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Objective Methods Results Significance For the pre‐surgical evaluation of patients with drug‐resistant focal epilepsy, stereo‐electroencephalographic (SEEG) signals are routinely recorded to identify the epileptogenic zone network (EZN). This network consists of remote brain regions involved in seizure initiation. However, the pathophysiological mechanisms underlying typical SEEG patterns that occur during the transition from interictal to ictal activity in distant brain nodes of the EZN remain poorly understood. The primary aim is to identify and explain these mechanisms using a novel physiologically‐plausible model of the EZN.We analyzed SEEG signals recorded from the EZN in 10 patients during the transition from interictal to ictal activity. This transition consisted of a sequence of periods during which SEEG signals from distant neocortical regions showed stereotypical patterns of activity: sustained preictal spiking activity preceding a fast activity occurring at seizure onset, followed by the ictal activity. Spectral content and non‐linear correlation of SEEG signals were analyzed. In addition, we developed a novel neuro‐inspired computational model consisting of bidirectionally coupled neuronal populations.The proposed model captured the essential characteristics of the patient signals, including the quasi‐synchronous onset of rapid discharges in distant interconnected epileptogenic zones. Statistical analysis confirmed the dynamic correlation/de‐decorrelation pattern observed in the patient signals and accurately reproduced in the simulated signals.This study provides insight into the abnormal dynamic changes in glutamatergic and γ‐aminobutyric acid (GABA)ergic synaptic transmission that occur during the transition to seizures. The results strongly support the hypothesis that bidirectional connections between distant neuronal populations of the EZN (from pyramidal cells to vaso‐intestinal peptide‐positive interneurons) play a key role in this transition, while parvalbumin‐positive interneurons intervene in the emergence of rapid discharges at seizure onset. [ABSTRACT FROM AUTHOR]

Gamma oscillations (30-120 Hz) in the brain are not periodic cycles, but they typically appear in short-time windows, often called oscillatory bursts. While the origin of this bursting phenomenon is still unclear, some recent studies hypothesize its origin in the external or endogenous noise of neural networks. We demonstrate that an exact neural mass model of excitatory and inhibitory quadratic-integrate and fire-spiking neurons theoretically predicts the emergence of a different regime of intrinsic bursting gamma (IBG) oscillations without any noise source, a phenomenon due to collective chaos. This regime is indeed observed in the direct simulation of spiking neurons, characterized by highly irregular spiking activity. IBGoscillations are distinguished by higher phase-amplitude coupling to slower theta oscillations concerning noise-induced bursting oscillations, thus indicating an increased capacity for information transfer between brain regions. We demonstrate that this phenomenon is present in both globally coupled and sparse networks of spiking neurons. These results propose a new mechanism for gamma oscillatory activity, suggesting deterministic collective chaos as a good candidate for the origin of gamma bursts. [ABSTRACT FROM AUTHOR]

Epilepsy, a neurological disorder characterized by recurrent seizures, presents a complex interplay of cellular and molecular mechanisms. The symptoms manifest themselves at various scales, from ion channels to brain regions to behavior in humans. Various screening, treatment, and preventive measures use this knowledge to tackle the disorder effectively. This article aims to summarize the current state of the art in epileptic markers from ion channels, astrocytes, and synaptic imbalance to whole brain Network Dynamics. Recent research has shed light on the critical involvement of astrocytes, the multifunctional glial cells, in the pathogenesis and modulation of epileptic seizures in humans. Astrocytes, once considered as mere supportive cells, are now recognized as active participants in the regulation of neuronal excitability, synaptic transmission, and brain homeostasis. Ion channel imbalance is one of the widely studied areas in the context of epilepsy and is partially addressed in the abstract. Recent advances in computational neuroscience have led to the development of whole brain network models, providing valuable tools for studying the complex dynamics of epileptic seizures. These models integrate diverse biological factors, including neuronal connectivity, synaptic dynamics, and cellular properties, to simulate the spatiotemporal patterns of epileptic activity across brain regions. Through computational simulations and analysis, whole brain network models offer insights into seizure initiation, propagation, and termination mechanisms, shedding light on the dynamic interactions between epileptic foci and distributed brain networks. Moreover, these models facilitate the exploration of network-based biomarkers for seizure prediction and intervention optimization. Challenges and limitations, such as model complexity and validation against experimental data, are also discussed. Despite these challenges, whole brain network models represent a promising approach for advancing our understanding of epilepsy and identifying novel therapeutic strategies. Future research efforts should focus on refining model fidelity, incorporating multimodal data, and translating computational findings into clinically relevant applications, ultimately improving the management and treatment of epilepsy patients.

