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 nonlinear 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.Comment: 8 pages. This errata note corrects typos and clarifies aspects related to equations presented in Proc IEEE EMBC (2019), pp. 4380 - 4386, doi 10.1109/EMBC.2019.8857101. A corrected version of the published article is included, followed by the detailed errata list and correction

Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excitatory-inhibitory oscillators are used to illustrate the approach.Comment: 20 pages, 4 figure

Motor “Binding:” Do Functional Assemblies in Primary Motor Cortex Have a Role?

AbstractIn this issue of Neuron, Jackson and colleagues describe a functional correlate of neural synchrony related to movement control. Synchrony strength in cortico-motoneuronal output neurons in primary motor cortex depended upon similarity of these neurons' connectivity pattern with the spinal cord. These results could form the foundation for subsequent investigations of motor binding

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 in-variant across seizures in a same patient, the source of traveling (2-3 Hz) spike-and-wave discharges (SWDs) during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. In addition, although most focal seizures terminate quasi-synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. To provide a unifying perspective on the observed diversity of spatiotemporal dynamics for seizure spread and termination, we introduce here the Epileptor neural field model. Two mechanisms play an essential role. First, while the slow ictal wavefront propagates as a front in excitable neural media, the faster SWDs propagation results from coupled-oscillator dynamics. Second, multiple time scales interact during seizure spread, allowing for low-voltage fast-activity (>10 Hz) to hamper seizure spread and for SWD propagation to affect the way a seizure terminates. These dynamics, together with variations in short and long-range connectivity strength, play a central role on seizure spread, maintenance and termination. We demonstrate how Epileptor field models incorporating the above mechanisms predict the previously reported diversity in seizure spread patterns. Furthermore, we confirm the predictions for synchronous or asynchronous (clustered) seizure termination in human seizures recorded via stereotactic EEG. Our new insights into seizure spatiotemporal dynamics may also contribute to the development of new closed-loop neuromodulation therapies for focal epilepsy.Comment: 10 pages + 9 pages Supporting Information (SI), 7 figures, 1 SI table, 7 SI figure

Efficient Decoding With Steady-State Kalman Filter in Neural Interface Systems

The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics.We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5[plus-over-minus sign]0.5 s (mean[plus-over-minus sign]s.d.) . The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25[plus-over-minus sign]3 single units by a factor of 7.0[plus-over-minus sign]0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.National Institutes of Health (U.S.) (Grant R01 DC009899)National Institutes of Health (U.S.) (Grant RC1 HD063931)National Institutes of Health (U.S.) (Grant N01 HD053403)National Institutes of Health (U.S.) (Grant 5K01 NS057389)National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant R01-EB006385)United States. Dept. of Veterans Affairs (Office of Research and Development, Rehabilitation R&D Service)Massachusetts General Hospital (Deane Institute for Integrated Research on Atrial Fibrillation and Stroke)Doris Duke Charitable FoundationSpaulding Rehabilitation Hospita

Dissociation between sustained single-neuron spiking β-rhythmicity and transient β-LFP oscillations in primate motor cortex

Determining the relationship between single-neuron spiking and transient (20 Hz) β-local field potential (β-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, β-LFP oscillations emerge, in contrast, as short transient events. Single-neuron mean firing rates within and outside transient β-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 β-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 β-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 β-LFP oscillations. The observed dissociation points to two different sources of variation in motor cortex β-LFPs: one that impacts single-neuron spiking dynamics and another related to the generation of mesoscopic β-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 β-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, β-local field potential (β-LFP) oscillations emerge, in contrast, as transient events. Furthermore, the β-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 β-LFPs

Single-neuron dynamics in human focal epilepsy

Epileptic seizures are traditionally characterized as the ultimate expression of monolithic, hypersynchronous neuronal activity arising from unbalanced runaway excitation. Here we report the first examination of spike train patterns in large ensembles of single neurons during seizures in persons with epilepsy. Contrary to the traditional view, neuronal spiking activity during seizure initiation and spread was highly heterogeneous, not hypersynchronous, suggesting complex interactions among different neuronal groups even at the spatial scale of small cortical patches. In contrast to earlier stages, seizure termination is a nearly homogenous phenomenon followed by an almost complete cessation of spiking across recorded neuronal ensembles. Notably, even neurons outside the region of seizure onset showed significant changes in activity minutes before the seizure. These findings suggest a revision of current thinking about seizure mechanisms and point to the possibility of seizure prevention based on spiking activity in neocortical neurons

Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution

Understanding the sources of variability in single-neuron spiking responses is an important open problem for the theory of neural coding. This variability is thought to result primarily from spontaneous collective dynamics in neuronal networks. Here, we investigate how well collective dynamics reflected in motor cortex local field potentials (LFPs) can account for spiking variability during motor behavior. Neural activity was recorded via microelectrode arrays implanted in ventral and dorsal premotor and primary motor cortices of non-human primates performing naturalistic 3-D reaching and grasping actions. Point process models were used to quantify how well LFP features accounted for spiking variability not explained by the measured 3-D reach and grasp kinematics. LFP features included the instantaneous magnitude, phase and analytic-signal components of narrow band-pass filtered (δ, θ, α, β) LFPs, and analytic signal and amplitude envelope features in higher-frequency bands. Multiband LFP features predicted single-neuron spiking (1ms resolution) with substantial accuracy as assessed via ROC analysis. Notably, however, models including both LFP and kinematics features displayed marginal improvement over kinematics-only models. Furthermore, the small predictive information added by LFP features to kinematic models was redundant to information available in fast-timescale (<100ms) spiking history. Overall, information in multiband LFP features, although predictive of single-neuron spiking during movement execution, was redundant to information available in movement parameters and spiking history. Our findings suggest that, during movement execution, collective dynamics reflected in motor cortex LFPs primarily relate to sensorimotor processes directly controlling movement output, adding little explanatory power to variability not accounted by movement parameters