec-97d9-483f-b1a6-6f952c81af26","added_by":"auto","created_at":"2026-04-21 01:33:21","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":6475664,"visible":true,"origin":"","legend":"","description":"","filename":"qeegbacktofuturebtopSupplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-9333312/v1/4682d3df40386577c76bad8d.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Back to the Future of Quantitative EEG: Normative Biomarkers from Spectral Ratios and Functional Indices for Diagnosis and Therapeutic Monitoring","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe electroencephalogram (EEG) occupies a singular position among clinical neurophysiological tools. Unlike functional magnetic resonance imaging (fMRI) or positron emission tomography (PET), which measure hemodynamic and metabolic correlates of neural activity with temporal resolution on the order of seconds, EEG directly records the electrical potentials generated by the postsynaptic currents of cortical neuronal populations with millisecond temporal resolution (Michel et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Rajkumar et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This direct access to neuronal dynamics, combined with its relatively low cost, portability, and bedside applicability, preserves the EEG's irreplaceable position in clinical neurology, cognitive neuroscience, and neurorehabilitation.\u003c/p\u003e \u003cp\u003eThe history of EEG analysis has followed a pendular trajectory. Following Hans Berger's seminal recordings in 1929, EEG established itself over several decades as the primary tool for evaluating brain function in clinical practice. During the 1970s and 1980s, the development of quantitative EEG (qEEG) introduced a fundamental conceptual shift: rather than relying solely on expert visual inspection of waveforms, EEG features could be extracted mathematically, characterized statistically, and interpreted against population norms. The pioneering work of Matoušek and Petersen (Matoušek and Petersen \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1973\u003c/span\u003e) on age-related EEG frequency analysis and the foundational contributions of E. Roy John and colleagues to the development of neurometrics (John \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1977\u003c/span\u003e; John et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) established the conceptual and methodological foundations for this approach. Neurometrics, as operationalized by John, constitutes a framework for quantitative EEG analysis that provides a precise and reproducible estimate of the deviation of an individual record from normality through statistical comparison with normative databases derived from large samples of healthy subjects (John et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1988\u003c/span\u003e), statistically, and interpreted against population norms.\u003c/p\u003e \u003cp\u003eThe 1990s witnessed a marked decline in the clinical prominence of qEEG. The rapid expansion of structural and functional neuroimaging\u0026mdash;MRI, PET, and functional MRI\u0026mdash;shifted scientific and clinical attention toward modalities offering superior spatial localization. This transition generated a partly unfounded belief that EEG was a diagnostic tool of relatively lower informative value compared to these emerging technologies (Turner \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBeginning in the early 2000s, however, a sustained renaissance of quantitative EEG started to consolidate, driven by the maturation of distributed electromagnetic source imaging methods, such as VARETA (Bosch-Bayard et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) and sLORETA (Pascual-Marqui \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), and the increasing availability of large-scale normative databases (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Valdes-Sosa et al., 2021; Bosch-Bayard et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Thatcher and Lubar 2009; Thatcher et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Valdes-Sosa et al., 1990; Szava et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e1994\u003c/span\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA).\u003c/p\u003e \u003cp\u003eAlongside these spectral and source imaging advances, a complementary tradition within quantitative EEG developed independently: the analysis of the global spatial configuration of the scalp potential field and its dynamics over time. Lehmann and colleagues established that the momentary electric field of the brain can be described by a small number of quasi-stable topographic configurations\u0026mdash;now termed EEG microstates\u0026mdash;whose spatial patterns, durations, and transition probabilities constitute fundamental descriptors of spontaneous brain dynamics (Lehmann et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Koenig, Michel, and collaborators subsequently demonstrated that the four canonical microstate classes follow systematic age-dependent normative trajectories across the human lifespan, with childhood-to-adulthood transitions in microstate duration and occurrence rates that parallel the maturational changes observed in spectral indices (Koenig et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The recent resurgence of interest in microstates\u0026mdash;driven by their robust correlation with large-scale resting-state fMRI networks (Rajkumar et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and their sensitivity to neurological and psychiatric conditions\u0026mdash;has established them as a complementary normative framework operating at the level of global field dynamics rather than frequency-domain features (Michel and Koenig \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The present work occupies a parallel and complementary niche: while microstate analysis characterizes the spatiotemporal architecture of brain electric fields, the spectral ratio and functional indices addressed here capture the frequency-domain composition of those same fields, providing clinically actionable biomarkers with direct electrode-level interpretability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDespite this methodological progress, routine clinical practice remains predominantly qualitative. EEG reports continue to rely primarily on expert visual descriptions, and, at best, on raw topographic maps of spectral power. The quantitative potential of normative maps, Z-scores, and derived functional indices is frequently underused. As a consequence, valuable information regarding how an individual's brain activity deviates from an age-typical population rarely enters formal clinical decision-making (Ko et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eA critical limitation of current clinical workflows is the reliance on raw pre and post\u0026ndash;treatment comparisons. Without reference to a normative framework, any observed change in an EEG index remains ambiguous: it is impossible to determine whether the observed shift represents movement toward neurotypical function, persistence within an abnormal range, or merely state-dependent fluctuation. Normative Z-score frameworks directly address this limitation by anchoring individual measurements to age-dependent population norms, enabling the clinician to quantify both the magnitude of initial deviation and the direction and significance of longitudinal change.\u003c/p\u003e \u003cp\u003eAn additional gap concerns the limited exploitation of multiple physiological states within qEEG protocols. Parameters assessed during eyes-open recording\u0026mdash;such as alpha rhythm reactivity to eye opening\u0026mdash;as well as responses to activation procedures (hyperventilation, photic stimulation) and EEG dynamics under cognitive load, provide complementary windows onto neurophysiological integrity absent from resting eyes-closed recordings alone. The individual alpha frequency (IAF) and its age-related developmental trajectory constitute particularly sensitive markers of neurophysiological maturation and thalamocortical integrity (Klimesch \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Pfurtscheller and Lopes da Silva \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1999\u003c/span\u003e), yet they are seldom quantified within normative frameworks in routine clinical reports.\u003c/p\u003e \u003cp\u003eThis limitation is clinically relevant because some electrophysiological abnormalities may remain subtle at rest but become evident during cognitive activation. In clinical practice, Swingle has explicitly recommended complementing eyes-closed and eyes-open conditions with a brief cognitive challenge such as reading or counting backwards, noting that certain patterns emerge only when the patient is cognitively challenged (Swingle \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). From a physiological perspective, the transition from eyes-closed to eyes-open already constitutes a shift toward higher EEG arousal (Barry and De Blasio \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Barry et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Beyond this basic manipulation, mental arithmetic and serial subtraction paradigms offer a practical and well-supported way to induce graded cognitive load without additional materials (Fairclough et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), while backward digit span provides a brief probe of working-memory manipulation (Onton et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Although normative lifespan references for these activation conditions remain largely unavailable, their integration into future normative protocols would substantially enrich the clinical interpretability of qEEG-derived biomarkers.\u003c/p\u003e \u003cp\u003eAlthough several normative qEEG databases have been developed for spectral power and related Z-score inference, and harmonized multinational norms are now available for cross-spectral EEG measures, the literature remains comparatively sparse regarding clinically standardized normative references for derived frequency ratios and composite functional metrics. Indices such as theta/beta, delta/beta, frontal alpha asymmetry-related measures, arousal-related EEG markers, and engagement metrics have been widely studied, but mostly as research variables, group discriminators, or task-sensitive markers rather than as integrated age-referenced biomarkers for individualized clinical inference.