Non-invasive brain stimulation, particularly transcranial electrical stimulation (tES), has been explored for its potential in controlling epileptic activity. Based on the whole-brain epilepsy model, this study proposes a mechanism of stimulus effects on excitatory synaptic levels within nodes to explain the lasting effect of tES on the control of epileptic oscillatory propagation. It is found that cathodal tES effectively controls seizure propagation and maintains it for a period of time by affecting excitatory synaptic levels. Further, we propose a closed-loop tES strategy based on amplitude control. The choice of feedback indicator determines the time of stimulus onset and is particularly important for stimulus effectiveness. An unsuitable feedback signal may shorten stimulus duration, reduce long-term effectiveness, or fail to suppress already widespread oscillations. Additionally, the duration after each stimulus trigger and synaptic decay rate also influence the lasting effectiveness of closed-loop tES. The construction of specific epilepsy network models based on information from six patients suggests that the choice of stimulation parameters should be based on patient-specific information. Although the stimulation parameters required varied across models, the overall trend indicates improved lasting effects with increased stimulation duration and synaptic decay rates. Finally, the study introduces a dual-target closed-loop tES approach for a patient with extensively distributed seizure zones, where single-target stimulation proved ineffective. This study provides theoretical support for the application of closed-loop tES technology for the treatment of epilepsy, highlighting the necessity of personalized treatment protocols based on detailed patient-specific information and the innovative potential of dual-target stimulation strategies in refractory cases. [ABSTRACT FROM AUTHOR]

We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonlinear NMDAR action is seen to be state-dependent and can have opposite effects depending on the type of neurons involved and the level of input firing rate received. The presented model can serve as a computationally efficient building block in whole brain network models for investigating the differential modulation of different types of synapses under neuromodulatory influence or receptor specific malfunction. [ABSTRACT FROM AUTHOR]

An epileptic seizure can usually be divided into three stages: interictal, preictal, and ictal. However, the seizure underlying the transition from interictal to ictal activities in the brain involves complex interactions between inhibition and excitation in groups of neurons. To explore this mechanism at the level of a single population, this paper employed a neural mass model, named the complete physiology-based model (cPBM), to reconstruct electroencephalographic (EEG) signals and to infer the changes in excitatory/inhibitory connections related to excitation–inhibition (E–I) balance based on an open dataset recorded for ten epileptic patients. Since epileptic signals display spectral characteristics, spectral dynamic causal modelling (DCM) was applied to quantify these frequency characteristics by maximizing the free energy in the framework of power spectral density (PSD) and estimating the cPBM parameters. In addition, to address the local maximum problem that DCM may suffer from, a hybrid deterministic DCM (H-DCM) approach was proposed, with a deterministic annealing-based scheme applied in two directions. The H-DCM approach adjusts the temperature introduced in the objective function by gradually decreasing the temperature to obtain relatively good initialization and then gradually increasing the temperature to search for a better estimation after each maximization. The results showed that (i) reconstructed EEG signals belonging to the three stages together with their PSDs can be reproduced from the estimated parameters of the cPBM; (ii) compared to DCM, traditional D-DCM and anti D-DCM, the proposed H-DCM shows higher free energies and lower root mean square error (RMSE), and it provides the best performance for all stages (e.g., the RMSEs between the reconstructed PSD computed from the reconstructed EEG signal and the sample PSD obtained from the real EEG signal are 0.33 ± 0.08, 0.67 ± 0.37 and 0.78 ± 0.57 in the interictal, preictal and ictal stages, respectively); and (iii) the transition from interictal to ictal activity can be explained by an increase in the connections between pyramidal cells and excitatory interneurons and between pyramidal cells and fast inhibitory interneurons, as well as a decrease in the self-loop connection of the fast inhibitory interneurons in the cPBM. Moreover, the E–I balance, defined as the ratio between the excitatory connection from pyramidal cells to fast inhibitory interneurons and the inhibitory connection with the self-loop of fast inhibitory interneurons, is also significantly increased during the epileptic seizure transition. [ABSTRACT FROM AUTHOR]

