Global Neuromagnetic Cortical Fields Have Non-Zero Velocity

Cortex-wide spontaneous activity non-linearly steers propagating sensory-evoked activity in awake mice

The brain responds highly variably to identical sensory inputs, but there is no consensus on the nature of this variability. We explore this question using cortex-wide optical voltage imaging and whisker stimulation in awake mice. Clustering analysis reveals that the sensory-evoked activity propagates over the cortex via distinct pathways associated with distinct behavioral states. The pathway taken by each trial is independent of the level of primary sensory-evoked activation but is partially predictable by the spatiotemporal features of the preceding cortical spontaneous activity patterns. The sensory inputs reduce trial-to-trial variability in brain activity and alter temporal autocorrelation in spatial activity pattern evolutions, suggesting non-linear interactions between evoked activities and spontaneous activities. Further, evoked activities and spontaneous activities occupy different positions in the state space, suggesting that sensory inputs can intricately interact with the internal state to generate large-scale evoked activity patterns not frequented by spontaneous brain states.

Cortical traveling waves reflect state-dependent hierarchical sequencing of local regions in the human connectome network

Recent human studies using electrocorticography have demonstrated that alpha and theta band oscillations form traveling waves on the cortical surface. According to neural synchronization theories, the cortical traveling waves may group local cortical regions and sequence them by phase synchronization; however these contributions have not yet been assessed. This study aimed to evaluate the functional contributions of traveling waves using connectome-based network modeling. In the simulation, we observed stable traveling waves on the entire cortical surface wherein the topographical pattern of these phases was substantially correlated with the empirically obtained resting-state networks, and local radial waves also appeared within the size of the empirical networks (< 50 mm). Importantly, individual regions in the entire network were instantaneously sequenced by their internal frequencies, and regions with higher intrinsic frequency were seen in the earlier phases of the traveling waves. Based on the communication-through-coherence theory, this phase configuration produced a hierarchical organization of each region by unidirectional communication between the arbitrarily paired regions. In conclusion, cortical traveling waves reflect the intrinsic frequency-dependent hierarchical sequencing of local regions, global traveling waves sequence the set of large-scale cortical networks, and local traveling waves sequence local regions within individual cortical networks.

Nonlinear analysis of periodic waves in a neural field model

Various types of brain activity, including motor, visual, and language, are accompanied by the propagation of periodic waves of electric potential in the cortex, possibly providing the synchronization of the epicenters involved in these activities. One example is cortical electrical activity propagating during sleep and described as traveling waves [Massimini et al., J. Neurosci. 24, 6862-6870 (2004)]. These waves modulate cortical excitability as they progress. Clinically related examples include cortical spreading depression in which a wave of depolarization propagates not only in migraine but also in stroke, hemorrhage, or traumatic brain injury [Whalen et al., Sci. Rep. 8, 1-9 (2018)]. Here, we consider the possible role of epicenters and explore a neural field model with two nonlinear integrodifferential equations for the distributions of activating and inhibiting signals. It is studied with symmetric connectivity functions characterizing signal exchange between two populations of neurons, excitatory and inhibitory. Bifurcation analysis is used to investigate the emergence of periodic traveling waves and of standing oscillations from the stationary, spatially homogeneous solutions, and the stability of these solutions. Both types of solutions can be started by local oscillations indicating a possible role of epicenters in the initiation of wave propagation.

Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation

The aim of this paper is to integrate different bodies of research including brain traveling waves, brain neuromodulation, neural field modeling and post-stroke language disorders in order to explore the opportunity of implementing model-guided, cortical neuromodulation for the treatment of post-stroke aphasia. Worldwide according to WHO, strokes are the second leading cause of death and the third leading cause of disability. In ischemic stroke, there is not enough blood supply to provide enough oxygen and nutrients to parts of the brain, while in hemorrhagic stroke, there is bleeding within the enclosed cranial cavity. The present paper focuses on ischemic stroke. We first review accumulating observations of traveling waves occurring spontaneously or triggered by external stimuli in healthy subjects as well as in patients with brain disorders. We examine the putative functions of these waves and focus on post-stroke aphasia observed when brain language networks become fragmented and/or partly silent, thus perturbing the progression of traveling waves across perilesional areas. Secondly, we focus on a simplified model based on the current literature in the field and describe cortical traveling wave dynamics and their modulation. This model uses a biophysically realistic integro-differential equation describing spatially distributed and synaptically coupled neural networks producing traveling wave solutions. The model is used to calculate wave parameters (speed, amplitude and/or frequency) and to guide the reconstruction of the perturbed wave. A stimulation term is included in the model to restore wave propagation to a reasonably good level. Thirdly, we examine various issues related to the implementation model-guided neuromodulation in the treatment of post-stroke aphasia given that closed-loop invasive brain stimulation studies have recently produced encouraging results. Finally, we suggest that modulating traveling waves by acting selectively and dynamically across space and time to facilitate wave propagation is a promising therapeutic strategy especially at a time when a new generation of closed-loop cortical stimulation systems is about to arrive on the market.

