Brain Topography

In the resting state (closed or open eyes) the electroencephalogram (EEG) and the magnetoencephalogram (MEG) exhibit rhythmic brain activity is typically the 10 Hz alpha rhythm. It has a topographic frequency spectral distribution that is, quite similar for both modalities--something not surprising since both EEG and MEG are generated by the same basic oscillations in thalamocortical circuitry. However, different physical aspects underpin the two types of signals. Does this difference lead to a different distribution of reconstructed sources for EEG and MEG rhythms? This question is important for the transferal of results from one modality to the other but has surprisingly received scant attention till now. We address this issue by comparing eyes open EEG source spectra recorded from 70 subjects from the Cuban Human Brain Mapping project with the MEG of 70 subjects from the Human Connectome Project. Source spectra for each voxel and frequencies between 0-50Hz with 100 frequency points were obtained via a novel sparse-covariance inverse method (BC-VARETA) based on individualized BEM head models with subject-specific regularization parameters (noise to signal ratio). We performed a univariate permutation-based rank test among sources of both modalities and found out no differences. To carry out an unbiased comparison we computed sources from eLORETA and LCMV, performed the same permutation-based comparison, and found the same results we got with BC-VARETA.

Neuronal avalanches are cascade-like events ubiquitously observed across imaging modalities and scales. Aperiodic timing and topographic distribution of these events have been related to the systemic physiology of brain states. However, it is still unknown whether neuronal avalanches are correlates of cognition, or purely reflect physiological properties. In this work, we investigate this question by analyzing intracranial recordings of epileptic participants during rest and passive listening of naturalistic speech and music stimuli. During speech or music listening, but not rest, participants brains "tick" together, as the timing of neuronal avalanches is stimulus-driven and hence correlated across participants. Auditory regions are strongly participating in coordinated neuronal avalanches, but also associative regions, indicating both the specificity and distributivity of cognitive processing. The subnetworks where such processing takes place during speech and music largely overlap, especially in auditory regions, but also diverge in associative cortical sites. Finally, differential pathways of avalanche propagation across auditory and non-auditory regions differentiate brain network dynamics during speech, music and rest. Overall, these results highlight the potential of neuronal avalanches as a neural index of cognition. Authors summaryNeuronal avalanches consist of collective network events propagating across the brain in short-lived and aperiodic instances. These salient events have garnered a great interest for studying the physics of cortical dynamics, and bear potential for studying brain data also in purely neuroscientific contexts. In this work we investigated neuronal avalanches to index cognition, analyzing an intracranial stereo electroencephalography (iEEG) dataset during speech, music listening and resting state in epileptic patients. We show that neuronal avalanches are consistently driven by music and speech stimuli: avalanches co-occur in participants listening to the same auditory stimulus; avalanche topography differs from resting state, presenting partial similarities during speech and music; avalanche propagation changes during speech, music, and rest conditions, especially along the pathways between auditory and non auditory regions. Our work underlines the distributed nature of auditory stimulus processing, supporting neuronal avalanches as a valuable and computationally advantageous framework for the study of cognition in humans.

Electrophysiological population signals contain oscillatory and fractal (1/frequency) components. So far research has largely focused on oscillatory activity and only recently interest in fractal population activity has gained momentum. Accordingly, while the cortical correlation structure of oscillatory population activity has been characterized, little is known about the correlation of fractal neuronal activity. To address this, we investigated fractal neuronal population activity in the human brain using resting-state magnetoencephalography (MEG). We combined source-analysis, signal orthogonalization and irregular-resampling auto-spectral analysis (IRASA) to systematically characterize the cortical distribution and correlation of fractal neuronal activity. We found that fractal population activity is robustly correlated across the cortex and that this correlation is spatially well structured. Furthermore, we found that the cortical correlation structure of fractal activity is similar but distinct from the correlation structure of oscillatory neuronal activity. Anterior cortical regions showed the strongest differences between oscillatory and fractal correlation patterns. Our results suggest that correlations of fractal population activity serve as robust markers of cortical network interactions. Furthermore, our results show that fractal and oscillatory signal components provide non-redundant information about large-scale neuronal correlations. This may reflect at least partly distinct neuronal mechanisms underlying and reflected by oscillatory and fractal neuronal population activity.

