Synchronization in the connectome: Metastable oscillatory modes emerge from interactions in the brain spacetime network

A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations and their link with neural activity remain unclear. Here, we hypothesise that the emergence of transient brain rhythms is a signature of weakly stable synchronization between spatially distributed brain areas, occurring at network-specific collective frequencies due to non-negligible conduction times. We test this hypothesis using a phenomenological network model to simulate interactions between neural mass potentials (resonating at 40Hz) in the structural connectome. Crucially, we identify a critical regime where metastable oscillatory modes emerge spontaneously in the delta (0.5-4Hz), theta (4-8Hz), alpha (8-13Hz) and beta (13-30Hz) frequency bands from weak synchronization of subsystems, closely approximating the MEG power spectra from 89 healthy individuals. Grounded in the physics of delay-coupled oscillators, these numerical analyses demonstrate the role of the spatiotemporal connectome in structuring brain activity in the frequency domain.

A personalizable autonomous neural mass model of epileptic seizures

The prospect of personalized computational modeling in neurological disorders, and in particular in epilepsy, is poised to revolutionize the field. Work in the last two decades has demonstrated that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by i) increasing excitation in NMM and ii) heuristically varying network inhibitory coupling parameters or, equivalently, inhibitory synaptic gains. Based on those studies, we provide here a laminar neural mass model capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input onto the pyramidal cell population, the model dynamics are autonomous --- all model parameters are static. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically plausible algorithm for chloride accumulation dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of Cl$^-$ in pyramidal cells, due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals to compare with real recordings performed in epileptic patients, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods using brain network models based on NMMs.

The Critical Modulatory Role of Spiny Stellate Cells in Seizure Onset Based on Dynamic Analysis of a Neural Mass Model

Growing evidence suggests that excitatory neurons in the brain play a significant role in seizure generation. Nonetheless, spiny stellate cells are cortical excitatory non-pyramidal neurons in the brain, whose basic role in seizure occurrence is not well understood. In the present research, we study the critical role of spiny stellate cells or the excitatory interneurons (EI), for the first time, in epileptic seizure generation using an extended neural mass model inspired by a thalamocortical model originally introduced by another research group. Applying bifurcation analysis on this modified model, we investigated the rich dynamics corresponding to the epileptic seizure onset and transition between interictal and ictal states caused by EI connectivity to other cell types. Our results indicate that the transition between interictal and ictal states (preictal signal) corresponds to a supercritical Hopf bifurcation, and thus, the extended model suggests that before seizure onset, the amplitude and frequency of neural activities gradually increase. Moreover, we showed that (1) the altered function of GABAergic and glutamatergic receptors of EI can cause seizure, and (2) the pathway between the thalamic relay nucleus and EI facilitates the transition from interictal to ictal activity by decreasing the preictal period. Thereafter, we considered both sensory and cortical periodic inputs to study model responses to various harmonic stimulations. Bifurcation analysis of the model, in this case, suggests that the initial state of the model might be the main cause for the transition between interictal and ictal states as the stimulus frequency changes. The extended thalamocortical model shows also that the amplitude jump phenomenon and non-linear resonance behavior result from the preictal state of the modified model. These results can be considered as a step forward to a deeper understanding of the mechanisms underlying the transition from normal activities to epileptic activities.

Extracting dynamical understanding from neural-mass models of mouse cortex

New brain atlases with high spatial resolution and whole-brain coverage have rapidly advanced our knowledge of the brain's neural architecture, including the systematic variation of excitatory and inhibitory cell densities across the mammalian cortex. But understanding how the brain's microscale physiology shapes brain dynamics at the macroscale has remained a challenge. While physiologically based mathematical models of brain dynamics are well placed to bridge this explanatory gap, their complexity can form a barrier to providing clear mechanistic interpretation of the dynamics they generate. In this work we develop a neural-mass model of the mouse cortex and show how bifurcation diagrams, which capture local dynamical responses to inputs and their variation across brain regions, can be used to understand the resulting whole-brain dynamics. We show that strong fits to resting-state functional magnetic resonance imaging (fMRI) data can be found in surprisingly simple dynamical regimes (including where all brain regions are confined to a stable fixed point) where regions are able to respond strongly to variations in their inputs, consistent with direct structural connections providing a strong constraint on functional connectivity in the anesthetized mouse. We also use bifurcation diagrams to show how perturbations to local excitatory and inhibitory coupling strengths across the cortex, constrained by cell-density data, provide spatially dependent constraints on resulting cortical activity, and support a greater diversity of coincident dynamical regimes. Our work illustrates methods for visualizing and interpreting model performance in terms of underlying dynamical mechanisms, an approach that is crucial for building explanatory and physiologically grounded models of the dynamical principles that underpin large-scale brain activity.

Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow us to classify the possible asynchronous and coherent behaviors emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. Analytic mean-field (MF) results show that both supra and sub-threshold balanced asynchronous regimes are observable in our system in the limit N >> K >> 1. Due to the heterogeneity, the asynchronous states are characterized at the microscopic level by the splitting of the neurons in to three groups: silent, fluctuation, and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism analogous to the pyramidal-interneuron gamma (PING), usually invoked for the emergence of γ-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations these collective rhythms can lock. This represents a novel mechanism of frequency locking in neural populations promoted by intrinsic fluctuations. COs are observable for any finite in-degree K, however, their existence in the limit N >> K >> 1 appears as uncertain.

Methods for inferring neural circuit interactions and neuromodulation from local field potential and electroencephalogram measures

Electrical recordings of neural mass activity, such as local field potentials (LFPs) and electroencephalograms (EEGs), have been instrumental in studying brain function. However, these aggregate signals lack cellular resolution and thus are not easy to be interpreted directly in terms of parameters of neural microcircuits. Developing tools for a reliable estimation of key neural parameters from these signals, such as the interaction between excitation and inhibition or the level of neuromodulation, is important for both neuroscientific and clinical applications. Over the years, we have developed tools based on neural network modeling and computational analysis of empirical data to estimate neural parameters from aggregate neural signals. This review article gives an overview of the main computational tools that we have developed and employed to invert LFPs and EEGs in terms of circuit-level neural phenomena, and outlines future challenges and directions for future research.

Realizing the Application of EEG Modeling in BCI Classification: Based on a Conditional GAN Converter

Electroencephalogram (EEG) modeling in brain-computer interface (BCI) provides a theoretical foundation for its development. However, limited by the lack of guidelines in model parameter selection and the inability to obtain personal tissue information in practice, EEG modeling in BCI is mainly focused on the theoretical qualitative level which shows a gap between the theory and its application. Based on such problems, this work combined the surface EEG simulation with a converter based on the generative adversarial network (GAN), to establish the connection from simulated EEG to its application in BCI classification. For the scalp EEGs modeling, a mathematical model was built according to the physics of surface EEG, which consisted of the parallel 3-population neural mass model, the equivalent dipole, and the forward computation. For application, a converter based on the conditional GAN was designed, to transfer the simulated theoretical-only EEG to its practical version, in the lack of individual bio-information. To verify the feasibility, based on the latest microexpression-assisted BCI paradigm proposed by our group, the converted simulated EEGs were used in the training of BCI classifiers. The results indicated that, compared with training with insufficient real data, by adding the simulated EEGs, the overall performance showed a significant improvement (P = 0.04 < 0.05), and the test performance can be improved by 2.17% ± 4.23, in which the largest increase was up to 12.60% ± 1.81. Through this work, the link from theoretical EEG simulation to BCI classification has been initially established, providing an enhanced novel solution for the application of EEG modeling in BCI.

Realistic alpha oscillations and transient responses in a cortical microcircuit model

Neural-mass modeling of neural population data (EEG, ECoG, or LFPs) has shown promise both in elucidating the neural processes underlying cortical rhythms and changes in brain state, as well as offering a framework for testing the interplay between these rhythms and information processing. Models of cortical alpha rhythms (8 - 12 Hz) and their impact in visual sensory processing have been at the forefront of this effort, with the Jansen-Rit being one of the more popular models in this domain. The Jansen-Rit model, however, fails in reproducing key physiological observations including the level of inputs that cortical neurons receive and their responses to visual transients. To address these issues we generated a neural mass model that complies better with synaptic mediated dynamics, intrinsic alpha behavior, and produces realistic responses. The model is robust to many changes in parameter values but critically depends on the ratio of excitation to inhibition, producing response transients whose features are dependent on this ratio and alpha phase and power. The model is sufficiently flexible so as to be able to easily replicate the range of low frequency oscillations observed in different studies. Consistent with experimental observations, we find phase-dependent response dynamics to both visual and electrical stimulation using this model. The model suggests that stimulation facilitates alpha at particular phases and suppresses it in others due to a phase dependent lag in inhibitory responses. Hence, the model generates insight into the physiological parameters responsible for intrinsic oscillations and testable hypotheses regarding the interactions between visual and electrical stimulation on those oscillations.