\u003c/p\u003e \u003cp\u003eThe present study aims to fill this gap by providing the first systematic normative models for this family of indices derived from the HarMNqEEG project database (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), comprising 1,564 neurologically healthy subjects from 9 countries spanning the full human lifespan (ages 5 to 97). We derive age-dependent normative trajectories and individualized Z-scores and define a unified normative framework with electrode-level spectral normalization (ESN) to ensure applicability across the full range of clinical recording contexts.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. The HarMNqEEG Multinational Database\u003c/h2\u003e \u003cp\u003eThe normative data used in this study were derived from the Harmonized-Multinational qEEG Norms (HarMNqEEG) project, an international collaborative initiative coordinated by the Global Brain Consortium (GBC) (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The database comprises resting-state EEG recordings from 1,564 neurologically healthy subjects, spanning the full human lifespan from 5 to 97 years of age, collected across 9 countries: Cuba, China, Malaysia, Russia, Germany, Switzerland, Canada, Colombia, and the United States. Data were obtained from 14 independent studies conducted with 12 different EEG acquisition systems, reflecting the diversity of equipment and protocols encountered in international multicenter research.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e2.1.1. Inclusion and Exclusion Criteria\u003c/h2\u003e \u003cp\u003eParticipants were selected according to strict clinical criteria designed to constitute a representative healthy population rather than a highly selected \"super-normal\" sample. Exclusion criteria included: history of neurological or psychiatric disorders; current or recent use of psychoactive medications or substances with known effects on the central nervous system; significant head trauma or loss of consciousness; systemic diseases with documented neurological impact (e.g., uncontrolled diabetes mellitus, severe arterial hypertension); and abnormalities identified on neurological examination. Where available, structural MRI and cognitive screening results were also used to confirm neurological health.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Data Preprocessing\u003c/h2\u003e \u003cp\u003eA central challenge in aggregating EEG data across multiple recording sites and device types is the presence of systematic inter-site variability\u0026mdash;commonly referred to as \"batch effects\"\u0026mdash;that can introduce spurious differences unrelated to neurophysiology. The pipeline used here addressed this through the following procedure:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eArtifact Rejection\u003c/b\u003e: Visual inspection and automated quality-control procedures were applied to select a minimum of 60 seconds of stationary, artifact-free EEG activity per participant.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eSpectral Estimation\u003c/b\u003e: Cross-spectral matrices were computed for the standard 19-electrode array of the International 10\u0026ndash;20 system using the Fast Fourier Transform (FFT) with a frequency resolution of 0.39 Hz.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eElectrode-level Spectral Normalization (ESN)\u003c/b\u003e: For each subject i and electrode ch, the Electrode-level Spectral Normalization factor is defined as ESN(ch, i) = mean_f[S(ch, f, i)] for f \u0026isin; [0.39, 19.11] Hz, where S(ch, f, i) is the spectral power density at electrode ch and frequency f, and the average is taken over all frequency bins used in index computation. Each spectral value is then normalized by division: S_norm(ch, f, i)\u0026thinsp;=\u0026thinsp;S(ch, f, i) / ESN(ch, i) (5). On a log scale, this is an additive correction \u0026mdash; equivalent to a multiplicative factor on a linear scale. The ESN simultaneously accounts for individual-level variability in scalp and skull conductivity and other multiplicative amplitude offsets that are flat across the analysis band. This universality is a key advantage over device-covariate approaches: ESN normalization is always applicable, including when the acquisition system is unknown, which is common in clinical practice.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eResidual variability\u003c/b\u003e: after ESN normalization, residual inter-site amplitude variability is absorbed within the normative dispersion term of the GAMLSS model, since the per-electrode ESN correction removes both individual-level and external-level multiplicative scale differences before index computation.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe complete computational pipeline proposed in this work is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It includes Eyes Open (EO) and Cognitive Load (CL), although at present, normative databases are available only for the Eyes Closed (EC) condition. It is our purpose to standardize some Cognitive Load tasks in the future (as proposed in section \u003cspan refid=\"Sec35\" class=\"InternalRef\"\u003e4.5.1\u003c/span\u003e) and gather databases recorded under these parameters to calculate norms for these physiological tasks, which can provide useful information for the clinical use of qEEG.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Calculation of Quantitative Indices\u003c/h2\u003e \u003cp\u003eFor each participant in the database, 18 quantitative indices were calculated from the spectral power densities obtained after preprocessing. Four canonical frequency bands were defined: Delta (δ: 1.5\u0026ndash;3.5 Hz), Theta (θ: 3.9\u0026ndash;7.5 Hz), Alpha (α: 7.9\u0026ndash;12.5 Hz), and Beta (β: 12.9\u0026ndash;19.14 Hz). Spectral power at a given electrode ch and band is denoted P_band(ch). Where an index is computed over a set of electrodes, the mean power across that set is used. All ratio-based indices are computed on log-transformed band powers, so that a ratio becomes a difference of logarithms: ln(P₁)\u0026thinsp;\u0026minus;\u0026thinsp;ln(P₂)\u0026thinsp;\u0026equiv;\u0026thinsp;ln(P₁/P₂). This log-ratio formulation is symmetric, improves distributional properties, and is standard in qEEG normative modeling (Bosch-Bayard et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Arns et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1. Electrode-Level Spectral Ratios\u003c/h2\u003e \u003cp\u003eThe following three ratios are computed separately for each of the 19 electrodes of the 10\u0026ndash;20 system, yielding 19 values per ratio. Each electrode\u0026ndash;ratio combination receives its own age-dependent normative model.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTheta/Beta Ratio (TBR, per electrode)\u003c/b\u003e: TBR(ch)\u0026thinsp;=\u0026thinsp;ln[θ(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[β(ch)]. Widely used as a marker of attentional regulation and cortical arousal (Arns et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Ogrim et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTheta/Alpha Ratio (TAR, per electrode)\u003c/b\u003e: TAR(ch)\u0026thinsp;=\u0026thinsp;ln[θ(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[α(ch)]. Reflects the relative dominance of theta over alpha; sensitive to vigilance level and cognitive fatigue (Klimesch \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1999\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAlpha/Beta Ratio (ABR, per electrode)\u003c/b\u003e: ABR(ch)\u0026thinsp;=\u0026thinsp;ln[α(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[β(ch)]. Indexes the balance between idling alpha states and active beta processing; elevated values are associated with reduced cortical arousal and drowsiness.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDelta/Beta Ratio (DBR, per electrode)\u003c/b\u003e: DBR(ch)\u0026thinsp;=\u0026thinsp;ln[δ(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[β(ch)]. Captures the balance between slow delta oscillations and fast beta activity; elevated DBR has been associated with cortical hypoactivation and is sensitive to disorders of consciousness and severe attentional dysregulation (Thatcher et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e1989\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDelta/Alpha Ratio (DAR, per electrode)\u003c/b\u003e: DAR(ch)\u0026thinsp;=\u0026thinsp;ln[δ(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[α(ch)]. Widely used as an indicator of cerebral ischemia, diffuse encephalopathy, and cognitive impairment, elevated DAR reflects pathological slow-wave dominance (Claassen et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDelta/Theta Ratio (DTR, per electrode)\u003c/b\u003e: DTR(ch)\u0026thinsp;=\u0026thinsp;ln[δ(ch)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[θ(ch)]. Reflects the relative contribution of infra-slow delta versus theta activity; sensitive to depth of sleep and severe cortical depression, and useful for distinguishing delta-dominant from theta-dominant slow-wave profiles.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2. Global Functional State Indices\u003c/h2\u003e \u003cp\u003eThese four indices characterize broad functional brain states and are computed from spatially averaged power across all 19 electrodes (denoted β̅, α̅, θ̅, δ̅), except where noted.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEngagement Index (EI)\u003c/b\u003e: EI = β̅ / (α̅ + θ̅), following Pope et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1995\u003c/span\u003e). Computed over all 19 electrodes. Captures the relative suppression of slow-wave activity during sustained cognitive engagement.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eArousal Index (AI)\u003c/b\u003e: AI\u0026thinsp;=\u0026thinsp;β_F̅ / (δ_F̅\u0026thinsp;+\u0026thinsp;θ_F̅), where the overbar denotes the mean over the frontal cluster F3, F4, Cz. Quantifies the balance between frontal fast and slow oscillations as a measure of CNS activation level (Bonnet and Arand \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eValence Index (Frontal Alpha Asymmetry, FAA)\u003c/b\u003e: FAA\u0026thinsp;=\u0026thinsp;α(F3)]/β(F3) \u0026minus; α(F4)/β(F4), computed from the alpha power at electrodes F3 and F4 individually. Operationalizes the frontal EEG asymmetry framework linking hemispheric alpha lateralization to emotional valence (Allen et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Davidson \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eCognitive-Affective Index (CAI)\u003c/b\u003e: CAI\u0026thinsp;=\u0026thinsp;FC-TBR \u0026times; FAA, where FC-TBR is the frontocentral theta/beta ratio defined in section \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e2.3.3\u003c/span\u003e, and FAA is the frontal alpha asymmetry defined above. This compound index captures the simultaneous contribution of frontocentral cognitive load and hemispheric emotional lateralization.