A challenge in interpreting features derived from source-space electroencephalography (EEG) and magnetoencephalography (MEG) signals is residual mixing of the true source signals. A common approach is to use features that are invariant under linear and instantaneous mixing. In the context of this approach, it is of interest to know which invariant features can be constructed from a given set of source-projected EEG/MEG signals. We address this question by exploiting the fact that invariant features can be viewed as functions on the Grassmann manifold. By embedding the Grassmann manifold in a vector space, coordinates are obtained that serve as building blocks for invariant features, in the sense that all invariant features can be constructed from them. We illustrate this approach by constructing several new bivariate, higher-order, and multidimensional functional connectivity measures for static and time-resolved analysis of time-domain EEG/MEG signals. Lastly, we apply such an invariant feature derived from the Grassmann manifold to EEG data from comatose survivors of cardiac arrest and show its superior sensitivity to identify changes in functional connectivity. Author SummaryElectroencephalography (EEG) and magnetoencephalography (MEG) are techniques to non-invasively measure brain activity in human subjects. This works by measuring the electric potentials on the scalp (EEG) or the magnetic fluxes surrounding the head (MEG) that are induced by currents flowing in the brains grey matter (the "brain activity"). However, reconstruction of brain activity from EEG/MEG sensor signals is an ill-posed inverse problem and, consequently, the reconstructed brain signals are linear superpositions of the true brain signals. This fact complicates the interpretation of the reconstructed brain activity. A common approach is to only use features of the reconstructed activity that are invariant under linear superpositions. In this study we show that all invariant features of reconstructed brain signals can be obtained by taking combinations of a finite set of fundamental features. The fundamental features are parametrized by a high-dimensional space known as the Grass-mann manifold, which has a rich geometric structure that can be exploited to construct new invariant features. Our study advances the systematic study of invariant properties of EEG/MEG data and can be used as a framework to systematize and interrelate existing results. We use the theory to construct a new invariant connectivity measure and apply it to EEG data from comatose survivors of cardiac arrest. We find that this measure enables superior identification of affected brain regions.

Despite several studies investigating the relationship between blood-oxygen-level-dependent functional MRI (BOLD-fMRI) and neuroelectric activity, our understanding is rather incomplete. For instance, the canonical hemodynamic response function (HRF) is commonly used, regardless of brain region, frequency of electric activity and functional networks. We studied this relationship between BOLD-fMRI and electroencephalography (EEG) signal of the human brain in detail using simultaneous fMRI and EEG in healthy awake human subjects at rest. Signals from EEG sensors were filtered into different frequency bands and reconstructed it in the three-dimensional source space. The correlation of the time courses of the two modalities were quantified on a voxel-by-voxel basis on full-brain level as well as separately for each resting state network, with different temporal shifts and EEG frequency bands. We found highly significant correlations between the BOLD-fMRI signal and simultaneously measured EEG, yet with varying time-lags for different frequency bands and different resting state networks. Additionally, we found significant negative correlations with a much longer delay in the fMRI BOLD signal. The positive correlations were mostly around 6-8 seconds delayed in the BOLD time course while the negative correlations were noticed with a BOLD delay of around 20 to 26 seconds. These positive and negative correlation patterns included the commonly reported alpha and gamma bands but also extend in other frequency bands giving characteristic profiles for different resting state networks. Our results confirm recent works that suggest that the relationship between the two modalities is rather brain region / network-specific than a global function and suggest that applying a global canonical HRF for electrophysiological data is probably insufficient to account for the different spatial and temporal dynamics of different brain networks. Moreover, our results suggest that the HRF also varies in different frequency bands giving way to further studies investigating cross-frequency coupling and its interplay with resting state networks.

