Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures.

The spread of seizures across brain networks is the main impairing factor, often leading to loss-of-consciousness, in people with epilepsy. Despite advances in recording and modeling brain activity, uncovering the nature of seizure spreading dynamics remains an important challenge to understanding and treating pharmacologically resistant epilepsy. To address this challenge, we introduce a new probabilistic model that captures the spreading dynamics in patient-specific complex networks. Network connectivity and interaction time delays between brain areas were estimated from white-matter tractography. The model's computational tractability allows it to play an important complementary role to more detailed models of seizure dynamics. We illustrate model fitting and predictive performance in the context of patient-specific Epileptor networks. We derive the phase diagram of spread size (order parameter) as a function of brain excitability and global connectivity strength, for different patient-specific networks. Phase diagrams allow the prediction of whether a seizure will spread depending on excitability and connectivity strength. In addition, model simulations predict the temporal order of seizure spread across network nodes. Furthermore, we show that the order parameter can exhibit both discontinuous and continuous (critical) phase transitions as neural excitability and connectivity strength are varied. Existence of a critical point, where response functions and fluctuations in spread size show power-law divergence with respect to control parameters, is supported by mean-field approximations and finite-size scaling analyses. Notably, the critical point separates two distinct regimes of spreading dynamics characterized by unimodal and bimodal spread-size distributions. Our study sheds new light on the nature of phase transitions and fluctuations in seizure spreading dynamics. We expect it to play an important role in the development of closed-loop stimulation approaches for preventing seizure spread in pharmacologically resistant epilepsy. Our findings may also be of interest to related models of spreading dynamics in epidemiology, biology, finance, and statistical physics.

Emergence of Distinct Neural Subspaces in Motor Cortical Dynamics during Volitional Adjustments of Ongoing Locomotion.

The ability to modulate ongoing walking gait with precise, voluntary adjustments is what allows animals to navigate complex terrains. However, how the nervous system generates the signals to precisely control the limbs while simultaneously maintaining locomotion is poorly understood. One potential strategy is to distribute the neural activity related to these two functions into distinct cortical activity coactivation subspaces so that both may be conducted simultaneously without disruptive interference. To investigate this hypothesis, we recorded the activity of primary motor cortex in male nonhuman primates during obstacle avoidance on a treadmill. We found that the same neural population was active during both basic unobstructed locomotion and volitional obstacle avoidance movements. We identified the neural modes spanning the subspace of the low-dimensional dynamics in primary motor cortex and found a subspace that consistently maintains the same cyclic activity throughout obstacle stepping, despite large changes in the movement itself. All of the variance corresponding to this large change in movement during the obstacle avoidance was confined to its own distinct subspace. Furthermore, neural decoders built for ongoing locomotion did not generalize to decoding obstacle avoidance during locomotion. Our findings suggest that separate underlying subspaces emerge during complex locomotion that coordinates ongoing locomotor-related neural dynamics with volitional gait adjustments. These findings may have important implications for the development of brain-machine interfaces.SIGNIFICANCE STATEMENT Locomotion and precise, goal-directed movements are two distinct movement modalities with known differing requirements of motor cortical input. Previous studies have characterized the cortical activity during obstacle avoidance while walking in rodents and felines, but, to date, no such studies have been completed in primates. Additionally, in any animal model, it is unknown how these two movements are represented in primary motor cortex (M1) low-dimensional dynamics when both activities are performed at the same time, such as during obstacle avoidance. We developed a novel obstacle avoidance paradigm in freely moving nonhuman primates and discovered that the rhythmic locomotion-related dynamics and the voluntary, gait-adjustment movement separate into distinct subspaces in M1 cortical activity. Our analysis of decoding generalization may also have important implications for the development of brain-machine interfaces.

CLoSES: A platform for closed-loop intracranial stimulation in humans.