Next-generation neural mass and field modeling

The Wilson-Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson-Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson-Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Large-scale cortical travelling waves predict localized future cortical signals

Predicting future brain signal is highly sought-after, yet difficult to achieve. To predict the future phase of cortical activity at localized ECoG and MEG recording sites, we exploit its predominant, large-scale, spatiotemporal dynamics. The dynamics are extracted from the brain signal through Fourier analysis and principal components analysis (PCA) only, and cast in a data model that predicts future signal at each site and frequency of interest. The dominant eigenvectors of the PCA that map the large-scale patterns of past cortical phase to future ones take the form of smoothly propagating waves over the entire measurement array. In ECoG data from 3 subjects and MEG data from 20 subjects collected during a self-initiated motor task, mean phase prediction errors were as low as 0.5 radians at local sites, surpassing state-of-the-art methods of within-time-series or event-related models. Prediction accuracy was highest in delta to beta bands, depending on the subject, was more accurate during episodes of high global power, but was not strongly dependent on the time-course of the task. Prediction results did not require past data from the to-be-predicted site. Rather, best accuracy depended on the availability in the model of long wavelength information. The utility of large-scale, low spatial frequency traveling waves in predicting future phase activity at local sites allows estimation of the error introduced by failing to account for irreducible trajectories in the activity dynamics.

Prediction is an important step in scientific progress, often leading to real-world applications. Prediction of future brain activity could lead to improvements in detecting driver and pilot error or real-time brain testing using transcranial magnetic stimulation. Previous studies have either supposed that the ‘noise’ level in the cortex is high, setting the prediction bar rather low; or used localized measurements to predict future activity, with modest success. A long-held but controversial hypothesis is that the cortex is best characterized as a multi-scale dynamic structure, in which the flow of activity at one scale, say, the area responsible for motor control, is inextricably tied to activity at smaller and larger scales, for example within a cortical column and the whole cortex. We test this hypothesis by analyzing large-scale traveling waves of cortical activity. Like waves arriving on a beach, the ongoing wave motion allows better prediction of future activity compared to monitoring the local rise and fall; in the best cases the future wave cycle is predicted with as low as 20° average error angle. The prediction techniques developed for the present research rely on mathematics related to quantifying large-scale weather patterns or analysis of fluid dynamics.

Metastable brain waves

Traveling patterns of neuronal activity-brain waves-have been observed across a breadth of neuronal recordings, states of awareness, and species, but their emergence in the human brain lacks a firm understanding. Here we analyze the complex nonlinear dynamics that emerge from modeling large-scale spontaneous neural activity on a whole-brain network derived from human tractography. We find a rich array of three-dimensional wave patterns, including traveling waves, spiral waves, sources, and sinks. These patterns are metastable, such that multiple spatiotemporal wave patterns are visited in sequence. Transitions between states correspond to reconfigurations of underlying phase flows, characterized by nonlinear instabilities. These metastable dynamics accord with empirical data from multiple imaging modalities, including electrical waves in cortical tissue, sequential spatiotemporal patterns in resting-state MEG data, and large-scale waves in human electrocorticography. By moving the study of functional networks from a spatially static to an inherently dynamic (wave-like) frame, our work unifies apparently diverse phenomena across functional neuroimaging modalities and makes specific predictions for further experimentation.