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3. Frontocentral Regional Ratios\u003c/h2\u003e \u003cp\u003eThese two indices restrict the spectral ratio computation to the frontocentral cluster comprising electrodes F3, F4, and Cz, yielding a single value per index, the mean ratio across those three electrodes.\u003c/p\u003e \u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eFrontoCentral Theta/Beta (FC-TBR)\u003c/b\u003e: FC-TBR\u0026thinsp;=\u0026thinsp;ln[θ_FC̅]\u0026thinsp;\u0026minus;\u0026thinsp;ln[β_FC̅], where the overbar denotes the mean over F3, F4, Cz. The regional counterpart of the per-electrode TBR, focusing on the frontocentral region relevant to executive control and attentional regulation (Arns et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eFrontoCentral Delta/Beta (FC-DBR)\u003c/b\u003e: FC-DBR\u0026thinsp;=\u0026thinsp;ln[δ_FC̅]\u0026thinsp;\u0026minus;\u0026thinsp;ln[β_FC̅], computed over the same cluster F3, F4, Cz. Captures the balance between frontocentral delta and beta activity.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4. Hemispheric Asymmetry Indices\u003c/h2\u003e \u003cp\u003eTwo families of asymmetry indices are computed, both using the log-difference formulation:\u003c/p\u003e \u003cp\u003e \u003cem\u003eAsymmetry\u0026thinsp;=\u0026thinsp;ln[M(left electrode)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[M(right electrode)]\u003c/em\u003e (A)\u003c/p\u003e \u003cp\u003ewhere M is either absolute band power or a spectral ratio. A positive value indicates left-hemisphere dominance; a negative value indicates right-hemisphere dominance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4a. Asymmetry Index (per band, per homologous pair)\u003c/h2\u003e \u003cp\u003eThe Asymmetry Index is computed as the log-difference of absolute band power between homologous electrode pairs, separately for each of the four canonical frequency bands:\u003c/p\u003e \u003cp\u003e \u003cem\u003eAI(band, pair)\u0026thinsp;=\u0026thinsp;ln[P_band(left)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[P_band(right)]\u003c/em\u003e (B)\u003c/p\u003e \u003cp\u003eThis yields a matrix of values indexed by band (δ, θ, α, β) and homologous pair. The pairs used are: Fp1/Fp2, F3/F4, F7/F8, C3/C4, T3/T4, T5/T6, P3/P4, and O1/O2. Each band\u0026ndash;pair combination receives its own age-dependent normative model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4b. Ratio-Based Asymmetry Indices\u003c/h2\u003e \u003cp\u003eEight indices combine spectral ratios with hemispheric asymmetry, computed at four clinically selected pairs of homologous electrodes using two ratios (δ/β and θ/β):\u003c/p\u003e \u003cp\u003e \u003cem\u003eAsym(ratio, pair)\u0026thinsp;=\u0026thinsp;ln[ratio(left)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[ratio(right)]\u003c/em\u003e (C)\u003c/p\u003e \u003cp\u003eThe eight indices are:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eδ/β Asymmetry F3\u0026thinsp;\u0026minus;\u0026thinsp;F4\u003c/b\u003e: ln[δ(F3)/β(F3)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[δ(F4)/β(F4)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eθ/β Asymmetry F3\u0026thinsp;\u0026minus;\u0026thinsp;F4\u003c/b\u003e: ln[θ(F3)/β(F3)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[θ(F4)/β(F4)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eδ/β Asymmetry F7\u0026thinsp;\u0026minus;\u0026thinsp;F8\u003c/b\u003e: ln[δ(F7)/β(F7)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[δ(F8)/β(F8)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eθ/β Asymmetry F7\u0026thinsp;\u0026minus;\u0026thinsp;F8\u003c/b\u003e: ln[θ(F7)/β(F7)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[θ(F8)/β(F8)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eδ/β Asymmetry T3\u0026thinsp;\u0026minus;\u0026thinsp;T4\u003c/b\u003e: ln[δ(T3)/β(T3)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[δ(T4)/β(T4)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eθ/β Asymmetry T3\u0026thinsp;\u0026minus;\u0026thinsp;T4\u003c/b\u003e: ln[θ(T3)/β(T3)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[θ(T4)/β(T4)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eδ/β Asymmetry T5\u0026thinsp;\u0026minus;\u0026thinsp;T6\u003c/b\u003e: ln[δ(T5)/β(T5)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[δ(T6)/β(T6)].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eθ/β Asymmetry T5\u0026thinsp;\u0026minus;\u0026thinsp;T6\u003c/b\u003e: ln[θ(T5)/β(T5)]\u0026thinsp;\u0026minus;\u0026thinsp;ln[θ(T6)/β(T6)].\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Normative Modeling and Z-Score Derivation\u003c/h2\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1. Distributional Transformation\u003c/h2\u003e \u003cp\u003eThe indices computed in this study are expressed as log-ratios or log-differences of band powers and therefore span negative and positive values with approximately symmetric distributions. No additional distributional transformation was applied before model fitting. This is consistent with the log-ratio formulation described in section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e2.3\u003c/span\u003e, which ensures that ratio-based indices are already on an approximately linear scale suitable for Gaussian normative modeling.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2. GAMLSS Normative Framework\u003c/h2\u003e \u003cp\u003eAge-dependent normative trajectories were estimated using a heteroscedastic regression framework consistent with the two-parameter GAMLSS family [Rigby \u0026amp; Stasinopoulos, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2005\u003c/span\u003e], with both the conditional mean (\u0026micro;) and the log-standard deviation (log σ) modeled as smooth functions of age via penalized B-splines (P-splines).\u003c/p\u003e \u003cp\u003eThe conditional distribution family was selected adaptively for each index using a three-criterion procedure evaluated on the raw (pre-transformation) data. Three diagnostic statistics were computed: excess kurtosis (kurt\u0026thinsp;\u0026minus;\u0026thinsp;3), skewness, and the p-value of a Shapiro\u0026ndash;Wilk test on a subsample of up to 2,000 observations. When at least two of the three criteria indicated non-normality (excess kurtosis\u0026thinsp;\u0026gt;\u0026thinsp;1, |skewness| \u0026gt; 0.5, or Shapiro\u0026ndash;Wilk p\u0026thinsp;\u0026lt;\u0026thinsp;0.05), a non-Normal family was attempted. For indices with strictly positive values, the Box\u0026ndash;Cox t (BCT) family was fitted on the raw data \u0026mdash; absorbing asymmetry and heavy tails through its shape parameters ν and τ, making a preliminary log-transformation redundant \u0026mdash; with fallback to BCPE and then Normal (NO) if BCT failed to converge (see Supplementary Table\u0026nbsp;3 for more details).\u003c/p\u003e \u003cp\u003eFor indices with values spanning the real line (e.g., Valence/FAA), the Normal family was retained regardless of the diagnostic criteria, as empirical testing confirmed that alternative families (JSU, SHASHo) did not improve centile calibration for the spike-and-slab marginal distribution (see Supplementary Fig.\u0026nbsp;8, Valence panel) characteristic of frontal alpha asymmetry in healthy populations. When fewer than two criteria indicated non-normality, the Normal family was used directly, with any requested pre-transformation (e.g., log for Arousal) applied before fitting.\u003c/p\u003e \u003cp\u003eLet Y\u003csub\u003ei\u003c/sub\u003e denote the (transformed) value of a given EEG-derived index for subject i. The conditional distribution of Y\u003csub\u003ei\u003c/sub\u003e is assumed to follow a parametric family:\u003c/p\u003e \u003cp\u003e \u003cem\u003eY\u003csub\u003ei\u003c/sub\u003e ~ D(\u0026micro;\u003csub\u003ei\u003c/sub\u003e, σ\u003csub\u003ei\u003c/sub\u003e, ν\u003csub\u003ei\u003c/sub\u003e, τ\u003csub\u003ei\u003c/sub\u003e)\u003c/em\u003e (1)\u003c/p\u003e \u003cp\u003ewhere \u0026micro;\u003csub\u003ei\u003c/sub\u003e is the conditional mean, σ\u003csub\u003ei\u003c/sub\u003e is the conditional standard deviation, and ν\u003csub\u003ei\u003c/sub\u003e and τ\u003csub\u003ei\u003c/sub\u003e are optional shape parameters governing skewness and kurtosis, respectively. For most EEG indices, modeling of \u0026micro;\u003csub\u003ei\u003c/sub\u003e and σ\u003csub\u003ei\u003c/sub\u003e was sufficient; higher-order parameters were included only when residual diagnostics indicated significant departure from distributional assumptions.\u003c/p\u003e \u003cp\u003eThe conditional mean and dispersion were modeled as:\u003c/p\u003e \u003cp\u003e \u003cem\u003e\u0026micro;\u003csub\u003ei\u003c/sub\u003e = f(age\u003csub\u003ei\u003c/sub\u003e)\u003c/em\u003e (2)\u003c/p\u003e \u003cp\u003e \u003cem\u003elog(σ\u003csub\u003ei\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;g(age\u003csub\u003ei\u003c/sub\u003e)\u003c/em\u003e (3)\u003c/p\u003e \u003cp\u003ewhere f(\u0026middot;) and g(\u0026middot;) are smooth functions of log(age) estimated as penalized B-splines (P-splines) using the pb() smoother of the gamlss R package (Rigby \u0026amp; Stasinopoulos, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). The degree of smoothing is selected automatically by minimizing a generalized Akaike information criterion (GAIC), avoiding the need to prespecify the number or location of knots. Both location and dispersion submodels are fitted jointly by alternating IRLS cycles (maximum 50 outer iterations). When residual diagnostics\u0026mdash;specifically, worm plots and Q\u0026ndash;Q plots of normalized quantile residuals\u0026mdash;indicated significant departure from normality, operationalized as excess kurtosis greater than 5, the Box\u0026ndash;Cox t (BCT) family was substituted for the Normal family to accommodate heavy-tailed distributions. For all remaining indices, the Normal (NO) conditional family was used. This adaptive family selection ensures distributional adequacy across the full set of indices, which differ substantially in tail behavior.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e2.4.3. Electrode-level Spectral Normalization (ESN)\u003c/h2\u003e \u003cp\u003eA key preprocessing step before normative modeling is the removal of multiplicative amplitude variability that reflects physiological and technical sources unrelated to the neurophysiological indices of interest. These sources include individual differences in scalp and skull conductivity\u0026mdash;which scale all electrode amplitudes by a subject-specific factor\u0026mdash;and other externally related differences in electrode impedance, which introduce electrode-specific scale offsets that vary across acquisition systems. Critically, these two sources of variability are confounded and cannot be separated without detailed knowledge of the recording hardware.