Recordings of electromagnetic fields from the human brain are widely used to study neurophysiological processes and their characterize functional changes across typical and clinical mental states. Non-invasive techniques, such as electroencephalography (EEG) and magnetoencephalography (MEG), are commonly employed to capture these recordings. These methods predominantly measure the integrated activity of post-synaptic and transmembrane currents generated by thousands of neurons (Lopes da Silva, 2013). Historically, EEG and MEG recordings have been interpreted primarily as reflecting rhythmic brain activity, commonly referred to as neural oscillations (Buzsáki and Draguhn, 2004).

EEG and MEG studies have traditionally compared properties of neural oscillatory across experimental groups or conditions by analyzing metrics averaged over a fixed recording period. However, this approach may overlook key aspects of temporal variability, in particular, rare events with extreme values near the maximum. Empirical evidence indicates that many brain parameters, such as firing rates or synapse counts, follow skewed distributions (Buzsáki and Mizuseki, 2014). This pattern extends to both functional and anatomical features of the brain across multiple hierarchical levels (Buzsáki and Mizuseki, 2014; Roberts et al., 2015).

Skewed distributions suggest that single representative values, such as the mean or median, fail to capture the full range of temporal variability in brain activity (Limpert and Stahel, 2011). For instance, no single “average” neuron exists in a population because the minority of fast-firing neurons disproportionately influences the group’s mean firing rate. Similarly, neuronal ensemble sizes cannot be accurately described by an average value, as their distribution often follows, if not a pure power law, then at least a hybrid distribution combining power-law scaling and exponential decay (Dehghani et al., 2012). These findings underscore the need to account for the heavy-tailed nature of brain activity distributions when analyzing neural dynamics.

Multiple studies have demonstrated associations between temporal variability in neurophysiological signals and various cognitive, behavioral, and sensory processes (Basalyga and Salinas, 2006; McIntosh et al., 2008; Pinneo, 1966). Signal variability have been proposed as an indicator of effective and optimal performance (Faisal et al., 2008). However, despite the substantial body of research in this area, many studies continue to rely on traditional averaging approaches to analyze neurophysiological data (Garrett et al., 2013). These approaches present significant limitations as they fail to account for the inherently skewed distributions that characterize the variability of parameters governing the behavior of the underlying dynamical systems.

There is no consensus on which temporal properties of neural activity are most sensitive to variations in mental states (Cohen, 2017). Several theoretical frameworks have been proposed to capture different aspects of temporal dynamics. Key concepts in this literature include brain microstates (Musso et al., 2010), neuronal avalanches (Beggs and Plenz, 2003), and metastability (Tognoli and Kelso, 2014). Brain microstates are defined as brief periods of quasi-stable brain activity, thought to result from the coordinated activation of neural ensembles within specific networks (Vakorin et al., 2013). The theory of neuronal avalanches describes neurophysiological activity as cascades of bursts, supported by neural networks of varying sizes (Plenz and Thiagarajan, 2007). Finally, metastability characterizes a sequence of relatively stable states in a complex dynamical system. These states emerge from interactions among multiple parameters within the system’s phase space (Naik et al., 2017). Metastability offers a theoretical framework for understanding the balance between the brain’s stable activity patterns and its transient dynamics (Deco and Kringelbach, 2016).

These frameworks have been adapted to characterize age-related changes in temporal properties of neural oscillations in the typical brain across the lifespan (Kahana, 2006). Using the concept of microstates, Vakorin et al. (2013) explored age-related changes across early adolescence in resting-state EEG dynamics in eyes open and closed conditions under the framework of microstates. They showed that the number of microstates increased with age, whereas their average durations decreased. Similarly, Brookes et al. (2018) reported that when the number of microstates are held constant, the mean time spent in each state increased with age, spanning mid-childhood to early adulthood. Other studies have focused on the relationships between neurodynamic events and ageing. For rexample, Fosque et al. (2022) analyzed age-related changes in neural avalanche properties in adults across a wide age range.