Targeted interrogation of brain networks through invasive brain stimulation has become an increasingly important research tool as well as therapeutic modality. The majority of work with this emerging capability has been focused on open-loop approaches. Closed-loop techniques, however, could improve neuromodulatory therapies and research investigations by optimizing stimulation approaches using neurally informed, personalized targets. Implementing closed-loop systems is challenging particularly with regard to applying consistent strategies considering inter-individual variability. In particular, during intracranial epilepsy monitoring, where much of this research is currently progressing, electrodes are implanted exclusively for clinical reasons. Thus, detection and stimulation sites must be participant- and task-specific. The system must run in parallel with clinical systems, integrate seamlessly with existing setups, and ensure safety features are in place. In other words, a robust, yet flexible platform is required to perform different tests with a single participant and to comply with clinical requirements. In order to investigate closed-loop stimulation for research and therapeutic use, we developed a Closed-Loop System for Electrical Stimulation (CLoSES) that computes neural features which are then used in a decision algorithm to trigger stimulation in near real-time. To summarize CLoSES, intracranial electroencephalography (iEEG) signals are acquired, band-pass filtered, and local and network features are continuously computed. If target features are detected (e.g. above a preset threshold for a certain duration), stimulation is triggered. Not only could the system trigger stimulation while detecting real-time neural features, but we incorporated a pipeline wherein we used an encoder/decoder model to estimate a hidden cognitive state from the neural features. CLoSES provides a flexible platform to implement a variety of closed-loop experimental paradigms in humans. CLoSES has been successfully used with twelve patients implanted with depth electrodes in the epilepsy monitoring unit. During cognitive tasks (N=5), stimulation in closed loop modified a cognitive hidden state on a trial by trial basis. Sleep spindle oscillations (N=6) and sharp transient epileptic activity (N=9) were detected in near real-time, and stimulation was applied during the event or at specified delays (N=3). In addition, we measured the capabilities of the CLoSES system. Total latency was related to the characteristics of the event being detected, with tens of milliseconds for epileptic activity and hundreds of milliseconds for spindle detection. Stepwise latency, the actual duration of each continuous step, was within the specified fixed-step duration and increased linearly with the number of channels and features. We anticipate that probing neural dynamics and interaction between brain states and stimulation responses with CLoSES will lead to novel insights into the mechanism of normal and pathological brain activity, the discovery and evaluation of potential electrographic biomarkers of neurological and psychiatric disorders, and the development and testing of patient-specific stimulation targets and control signals before implanting a therapeutic device.

Phase reorganization leads to transient ß-LFP spatial wave patterns in motor cortex during steady-state movement preparation.

Previous studies on the origin and properties of spatial patterns in motor cortex ß-local field potential (ß-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether ß-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in ß-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) ß-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) ß-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) ß-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, ß-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient ß-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of ß-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient ß-local field potential (ß-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, ß-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex ß-LFP wave patterns.

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Optogenetic Stimulation Shifts the Excitability of Cerebral Cortex from Type I to Type II: Oscillation Onset and Wave Propagation.

Constant optogenetic stimulation targeting both pyramidal cells and inhibitory interneurons has recently been shown to elicit propagating waves of gamma-band (40-80 Hz) oscillations in the local field potential of non-human primate motor cortex. The oscillations emerge with non-zero frequency and small amplitude-the hallmark of a type II excitable medium-yet they also propagate far beyond the stimulation site in the manner of a type I excitable medium. How can neural tissue exhibit both type I and type II excitability? We investigated the apparent contradiction by modeling the cortex as a Wilson-Cowan neural field in which optogenetic stimulation was represented by an external current source. In the absence of any external current, the model operated as a type I excitable medium that supported propagating waves of gamma oscillations similar to those observed in vivo. Applying an external current to the population of inhibitory neurons transformed the model into a type II excitable medium. The findings suggest that cortical tissue normally operates as a type I excitable medium but it is locally transformed into a type II medium by optogenetic stimulation which predominantly targets inhibitory neurons. The proposed mechanism accounts for the graded emergence of gamma oscillations at the stimulation site while retaining propagating waves of gamma oscillations in the non-stimulated tissue. It also predicts that gamma waves can be emitted on every second cycle of a 100 Hz oscillation. That prediction was subsequently confirmed by re-analysis of the neurophysiological data. The model thus offers a theoretical account of how optogenetic stimulation alters the excitability of cortical neural fields.