Phase coherence and amplitude correlations across brain regions are two main mechanisms of connectivity that govern brain dynamics at multiple scales. However, despite the increasing evidence that associates these mechanisms with brain functions and cognitive processes, the relationship between these different coupling modes is not well understood. Here, we study the causal relation between both types of functional coupling across multiple cortical areas. While most of the studies adopt a definition based on pairs of electrodes or regions of interest, we here employ a multichannel approach that provides us with a time-resolved definition of phase and amplitude coupling parameters. Using data recorded with a multichannel {micro}ECoG array from the ferret brain, we found that the transmission of information between both modes can be unidirectional or bidirectional, depending on the frequency band of the underlying signal. These results were reproduced in magnetoencephalography (MEG) data recorded during resting from the human brain. We show that this transmission of information occurs in a model of coupled oscillators and may represent a generic feature of a dynamical system. Together, our findings open the possibility of a general mechanism that may govern multi-scale interactions in brain dynamics.

Synchronous oscillations of neuronal populations support resting-state cortical activity. Recent studies indicate that resting-state functional connectivity is not static, but exhibits complex dynamics. The mechanisms underlying the complex dynamics of cortical activity have not been well characterised. Here, we directly apply singular value decomposition (SVD) in source-reconstructed electroencephalography (EEG) in order to characterise the dynamics of spatiotemporal patterns of resting-state functional connectivity. We found that changes in resting-state functional connectivity were associated with distinct complex topological features, "Rich-Club organisation", of the default mode network, salience network, and motor network. Rich-club topology of the salience network revealed greater functional connectivity between ventrolateral prefrontal cortex and anterior insula, whereas Rich-club topologies of the default mode networks revealed bilateral functional connectivity between fronto-parietal and posterior cortices. Spectral analysis of the dynamics underlying Rich-club organisations of these source-space network patterns revealed that resting-state cortical activity exhibit distinct dynamical regimes whose intrinsic expressions contain fast oscillations in the alpha-beta band and with the envelope-signal in the timescale of < 0.1 Hz. Our findings thus demonstrated that multivariate eigen-decomposition of source-reconstructed EEG is a reliable computational technique to explore how dynamics of spatiotemporal features of the resting-state cortical activity occur that oscillate at distinct frequencies.

Laminar fMRI holds the potential to study connectivity at the laminar level in humans. Here we analyze simultaneously recorded EEG and high resolution fMRI data to investigate how EEG power modulations, induced by a task with an attentional component, relate to changes in fMRI laminar connectivity between and within brain regions. Our results indicate that our task induced decrease in beta power relates to an increase in deep-to-deep layer coupling between regions and to an increase in deep/middle-to-superficial layer connectivity within brain regions. The attention-related alpha power decrease predominantly relates to reduced connectivity between deep and superficial layers within brain regions, since, unlike beta power, alpha power was found to be positively correlated to connectivity. We observed no strong relation between laminar connectivity and gamma band oscillations. These results indicate that especially beta band, and to a lesser extent alpha band oscillations relate to laminar specific fMRI connectivity. These differential effects for the alpha and beta bands suggest a complex picture of possibly co-occurring neural processes that can differentially affect laminar connectivity.