Also, the concept of brain metastability has been used to quantify the signal complexity of neural oscillations. Signal complexity reflects the amount of information in neural signals, representing the collective activity of neuronal ensembles (Deco et al., 2017). Lippe et al. (2009) observed age-related increases in the complexity of resting-state EEG signals across infants and children. They also examined the relationship between maturation and signal complexity during a rapid face recognition task in children and young adults, reporting increased complexity with age.

In this study, we aimed to investigate extreme neural dynamics, characterized by the tails of skewed distributions of brain parameters, using skewness and kurtosis. Skewness quantifies the asymmetry of a probability distribution, while kurtosis measures the extremity of the tails without reflecting the shape of the central peak (Westfall, 2014). Both metrics capture properties of the signal tails, which may indicate periods of intense cognitive processing or heightened attention, as well as potential markers of cognitive impairment or neural dysfunction (Buzsáki and Mizuseki, 2014).

The tails of skewed distributions likely reflect moments of long-range synchronized neural activity, a process believed to play a critical role in both cognitive function and pathological conditions (Meijer et al., 2020; Nowak et al., 2017). Heightened synchronization during these moments may optimize neural processing but can also lead to pathological outcomes, such as seizures, when excessive (Jiruska et al., 2013). For example, several studies have examined extreme values in cortical oscillations under clinical conditions such as epilepsy, demonstrating their utility in facilitating seizure detection from EEG recordings (Xiang et al., 2020; Karpov et al., 2022). Other studies have identified differences in signal power distributions under varying conditions, such as the transitions between eyes-open and eyes-closed states, emphasizing the relevance of extreme values in characterizing the temporal variability of neurophysiological recordings (Mišić et al., 2011).

Statistical properties of distribution tails, such as skewness and kurtosis, provide practical insights into cognitive and clinical states. Skewness has proven effective in distinguishing cognitive states, such as meditation, mathematical problem-solving, and open-eye conditions, highlighting its potential for cognitive state monitoring (Joshua Davis et al., 2020). Similarly, kurtosis has demonstrated clinical relevance in multiple domains. In pediatric epilepsy, high-frequency brain signals exhibit significantly elevated kurtosis in patients compared to controls, particularly in epileptogenic zones (Xiang et al., 2020). This makes kurtosis a useful biomarker for identifying seizure onset regions and guiding clinical interventions. Also, kurtosis-based methods have been developed for detecting high-frequency oscillations in intracranial EEG, which are critical for localizing seizure onset zones in epilepsy patients (Quitadamo et al., 2018).

Kurtosis has also been implicated in neurodegenerative disorders. EEG studies in Alzheimer’s patients reveal higher kurtosis values compared to controls, leading to the development of kurtosis-based denoising techniques that enhance diagnostic accuracy (Liu et al., 2015). Furthermore, brain-computer interface (BCI) research has used kurtosis to classify motor imagery tasks in EEG data, achieving high accuracy in distinguishing between imagined left- and right-hand movements (Wu and Ye, 2006).

Empirical evidence on age-related changes in the maximal capacities of neurophysiological parameters remains limited, particularly when examined across the lifespan. In this study, we aimed to investigate brain ageing by focusing on extreme events in neurodynamics across adulthood, spanning young to elderly adults. We hypothesized that ageing would be associated with frequency-specific trajectories in the brain’s capacity to generate extreme neurodynamic events.

To quantify these age-related changes, we analyzed resting-state magnetoencephalography (MEG) recordings from the Cam-CAN repository (Shafto et al., 2014). Our analysis focused on frequency-specific temporal variations in MEG amplitude, assessing their statistical properties through the metrics of skewness and kurtosis. These metrics characterized the tails of the amplitude distributions, capturing extreme dynamics in brain activity. We then examined how these parameters evolved with age, identifying spatio-spectral patterns of age-related trajectories in extreme neurodynamics throughout adulthood.

We performed 10 group analyses with PLS (five frequencies times two MEG measures), reporting the data-driven overall group contrasts with the largest variance explained. The group contrast was significant at all frequencies except for the kurtosis measure at lower gamma oscillations.