Dissociation between sustained single-neuron spiking and transient ß-LFP oscillations in primate motor cortex.

Determining the relationship between single-neuron spiking and transient (20 Hz) ß-local field potential (ß-LFP) oscillations is an important step for understanding the role of these oscillations in motor cortex. We show that whereas motor cortex firing rates and beta spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-LFP oscillations emerge, in contrast, as short transient events. Single-neuron mean firing rates within and outside transient ß-LFP events showed no differences, and no consistent correlation was found between the beta oscillation amplitude and firing rates, as was the case for movement- and visual cue-related ß-LFP suppression. Importantly, well-isolated single units featuring beta-rhythmic spiking (43%, 125/292) showed no apparent or only weak phase coupling with the transient ß-LFP oscillations. Similar results were obtained for the population spiking. These findings were common in triple microelectrode array recordings from primary motor (M1), ventral (PMv), and dorsal premotor (PMd) cortices in nonhuman primates during movement preparation. Although beta spiking rhythmicity indicates strong membrane potential fluctuations in the beta band, it does not imply strong phase coupling with ß-LFP oscillations. The observed dissociation points to two different sources of variation in motor cortex ß-LFPs: one that impacts single-neuron spiking dynamics and another related to the generation of mesoscopic ß-LFP signals. Furthermore, our findings indicate that rhythmic spiking and diverse neuronal firing rates, which encode planned actions during movement preparation, may naturally limit the ability of different neuronal populations to strongly phase-couple to a single dominant oscillation frequency, leading to the observed spiking and ß-LFP dissociation.NEW & NOTEWORTHY We show that whereas motor cortex spiking rates and beta (~20 Hz) spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-local field potential (ß-LFP) oscillations emerge, in contrast, as transient events. Furthermore, the ß-LFP phase at which neurons spike drifts: phase coupling is typically weak or absent. This dissociation points to two sources of variation in the level of motor cortex beta: one that impacts single-neuron spiking and another related to the generation of measured mesoscopic ß-LFPs.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures.

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Neuronal ensemble synchrony during human focal seizures.

Seizures are classically characterized as the expression of hypersynchronous neural activity, yet the true degree of synchrony in neuronal spiking (action potentials) during human seizures remains a fundamental question. We quantified the temporal precision of spike synchrony in ensembles of neocortical neurons during seizures in people with pharmacologically intractable epilepsy. Two seizure types were analyzed: those characterized by sustained gamma (∼40-60 Hz) local field potential (LFP) oscillations or by spike-wave complexes (SWCs; ∼3 Hz). Fine (<10 ms) temporal synchrony was rarely present during gamma-band seizures, where neuronal spiking remained highly irregular and asynchronous. In SWC seizures, phase locking of neuronal spiking to the SWC spike phase induced synchrony at a coarse 50-100 ms level. In addition, transient fine synchrony occurred primarily during the initial ∼20 ms period of the SWC spike phase and varied across subjects and seizures. Sporadic coherence events between neuronal population spike counts and LFPs were observed during SWC seizures in high (∼80 Hz) gamma-band and during high-frequency oscillations (∼130 Hz). Maximum entropy models of the joint neuronal spiking probability, constrained only on single neurons' nonstationary coarse spiking rates and local network activation, explained most of the fine synchrony in both seizure types. Our findings indicate that fine neuronal ensemble synchrony occurs mostly during SWC, not gamma-band, seizures, and primarily during the initial phase of SWC spikes. Furthermore, these fine synchrony events result mostly from transient increases in overall neuronal network spiking rates, rather than changes in precise spiking correlations between specific pairs of neurons.

