Neural Mass Research Articles

Brain model state space reconstruction using an LSTM neural network

Objective. Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to electroencephalography (EEG). However, this approach lacks a reliable method to determine the initial filter conditions and assumes that the distribution of states remains Gaussian. This study presents an alternative, data-driven method to track the states and parameters of neural mass models (NMMs) from EEG recordings using deep learning techniques, specifically a long short-term memory (LSTM) neural network. Approach. An LSTM filter was trained on simulated EEG data generated by a NMM using a wide range of parameters. With an appropriately customised loss function, the LSTM filter can learn the behaviour of NMMs. As a result, it can output the state vector and parameters of NMMs given observation data as the input. Main results. Test results using simulated data yielded correlations with R squared of around 0.99 and verified that the method is robust to noise and can be more accurate than a nonlinear Kalman filter when the initial conditions of the Kalman filter are not accurate. As an example of real-world application, the LSTM filter was also applied to real EEG data that included epileptic seizures, and revealed changes in connectivity strength parameters at the beginnings of seizures. Significance. Tracking the state vector and parameters of mathematical brain models is of great importance in the area of brain modelling, monitoring, imaging and control. This approach has no need to specify the initial state vector and parameters, which is very difficult to do in practice because many of the variables being estimated cannot be measured directly in physiological experiments. This method may be applied using any NMM and, therefore, provides a general, novel, efficient approach to estimate brain model variables that are often difficult to measure.

Integrating semi-analytically and efficiently extended Neural Mass Models with distributed transmission delays

Integrating semi-analytically and efficiently extended Neural Mass Models with distributed transmission delays

Exploration of interictal to ictal transition in epileptic seizures using a neural mass model.

The online version contains supplementary material available at 10.1007/s11571-023-09976-6.

Improved Neurophysiological Process Imaging Through Optimization of Kalman Filter Initial Conditions

Recent work presented a framework for space-time-resolved neurophysiological process imaging that augments existing electromagnetic source imaging techniques. In particular, a nonlinear Analytic Kalman filter (AKF) has been developed to efficiently infer the states and parameters of neural mass models believed to underlie the generation of electromagnetic source currents. Unfortunately, as the initialization determines the performance of the Kalman filter, and the ground truth is typically unavailable for initialization, this framework might produce suboptimal results unless significant effort is spent on tuning the initialization. Notably, the relation between the initialization and overall filter performance is only given implicitly and is expensive to evaluate; implying that conventional optimization techniques, e.g. gradient or sampling based, are inapplicable. To address this problem, a novel efficient framework based on blackbox optimization has been developed to find the optimal initialization by reducing the signal prediction error. Multiple state-of-the-art optimization methods were compared and distinctively, Gaussian process optimization decreased the objective function by 82.1% and parameter estimation error by 62.5% on average with the simulation data compared to no optimization applied. The framework took only 1.6[Formula: see text]h and reduced the objective function by an average of 13.2% on 3.75[Formula: see text]min 4714-source channel magnetoencephalography data. This yields an improved method of neurophysiological process imaging that can be used to uncover complex underpinnings of brain dynamics.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen and Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks.

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.

Tracking the effects of propofol, sevoflurane and (S)-ketamine anesthesia using an unscented Kalman filter-based neural mass model