\u003c/p\u003e \u003cp\u003eTo address this, an Electrode-level Spectral Normalization factor (ESN) is computed for each subject i and electrode ch as:\u003c/p\u003e \u003cp\u003eESN(ch, i) = mean_f [ S(ch, f, i) ], f \u0026isin; [0.39, 19.11] Hz (4)\u003c/p\u003e \u003cp\u003ewhere S(ch, f, i) is the spectral power density at electrode ch, frequency bin f, and subject i, and the mean is taken over all frequency bins used in the computation of normative indices. The frequency range [0.39, 19.11] Hz is fixed and identical for all subjects and studies, ensuring that the ESN factor is strictly comparable across individuals and recording systems. Each spectral value is then normalized by division:\u003c/p\u003e \u003cp\u003eS_norm(ch, f, i)\u0026thinsp;=\u0026thinsp;S(ch, f, i) / ESN(ch, i) (5)\u003c/p\u003e \u003cp\u003eIn log-scale, this corresponds to a subtraction: ln[Sₙₒ℠ₘ]\u0026thinsp;=\u0026thinsp;ln[S]\u0026thinsp;\u0026minus;\u0026thinsp;ln[ESN], making the ESN correction additive on the scale on which normative models are fitted. Equivalently, on the original power scale, the correction is multiplicative. This distinction is methodologically important: multiplicative normalization preserves the relative spectral structure within each subject while removing between-subject and between other recording-conditions-related scale differences.\u003c/p\u003e \u003cp\u003eESN corrects multiplicative amplitude differences per electrode within the analysis band but does not account for frequency-dependent transfer function differences across devices (e.g., differential roll-off slopes or filter characteristics). Studies combining equipment with substantially different spectral response characteristics should verify residual device effects in GAMLSS model residuals.\u003c/p\u003e \u003cp\u003eA fundamental advantage of ESN normalization over device-covariate approaches is that it requires no knowledge of the recording equipment. It is therefore universally applicable: it can be applied to any EEG recording, including archival data, referral recordings, and recordings from systems not represented in the normative database\u0026mdash;contexts in which a device covariate cannot be specified. This universality ensures that the normative framework developed here can be applied in the full range of clinical and research settings encountered in practice.\u003c/p\u003e \u003cp\u003eFollowing ESN normalization, the conditional mean of the GAMLSS model contains only the age-dependent smooth term:\u003c/p\u003e \u003cp\u003e\u0026micro;\u003csub\u003ei\u003c/sub\u003e = f(age\u003csub\u003ei\u003c/sub\u003e) (6)\u003c/p\u003e \u003cp\u003elog(σ\u003csub\u003ei\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;g(age\u003csub\u003ei\u003c/sub\u003e) (7)\u003c/p\u003e \u003cp\u003ewhere f(\u0026middot;) and g(\u0026middot;) are P-spline smoothers on log(age). The individualized Z-score for subject i with index value Y\u003csub\u003ei\u003c/sub\u003e is:\u003c/p\u003e \u003cp\u003eZ\u003csub\u003ei\u003c/sub\u003e = [Y\u003csub\u003ei\u003c/sub\u003e \u0026minus; \u0026micro;̂\u003csub\u003ei\u003c/sub\u003e] / σ̂\u003csub\u003ei\u003c/sub\u003e (8)\u003c/p\u003e \u003cp\u003ewhere \u0026micro;̂\u003csub\u003ei\u003c/sub\u003e and σ̂\u003csub\u003ei\u003c/sub\u003e are the age-adjusted normative mean and standard deviation derived from the GAMLSS model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e2.4.4. Computation of Individualized Deviation Scores\u003c/h2\u003e \u003cp\u003eFor any individual subject i with index value Y\u003csub\u003ei\u003c/sub\u003e measured at age t, the individualized Z-score under either normalization mode is interpreted as the number of age-adjusted standard deviations by which the observed measurement deviates from the normative expectation:\u003c/p\u003e \u003cp\u003eUnder conventional probabilistic thresholds:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e|Z| \u0026gt; 2.0 corresponds to approximately the 2.5th or 97.5th percentile of the normative population, indicating a borderline deviation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e|Z| \u0026gt; 3.0 indicates a strong deviation, expected in fewer than 0.15% of neurotypical individuals of the same age.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eIn addition to Z-scores, smooth age-dependent centile curves (5th, 10th, 25th, 50th, 75th, 90th, and 95th centiles) were generated for each index and electrode region, providing a reference for clinical and research use (\u003cem\u003esee Supplementary Table\u0026nbsp;2\u003c/em\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e2.4.5. Model Validation\u003c/h2\u003e \u003cp\u003eThe stability and predictive performance of the normative models were evaluated using several complementary procedures:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003ek-fold cross-validation\u003c/b\u003e: Models were fitted on training subsets and evaluated on held-out data, with prediction error assessed separately within each age stratum.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eResidual diagnostics\u003c/b\u003e: Worm plots and Q-Q plots of normalized quantile residuals were inspected to verify distributional adequacy of the fitted models.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eCentile calibration\u003c/b\u003e: Empirical coverage of predicted centile intervals was compared against theoretical expectations across the full age range.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAssessment of ESN normalization and model calibration\u003c/b\u003e: Assessment of ESN normalization: The reduction in inter-subject spectral amplitude variability following per-electrode ESN correction was quantified, and centile calibration was verified after normalization (\u003cem\u003esee Supplementary Fig.\u0026nbsp;10\u003c/em\u003e).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eModel calibration was assessed through two complementary procedures reported in Supplementary Tables\u0026nbsp;1 and 2: (1) the percentage of normative subjects with normalized quantile residuals |Z| \u0026gt; 1.96, computed using R's internal quantile residual diagnostics and expected to approximate 5.0% under a well-calibrated model; and (2) empirical centile coverage, evaluated by comparing each subject's observed value against the age-interpolated centile curve across seven thresholds (p2.5 through p97.5).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Software and Implementation\u003c/h2\u003e \u003cp\u003eSpectral analysis and preprocessing were implemented in MATLAB (R2015a). Normative modeling was performed in R (v4.3) using the gamlss package (Rigby \u0026amp; Stasinopoulos, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Stasinopoulos \u0026amp; Rigby, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2007\u003c/span\u003e (Stasinopoulos and Rigby \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2007\u003c/span\u003e)). For each index, a two-parameter GAMLSS model with P-spline smoothers on log(age) was fitted using the pb() function, with automatic smoothing parameter selection via GAIC. Inter-site and inter-individual amplitude variability was addressed through Electrode-level Spectral Normalization (ESN) applied at the electrode level before index computation (see Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e2.4.3\u003c/span\u003e) rather than as a separate preprocessing step. Topographic Z-score interpolation for electrode-level surfaces was performed using spherical spline interpolation of order 4 [Perrin et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1989\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Distribution of EEG Spectral Indices and Transformation Assessment\u003c/h2\u003e \u003cp\u003eThe distribution of each spectral index was first examined across the full normative sample. Most indices displayed moderate skewness, typical of ratio-based measures derived from spectral power. Log-transformations were applied when appropriate to stabilize variance and improve model fit. Gaussian models for all major indices satisfactorily approximated post-transformation residual distributions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Age-Dependent Normative Trajectories\u003c/h2\u003e \u003cp\u003eNormative trajectories estimated via GAMLSS revealed significant nonlinear developmental patterns for several indices (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The theta/beta ratio decreased markedly from childhood to early adulthood, consistent with the maturation of attentional networks and the progressive reduction in slow oscillatory activity. The delta/beta ratio showed a similar decreasing trajectory. In contrast, the alpha/delta ratio and IAF exhibited progressive increases during adolescence followed by stabilization in adulthood, consistent with well-known developmental strengthening of alpha oscillations and thalamocortical maturation.\u003c/p\u003e \u003cp\u003eComplete normative centile trajectories for all 19 electrode-level indices are provided as Supplementary Figures. Each supplementary figure displays, for a given index, the age-dependent normative mean and \u0026plusmn;\u0026thinsp;1.96σ interval estimated by the GAMLSS model alongside individual observations from the HarMNqEEG normative database, arranged by electrode according to the standard 10\u0026ndash;20 spatial layout.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Normative Centile Curves and Z-score Distributions\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFormal calibration diagnostics confirmed adequate model performance for all indices. In Supplementary Tables\u0026nbsp;1 and 2, we show the results for three of the most popular and used indices: Arousal, Valence, and TBR (Theta/Beta Ratio). TBR and Arousal Index models showed excellent calibration across all centile thresholds (max |Δ| \u0026lt; 1.4 pp and \u0026lt;\u0026thinsp;1.0 pp, respectively; residual rates within 0.1 pp of the nominal 5.0%). The Valence Index showed adequate global calibration (5.11% residuals outside \u0026plusmn;\u0026thinsp;1.96σ) but systematic underdispersion in the central quantiles (p25: \u0026minus;10 pp; p75: +10 pp), reflecting the spike-and-slab character of the FAA distribution in healthy populations (see Supplementary Fig.