Local field potentials in primate motor cortex encode grasp kinetic parameters.

Reach and grasp kinematics are known to be encoded in the spiking activity of neuronal ensembles and in local field potentials (LFPs) recorded from primate motor cortex during movement planning and execution. However, little is known, especially in LFPs, about the encoding of kinetic parameters, such as forces exerted on the object during the same actions. We implanted two monkeys with microelectrode arrays in the motor cortical areas MI and PMd to investigate encoding of grasp-related parameters in motor cortical LFPs during planning and execution of reach-and-grasp movements. We identified three components of the LFP that modulated during grasps corresponding to low (0.3-7Hz), intermediate (~10-~40Hz) and high (~80-250Hz) frequency bands. We show that all three components can be used to classify not only grip types but also object loads during planning and execution of a grasping movement. In addition, we demonstrate that all three components recorded during planning or execution can be used to continuously decode finger pressure forces and hand position related to the grasping movement. Low and high frequency components provide similar classification and decoding accuracies, which were substantially higher than those obtained from the intermediate frequency component. Our results demonstrate that intended reach and grasp kinetic parameters are encoded in multiple LFP bands during both movement planning and execution. These findings also suggest that the LFP is a reliable signal for the control of parameters related to object load and applied pressure forces in brain-machine interfaces.

Microscale spatiotemporal dynamics during neocortical propagation of human focal seizures.

Some of the most clinically consequential aspects of focal epilepsy, e.g. loss of consciousness, arise from the generalization or propagation of seizures through local and large-scale neocortical networks. Yet, the dynamics of such neocortical propagation remain poorly understood. Here, we studied the microdynamics of focal seizure propagation in neocortical patches (4×4 mm) recorded via high-density microelectrode arrays (MEAs) implanted in people with pharmacologically resistant epilepsy. Our main findings are threefold: (1) a newly developed stage segmentation method, applied to local field potentials (LFPs) and multiunit activity (MUA), revealed a succession of discrete seizure stages, each lasting several seconds. These different stages showed characteristic evolutions in overall activity and spatial patterns, which were relatively consistent across seizures within each of the 5 patients studied. Interestingly, segmented seizure stages based on LFPs or MUA showed a dissociation of their spatiotemporal dynamics, likely reflecting different contributions of non-local synaptic inputs and local network activity. (2) As previously reported, some of the seizures showed a peak in MUA that happened several seconds after local seizure onset and slowly propagated across the MEA. However, other seizures had a more complex structure characterized by, for example, several MUA peaks, more consistent with the succession of discrete stages than the slow propagation of a simple wavefront of increased MUA. In both cases, nevertheless, seizures characterized by spike-wave discharges (SWDs, ~2-3 Hz) eventually evolved into patterns of phase-locked MUA and LFPs. (3) Individual SWDs or gamma oscillation cycles (25-60 Hz), characteristic of two different types of recorded seizures, tended to propagate with varying degrees of directionality, directions of propagation and speeds, depending on the identified seizure stage. However, no clear relationship was observed between the MUA peak onset time (in seizures where such peak onset occurred) and changes in MUA or LFP propagation patterns. Overall, our findings indicate that the recruitment of neocortical territories into ictal activity undergoes complex spatiotemporal dynamics evolving in slow discrete states, which are consistent across seizures within each patient. Furthermore, ictal states at finer spatiotemporal scales (individual SWDs or gamma oscillations) are organized by slower time scale network dynamics evolving through these discrete stages.

Spatiotemporal dynamics of optogenetically induced and spontaneous seizure transitions in primary generalized epilepsy.