Objective. Neural mass model (NMM) has been widely used to investigate the neurophysiological mechanisms of anesthetic drugs induced general anesthesia (GA). However, whether the parameters of NMM could track the effects of anesthesia still unknown. Approach. We proposed using the cortical NMM (CNMM) to infer the potential neurophysiological mechanism of three different anesthetic drugs (i.e. propofol, sevoflurane, and (S)-ketamine) induced GA, and we employed unscented Kalman filter (UKF) to track any change in raw electroencephalography (rEEG) in frontal area during GA. We did this by estimating the parameters of population gain [i.e. excitatory/inhibitory postsynaptic potential (EPSP/IPSP, i.e. parameter A/B in CNMM) and the time constant rate of EPSP/IPSP (i.e. parameter a/b in CNMM). We compared the rEEG and simulated EEG (sEEG) from the perspective of spectrum, phase-amplitude coupling (PAC), and permutation entropy (PE). Main results. Under three estimated parameters (i.e. A, B, and a for propofol/sevoflurane or b for (S)-ketamine), the rEEG and sEEG had similar waveforms, time-frequency spectra, and PAC patterns during GA for the three drugs. The PE curves derived from rEEG and sEEG had high correlation coefficients (propofol: 0.97 ± 0.03, sevoflurane: 0.96 ± 0.03, (S)-ketamine: 0.98 ± 0.02) and coefficients of determination (R 2) (propofol: 0.86 ± 0.03, sevoflurane: 0.68 ± 0.30, (S)-ketamine: 0.70 ± 0.18). Except for parameter A for sevoflurane, the estimated parameters for each drug in CNMM can differentiate wakefulness and non-wakefulness states. Compared with the simulation of three estimated parameters, the UKF-based CNMM had lower tracking accuracy under the simulation of four estimated parameters (i.e. A, B, a, and b) for three drugs. Significance. The results demonstrate that a combination of CNMM and UKF could track the neural activities during GA. The EPSP/IPSP and their time constant rate can interpret the anesthetic drug’s effect on the brain, and can be used as a new index for depth of anesthesia monitoring.

Global nonlinear approach for mapping parameters of neural mass models.

Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively compare the output of NMMs with data, and thereby find parameter values for which the model can produce the observed dynamics. Mapping dynamics to NMM parameter values in this way has the potential to improve our understanding of the brain in health and disease. Though abstract, NMMs still comprise of many parameters that are difficult to constrain a priori. This makes it challenging to explore the dynamics of NMMs and elucidate regions of parameter space in which their dynamics best approximate data. Existing approaches to overcome this challenge use a combination of linearising models, constraining the values they can take and exploring restricted subspaces by fixing the values of many parameters a priori. As such, we have little knowledge of the extent to which different regions of parameter space of NMMs can yield dynamics that approximate data, how nonlinearities in models can affect parameter mapping or how best to quantify similarities between model output and data. These issues need to be addressed in order to fully understand the potential and limitations of NMMs, and to aid the development of new models of brain dynamics in the future. To begin to overcome these issues, we present a global nonlinear approach to recovering parameters of NMMs from data. We use global optimisation to explore all parameters of nonlinear NMMs simultaneously, in a minimally constrained way. We do this using multi-objective optimisation (multi-objective evolutionary algorithm, MOEA) so that multiple data features can be quantified. In particular, we use the weighted horizontal visibility graph (wHVG), which is a flexible framework for quantifying different aspects of time series, by converting them into networks. We study EEG alpha activity recorded during the eyes closed resting state from 20 healthy individuals and demonstrate that the MOEA performs favourably compared to single objective approaches. The addition of the wHVG objective allows us to better constrain the model output, which leads to the recovered parameter values being restricted to smaller regions of parameter space, thus improving the practical identifiability of the model. We then use the MOEA to study differences in the alpha rhythm observed in EEG recorded from 20 people with epilepsy. We find that a small number of parameters can explain this difference and that, counterintuitively, the mean excitatory synaptic gain parameter is reduced in people with epilepsy compared to control. In addition, we propose that the MOEA could be used to mine for the presence of pathological rhythms, and demonstrate the application of this to epileptiform spike-wave discharges.

Characterization of regional differences in resting-state fMRI with a data-driven network model of brain dynamics

Model-based data analysis of whole-brain dynamics links the observed data to model parameters in a network of neural masses. Recently, studies focused on the role of regional variance of model parameters. Such analyses however necessarily depend on the properties of preselected neural mass model. We introduce a method to infer from the functional data both the neural mass model representing the regional dynamics and the region- and subject-specific parameters while respecting the known network structure. We apply the method to human resting-state fMRI. We find that the underlying dynamics can be described as noisy fluctuations around a single fixed point. The method reliably discovers three regional parameters with clear and distinct role in the dynamics, one of which is strongly correlated with the first principal component of the gene expression spatial map. The present approach opens a novel way to the analysis of resting-state fMRI with possible applications for understanding the brain dynamics during aging or neurodegeneration.