Magnetoencephalography (MEG) is used extensively to study functional connectivity (FC) networks of phase-synchronization, but the relationship of these networks to their biophysical substrates is poorly understood. Biophysical Network Models (BNMs) have been used to produce networks corresponding to MEG-derived networks of phase-synchronization, but the roles of inter-regional conduction delays, the structural connectome and dynamics of model of individual brain regions, in obtaining this correspondence remain unknown. In this study, we investigated the roles of conduction delays, the structural connectome, and dynamics of models of individual regions, in obtaining a correspondence between model-generated and MEG-derived networks between left-hemispheric regions. To do this, we compared three BNMs, respectively comprising Wilson-Cowan oscillators interacting with diffusion Magnetic Resonance Imaging (MRI)-based patterns of structural connections through zero delays, constant delays and distance-dependent delays respectively. For the BNM whose networks corresponded most closely to the MEG-derived network, we used comparisons against null models to identify specific features of each model component, e.g. the pattern of connections in the structure connectome, that contributed to the observed correspondence. The Wilson-Cowan zero delays model produced networks with a closer correspondence to the MEG-derived network than those produced by the constant delays model, and the same as those produced by the distance-dependent delays model. Hence, there is no evidence that including conduction delays improves the correspondence between model-generated and MEG-derived networks. Given this, we chose the Wilson-Cowan zero delays model for further investigation. Comparing the Wilson-Cowan zero delays model against null models revealed that both the pattern of structural connections and Wilson-Cowan oscillatory dynamics contribute to the correspondence between model-generated and MEG-derived networks. Our investigations yield insight into the roles of conduction delays, the structural connectome and dynamics of models of individual brain regions, in obtaining a correspondence between model-generated and MEG-derived networks. These findings result in a parsimonious BNM that produces networks corresponding closely to MEG-derived networks of phase-synchronization. HighlightsO_LISimple biophysical model produces close match ({rho}=0.49) between model and MEG networks C_LIO_LINo evidence for conduction delays improving match between model and MEG networks C_LIO_LIPattern of structural connections contributes to match between model and MEG networks C_LIO_LIWilson-Cowan oscillatory dynamics contribute to match between model and MEG networks C_LI

Recent years have seen an increasing interest in the spatiotemporal dynamics of oscillatory brain activity. Recordings at various scales have shown oscillations propagating as waves over cortical space, both at small and large scales. The most common waves observed in the EEG are planar waves, formed by a synchronized wavefront propagating in a consistent direction (e.g., posterior-anterior). These waves have been linked to diverse perceptual and cognitive measures. However, their quantification has faced issues due to the inherently noisy EEG signal and its ambiguous spatial localization. Existing methods employ restrictive windows of analysis (e.g., lines of electrodes) or rely on wave motifs extracted from the data. A specific algorithm for detecting planar waves is still lacking. Here, we present a comprehensive analysis pipeline for this purpose, comprising three steps: first, genuine oscillatory activity is extracted from the EEG as clusters. The spatial phase gradient is then fit using a spherical wave model. Finally, stable waves are extracted from the time series of fits. We validate our method using simulations over a physiological range of parameters. Using a forward model, we test EEG wave detection for propagation along different pathways at the source level. Lastly, we apply our analysis to real EEG recordings, targeting alpha oscillations during visual stimulation and at rest. In summary, our method provides a reliable algorithm for detecting planar waves in the EEG. Given the emerging functional roles of traveling waves in perception and cognition, this could potentially be utilized in a wide range of future studies.

Understanding intelligence-related variations in electroencephalographic (EEG) activity requires advanced mathematical approaches capable of capturing geometric transformations and long-range dependencies in neural dynamics. These approaches may provide methodological advantages over conventional spectral and connectivity-based techniques by offering deeper insights into the structural and functional organization of neural networks. In this study, we integrate Clifford algebra, Noethers theorem and fractional calculus to analyze EEG signals from high- and low-IQ individuals, looking for key intelligence-related differences in cortical organization. Clifford algebra enables the representation of EEG signals as multivectors, preserving both magnitude and directional relationships across cortical regions. Noethers theorem provides a quantitative measure of symmetry properties linked to spectral features, identifying conserved functional patterns across distinct brain regions. Mittag-Leffler functions, derived from fractional calculus, characterize long-range dependencies in neural oscillations, allowing for the detection of memory effects and scale-invariant properties often overlooked by traditional methods. We found significant differences between high- and low-IQ individuals in geometric trajectories, hemispheric connectivity, spectral properties and fractional-order dynamics. High-IQ individuals exhibited increased spectral asymmetry, enhanced spectral differentiation, distinct geometric trajectories and greater fractional connectivity, particularly in frontal and central regions. In contrast, low-IQ individuals displayed more uniform hemispheric connectivity and heightened fractional activity in occipital areas. Mittag-Leffler fractional exponents further indicated that high-IQ individuals possessed more varied neural synchronization patterns. Overall, our multi-faceted approach suggests that intelligence-related neural dynamics are characterized by an asymmetric, functionally specialized and fractionally complex cortical organization. This results in significant differences in network topology, efficiency, modularity and long-range dependencies.