Presaccadic EEG activity predicts visual saliency in free-viewing contour integration

While viewing a scene, the eyes are attracted to salient stimuli. We set out to identify the brain signals controlling this process. In a contour integration task, in which participants searched for a collinear contour in a field of randomly oriented Gabor elements, a previously established model was applied to calculate a visual saliency value for each fixation location. We studied brain activity related to the modeled saliency values, using coregistered eye tracking and EEG. To disentangle EEG signals reflecting salience in free viewing from overlapping EEG responses to sequential eye movements, we adopted generalized additive mixed modeling (GAMM) to single epochs of saccade-related EEG. We found that, when saliency at the next fixation location was high, amplitude of the presaccadic EEG activity was low. Since presaccadic activity reflects covert attention to the saccade target, our results indicate that larger attentional effort is needed for selecting less salient saccade targets than more salient ones. This effect was prominent in contour-present conditions (half of the trials), but ambiguous in the contour-absent condition. Presaccadic EEG activity may thus be indicative of bottom-up factors in saccade guidance. The results underscore the utility of GAMM for EEG-eye movement coregistration research.

Large-Scale Traveling Waves in EEG Activity Following Eye Movement

In spontaneous, stimulus-evoked, and eye-movement evoked EEG, the oscillatory signal shows large scale, dynamically organized patterns of phase. We investigated eye-movement evoked patterns in free-viewing conditions. Participants viewed photographs of natural scenes in anticipation of a memory test. From 200 ms intervals following saccades, we estimated the EEG phase gradient over the entire scalp, and the wave activity, i.e. the goodness of fit of a wave model involving a phase gradient assumed to be smooth over the scalp. In frequencies centered at 6.5 Hz, large-scale phase organization occurred, peaking around 70 ms after fixation onset and taking the form of a traveling wave. According to the wave gradient, most of the times the wave spreads from the posterior-inferior to anterior-superior direction. In these directions, the gradients depended on the size and direction of the saccade. Wave propagation velocity decreased in the course of the fixation, particularly in the interval from 50 to 150 ms after fixation onset. This interval corresponds to the fixation-related lambda activity, which reflects early perceptual processes following fixation onset. We conclude that lambda activity has a prominent traveling wave component. This component consists of a short-term whole-head phase pattern of specific direction and velocity, which may reflect feedforward propagation of visual information at fixation.

Towards plasma-like collisionless trajectories in the brain

Plasma studies depict collisionless, collective movements of charged particles. In touch with these concepts, originally developed by the far-flung branch of high energy physics, here we evaluate the role of collective behaviors and long-range functional couplingsof charged particlesin brain dynamics. We build a novel, empirically testable, brain model which takes into account collisionless movements of charged particles in a system, the brain, equipped with oscillations. The model is cast in a mathematical fashion with the potential of being operationalized, because it can be assessed in terms of McKean-Vlasov equations, derived from the classical Vlasov equations for plasma. A plasma-like brain also elucidates cortical phase transitions in the context of a brain at the edge of chaos, describing the required order parameters. In sum, showing how the brain might exhibit plasma-like features,we go through the concept of holistic behavior of nervous functions.

Relationships between short and fast brain timescales

Brain electric activity exhibits two important features: oscillations with different timescales, characterized by diverse functional and psychological outcomes, and a temporal power law distribution. In order to further investigate the relationships between low- and high- frequency spikes in the brain, we used a variant of the Borsuk-Ulam theorem which states that, when we assess the nervous activity as embedded in a sphere equipped with a fractal dimension, we achieve two antipodal points with similar features (the slow and fast, scale-free oscillations). We demonstrate that slow and fast nervous oscillations mirror each other over time via a sinusoid relationship and provide, through the Bloch theorem from solid-state physics, the possible equation which links the two timescale activities. We show that, based on topological findings, nervous activities occurring in micro-levels are projected to single activities at meso- and macro-levels. This means that brain functions assessed at the higher scale of the whole brain necessarily display a counterpart in the lower ones, and vice versa. Our topological approach makes it possible to assess brain functions both based on entropy, and in the general terms of particle trajectories taking place on donut-like manifolds. Condensed brain activities might give rise to ideas and concepts by combination of different functional and anatomical levels. Furthermore, cognitive phenomena, as well as social activity can be described by the laws of quantum mechanics; memories and decisions exhibit holographic organization. In physics, the term duality refers to a case where two seemingly different systems turn out to be equivalent. This topological duality holds for all the types of spatio-temporal brain activities, independent of their inter- and intra-level relationships, strength, magnitude and boundaries, allowing us to connect the physiological manifestations of consciousness to the electric activities of the brain.