Transitions into primary generalized epileptic seizures occur abruptly and synchronously across the brain. Their potential triggers remain unknown. We used optogenetics to causally test the hypothesis that rhythmic population bursting of excitatory neurons in a local neocortical region can rapidly trigger absence seizures. Most previous studies have been purely correlational, and it remains unclear whether epileptiform events induced by rhythmic stimulation (e.g., sensory/electrical) mimic actual spontaneous seizures, especially regarding their spatiotemporal dynamics. In this study, we used a novel combination of intracortical optogenetic stimulation and microelectrode array recordings in freely moving WAG/Rij rats, a model of absence epilepsy with a cortical focus in the somatosensory cortex (SI). We report three main findings: 1) Brief rhythmic bursting, evoked by optical stimulation of neocortical excitatory neurons at frequencies around 10 Hz, induced seizures consisting of self-sustained spike-wave discharges (SWDs) for about 10% of stimulation trials. The probability of inducing seizures was frequency-dependent, reaching a maximum at 10 Hz. 2) Local field potential power before stimulation and response amplitudes during stimulation both predicted seizure induction, demonstrating a modulatory effect of brain states and neural excitation levels. 3) Evoked responses during stimulation propagated as cortical waves, likely reaching the cortical focus, which in turn generated self-sustained SWDs after stimulation was terminated. Importantly, SWDs during induced and spontaneous seizures propagated with the same spatiotemporal dynamics. Our findings demonstrate that local rhythmic bursting of excitatory neurons in neocortex at particular frequencies, under susceptible ongoing brain states, is sufficient to trigger primary generalized seizures with stereotypical spatiotemporal dynamics.

Optogenetically induced spatiotemporal gamma oscillations and neuronal spiking activity in primate motor cortex.

Transient gamma-band (40-80 Hz) spatiotemporal patterns are hypothesized to play important roles in cortical function. Here we report the direct observation of gamma oscillations as spatiotemporal waves induced by targeted optogenetic stimulation, recorded by intracortical multichannel extracellular techniques in macaque monkeys during their awake resting states. Microelectrode arrays integrating an optical fiber at their center were chronically implanted in primary motor (M1) and ventral premotor (PMv) cortices of two subjects. Targeted brain tissue was transduced with the red-shifted opsin C1V1(T/T). Constant (1-s square pulses) and ramp stimulation induced narrowband gamma oscillations during awake resting states. Recordings across 95 microelectrodes (4 × 4-mm array) enabled us to track the transient gamma spatiotemporal patterns manifested, e.g., as concentric expanding and spiral waves. Gamma oscillations were induced well beyond the light stimulation volume, via network interactions at distal electrode sites, depending on optical power. Despite stimulation-related modulation in spiking rates, neuronal spiking remained highly asynchronous during induced gamma oscillations. In one subject we examined stimulation effects during preparation and execution of a motor task and observed that movement execution largely attenuated optically induced gamma oscillations. Our findings demonstrate that, beyond previously reported induced gamma activity under periodic drive, a prolonged constant stimulus above a certain threshold may carry primate motor cortex network dynamics into gamma oscillations, likely via a Hopf bifurcation. More broadly, the experimental capability in combining microelectrode array recordings and optogenetic stimulation provides an important approach for probing spatiotemporal dynamics in primate cortical networks during various physiological and behavioral conditions.

Spatiotemporal conditional inference and hypothesis tests for neural ensemble spiking precision.

The collective dynamics of neural ensembles create complex spike patterns with many spatial and temporal scales. Understanding the statistical structure of these patterns can help resolve fundamental questions about neural computation and neural dynamics. Spatiotemporal conditional inference (STCI) is introduced here as a semiparametric statistical framework for investigating the nature of precise spiking patterns from collections of neurons that is robust to arbitrarily complex and nonstationary coarse spiking dynamics. The main idea is to focus statistical modeling and inference not on the full distribution of the data, but rather on families of conditional distributions of precise spiking given different types of coarse spiking. The framework is then used to develop families of hypothesis tests for probing the spatiotemporal precision of spiking patterns. Relationships among different conditional distributions are used to improve multiple hypothesis-testing adjustments and design novel Monte Carlo spike resampling algorithms. Of special note are algorithms that can locally jitter spike times while still preserving the instantaneous peristimulus time histogram or the instantaneous total spike count from a group of recorded neurons. The framework can also be used to test whether first-order maximum entropy models with possibly random and time-varying parameters can account for observed patterns of spiking. STCI provides a detailed example of the generic principle of conditional inference, which may be applicable to other areas of neurostatistical analysis.

