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.

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.

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.

Forecasting seizure risk in adults with focal epilepsy: a development and validation study.

BACKGROUND: People with epilepsy are burdened with the apparent unpredictability of seizures. In the past decade, converging evidence from studies using chronic EEG (cEEG) revealed that epileptic brain activity shows robust cycles, operating over hours (circadian) and days (multidien). We hypothesised that these cycles can be leveraged to estimate future seizure probability, and we tested the feasibility of forecasting seizures days in advance. METHODS: We did a feasibility study in distinct development and validation cohorts, involving retrospective analysis of cEEG data recorded with an implanted device in adults (age ≥18 years) with drug-resistant focal epilepsy followed at 35 centres across the USA between Jan 19, 2004, and May 18, 2018. Patients were required to have had 20 or more electrographic seizures (development cohort) or self-reported seizures (validation cohort). In all patients, the device recorded interictal epileptiform activity (IEA; ≥6 months of continuous hourly data), the fluctuations in which helped estimate varying seizure risk. Point process statistical models trained on initial portions of each patient's cEEG data (both cohorts) generated forecasts of seizure probability that were tested on subsequent unseen seizure data and evaluated against surrogate time-series. The primary outcome was the percentage of patients with forecasts showing improvement over chance (IoC). FINDINGS: We screened 72 and 256 patients, and included 18 and 157 patients in the development and validation cohorts, respectively. Models incorporating information about multidien IEA cycles alone generated daily seizure forecasts for the next calendar day with IoC in 15 (83%) patients in the development cohort and 103 (66%) patients in the validation cohort. The forecasting horizon could be extended up to 3 days while maintaining IoC in two (11%) of 18 patients and 61 (39%) of 157 patients. Forecasts with a shorter horizon of 1 h, possible only for electrographic seizures in the development cohort, showed IoC in all 18 (100%) patients. INTERPRETATION: This study shows that seizure probability can be forecasted days in advance by leveraging multidien IEA cycles recorded with an implanted device. This study will serve as a basis for prospective clinical trials to establish how people with epilepsy might benefit from seizure forecasting over long horizons. FUNDING: None. VIDEO ABSTRACT.

Corrigendum: Low-Dimensional Motor Cortex Dynamics Preserve Kinematics Information During Unconstrained Locomotion in Nonhuman Primates.

[This corrects the article DOI: 10.3389/fnins.2019.01046.].

Effect of Closed-Loop Direct Electrical Stimulation during Sleep Spindles in Humans.

Sleep spindles are transient oscillations in the brain related to sleep consolidation and memory. We investigated if brief, localized electrical pulses could perturb spindles on five human patients with intracerebral electrodes implanted for clinical purpose. We used a closed-loop setup to specifically detect spindles and stimulate in real-time during these events. Stimulation latency was 200-400 ms following spindle onset. Analyzing the intracranial electro-encephalographic (iEEG) data both locally and globally, we found, in two of the patients, that single pulse stimulation could stop the spindles locally. Spindles were shorter than those without stimulation and a decrease in power at the same frequency as spindles was observed following stimulation.Clinical Relevance- This study shows that brief and precise electrical stimulation may be used to modulate oscillatory behavior of the human brain. Applied to sleep spindles, further studies may establish that single pulses applied in a closed-loop manner could be used to modulate memory and could help understand effect of neuromodulation in sleep disruption.

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.

Early Detection of Human Epileptic Seizures Based on Intracortical Microelectrode Array Signals.

OBJECTIVE: We examine, for the first time, the use of intracortical microelectrode array (MEA) signals for early detection of human epileptic seizures. METHODS: 4×4 mm2 96-channel-MEA recordings were obtained during neuro-monitoring preceding resective surgery in five participants. The participant-specific seizure-detection framework consisted of: first, feature extraction from local field potentials (LFPs) and multiunit activity (MUA); second, nonlinear cost-sensitive support vector machine (SVM) classification of ictal and interictal states based on LFP, MUA, and combined LFP-MUA (a SVM was trained for each participant separately); and third, Kalman filter postprocessing of SVM scoring functions. Performance was assessed on data including 17 seizures and 39.0 h interictal and preictal recordings. RESULTS: The use of combined LFP-MUA features resulted in 100% sensitivity with short detection latency (average: 2.7 s; median: 2.5 s) and five false alarms (0.13/h). The average detection performance based on the area under the receiver operating characteristic corresponded to 0.97. Importantly, technically false alarms were related to epileptiform activity, subclinical seizures, and recording artifacts. Extreme gradient boosting classifiers ranked features based on LFP spectral coherence or MUA count among the top features for seizures characterized by spike-wave complexes, whereas features related to LFP power spectra were ranked higher for seizures characterized by sustained gamma LFP oscillations. CONCLUSION: The combination of intracortical LFP and MUA signals may allow reliable detection of human epileptic seizures by improving latency and false alarm rate. SIGNIFICANCE: Intracortical MEAs provide promising signals for closed-loop seizure-control systems based on seizure early-detection in people with pharmacologically resistant epilepsies.