\u0026nbsp;10 for the Valence Index individual distribution along the age). This limits normative precision in the intermediate range (|Z| \u0026lt; 2) but does not affect the primary clinical use of this index \u0026mdash; detection of pathological hemispheric lateralization (|Z| \u0026gt; 2). Device-stratified residual diagnostics confirmed the absence of clinically meaningful equipment-related bias across all indices (see Supplementary Fig.\u0026nbsp;10, panel A).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Clinical Case Illustrations\u003c/h2\u003e \u003cp\u003eTo illustrate the clinical utility of the normative framework developed in this study, we present a representative pre\u0026ndash;post intervention case from a neurorehabilitation program. This case demonstrates several key measurement dimensions covered by the normative models: broadband spectral amplitudes, functional state indices (arousal, emotional valence), and spectral ratios across multiple recording conditions (eyes-closed, eyes-open, and cognitive load).\u003c/p\u003e \u003cdiv id=\"Sec25\" class=\"Section3\"\u003e \u003ch2\u003e3.4.1. Case Description\u003c/h2\u003e \u003cp\u003eThe participant is an 8-year-old male (initials B.M., data used with institutional consent) from Mexico, presenting with a clinical diagnosis of dysexecutive syndrome\u0026mdash;characterized by deficits in working memory, cognitive flexibility, inhibitory control, and goal-directed behavior. He received 21 sessions of transcranial direct current stimulation (tDCS) combined with cognitive-motor neurorehabilitation using the Kinestesia therapeutic video-game platform, targeting frontal executive networks. Quantitative EEG (qEEG) was recorded under standardized eyes-closed (EC), eyes-open (EO), and cognitive load (CL) conditions before and after the intervention. Broadband spectral power (absolute power, relative power, mean frequency), spectral ratios, and functional state indices were computed following the pipeline described in Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e2.3\u003c/span\u003e. For the EC condition, normative Z-scores were derived using the age-matched models developed in this study.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section3\"\u003e \u003ch2\u003e3.4.2. Spectral Changes\u003c/h2\u003e \u003cp\u003ePre-intervention qEEG showed a global mean EEG frequency between 5.86 and 7.81 Hz \u0026mdash; below the age-expected range for an 8-year-old \u0026mdash; with slow-frequency dominance consistent with the attentional and executive profile. Following intervention, mean EEG frequency increased to 5.86\u0026ndash;8.3 Hz overall, reaching 8.3 Hz in posterior regions, indicating a shift toward a more mature, faster-dominant spectral composition. This change was accompanied by a well-defined anterior-to-posterior frequency gradient, which was less organized pre-intervention. No deviations from normative references were detected post-intervention in broadband or narrowband spectral analyses, except for a mild and circumscribed increase in spectral energy in the 10.16\u0026ndash;10.55 Hz sub-band.\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB illustrate electrode-level spectral ratios (delta/beta, theta/alpha, theta/beta, delta/alpha) and absolute spectral amplitudes in the eyes-open condition. Consistent reductions in slow-to-fast ratios were observed post-intervention across frontal and central sites, with the largest changes in theta/beta and delta/beta. Absolute spectral amplitudes confirmed this pattern: marked reductions in delta and theta were observed at nearly all electrode sites, particularly prominent at Cz and frontal locations (delta: Cz pre\u0026thinsp;\u0026asymp;\u0026thinsp;95 \u0026micro;V, post\u0026thinsp;\u0026asymp;\u0026thinsp;25 \u0026micro;V; theta: Cz pre\u0026thinsp;\u0026asymp;\u0026thinsp;85 \u0026micro;V, post\u0026thinsp;\u0026asymp;\u0026thinsp;40 \u0026micro;V). Beta amplitude showed selective increases at Cz and F4, consistent with enhanced frontocentral activation. The Z-score theta/beta ratio at F3 decreased from 0.48 to 0.03 (\u0026minus;\u0026thinsp;93.7%) and at F4 from 0.47 to 0.30 (\u0026minus;\u0026thinsp;36.2%), representing near-complete normalization of frontal attentional regulation indices (Arns et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Ogrim et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). The individual alpha peak frequency increased from 9.38 to 9.77 Hz (+\u0026thinsp;4.1%), consistent with accelerated thalamocortical maturation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section3\"\u003e \u003ch2\u003e3.4.3. Functional State Indices and Z-Score Normalization\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. \u003cem\u003ePre\u0026ndash;post neurorehabilitation EEG changes in a representative clinical case (B.M., 8 years, dysexecutive syndrome). Quantitative EEG was recorded before and after the therapeutic intervention under eyes-open (OA) and cognitive load (UT) conditions. Blue: pre-intervention; orange: post-intervention. (A) Spectral ratios \u0026mdash; eyes open. Pre\u0026ndash;post trajectories of four log-ratio indices (delta/beta, theta/alpha, theta/beta, delta/alpha) across eight electrodes (Fz, Cz, F3, F4, T5, T6, O1, O2). Green shading indicates post\u0026thinsp;\u0026gt;\u0026thinsp;pre (increase); red shading indicates post\u0026thinsp;\u0026lt;\u0026thinsp;pre (reduction). Consistent reductions in slow-to-fast ratios are observed across frontal and central sites, with the largest changes in theta/beta and delta/beta, reflecting reduced slow-wave dominance and improved cortical activation. (B) Spectral amplitudes \u0026mdash; eyes open. Absolute spectral power (\u0026micro;V) pre and post for delta, theta, alpha, and beta bands across the same electrode set. Arrows indicate the direction of change at each electrode; orange arrows indicate reduction (post\u0026thinsp;\u0026lt;\u0026thinsp;pre), green arrows indicate increase (post\u0026thinsp;\u0026gt;\u0026thinsp;pre). Marked reductions in delta and theta amplitude are observed at frontal and central sites (notably Cz and F3), alongside selective beta increases at Cz and F4, consistent with enhanced frontocentral activation. (C) Functional state indices. Pre\u0026ndash;post bar comparison of the Arousal and Valence (frontal alpha asymmetry) indices under OA and UT conditions. Arrows indicate the magnitude and direction of change (Δ). Post-intervention increases in Arousal and Valence under OA reflect enhanced cortical activation; the reduction in Valence under UT suggests a shift toward right-hemisphere dominance under cognitive demand, consistent with reduced frontal cognitive load. (D) Emotional regulation Z-scores (eyes-closed condition). Pre\u0026ndash;post comparison of Valence and Arousal expressed as normative Z-scores derived from the age-matched models developed in this study. The shaded band indicates the \u0026plusmn;\u0026thinsp;1 SD normative range (Z\u0026thinsp;=\u0026thinsp;\u0026plusmn;\u0026thinsp;1). Pre-intervention Valence deviated markedly from the norm (Z\u0026thinsp;=\u0026thinsp;+\u0026thinsp;2.20), returning to within the normative range post-intervention (Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.50). Arousal showed a smaller but consistent shift toward normalization. The dashed line marks Z\u0026thinsp;=\u0026thinsp;0 (population mean).\u003c/em\u003e\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eD shows the pre\u0026ndash;post Z-score comparison of Valence and Arousal in the eyes-closed condition, anchored to the age-matched normative models developed in this study. The Valence index (frontal alpha asymmetry, FAA) shifted from Z\u0026thinsp;=\u0026thinsp;+\u0026thinsp;2.20 pre-intervention to Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.50 post-intervention \u0026mdash; a reduction of more than 2.7 standard deviations into the normative range \u0026mdash; consistent with normalization of pathological left-hemisphere alpha dominance. The Arousal index showed a parallel shift from Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.62 to Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.50, remaining within the normative band throughout but moving toward the population mean. These shifts in the eyes-closed condition are complemented by the broader pattern of functional index changes observed across states: in the eyes-closed condition, the Valence index had shown a marked deviation of Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.82 pre-intervention, returning to Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.61 post-intervention, while the Arousal index decreased by 0.10, together reflecting a generalized normalization of the neurophysiological state at rest.\u003c/p\u003e \u003cp\u003eThese results are clinically corroborated by the expert neurologist's assessment, which noted improved organization of the resting EEG, a stable and well-organized posterior alpha rhythm, and only mild intermittent disturbance of frontal-temporal activity \u0026mdash; a substantially improved profile relative to the pre-intervention recording. The quantitative indices provide an objective, reproducible complement to visual inspection, anchoring the observed changes within a normative probabilistic framework and enabling their direct comparison against age-expected population distributions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section3\"\u003e \u003ch2\u003e3.4.4. The Need for Multi-State Normative References\u003c/h2\u003e \u003cp\u003eThis case also highlights a methodological gap that the present framework only partially addresses. The most clinically informative changes were observed not only in the eyes-closed resting condition\u0026mdash;for which normative models are available\u0026mdash;but in the EO and CL conditions (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA\u0026ndash;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB). The reduction in theta/beta ratio under cognitive load, the increase in beta amplitude at frontal sites during EO, and the modulation of Arousal and Valence indices across conditions all constitute evidence of improved neurophysiological function that cannot currently be anchored to age-expected norms, because lifespan normative references for EO and cognitive activation conditions remain unavailable. This observation reinforces the call for future normative databases incorporating multi-state recording protocols (see Section \u003cspan refid=\"Sec35\" class=\"InternalRef\"\u003e4.5.1\u003c/span\u003e) and underscores that the clinical interpretability of qEEG as a therapeutic monitoring tool depends critically on the availability of condition-specific normative references.