Human seizures self-terminate across spatial scales via a critical transition.

Why seizures spontaneously terminate remains an unanswered fundamental question of epileptology. Here we present evidence that seizures self-terminate via a discontinuous critical transition or bifurcation. We show that human brain electrical activity at various spatial scales exhibits common dynamical signatures of an impending critical transition--slowing, increased correlation, and flickering--in the approach to seizure termination. In contrast, prolonged seizures (status epilepticus) repeatedly approach, but do not cross, the critical transition. To support these results, we implement a computational model that demonstrates that alternative stable attractors, representing the ictal and postictal states, emulate the observed dynamics. These results suggest that self-terminating seizures end through a common dynamical mechanism. This description constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.

Population interactions between parietal and primary motor cortices during reach.

Neural interactions between parietal area 2/5 and primary motor cortex (M1) were examined to determine the timing and behavioral correlates of cortico-cortical interactions. Neural activity in areas 2/5 and M1 was simultaneously recorded with 96-channel microelectrode arrays in three rhesus monkeys performing a center-out reach task. We introduce a new method to reveal parietal-motor interactions at a population level using partial spike-field coherence (PSFC) between ensembles of neurons in one area and a local field potential (LFP) in another. PSFC reflects the extent of phase locking between spike times and LFP, after removing the coherence between LFPs in the two areas. Spectral analysis of M1 LFP revealed three bands: low, medium, and high, differing in power between movement preparation and performance. We focus on PSFC in the 1-10 Hz band, in which coherence was strongest. PSFC was also present in the 10-40 Hz band during movement preparation in many channels but generally nonsignificant in the 60-200 Hz band. Ensemble PSFC revealed stronger interactions than single cell-LFP pairings. PSFC of area 2/5 ensembles with M1 LFP typically rose around movement onset and peaked ∼500 ms afterward. PSFC was typically stronger for subsets of area 2/5 neurons and M1 LFPs with similar directional bias than for those with opposite bias, indicating that area 2/5 contributes movement direction information. Together with linear prediction of M1 LFP by area 2/5 spiking, the ensemble-LFP pairing approach reveals interactions missed by single neuron-LFP pairing, demonstrating that cortico-cortical communication can be more readily observed at the ensemble level.

Neural manifolds carry reactivation of phonetic representations during semantic processing.

Traditional models of speech perception posit that neural activity encodes speech through a hierarchy of cognitive processes, from low-level representations of acoustic and phonetic features to high-level semantic encoding. Yet it remains unknown how neural representations are transformed across levels of the speech hierarchy. Here, we analyzed unique microelectrode array recordings of neuronal spiking activity from the human left anterior superior temporal gyrus, a brain region at the interface between phonetic and semantic speech processing, during a semantic categorization task and natural speech perception. We identified distinct neural manifolds for semantic and phonetic features, with a functional separation of the corresponding low-dimensional trajectories. Moreover, phonetic and semantic representations were encoded concurrently and reflected in power increases in the beta and low-gamma local field potentials, suggesting top-down predictive and bottom-up cumulative processes. Our results are the first to demonstrate mechanisms for hierarchical speech transformations that are specific to neuronal population dynamics.

Decoding 3D reach and grasp from hybrid signals in motor and premotor cortices: spikes, multiunit activity, and local field potentials.