Our findings revealed that extreme events in the temporal variability of MEG signal amplitude, as quantified by skewness and kurtosis, exhibited distinct ageing trajectories across adulthood. These trajectories varied spectrally across the five canonical frequency bands: delta, theta, alpha, beta, and lower gamma. Furthermore, the spatial distributions of these age-related changes were region-specific, highlighting unique patterns of neurophysiological ageing across the brain. This study is the initial attempt to investigate the skewed nature of frequency-specific oscillations and to quantify empirical distributions of brain rhythm variability across the full adult lifespan, from young to elderly individuals. Importantly, we introduced a novel framework that focuses on extreme events in neurophysiological variability. This aspect is commonly overlooked in traditional neurophysiological studies, which typically emphasize average values and fail to capture the broader spectrum of temporal variability.

Our findings can be interpreted within the framework of the brain criticality hypothesis (O'Byrne and Jerbi, 2022). This hypothesis posits that optimal information processing in a healthy brain occurs at a phase transition point between synchronous and asynchronous, or regular and irregular, states. A brain operating near criticality can rapidly transition between these states, with small bursts of neurodynamic activity potentially giving rise to extreme value events. According to this framework, critical neural networks are essential for achieving optimal information transfer, which may explain the occurrence of extreme events in brain dynamics.

Our analysis revealed that the skewness and kurtosis of delta oscillations increased with age, indicating greater deviations from white noise in the form of extreme value events in MEG signal amplitude (Figures 4C,F). These findings align with recent work by Fosque et al. (2022), which investigated the brain’s functional organization across the lifespan under the framework of quasicriticality. Using the same MEG dataset from the Cam-CAN repository, Fosque et al. (2022) suggested that the brain operates near a line of maximal dynamic susceptibility, achieving a critical point for optimal information processing without external stimuli, noise, or dissipation. In this state, neuronal networks are activated successively through neuronal avalanches, whose size and duration follow scale-free or power-law distributions. Fosque et al. (2022) identified a positive correlation between the variance of avalanche size and age across adulthood. They did not consider individual frequency bands. However, considering that MEG spectral power approximately follows a 1/f distribution, the lowest frequencies, such as delta rhythms, are expected to significantly contribute to the reported correlations.

Further evidence supporting our results aronf the delta frequencies comes from Vakorin et al. (2013), who investigated age-related changes in adolescence by examining the non-stationarity of EEG rhythms as a sequence of quasi-stable patterns. They segmented EEG recordings into clusters of similar dynamics and quantified them in terms of the number of quasi-stationary microstates and their durations. They found that the mean duration of stationary EEG segments decreased with age, and these changes were correlated with variability in the signal power of delta oscillations. These findings suggest greater non-stationarity and complexity of delta oscillations during adolescence. Such a pattern resonates with our current results, which show an increase in extreme value events of delta oscillations with age. Collectively, these studies provide convergent evidence that changes in extreme value dynamics, particularly in lower frequency bands like delta rhythms, play a critical role in both developmental and ageing processes.

Our results revealed age-related changes in the theta (Figure 5) and beta rhythms (Figure 3), characterized by both increases and decreases in the skewness and kurtosis of temporal variability in neuromagnetic signal amplitude. The underlying spatial re-distribution of energy associated with these changes remains unclear. Previous research has linked similar spatial changes during ageing to a balance between localized neural processing and long-range communication (McIntosh et al., 2014). McIntosh and colleagues examined the signal complexity of EEG and MEG oscillations across young, middle-aged, and elderly adults. Using metrics such as entropy, they found that local entropy increased with age, which was associated with functional connectivity within each hemisphere. Conversely, distributed or global entropy decreased with age, particularly for interhemispheric connections.