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe present study contributes to the ongoing revival of quantitative EEG by embedding a clinically relevant family of derived spectral indices within age-dependent probabilistic normative frameworks. The resulting models enable individualized inference\u0026mdash;answering not merely whether brain activity is atypical, but by how much and in which direction relative to the population norm for a given age. In doing so, this work revisits the original vision of neurometrics while integrating the computational and data-harmonization advances of modern neuroscience.\u003c/p\u003e \u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e4.1. From Qualitative Heuristics to Normative Precision\u003c/h2\u003e \u003cp\u003eFor decades, clinical EEG practice has relied on expert visual inspection to identify paroxysmal activity, focal slowing, or diffuse abnormalities. While this remains essential for the detection of unambiguous pathology, it systematically discards the wealth of information encoded in quantitative spectral features. The neurometrics framework proposed by John et al. (John \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1977\u003c/span\u003e; John et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) articulated a compelling alternative: brain function follows predictable statistical trajectories across the lifespan that can be modeled, and departures from these trajectories can be expressed as probabilistic scores amenable to clinical interpretation.\u003c/p\u003e \u003cp\u003eThe present results demonstrate that this principle extends naturally to derived spectral ratios and composite functional indices. A theta/beta ratio reported as a raw value has no intrinsic clinical meaning; the same value expressed as a Z-score of +\u0026thinsp;2.5 relative to an age-matched normative distribution immediately communicates a meaningful deviation, with a probability of occurrence below 1.2% in a neurotypical population of that age. This translation from measurement to inference is what distinguishes a normative biomarker from a descriptive metric, and it is precisely the translation that routine clinical reports currently fail to provide (Ko et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Prichep \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Functional Indices as Evidence of Therapeutic Efficacy\u003c/h2\u003e \u003cp\u003eOne of the most clinically significant contributions of this framework lies in the extension of normative modeling beyond simple spectral power to functional indices of arousal, emotional valence, and cognitive engagement. These composite metrics have been repeatedly linked to neuropsychiatric conditions and to the outcomes of therapeutic interventions: theta/beta elevation in attentional dysregulation (Arns et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Ogrim et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), frontal alpha asymmetry in mood disorders and affective valence (Davidson \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Smith et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), engagement index reduction in fatigue and inattention (Pope et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1995\u003c/span\u003e), and arousal index perturbations in vigilance disorders (Hegerl et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Olbrich et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHowever, the clinical utility of these indices has been severely constrained by the absence of normative reference values. Without such references, pre\u0026ndash;post comparisons in therapeutic monitoring yield only directional information\u0026mdash;the index increased or decreased\u0026mdash;without any indication of whether the change represents movement toward, arrival at, or departure from normotypical function. A patient whose frontal alpha asymmetry shifts from Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;2.8 to Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;1.2 following treatment has improved substantially in neurophysiological terms, even if the absolute index value remains in a range that appears clinically abnormal without normative context. Conversely, a patient who moves from Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.4 to Z\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.8 may show a numerically similar absolute change that is actually a mild deterioration within the normative range.\u003c/p\u003e \u003cp\u003eThe normative Z-score framework resolves this ambiguity by providing a principled measure of the direction and magnitude of neurophysiological change relative to the population distribution. This constitutes a qualitative upgrade in the evidential value of longitudinal qEEG monitoring\u0026mdash;from a descriptive record of change to a quantitative index of normalization\u0026mdash;that is directly relevant to evidence-based neurorehabilitation (Kropotov \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Kropotov \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Collura et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Electrode-level Spectral Normalization: A Universal and Principled Preprocessing Step\u003c/h2\u003e \u003cp\u003eA distinctive methodological contribution of this work is the adoption of Electrode-level Spectral Normalization (ESN) as a universal preprocessing step applied to each electrode\u0026rsquo;s spectral values before index computation. Technical variability between EEG acquisition systems\u0026mdash;arising from differences in amplifier characteristics, electrode impedance standards, reference schemes, and digital filtering\u0026mdash;constitutes a well-documented source of systematic variance in spectral estimates that is unrelated to neurophysiology (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). At the same time, individual differences in scalp and skull conductivity introduce subject-specific multiplicative scale factors that affect all electrodes simultaneously. Both sources of variability are multiplicative on the power scale and therefore appear as additive offsets in log-transformed spectral values\u0026mdash;precisely the scale on which normative indices are computed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec33\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Relation to the Normative Modeling Tradition in Neuroscience\u003c/h2\u003e \u003cp\u003eThe present work aligns with a broader movement in computational neuroscience toward normative modeling as a framework for understanding individual variability in brain measurements (Marquand et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Marquand et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) articulated the key insight that heterogeneous clinical populations cannot be understood through group-mean comparisons alone but require individual-level deviation scores relative to a well-characterized healthy distribution. Subsequent applications of this paradigm to structural MRI\u0026mdash;including the large-scale lifespan brain charts of Bethlehem et al. (Bethlehem et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u0026mdash;have demonstrated its value for identifying individuals whose brain measurements deviate from typical developmental trajectories, independently of diagnostic category.\u003c/p\u003e \u003cp\u003eQuantitative EEG is particularly well-suited for this approach. Its low cost, temporal resolution, and widespread clinical availability make it a practical complement to MRI-based normative atlases, extending the reach of normative modeling to settings where structural or functional neuroimaging is unavailable. The HarMNqEEG database (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), with its multinational harmonized design and lifespan coverage, provides a foundation for qEEG normative modeling that is broadly comparable in scope\u0026mdash;if not yet in spatial resolution\u0026mdash;to the large neuroimaging datasets underlying MRI brain charts.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec34\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Limitations and Future Directions\u003c/h2\u003e \u003cp\u003eComplementarity with EEG Microstate Normative Frameworks. The spectral normative framework developed here is complementary to the microstate-based normative tradition pioneered by Koenig, Michel, and colleagues (Koenig et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Michel and Koenig \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The two frameworks address orthogonal dimensions of spontaneous brain dynamics: momentary global field topography (microstates) versus frequency-domain composition (spectral ratios). Both have converged on the same normative imperative: individual measurements acquire clinical meaning only when anchored to age-expected population distributions (Koenig et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Marquand et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Bethlehem et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Future work integrating both frameworks within a unified lifespan reference would provide a substantially richer normative atlas of human brain electrophysiology.\u003c/p\u003e \u003cp\u003eSeveral limitations of the present work merit explicit acknowledgment. First, the HarMNqEEG database is exclusively restricted to eyes-closed resting-state recordings. While this condition provides the most stable and reproducible baseline for normative reference, it necessarily leaves uncharacterized a clinically important dimension of EEG dynamics: the brain's response to external stimulation and cognitive demand. Alpha reactivity upon eye opening\u0026mdash;a robust index of thalamocortical integrity (Pfurtscheller and Lopes da Silva \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Fonseca et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2011\u003c/span\u003e)\u0026mdash;and electrophysiological changes during mental arithmetic, working-memory tasks, or hyperventilation may reveal abnormalities that are invisible at rest. Future normative databases should prioritize the harmonized collection of eyes-open and cognitive activation recordings to enable \"functional neurometrics\" that capture the full dynamic repertoire of the human brain.\u003c/p\u003e \u003cp\u003eSecond, inter-site technical variability is addressed through ESN rather than Riemannian harmonization of the cross-spectral matrices (Li et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This choice is deliberate: Riemannian harmonization operates on the full cross-spectral tensor and efficiently removes site-level biases in the covariance geometry, but it introduces cross-electrode mixing that removes the direct neurophysiological interpretation of per-electrode spectral ratios and asymmetry indices. ESN corrects for multiplicative amplitude offsets while preserving the electrode-level meaning of each index, without requiring knowledge of the acquisition system. Riemannian harmonization remains a valuable approach for applications where the full covariance structure is the object of interest, such as source imaging and functional connectivity analysis.