Complexity of cortical wave patterns of the wake mouse cortex

Rich spatiotemporal dynamics of cortical activity, including complex and diverse wave patterns, have been identified during unconscious and conscious brain states. Yet, how these activity patterns emerge across different levels of wakefulness remain unclear. Here we study the evolution of wave patterns utilizing data from high spatiotemporal resolution optical voltage imaging of mice transitioning from barbiturate-induced anesthesia to wakefulness (N = 5) and awake mice (N = 4). We find that, as the brain transitions into wakefulness, there is a reduction in hemisphere-scale voltage waves, and an increase in local wave events and complexity. A neural mass model recapitulates the essential cellular-level features and shows how the dynamical competition between global and local spatiotemporal patterns and long-range connections can explain the experimental observations. These mechanisms possibly endow the awake cortex with enhanced integrative processing capabilities.

The role of additive and diffusive coupling on the dynamics of neural populations

Dynamical models consisting of networks of neural masses commonly assume that the interactions between neural populations are via additive or diffusive coupling. When using the additive coupling, a population’s activity is affected by the sum of the activities of neighbouring populations. In contrast, when using the diffusive coupling a neural population is affected by the sum of the differences between its activity and the activity of its neighbours. These two coupling functions have been used interchangeably for similar applications. In this study, we show that the choice of coupling can lead to strikingly different brain network dynamics. We focus on a phenomenological model of seizure transitions that has been used both with additive and diffusive coupling in the literature. We consider small networks with two and three nodes, as well as large random and scale-free networks with 64 nodes. We further assess resting-state functional networks inferred from magnetoencephalography (MEG) from people with juvenile myoclonic epilepsy (JME) and healthy controls. To characterize the seizure dynamics on these networks, we use the escape time, the brain network ictogenicity (BNI) and the node ictogenicity (NI), which are measures of the network’s global and local ability to generate seizure activity. Our main result is that the level of ictogenicity of a network is strongly dependent on the coupling function. Overall, we show that networks with additive coupling have a higher propensity to generate seizures than those with diffusive coupling. We find that people with JME have higher additive BNI than controls, which is the hypothesized BNI deviation between groups, while the diffusive BNI provides opposite results. Moreover, we find that the nodes that are more likely to drive seizures in the additive coupling case are more likely to prevent seizures in the diffusive coupling case, and that these features correlate to the node’s number of connections. Consequently, previous results in the literature involving such models to interrogate functional or structural brain networks could be highly dependent on the choice of coupling. Our results on the MEG functional networks and evidence from the literature suggest that the additive coupling may be a better modeling choice than the diffusive coupling, at least for BNI and NI studies. Thus, we highlight the need to motivate and validate the choice of coupling in future studies involving network models of brain activity.

Effect of channel density, inverse solutions and connectivity measures on EEG resting-state networks reconstruction: A simulation study