Neuronal oscillations in different frequency bands have been linked to a wide variety of cognitive functions, and may even be a fundamental mechanism of inter-regional communication. For this reason, manipulation of oscillatory activity via brain stimulation is a central goal in neuroscience research. However, the vast majority of studies characterise oscillatory activity solely in terms of amplitude and frequency. Oscillations can also be characterised by their waveform shape; the degree to which they resemble or deviate from sinusoids. Here we exploit Empirical Mode Decomposition (EMD), a novel method that allows quantification of oscillatory waveform shape. We show for the first time that transcranial direct current stimulation (tDCS) alters the waveform shape of gamma oscillatory activity in the visual cortex. Notably, changes in waveform shape were limited to one half of the phase cycle; anodal stimulation led to a relatively slower, and cathodal to a relatively faster, descending half-wave. tDCS is generally believed to affect cortical excitability via alteration of resting membrane potential. Interestingly, simulations of altered cortical excitability in a gamma-generating neuronal population indicated the waveform shape changes observed experimentally likely stem from stimulation of pyramidal neurons. These findings have implications for understanding the neural consequences of tDCS at the level of neuronal population phenomena such as cortical oscillations and underscore the importance of waveform shape as an important feature of neuronal oscillations.

Our moment-to-moment conscious experience is paced by transitions between states, each one corresponding to a change in the electromagnetic brain activity. One consolidated analytical choice is to characterize these changes in the frequency domain, such that the transition from one state to the other corresponds to a difference in the strength of oscillatory power, often in pre-defined, theory-driven frequency bands of interest. Today, the huge leap in available computational power allows us to explore new ways to characterize electromagnetic brain activity and its changes. Here we leveraged an innovative set of features on an MEG dataset with 29 human participants, to test how these features described some of those state transitions known to elicit prominent changes in the frequency spectrum, such as eyes-closed vs eyes-open resting-state or the occurrence of visual stimulation. We then compared the informativeness of multiple sets of features by submitting them to a multivariate classifier (SVM). We found that the new features outperformed traditional ones in generalizing states classification across participants. Moreover, some of these new features yielded systematically better decoding accuracy than the power in canonical frequency bands that has been often considered a landmark in defining these state changes. Critically, we replicated these findings, after pre-registration, in an independent EEG dataset (N=210). In conclusion, the present work highlights the importance of a full characterization of the state changes in the electromagnetic brain activity, which takes into account also other dimensions of the signal on top of its description in theory-driven frequency bands of interest.

One frequently studied biomarker for health and disease conditions is the P3 component extracted from scalp recorded electroencephalography (EEG). The spatial origin of this significant neural signal is known to be distributed, typically involving large regions of the cerebral cortex as well as subcortical structures. Unlike the temporal characterization of the P3 by amplitude or latency measures from event-related potentials (ERPs), the spatial characterization of the P3 component is relatively rare, typically qualitative, and often reported as differences between populations (group differences between healthy controls and clinical groups). Here we introduce a novel approach to quantitatively characterize the spatial origin of the P3 component by (1) applying second-order blind identification (SOBI) to continuous, high-density EEG data to extract the P3 component, (2) modeling the underlying generators of the SOBI P3 component as a set of equivalent current dipoles (ECDs) in Talairach space using BESA; (3) using the application Talairach Client to determine the "hits" associated with the anatomical structures at three level of resolution (lobe, gyrus, and cell type). We show that the hits information provided by Talairach Client can enable a quantitative characterization of the spatial configuration of the network underlying the P3 component (P3N) via two quantities: cross-individual reliability (or consistency) of a given brain structure as a part of the P3N, and within-individual contribution of a given brain structure to the whole P3N network. We suggest that this method may be used to further differentiate individuals in the absence of differences in P3 amplitude or latency, or when scientific questions or practical application cannot be supported by a yes-no answer regarding the source of a P3 component. Finally, application of our method to a group of 13 participants revealed that frontal structures, particularly BA10, play a special role in the function of a global cortical network underlying novelty processing.