Background: Mathematical modeling and computer simulation are important methods for understanding complex neural systems. The whole-brain network model can help people understand the neurophysiological mechanisms of brain cognition and functional diseases of the brain. Methods: In this study, we constructed a resting-state whole-brain network model (WBNM) by using the Wendling neural mass model as the node and a real structural connectivity matrix as the edge of the network. By analyzing the correlation between the simulated functional connectivity matrix in the resting state and the empirical functional connectivity matrix, an optimal global coupling coefficient was obtained. Then, the waveforms and spectra of simulated EEG signals and four commonly used measures from graph theory and small-world network properties of simulated brain networks under different thresholds were analyzed. Results: The results showed that the correlation coefficient of the functional connectivity matrix of the simulated WBNM and empirical brain networks could reach a maximum value of 0.676 when the global coupling coefficient was set to 20.3. The simulated EEG signals showed rich waveform and frequency-band characteristics. The commonly used graph-theoretical measures and small-world properties of the constructed WBNM were similar to those of empirical brain networks. When the threshold was set to 0.22, the maximum correlation between the simulated WBNM and empirical brain networks was 0.709. Conclusions: The constructed resting-state WBNM is similar to a real brain network to a certain extent and can be used to study the neurophysiological mechanisms of complex brain networks. [ABSTRACT FROM AUTHOR]

Gamma oscillations (30–120 Hz) in the brain are not periodic cycles, but they typically appear in short-time windows, often called oscillatory bursts. While the origin of this bursting phenomenon is still unclear, some recent studies hypothesize its origin in the external or endogenous noise of neural networks. We demonstrate that an exact neural mass model of excitatory and inhibitory quadratic-integrate and fire-spiking neurons theoretically predicts the emergence of a different regime of intrinsic bursting gamma (IBG) oscillations without any noise source, a phenomenon due to collective chaos. This regime is indeed observed in the direct simulation of spiking neurons, characterized by highly irregular spiking activity. IBG oscillations are distinguished by higher phase-amplitude coupling to slower theta oscillations concerning noise-induced bursting oscillations, thus indicating an increased capacity for information transfer between brain regions. We demonstrate that this phenomenon is present in both globally coupled and sparse networks of spiking neurons. These results propose a new mechanism for gamma oscillatory activity, suggesting deterministic collective chaos as a good candidate for the origin of gamma bursts.

Excessive neural synchronization of neural populations in the beta (β) frequency range (12–35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications. [ABSTRACT FROM AUTHOR]

Transcranial direct current stimulation (tDCS) is a noninvasive technique that uses constant, low-intensity direct current to regulate brain activities. Clinical studies have shown that cathode-tDCS (c-tDCS) is effective in reducing seizure frequency in patients with epilepsy. Due to the heterogeneity and patient specificity of seizures, patient-specific epilepsy networks are increasingly important in exploring the regulatory role of c-tDCS. In this study, we first set the left hippocampus, para-hippocampus, and amygdala as the epileptogenic zone (EZ), and the left inferior temporal cortex and ventral temporal cortex as the initial propagation zone (PZ) to establish a large-scale epilepsy network model. Then we set tDCS cathode locations according to the maximum average energy of the simulated EEG signals and systematically study c-tDCS inhibitory effects on the propagation of epileptic activity. The results show that c-tDCS is effective in suppressing the propagation of epileptic activity. Further, to consider the patient specificity, we set specific EZ and PZ according to the clinical diagnosis of 6 patients and establish patient-specific epileptic networks. We find that c-tDCS can suppress the propagation of abnormal activity in most patient-specific epileptic networks. However, when the PZ is widely distributed in both hemispheres, the treatment effect of c-tDCS is not satisfactory. Hence, we propose dual-cathode tDCS. For epilepsy models with a wide distribution of PZ, it can inhibit the propagation of epileptiform activity in other nodes except EZ and PZ without increasing the tDCS current strength. Our results provide theoretical support for the treatment of epilepsy with tDCS. [ABSTRACT FROM AUTHOR]