Along with the study of brain activity evoked by external stimuli, the past two decades witnessed an increased interest in characterizing the spontaneous brain activity occurring during resting conditions. The identification of connectivity patterns in this so-called "resting-state" has been the subject of a great number of electrophysiology-based studies, using the Electro/Magneto-Encephalography (EEG/MEG) source connectivity method. However, no consensus has been reached yet regarding a unified (if possible) analysis pipeline, and several involved parameters and methods require cautious tuning. This is particularly challenging when different analytical choices induce significant discrepancies in results and drawn conclusions, thereby hindering the reproducibility of neuroimaging research. Hence, our objective in this study was to shed light on the effect of analytical variability on outcome consistency by evaluating the implications of parameters involved in the EEG source connectivity analysis on the accuracy of resting-state networks (RSNs) reconstruction. We simulated, using neural mass models, EEG data corresponding to two RSNs, namely the default mode network (DMN) and dorsal attentional network (DAN). We investigated the impact of five channel densities (19, 32, 64, 128, 256), three inverse solutions (weighted minimum norm estimate (wMNE), exact low-resolution brain electromagnetic tomography (eLORETA), and linearly constrained minimum variance (LCMV) beamforming) and four functional connectivity measures (phase-locking value (PLV), phase-lag index (PLI), and amplitude envelope correlation (AEC) with and without source leakage correction), on the correspondence between reconstructed and reference networks. We showed that, with different analytical choices related to the number of electrodes, source reconstruction algorithm, and functional connectivity measure, high variability is present in the results. More specifically, our results show that a higher number of EEG channels significantly increased the accuracy of the reconstructed networks. Additionally, our results showed significant variability in the performance of the tested inverse solutions and connectivity measures. Such methodological variability and absence of analysis standardization represent a critical issue for neuroimaging studies that should be prioritized. We believe that this work could be useful for the field of electrophysiology connectomics, by increasing awareness regarding the challenge of variability in methodological approaches and its implications on reported results.

Predictive neuromodulation of cingulo-frontal neural dynamics in major depressive disorder using a brain-computer interface system: A simulation study.

Deep brain stimulation (DBS) is a promising therapy for treatment-resistant major depressive disorder (MDD). MDD involves the dysfunction of a brain network that can exhibit complex nonlinear neural dynamics in multiple frequency bands. However, current open-loop and responsive DBS methods cannot track the complex multiband neural dynamics in MDD, leading to imprecise regulation of symptoms, variable treatment effects among patients, and high battery power consumption. Here, we develop a closed-loop brain-computer interface (BCI) system of predictive neuromodulation for treating MDD. We first use a biophysically plausible ventral anterior cingulate cortex (vACC)-dorsolateral prefrontal cortex (dlPFC) neural mass model of MDD to simulate nonlinear and multiband neural dynamics in response to DBS. We then use offline system identification to build a dynamic model that predicts the DBS effect on neural activity. We next use the offline identified model to design an online BCI system of predictive neuromodulation. The online BCI system consists of a dynamic brain state estimator and a model predictive controller. The brain state estimator estimates the MDD brain state from the history of neural activity and previously delivered DBS patterns. The predictive controller takes the estimated MDD brain state as the feedback signal and optimally adjusts DBS to regulate the MDD neural dynamics to therapeutic targets. We use the vACC-dlPFC neural mass model as a simulation testbed to test the BCI system and compare it with state-of-the-art open-loop and responsive DBS treatments of MDD. We demonstrate that our dynamic model accurately predicts nonlinear and multiband neural activity. Consequently, the predictive neuromodulation system accurately regulates the neural dynamics in MDD, resulting in significantly smaller control errors and lower DBS battery power consumption than open-loop and responsive DBS. Our results have implications for developing future precisely-tailored clinical closed-loop DBS treatments for MDD.

Decreased coherence in the model of the dorsal visual pathway associated with Alzheimer’s disease

Decreased coherence in electroencephalogram (EEG) has been reported in Alzheimer’s disease (AD) experimentally, which could be considered as a typical electrophysiological characteristic in AD. This work aimed to investigate the effect of AD on coherence in the dorsal visual pathway by the technique of neurocomputation. Firstly, according to the hierarchical organization of the cerebral cortex and the information flows of the dorsal visual pathway, a more physiologically plausible neural mass model including cortical areas v1, v2, and v5 was established in the dorsal visual pathway. The three interconnected cortical areas were connected by ascending and descending projections. Next, the pathological condition of loss of long synaptic projections in AD was simulated by reducing the parameters of long synaptic projections in the model. Then, the loss of long synaptic projections on coherence among different visual cortex areas was explored by means of power spectral analysis and coherence function. The results demonstrate that the coherence between these interconnected cortical areas showed an obvious decline with the gradual decrease of long synaptic projections, i.e. decrease in descending projections from area v2 to v1 and v5 to v2 and ascending projection from area v2 to v5. Hopefully, the results of this study could provide theoretical guidance for understanding the dynamical mechanism of AD.