Neural activity in motor cortex during reach and grasp movements shows modulations in a broad range of signals from single-neuron spiking activity (SA) to various frequency bands in broadband local field potentials (LFPs). In particular, spatiotemporal patterns in multiband LFPs are thought to reflect dendritic integration of local and interareal synaptic inputs, attentional and preparatory processes, and multiunit activity (MUA) related to movement representation in the local motor area. Nevertheless, the relationship between multiband LFPs and SA, and their relationship to movement parameters and their relative value as brain-computer interface (BCI) control signals, remain poorly understood. Also, although this broad range of signals may provide complementary information channels in primary (MI) and ventral premotor (PMv) areas, areal differences in information have not been systematically examined. Here, for the first time, the amount of information in SA and multiband LFPs was compared for MI and PMv by recording from dual 96-multielectrode arrays while monkeys made naturalistic reach and grasp actions. Information was assessed as decoding accuracy for 3D arm end point and grip aperture kinematics based on SA or LFPs in MI and PMv, or combinations of signal types across areas. In contrast with previous studies with ≤16 simultaneous electrodes, here ensembles of >16 units (on average) carried more information than multiband, multichannel LFPs. Furthermore, reach and grasp information added by various LFP frequency bands was not independent from that in SA ensembles but rather typically less than and primarily contained within the latter. Notably, MI and PMv did not show a particular bias toward reach or grasp for this task or for a broad range of signal types. For BCIs, our results indicate that neuronal ensemble spiking is the preferred signal for decoding, while LFPs and combined signals from PMv and MI can add robustness to BCI control.

Critical dynamics in the spread of focal epileptic seizures: Network connectivity, neural excitability and phase transitions.

Focal epileptic seizures can remain localized or, alternatively, spread across brain areas, often resulting in impairment of cognitive function and loss of consciousness. Understanding the factors that promote spread is important for developing better therapeutic approaches. Here, we show that: (1) seizure spread undergoes "critical" phase transitions in models (epileptor-networks) that capture the neural dynamics of spontaneous seizures while incorporating patient-specific brain network connectivity, axonal delays and identified epileptogenic zones (EZs). We define a collective variable for the spreading dynamics as the spread size, i.e. the number of areas or nodes in the network to which a seizure has spread. Global connectivity strength and excitability in the surrounding non-epileptic areas work as phase-transition control parameters for this collective variable. (2) Phase diagrams are predicted by stability analysis of the network dynamics. (3) In addition, the components of the Jacobian's leading eigenvector, which tend to reflect the connectivity strength and path lengths from the EZ to surrounding areas, predict the temporal order of network-node recruitment into seizure. (4) However, stochastic fluctuations in spread size in a near-criticality region make predictability more challenging. Overall, our findings support the view that within-patient seizure-spread variability can be characterized by phase-transition dynamics under transient variations in network connectivity strength and excitability across brain areas. Furthermore, they point to the potential use and limitations of model-based prediction of seizure spread in closed-loop interventions for seizure control.

Grasp-squeeze adaptation to changes in object compliance leads to dynamic beta-band communication between primary somatosensory and motor cortices.

In asking the question of how the brain adapts to changes in the softness of manipulated objects, we studied dynamic communication between the primary sensory and motor cortical areas when nonhuman primates grasp and squeeze an elastically deformable manipulandum to attain an instructed force level. We focused on local field potentials recorded from S1 and M1 via intracortical microelectrode arrays. We computed nonparametric spectral Granger Causality to assess directed cortico-cortical interactions between these two areas. We demonstrate that the time-causal relationship between M1 and S1 is bidirectional in the beta-band (15-30 Hz) and that this interareal communication develops dynamically as the subjects adjust the force of hand squeeze to reach the target level. In particular, the directed interaction is strongest when subjects are focused on maintaining the instructed force of hand squeeze in a steady state for several seconds. When the manipulandum's compliance is abruptly changed, beta-band interareal communication is interrupted for a short period (~ 1 s) and then is re-established once the subject has reached a new steady state. These results suggest that transient beta oscillations can provide a communication subspace for dynamic cortico-cortical S1-M1 interactions during maintenance of steady sensorimotor states.