Decoding speech from spike-based neural population recordings in secondary auditory cortex of non-human primates.

Direct electronic communication with sensory areas of the neocortex is a challenging ambition for brain-computer interfaces. Here, we report the first successful neural decoding of English words with high intelligibility from intracortical spike-based neural population activity recorded from the secondary auditory cortex of macaques. We acquired 96-channel full-broadband population recordings using intracortical microelectrode arrays in the rostral and caudal parabelt regions of the superior temporal gyrus (STG). We leveraged a new neural processing toolkit to investigate the choice of decoding algorithm, neural preprocessing, audio representation, channel count, and array location on neural decoding performance. The presented spike-based machine learning neural decoding approach may further be useful in informing future encoding strategies to deliver direct auditory percepts to the brain as specific patterns of microstimulation.

Low-Dimensional Motor Cortex Dynamics Preserve Kinematics Information During Unconstrained Locomotion in Nonhuman Primates.

The dynamical systems view of movement generation in motor cortical areas has emerged as an effective way to explain the firing properties of populations of neurons recorded from these regions. Recently, many studies have focused on finding low-dimensional representations of these dynamical systems during voluntary reaching and grasping behaviors carried out by the forelimbs. One such model, the Poisson linear-dynamical-system (PLDS) model, has been shown to extract dynamics which can be used to decode reaching kinematics. However, few have investigated these dynamics, especially in non-human primates, during behaviors such as locomotion, which may involve motor cortex to a lesser degree. Here, we focused on unconstrained quadrupedal locomotion, and investigated whether unsupervised latent state-space models can extract low-dimensional dynamics while preserving information about hind-limb kinematics. Spiking activity from the leg area of primary motor cortex of rhesus macaques was recorded simultaneously with hind-limb joint positions during ambulation across a corridor, ladder, and on a treadmill at various speeds. We found that PLDS models can extract stereotyped low-dimensional neural trajectories from these neurons phase-locked to the gait cycle, and that distinct trajectories emerge depending on the speed and class of behavior. Additionally, it was possible to decode both the hind-limb kinematics and the gait phase from these inferred trajectories just as well or better than from the full neural population (18-80 neurons) with only 12 dimensions. Our results demonstrate that kinematics and gait phase during various locomotion tasks are well represented in low-dimensional latent dynamics inferred from motor cortex population activity.

Intracortical neural activity distal to seizure-onset-areas predicts human focal seizures.

The apparent unpredictability of epileptic seizures has a major impact in the quality of life of people with pharmacologically resistant seizures. Here, we present initial results and a proof-of-concept of how focal seizures can be predicted early in advance based on intracortical signals recorded from small neocortical patches away from identified seizure onset areas. We show that machine learning algorithms can discriminate between interictal and preictal periods based on multiunit activity (i.e. thresholded action potential counts) and multi-frequency band local field potentials recorded via 4 X 4 mm2 microelectrode arrays. Microelectrode arrays were implanted in 5 patients undergoing neuromonitoring for resective surgery. Post-implant analysis revealed arrays were outside the seizure onset areas. Preictal periods were defined as the 1-hour period leading to a seizure. A 5-minute gap between the preictal period and the putative seizure onset was enforced to account for potential errors in the determination of actual seizure onset times. We used extreme gradient boosting and long short-term memory networks for prediction. Prediction accuracy based on the area under the receiver operating characteristic curves reached 90% for at least one feature type in each patient. Importantly, successful prediction could be achieved based exclusively on multiunit activity. This result indicates that preictal activity in the recorded neocortical patches involved not only subthreshold postsynaptic potentials, perhaps driven by the distal seizure onset areas, but also neuronal spiking in distal recurrent neocortical networks. Beyond the commonly identified seizure onset areas, our findings point to the engagement of large-scale neuronal networks in the neural dynamics building up toward a seizure. Our initial results obtained on currently available human intracortical microelectrode array recordings warrant new studies on larger datasets, and open new perspectives for seizure prediction and control by emphasizing the contribution of multiscale neural signals in large-scale neuronal networks.