Next generation neural population models

Low-dimensional neural mass models are often invoked to model the coarse-grained activity of large populations of neurons and synapses and have been used to help understand the coordination of large scale brain rhythms. However, they are phenomenological in nature and, although motivated by neurobiological considerations, the absence of a direct link to an underlying biophysical reality is a weakness that means they may not be best suited to capturing some of the rich behaviors seen in real neuronal tissue. In this perspective article I discuss a simple spiking neuron network model that has recently been shown to admit to an exact mean-field description for synaptic interactions. This has many of the features of a neural mass model coupled to an additional dynamical equation that describes the evolution of population synchrony. Thisnext generationneural mass model is ideally suited to understanding the patterns of brain activity that are ubiquitously seen in neuroimaging recordings. Here I review the mean-field equations, the way in which population synchrony, firing rate, and average voltage are intertwined, together with their application in large scale brain modeling. As well as natural extensions of this new approach to modeling the dynamics of neuronal populations I discuss some of the open mathematical challenges in developing a statistical neurodynamics that can generalize the one discussed here.

Population spiking and bursting in next-generation neural masses with spike-frequency adaptation.

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the θ-γ range has revealed that a reduction of SFA leads to an increase of the θ frequency joined to a decrease of the γ one. This is analogous to what has been reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, which is known to reduce SFA.

Neural adaptation and fractional dynamics as a window to underlying neural excitability.

The relationship between macroscale electrophysiological recordings and the dynamics of underlying neural activity remains unclear. We have previously shown that low frequency EEG activity (<1 Hz) is decreased at the seizure onset zone (SOZ), while higher frequency activity (1-50 Hz) is increased. These changes result in power spectral densities (PSDs) with flattened slopes near the SOZ, which are assumed to be areas of increased excitability. We wanted to understand possible mechanisms underlying PSD changes in brain regions of increased excitability. We hypothesized that these observations are consistent with changes in adaptation within the neural circuit. We developed a theoretical framework and tested the effect of adaptation mechanisms, such as spike frequency adaptation and synaptic depression, on excitability and PSDs using filter-based neural mass models and conductance-based models. We compared the contribution of single timescale adaptation and multiple timescale adaptation. We found that adaptation with multiple timescales alters the PSDs. Multiple timescales of adaptation can approximate fractional dynamics, a form of calculus related to power laws, history dependence, and non-integer order derivatives. Coupled with input changes, these dynamics changed circuit responses in unexpected ways. Increased input without synaptic depression increases broadband power. However, increased input with synaptic depression may decrease power. The effects of adaptation were most pronounced for low frequency activity (< 1Hz). Increased input combined with a loss of adaptation yielded reduced low frequency activity and increased higher frequency activity, consistent with clinical EEG observations from SOZs. Spike frequency adaptation and synaptic depression, two forms of multiple timescale adaptation, affect low frequency EEG and the slope of PSDs. These neural mechanisms may underlie changes in EEG activity near the SOZ and relate to neural hyperexcitability. Neural adaptation may be evident in macroscale electrophysiological recordings and provide a window to understanding neural circuit excitability.

A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM) that represent the mean activity of large numbers of neurons. Here, we provide first a new framework called laminar NMM, or LaNMM for short, where we combine conduction physics with NMMs to simulate electrophysiological measurements. Then, we employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define a minimal model capable of generating coupled slow and fast oscillations, and we optimize LaNMM-specific parameters to fit multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology by selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals. In closing, we discuss how this hybrid modeling framework can be more generally used to infer cortical circuitry.

Global dynamics of neural mass models

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings

Objective. Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements. Approach. We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept. Main results. CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer). Significance. Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.