\u003c/p\u003e \u003cp\u003eThird, the present normative models were derived exclusively from resting-state spectral features and do not incorporate source-level information. The integration of electromagnetic source imaging methods such as VARETA (Bosch-Bayard et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) and sLORETA (Pascual-Marqui \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) within a normative framework would allow the localization of deviating generators, adding a spatial dimension to the probabilistic biomarker approach. This extension is technically feasible within the HarMNqEEG infrastructure and constitutes a natural next step toward a comprehensive normative atlas of human brain electrophysiology.\u003c/p\u003e \u003cp\u003eFinally, the clinical validation of these normative indices as diagnostic or prognostic biomarkers in specific neurological and psychiatric conditions\u0026mdash;ADHD, mood disorders, mild cognitive impairment, epilepsy\u0026mdash;requires prospective studies comparing Z-score profiles against gold-standard clinical diagnoses and longitudinal outcomes. The normative models presented here provide the infrastructure for such studies; their clinical sensitivity and specificity remain to be established across patient populations.\u003c/p\u003e \u003cdiv id=\"Sec35\" class=\"Section3\"\u003e \u003ch2\u003e4.5.1. Toward Cognitive Activation Norms: A Proposed Protocol\u003c/h2\u003e \u003cp\u003eTo our knowledge, normative qEEG frameworks have focused predominantly on eyes-closed resting conditions. However, the inclusion of brief cognitive challenge blocks may substantially enrich clinical interpretation by revealing how EEG-derived biomarkers change under increasing mental demand. Existing literature supports the use of such tasks as practical probes of arousal, workload, and executive function (Fairclough et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Onton et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Borghini et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), although normative lifespan references for these activation conditions remain largely unavailable.\u003c/p\u003e \u003cp\u003e From a practical standpoint, the most clinically defensible approach is a short sequential protocol that establishes a graded continuum from baseline resting state to executive load, using only verbal instructions and no additional materials. Based on the available EEG literature on cognitive workload (Fairclough et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Onton et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Borghini et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and clinical practice guidelines (Swingle \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), the following six-block protocol is proposed as a future standard for normative expansion (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 1 \u0026mdash; Eyes closed (EC)\u003c/b\u003e: 2\u0026ndash;3 min. Thalamocortical baseline; standard HarMNqEEG reference condition.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 2 \u0026mdash; Eyes open (EO)\u003c/b\u003e: 1\u0026ndash;2 min. Physiological activation; alpha reactivity and EC\u0026rarr;EO modulation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 3 \u0026mdash; Backward counting (easy)\u003c/b\u003e: 30\u0026ndash;60 s. Count backward from 100 by 1s. Sustained attention and executive control.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 4 \u0026mdash; Serial subtraction (hard)\u003c/b\u003e: 30\u0026ndash;90 s. Subtract 7s from 100 mentally. Cognitive load, working memory, and inhibitory control.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 5 \u0026mdash; Backward digit span\u003c/b\u003e: 1\u0026ndash;2 min. Repeat digit sequences in reverse. Working-memory manipulation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBlock 6 \u0026mdash; Covert verbal fluency\u003c/b\u003e: 30\u0026ndash;60 s. Generate as many animal names as possible mentally. Lexical retrieval and executive search.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis gradient ranges from simple physiological activation (EC\u0026rarr;EO) to genuine executive and working-memory demands. Swingle explicitly recommends including an eyes-open condition and a cognitive challenge, such as reading or counting backwards, noting that certain EEG patterns emerge only under cognitive demand and are invisible at rest (Swingle \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Tasks involving overt speech should be avoided due to electromyographic contamination; covert or minimal-response variants are strongly preferred. Table\u0026nbsp;2 summarizes the key properties of the proposed tasks.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBrief cognitive challenge tasks that can be integrated into a resting-state qEEG protocol, ordered by increasing cognitive demand. Tasks are proposed as a future extension of eyes-closed normative protocols to capture EEG dynamics under graded activation conditions.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTask\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDomain probed\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTypical instruction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDuration\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMain advantages\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLimitations / artifacts\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eClinical utility in qEEG\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEyes open (EO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eArousal/alpha reactivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\"Eyes open, look straight ahead.\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u0026ndash;3 min\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo materials; standardized\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEye blinks, saccades\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAlpha reactivity; EC\u0026rarr;EO modulation (Barry et al., 2017)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBackward counting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSustained attention, executive control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\"Count backward from 100 to 1.\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u0026ndash;60 s\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEasy; scalable; no materials\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eOvert speech adds EMG; use covert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePractical challenge; recommended by Swingle/ClinicalQ (Swingle \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2015\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSerial subtraction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCognitive load, working memory, inhibitory control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\"Subtract 7s from 100 mentally.\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u0026ndash;90 s\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStrong EEG workload literature; adjustable difficulty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eOvert response contaminates the EEG; arithmetic skill confound\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBest no-equipment workload task for brief EEG blocks (Fairclough et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBackward digit span\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWorking memory manipulation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\"Repeat these digits backwards.\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u0026ndash;2 min\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWell-defined executive demand; adaptable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eExaminer timing required; overt artifacts\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFrontal-executive probe; sensitive to WM capacity (Onton et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2005\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCovert verbal fluency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLexical retrieval, executive search\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\"Think of as many animals as possible.\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u0026ndash;60 s\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo materials; language/executive load\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCompliance harder to verify if fully covert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFrontal/language network assessment (Borghini et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eEC\u0026thinsp;=\u0026thinsp;eyes closed; EO\u0026thinsp;=\u0026thinsp;eyes open; EMG\u0026thinsp;=\u0026thinsp;electromyographic artifact; WM\u0026thinsp;=\u0026thinsp;working memory. Covert or minimal-response variants are preferred to minimize signal contamination. References in brackets correspond to citations in the main text.\u003c/em\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eReclaiming quantitative EEG as a primary diagnostic and monitoring instrument is not a nostalgic return to the past, but a scientifically grounded necessity for modern precision neurophysiology. The normative models presented here\u0026mdash;for spectral power ratios, cognitive-emotional state indices, and physiological parameters\u0026mdash;provide the statistical infrastructure required to transform descriptive EEG metrics into probabilistic clinical biomarkers. By anchoring individual measurements to age-adjusted population distributions and expressing deviations as Z-scores under the unified ESN-normalized framework, clinicians gain direct, interpretable answers to the questions that matter most in practice: Is this patient's brain activity typical for their age? Has treatment produced a neurophysiologically meaningful change toward normotypical function?