Uncovering low-dimensional structure in high-dimensional representations of long-term recordings in people with epilepsy.

Effective representations of recordings of epileptic activity for seizure prediction are high-dimensional, which prevents their visualization. Here we introduce and evaluate methods to find low-dimensional (2D or 3D) descriptors of these high-dimensional representations, which are amenable for visualization. Once low-dimensional descriptors are found, it is useful to identify structure in them. We evaluate clustering algorithms to automatically identify this structure. In addition, typical recordings of epileptic activity are long, extending for several days or weeks. We present and assess extensions of the previous methods to handle large datasets.

Ongoing intracortical neural activity predicts upcoming interictal epileptiform discharges in human epilepsy.

Interictal epileptiform discharges (IEDs) are a hallmark of focal epilepsies. Most previous studies have focused on whether IED events increase seizure likelihood or, on the contrary, act as a protective mechanism. Here, we study instead whether IED events themselves can be predicted based on measured ongoing neural activity. We examined local field potentials (LFPs) and multi-unit activity (MUA) recorded via intracortical 10 × 10 (4 × 4 mm) arrays implanted in two patients with pharmacologically resistant seizures. Seizures in one patient (P1) were characterized by low-voltage fast-activity (LVFA), and IEDs occurred as isolated (100 - 200 ms) spike-wave events. In the other patient (P2), seizures were characterized by complex spike-wave discharges (2 - 3 Hz) and IEDs consisted of bursts of ~ 2 - 3 spike-wave discharges each lasting ~ 300 - 500 ms. We used extreme gradient boosting (XGBoost) classifiers for IED prediction. Inputs to the classifiers consisted of LFP power spectra; In addition, counts of MUA (1-ms and 100-ms time bins) and envelope, as well as leading eigenvalues/eigenvectors of MUA correlation matrices were used as features. Features were computed from moving short-time windows (1 second) immediately preceding IED events (0.3 - 0.5 preictal gap). Classifiers allowed successful IED prediction in both patients, with better results in the case of IED occurring in the LVFA case (area under ROC curve: 0.86). In comparison, LFP features performed comparatively for P1 datasets, while MUA appeared not predictive in the case of P2. Our preliminary results suggest that features of ongoing activity, predictive of upcoming IED events, can be identified based on intracortical recordings, and warrant further investigation in larger datasets. We expect this type of prediction analyses to contribute to a better understanding of the mechanisms underlying the generation of IED events and their contribution to seizure onset.

Stability of stochastic finite-size spiking-neuron networks: Comparing mean-field, 1-loop correction and quasi-renewal approximations.

We examine the stability and qualitative dynamics of stochastic neuronal networks specified as multivariate non-linear Hawkes processes and related point-process generalized linear models that incorporate both auto- and cross-history effects. In particular, we adapt previous theoretical approximations based on mean field and mean field plus 1-loop correction to incorporate absolute refractory periods and other auto-history effects. Furthermore, we extend previous quasi-renewal approximations to the multivariate case, i.e. neuronal networks. The best sensitivity and specificity performance, in terms of predicting stability and divergence to nonphysiologically high firing rates in the examined simulations, was obtained by a variant of the quasi-renewal approximation.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation.

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy.

Recent studies have shown that seizures can spread and terminate across brain areas via a rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset area is usually invariant across seizures in an individual patient, the source of traveling (2-3 Hz) spike-and-wave discharges during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. Furthermore, although many focal seizures terminate synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. Here, we introduce a unifying perspective based on a new neural field model of epileptic seizure dynamics. Two main mechanisms, the co-existence of wave propagation in excitable media and coupled-oscillator dynamics, together with the interaction of multiple time scales, account for the reported diversity. We confirm our predictions in seizures and tractography data obtained from patients with pharmacologically resistant epilepsy. Our results contribute toward patient-specific seizure modeling.

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.