Growing evidence suggests that travelling waves are functionally relevant for cognitive operations in the brain. Several electroencephalography (EEG) studies report on a perceptual alpha-echo, representing the brain response to a random visual flicker, propagating as a travelling wave across the cortical surface. In this study, we ask if the propagating activity of the alpha-echo is best explained by a set of discrete sources mixing at the sensor level rather than a cortical travelling wave. To this end, we presented participants with gratings modulated by random noise and simultaneously acquired the ongoing MEG. The perceptual alpha-echo was estimated using the temporal response function linking the visual input to the brain response. At the group level, we observed a spatial decay of the amplitude of the alpha-echo with respect to the sensor where the alpha-echo was the largest. Importantly, the propagation latencies consistently increased with the distance. Interestingly, the propagation of the alpha-echoes was predominantly centro-lateral, while EEG studies reported mainly posterior-frontal propagation. Moreover, the propagation speed of the alpha-echoes derived from the MEG data was around 10 m/s, which is higher compared to the 2 m/s reported in EEG studies. Using source modelling, we found an early component in the primary visual cortex and a phase-lagged late component in the parietal cortex, which may underlie the travelling alpha-echoes at the sensor level. We then simulated the alpha-echoes using realistic EEG and MEG forward models by placing two sources in the parietal and occipital cortices in accordance with our empirical findings. The two-source model could account for both the direction and speed of the observed alpha-echoes in the EEG and MEG data. Our results demonstrate that the propagation of the perceptual echoes observed in EEG and MEG data can be explained by two sources mixing at the scalp level equally well as by a cortical travelling wave. This conclusion however does not put into question continuous travelling waves reported in intracranial recordings.

Several studies have shown that coordination among neural ensembles is a key to understand human cognition. A well charted path is to identify coordination states associated with cognitive functions from spectral changes in the oscillations of EEG or MEG. A growing number of studies suggest that the tendency to switch between coordination states, sculpts the dynamic repertoire of the brain and can be indexed by a measure known as metastability. In this article, we characterize perturbations in the metastability of global brain network dynamics following Transcranial Magnetic Stimulation that could quantify the duration for which information processing is altered, thus, allowing researchers to understand the network effects of brain stimulation, standardise stimulation protocols and design experimental tasks. We demonstrate the effect empirically using publicly available datasets and use a digital twin (a whole brain connectome model) to understand the dynamic principles that generate such observations. We observed a significant reduction in metastability, concurrent with an increase in coherence following single-pulse TMS reflecting the existence of a window where neural coordination is altered. The reduction in complexity was validated by an additional measure based on the Lempel-Ziv complexity of microstate labelled EEG data. Interestingly, higher frequencies in the EEG signal showed faster recovery in metastability than lower frequencies. The digital twin shed light on how the phase resetting introduced by the single-pulse TMS in local cortical networks can propagate globally across the whole brain and give rise to changes in metastability and coherence.