Interestingly, in our study, the spatial patterns of age-related changes in the probability of extreme events for the theta and beta rhythms appeared visually similar. This observation may reflect cross-frequency coupling, a mechanism by which local dynamics could be integrated into long-range communication (Buzsáki and Watson, 2012). Cross-frequency coupling allows slower oscillations to propagate across broader spatial scales, facilitating neural coordination (Canolty and Knight, 2010). Specifically, coupling between theta and beta oscillations may play a critical role in sustaining healthy sensory networks (Cravo et al., 2011). This potential interaction between rhythms underscores the importance of exploring how cross-frequency dynamics contribute to changes in neural function across the lifespan. In addition to theta-beta coupling, due to the prominence of changes in alpha power across age (Broitman et al., 2024), we suggest that future studies also analyze coupling effects between alpha and other frequency bands, in the context of extreme events.

Our findings also can be considered in the context of previous studies investigating age-related changes in the aperiodic component of neural signals. This component is characterized by a 1/f spectral trend and is distinct from the rhythmic oscillations traditionally associated with EEG. The 1/f component is thought to reflect aperiodic neural activity that can influence the interpretation of EEG data, particularly in the context of brain network organization (Brake et al., 2024). Furtehrmore, it may reflect the baseline level of neural activity which has been linked to processing speed and cognitive decline in ageing populations (Tran et al., 2020), and more generally may be related to excitatory-inhibitory balance (Salvatore et al., 2024). The 1/f component has been shown to shift with ageing (Voytek et al., 2015). Since changes in the 1/f component likely influence the maximum values of neural signals, variations in the kurtosis and skewness of the signal may partially reflect this underlying shift in the aperiodic component. While our analysis focused explicitly on extreme events within the spectral bands, incorporating the 1/f exponent in future studies could provide a more comprehensive understanding of extreme neurodynamic events. This approach may help clarify how aperiodic shifts interact with rhythmic brain activity. Future research could benefit from using mathematical models that explain the generation of EEG signals (Brake et al., 2024).

We note that the two metrics we used in our analysis, skewness and kurtosis, produced similar results. These metrics are sensitive to extreme values, which makes them useful in neurological applications (Karpov et al., 2022; Xiang et al., 2020). For unimodal distributions such as the log-normal distribution, both skewness and kurtosis can be expected to reflect tail properties. Hence, it is not surprising that we found qualitatively similar results using both metrics in all frequency bands of interest, except for the gamma band. For instance, a previous study found that both higher skewness and kurtosis of MEG signals in three frequency bands (theta to lower gamma oscillations, ripples, and fast ripples) were associated with pediatric epilepsy compared to the control group (Xiang et al., 2020). Although it was not our explicit goal, our study confirms that skewness and kurtosis provide virtually identical results for our data set.

Our study has limitations. First, we used cross-sectional data to examine age-related changes, which limits our ability to quantify ageing trajectories. Cohort differences may influence the comparisons across age groups, as noted by Salthouse (2019). Second, our study does not account for the heterogeneity or sub-types within the ageing population, as recent research by Rodrigues et al. (2022), Nyberg et al. (2023), and Hinault et al. (2023) has highlighted. These studies suggest that the ageing population should not be treated as a homogeneous group, opening new avenues for future research. Potentially, our patterns of age-related changes may be affected by muscle artifacts. We aggregate our estimates by computing the median metrics across segments, which may help to mitigate the influence of artificial patterns within individual subjects.

In conclusion, our study introduces and validates a new framework focusing on extreme neurodynamic events to investigate brain processing across the adult lifespan. We found that ageing is characterized by shifts in the occurrence of large-amplitude neurodynamic events. These extreme events, measured through sample skewness and kurtosis of the MEG signal amplitude distributions, exhibit distinct temporal and spatial patterns across all frequency bands, from theta to lower gamma. These markers may offer a complementary view for defining age-related trajectories of healthy brain processing. By emphasizing extreme events rather than typical or mean values, our framework provides a novel approach to understanding brain function. Our findings highlight the potential of extreme events in neurodynamics for exploring maximal capacities, thereby contributing to a more comprehensive understanding of the neural mechanisms underlying ageing.