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

BackgroundNeuronal- and circuit-level abnormalities of excitation and inhibition are shown to be associated with tau and amyloid-beta (Aβ) in preclinical models of Alzheimer's disease (AD). These relationships remain poorly understood in patients with AD.MethodsUsing empirical spectra from magnetoencephalography and computational modeling (neural mass model), we examined excitatory and inhibitory parameters of neuronal subpopulations and investigated their specific associations to regional tau and Aβ, measured by positron emission tomography, in patients with AD.ResultsPatients with AD showed abnormal excitatory and inhibitory time-constants and neural gains compared to age-matched controls. Increased excitatory time-constants distinctly correlated with higher tau depositions while increased inhibitory time-constants distinctly correlated with higher Aβ depositions.ConclusionsOur results provide critical insights about potential mechanistic links between abnormal neural oscillations and cellular correlates of impaired excitatory and inhibitory synaptic functions associated with tau and Aβ in patients with AD.FundingThis study was supported by the National Institutes of Health grants: K08AG058749 (KGR), F32AG050434-01A1 (KGR), K23 AG038357 (KAV), P50 AG023501, P01 AG19724 (BLM), P50-AG023501 (BLM and GDR), R01 AG045611 (GDR); AG034570, AG062542 (WJ); NS100440 (SSN), DC176960 (SSN), DC017091 (SSN), AG062196 (SSN); a grant from John Douglas French Alzheimer's Foundation (KAV); grants from Larry L. Hillblom Foundation: 2015-A-034-FEL (KGR), 2019-A-013-SUP (KGR); grants from the Alzheimer's Association: AARG-21-849773 (KGR); PCTRB-13-288476 (KAV), and made possible by Part the CloudTM (ETAC-09-133596); a grant from Tau Consortium (GDR and WJJ), and a gift from the S. D. Bechtel Jr. Foundation.

Background: The role of delayed feedback stimulation in the discussion of Parkinson's disease (PD) has recently received increasing attention. Stimulation of pedunculopontine nucleus (PPN) is an emerging treatment for PD. However, the effect of PPN in regulating PD is ignored, and the delayed feedback stimulation algorithm is facing some problems in parameter selection. Methods: On the basis of a neural mass model, we established a new network for PPN. Four types of delayed feedback stimulation schemes were designed, such as stimulating subthalamic nucleus (STN) with the local field potentials (LFPs) of STN nucleus, globus pallidus (GPe) with the LFPs of Gpe nucleus, PPN with the LFPs of Gpe nucleus, and STN with the LFPs of PPN nucleus. Results: In this study, we found that all four kinds of delayed feedback schemes are effective, suggesting that the algorithm is simple and more effective in experiments. More specifically, the other three control schemes improved the control performance and reduced the stimulation energy expenditure compared with traditional stimulating STN itself only. Conclusion: PPN stimulation can affect the new network and help to suppress pathological oscillations for each neuron. We hope that our results can gain an insight into the future clinical treatment. [ABSTRACT FROM AUTHOR]

Strong inhibitory recurrent connections can reduce the tendency for a neural network to become unstable. This is known as inhibitory stabilization; networks that are unstable in the absence of strong inhibitory feedback because of their unstable excitatory recurrent connections are known as Inhibition Stabilized Networks (ISNs). One of the characteristics of ISNs is their "paradoxical response", where perturbing the inhibitory neurons with additional excitatory input results in a decrease in their activity after a temporal delay instead of increasing their activity. Here, we develop a model of populations of neurons across different layers of cortex. Within each layer, there is one population of inhibitory neurons and one population of excitatory neurons. The connectivity weights across different populations in the model are derived from a synaptic physiology database provided by the Allen Institute. The model shows a gradient of excitation–inhibition balance across different layers in the cortex, where superficial layers are more inhibitory dominated compared to deeper layers. To investigate the presence of ISNs across different layers, we measured the membrane potentials of neural populations in the model after perturbing inhibitory populations. The results show that layer 2/3 in the model does not operate in the ISN regime but layers 4 and 5 do operate in the ISN regime. These results accord with neurophysiological findings that explored the presence of ISNs across different layers in the cortex. The results show that there may be a systematic macroscopic gradient of inhibitory stabilization across different layers in the cortex that depends on the level of excitation–inhibition balance, and that the strength of the paradoxical response increases as the model moves closer to bifurcation points. [ABSTRACT FROM AUTHOR]