Efficient language production requires rapid interactions between different brain areas. These interactions can be severely affected by brain lesions. However, the neurophysiological correlates of the spatiotemporal dynamics during language production are not well understood. The current pilot study explores differences in spatiotemporal cortical dynamics between five subjects with post-stroke aphasia and five control subjects. Electroencephalography was recorded during picture naming in both groups. Average-based analyses (event-related potential (ERP), frequency-specific Global Field Power (GFP)), reveal a strong synchronization of cortical oscillations, especially within the first 600ms post-stimulus, with a time shift between participants with aphasia and control subjects. ERPs and the corresponding brain microstates indicate coordinated brain activity alternating mainly between frontal and occipital zones. This behavior can be described as standing waves between two main sources. At the single-trial scale, traveling waves (TW) were identified from both phase and amplitude analyses. The spatiotemporal distribution of amplitude TW reveals subject-specific organization of several interconnected hubs. In patients with aphasia this spatial organization of TW reveals zones with no TW notably in the vicinity of stroke lesions. The present results provide important hints for the hypothesis that TW contribute to the synchronization and communication between different brain areas especially by interconnecting cortical hubs. Moreover, our findings show that cortical dynamics is affected by brain lesions. Contribution to the FieldO_LISpatiotemporal cortical dynamics of individual trials reveals the presence of phase and amplitude traveling waves. C_LIO_LIExploration of traveling waves on the 2D cortical surface reveals the presence of interconnected epicenters or hubs in all subjects. C_LIO_LIThe spatiotemporal distribution of traveling waves shows a higher density in the prefrontal area for people with aphasia than for healthy subjects. C_LIO_LIFor subjects with aphasia, a sparser density of traveling waves is observed in the approximated lesion area. C_LIO_LIEvent-related potential analyses reveal a consistent alternating activity between the frontal and occipital regions. C_LIO_LISubjects with aphasia present a larger and/or delayed contribution in the delta range in the GFP patterns compared to control subjects. C_LI

Whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. This seemingly worthless sentence is an informal description of the hairy ball theorem, an invaluable mathematical weapon that has been proven useful to describe a variety of physical/biological processes/phenomena in terms of topology, rather than classical cause/effect relationships. In this paper we will focus on the electrical brain field - electroencephalogram (EEG). As a starting point we consider the recently-raised observation that, when electromagnetic oscillations propagate with a spherical wave front, there must be at least one point where the electromagnetic field vanishes. We show how this description holds also for the electric waves produced by the brain and detectable by EEG. Once located these zero-points in EEG traces, we confirm that they are able to modify the electric wave fronts detectable in the brain. This sheds new light on the functional features of a nonlinear, metastable nervous system at the edge of chaos, based on the neuroscientific model of Operational Architectonics of brain-mind functioning. As an example of practical application of this theorem, we provide testable previsions, suggesting the proper location of transcranial magnetic stimulations coils to improve the clinical outcomes of drug-resistant epilepsy.

A particular yet computationally successful solution of an inverse transcranial magnetic stimulation (TMS) problem is reported. The goal has been focusing the normal unsigned electric field at the inner cortical surface and its vicinity (the D wave activation site) given a unique high-resolution gyral pattern of a subject and a precise coil model. For 16 subjects and 32 arbitrary target points, the solution decreases the mean deviation of the maximum-field domain from the target by a factor of 2 on average. The reduction in the maximum-field area is expected to quadruple. The average final deviation is 6 mm. Rotation about the coil axis is the most significantly altered parameter, and the coil moves 10 mm on average during optimization. The maximum electric field magnitude decreases by 16% on average. Stability of the solution is enforced. The relative average de-focalization is below 1.2 when position/orientation accuracies are within 3 mm/6 degrees, respectively. The solution for the maximum normal field may also maximize the total field and its gradient for neighboring cortical layers III-V (I wave activation).

A fundamental view of neuroscience is that, in addition to neuronal activity, the structure of the brain constrains and explains brain function. An alluring formalism in computational neuroscience has been the generation of structural eigenmodes of neural activity from a matrix representing the anatomy of the brain. Traditionally, brain connectomics has been the gold standard for the coupling between structure and function. However, it has recently been suggested that simpler brain geometry can provide more explanatory power in fMRI. An adjacent modality is the source localisation problem of EEG, which aims to identify the underlying generators of EEG recordings. The underdetermined nature of the problem requires sufficient constraints to produce realistic and unique solutions of source activity. In this work, we presented a simple framework for incorporating different forms of structural brain eigenmodes to constrain the source localisation problem in epilepsy. We found that geometric eigenmodes were able to reconstruct the spread of a seizure through the brain slightly better than connectome eigenmodes, and both types of structural modes significantly outperformed commonly used approaches.