\u003c/p\u003e \u003cp\u003eThe use of GAMLSS modeling captures the non-linear developmental trajectories of EEG indices across the lifespan and appropriately represents age-dependent changes in both expected values and inter-individual variability\u0026mdash;properties that earlier normative approaches based on fixed-variance linear models could not accommodate. The ESN normalization strategy ensures that the framework remains applicable across the full spectrum of clinical recording contexts, from well-documented research-grade EEG to legacy or minimally documented clinical files, without sacrificing methodological transparency.\u003c/p\u003e \u003cp\u003eTo our knowledge, this represents the first systematic effort to construct harmonized, multinational normative models for this family of derived functional qEEG indices. The work establishes the foundational normative layer for eyes-closed resting-state conditions. Future extensions\u0026mdash;incorporating eyes-open, cognitive activation, hyperventilation, and photic stimulation conditions, and integrating source-level normative mapping\u0026mdash;will complete the transition from static to functional neurometrics and fulfill the original promise of quantitative EEG as an objective, individualized tool for evidence-based neurorehabilitation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors thank the HarMNqEEG consortium for making the multinational normative database publicly available, and the participants of all contributing sites. The clinical case illustration was provided by CIMMCO (Quer\u0026eacute;taro, M\u0026eacute;xico).\u003c/p\u003e\n\n\u003cp\u003eCompeting Interests\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eJBB was partially funded by the German Research Foundation core facility, grant INST 184/216-1.\u003c/p\u003e\n\u003cp\u003eAuthor Contributions\u003c/p\u003e\n\u003cp\u003eJorge Bosch-Bayard: Conceptualization, Methodology, Formal analysis, Software, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing, Data curation, Supervision. J. Guerrero-Sauzameda: Conceptualization, Formal analysis, Visualization, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing. R. Bosch-Bayard: Conceptualization; Writing \u0026ndash; review \u0026amp; editing. R. P\u0026eacute;rez-Elvira: Writing \u0026ndash; review \u0026amp; editing. A. Bosch-Castro, J. S\u0026aacute;nchez-Rodr\u0026iacute;guez, A. Flores, K. Flores, E. Resendiz-Flores: Visualization, Figures Design, testing, review \u0026amp; editing. A. Ferrando, P. Ferrando: Data curation, Writing \u0026ndash; review \u0026amp; editing. L. Gal\u0026aacute;n-Garc\u0026iacute;a: Methodology, Data curation, Writing \u0026ndash; review \u0026amp; editing. P. Valdes-Sosa: Methodology, Data curation, Writing \u0026ndash; review \u0026amp; editing. G.A. Chiarenza: Conceptualization; Writing \u0026ndash; review \u0026amp; editing. R.J. Biscay: Methodology, Conceptualization; Writing \u0026ndash; review \u0026amp; editing. L. Morales-Chac\u0026oacute;n: Conceptualization, Methodology, Formal analysis, Data curation, Supervision, Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003eEthics Approval and Informed Consent\u003c/p\u003e\n\u003cp\u003eThe HarMNqEEG normative dataset was derived from retrospectively harmonized data collected under institutional ethics approvals at each contributing site (Li et al. 2022). The clinical case illustration (Section 3.4) was obtained with institutional approval and written informed consent from the participant\u0026rsquo;s legal guardian. All procedures comply with the Declaration of Helsinki.\u003c/p\u003e\n\u003cp\u003eData Availability\u003c/p\u003e\n\u003cp\u003eThe HarMNqEEG normative database is publicly available at https://github.com/CCC-members/HarMNqEEG. GAMLSS model parameters, centile curves, and Z-score computation scripts (MATLAB/R) will be released under an open-source license upon acceptance.\u003c/p\u003e\n\u003cp\u003eArtificial Intelligence Disclosure\u003c/p\u003e\n\u003cp\u003eThe authors used Claude (Anthropic, claude.ai) to assist with the following tasks during manuscript preparation: Python scripting for statistical analysis and figure generation, editing and revision of manuscript text for clarity and concision, and formatting of the reference list. All analytical decisions, interpretation of results, and final manuscript content were made by and remain the responsibility of the authors. The use of this tool was reviewed and approved by all co-authors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlexander LM, Escalera J, Cao L, Doyle C, Taber-Thomas B, Craddock C, Danz D, Esler A, Finegan S, Gupta S, Hamilton AJ, Kopylova O, Milham MP (2017) An open resource for transdiagnostic research in child and adolescent mental health. Sci Data 4:170181. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/sdata.2017.181\u003c/span\u003e\u003cspan address=\"10.1038/sdata.2017.181\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen JJB, Coan JA, Nazarian M (2018) The role of frontal EEG asymmetry in emotion. 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Sci Data 8:45. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41597-021-00829-7\u003c/span\u003e\u003cspan address=\"10.1038/s41597-021-00829-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVald\u0026eacute;s-Sosa et al (1990) Esta referencia corresponde a las developmental surfaces \u0026mdash; las ecuaciones normativas de alta resoluci\u0026oacute;n espectral en. Springer, Brain Topography\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVald\u0026eacute;s-Sosa PA, Biscay R, Gal\u0026aacute;n L, Bosch J, Szava S, Virues T (1990) High resolution spectral EEG norms for topography. Brain Topogr 3:281\u0026ndash;282. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/BF01187711\u003c/span\u003e\u003cspan address=\"10.1007/BF01187711\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"brain-topography","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"btop","sideBox":"Learn more about [Brain Topography](http://link.springer.com/journal/10548)","snPcode":"10548","submissionUrl":"https://submission.nature.com/new-submission/10548/3","title":"Brain Topography","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"quantitative EEG, normative models, GAMLSS, spectral ratios (theta/beta, arousal), electrode-level spectral normalization, therapeutic monitoring","lastPublishedDoi":"10.21203/rs.3.rs-9333312/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9333312/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eQuantitative EEG (qEEG) provides objective, millisecond-resolution measures of brain dynamics. Despite decades of methodological advances, clinically relevant derived indices\u0026mdash;spectral power ratios, cognitive-emotional state markers, and physiological parameters\u0026mdash;are typically reported as raw values without the normative context required for individualized clinical inference.\u003c/p\u003e\u003ch2\u003eObjective\u003c/h2\u003e \u003cp\u003eTo develop the first systematic age-dependent normative models for this family of derived qEEG indices using a multinational database, enabling probabilistic Z-score interpretation at the individual level and objective therapeutic monitoring.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eNormative modeling was applied to the HarMNqEEG database (n\u0026thinsp;=\u0026thinsp;1,564 neurologically healthy participants, ages 5\u0026ndash;97, 9 countries, eyes-closed resting state). Electrode-level Spectral Normalization (ESN) removed inter-individual and inter-device amplitude variability while preserving the neurophysiological interpretability of each index. Age-dependent normative trajectories were estimated using Generalized Additive Models for Location, Scale, and Shape (GAMLSS) with P-splines on log(age), allowing conditional mean and variance to vary non-linearly across the lifespan.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eGAMLSS modeling revealed significant non-linear age-dependent trajectories for all indices. Slow-wave-dominated ratios showed steep decreases from childhood to early adulthood, consistent with cortical maturation; alpha-dominated indices increased during adolescence before stabilizing. ESN normalization yielded well-calibrated normative residuals across the full age range and across all nine recording devices.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThese normative models enable principled, age-adjusted probabilistic inference at the individual level, bridging the historical gap between advanced qEEG methodology and routine clinical practice. The ESN strategy requires no knowledge of recording equipment, ensuring broad applicability. The framework provides an objective tool for monitoring neurophysiological change during therapeutic interventions.\u003c/p\u003e","manuscriptTitle":"Back to the Future of Quantitative EEG: Normative Biomarkers from Spectral Ratios and Functional Indices for Diagnosis and Therapeutic Monitoring","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-21 01:33:16","doi":"10.21203/rs.3.rs-9333312/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-15T13:05:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-07T04:52:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"163116949390165393533044038191248538901","date":"2026-05-06T00:45:57+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-02T07:36:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"311485111396228016917364917305163799064","date":"2026-04-13T15:37:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-13T14:25:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-08T15:05:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-08T10:52:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Brain Topography","date":"2026-04-06T11:10:36+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"brain-topography","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"btop","sideBox":"Learn more about [Brain Topography](http://link.springer.com/journal/10548)","snPcode":"10548","submissionUrl":"https://submission.nature.com/new-submission/10548/3","title":"Brain Topography","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"fefe82f9-8268-49e9-b149-4181638e6144","owner":[],"postedDate":"April 21st, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-15T13:05:02+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-07T04:52:41+00:00","index":14,"fulltext":""},{"type":"reviewerAgreed","content":"163116949390165393533044038191248538901","date":"2026-05-06T00:45:57+00:00","index":13,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-02T07:36:43+00:00","index":12,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-15T13:10:04+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-21 01:33:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9333312","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9333312","identity":"rs-9333312","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}