Evoked neural responses to sensory stimuli have been extensively investigated in humans and animal models both to enhance our understanding of brain function and to aid in clinical diagnosis of neurological and neuropsychiatric conditions. Recording and imaging techniques such as electroencephalography (EEG), magnetoencephalography (MEG), local field potentials (LFPs), and calcium imaging provide complementary information about different aspects of brain activity at different spatial and temporal scales. Modeling and simulations provide a way to integrate these different types of information to clarify underlying neural mechanisms.In this study, we aimed to shed light on the neural dynamics underlying auditory evoked responses by fitting a rate-based model to LFPs recorded via multi-contact electrodes which simultaneously sampled neural activity across cortical laminae. Recordings included neural population responses to best-frequency (BF) and non-BF tones at four representative sites in primary auditory cortex (A1) of awake monkeys. The model considered major neural populations of excitatory, parvalbumin-expressing (PV), and somatostatin-expressing (SOM) neurons across layers 2/3, 4, and 5/6. Unknown parameters, including the connection strength between the populations, were fitted to the data. Our results revealed similar population dynamics, fitted model parameters, predicted equivalent current dipoles (ECD), tuning curves, and lateral inhibition profiles across recording sites and animals, in spite of quite different extracellular current distributions. We found that PV firing rates were higher in BF than in non-BF responses, mainly due to different strengths of tonotopic thalamic input, whereas SOM firing rates were higher in non-BF than in BF responses due to lateral inhibition.In conclusion, we demonstrate the feasibility of the model-fitting approach in identifying the contributions of cell-type specific population activity to stimulus-evoked LFPs across cortical laminae, providing a foundation for further investigations into the dynamics of neural circuits underlying cortical sensory processing.

Abstract Background The role of delayed feedback stimulation in the discussion of Parkinson's disease (PD) has recently received increasing attention. Stimulation of pedunculopontine nucleus (PPN) is an emerging treatment for PD. However, the effect of PPN in regulating PD is ignored, and the delayed feedback stimulation algorithm is facing some problems in parameter selection. Methods On the basis of a neural mass model, we established a new network for PPN. Four types of delayed feedback stimulation schemes were designed, such as stimulating subthalamic nucleus (STN) with the local field potentials (LFPs) of STN nucleus, globus pallidus (GPe) with the LFPs of Gpe nucleus, PPN with the LFPs of Gpe nucleus, and STN with the LFPs of PPN nucleus. Results In this study, we found that all four kinds of delayed feedback schemes are effective, suggesting that the algorithm is simple and more effective in experiments. More specifically, the other three control schemes improved the control performance and reduced the stimulation energy expenditure compared with traditional stimulating STN itself only. Conclusion PPN stimulation can affect the new network and help to suppress pathological oscillations for each neuron. We hope that our results can gain an insight into the future clinical treatment.

Alzheimer's disease (AD) is a degenerative brain disease, and the condition is difficult to assess. In the past, numerous brain dynamics models have made remarkable contributions to neuroscience and the brain from the microcosmic to the macroscopic scale. Recently, large-scale brain dynamics models have been developed based on dual-driven multimodal neuroimaging data and neurodynamics theory. These models bridge the gap between anatomical structure and functional dynamics and have played an important role in assisting the understanding of the brain mechanism. Large-scale brain dynamics have been widely used to explain how macroscale neuroimaging biomarkers emerge from potential neuronal population level disturbances associated with AD. In this review, we describe this emerging approach to studying AD that utilizes a biophysically large-scale brain dynamics model. In particular, we focus on the application of the model to AD and discuss important directions for the future development and analysis of AD models. This will facilitate the development of virtual brain models in the field of AD diagnosis and treatment and add new opportunities for advancing clinical neuroscience. [ABSTRACT FROM AUTHOR]

neurolib is a computational framework for whole-brain modeling written in Python. It provides a set of neural mass models that represent the average activity of a brain region on a mesoscopic scale. In a whole-brain network model, brain regions are connected with each other based on biologically informed structural connectivity, i.e., the connectome of the brain. neurolib can load structural and functional datasets, set up a whole-brain model, manage its parameters, simulate it, and organize its outputs for later analysis. The activity of each brain region can be converted into a simulated BOLD signal in order to calibrate the model against empirical data from functional magnetic resonance imaging (fMRI). Extensive model analysis is made possible using a parameter exploration module, which allows one to characterize a model's behavior as a function of changing parameters. An optimization module is provided for fitting models to multimodal empirical data using evolutionary algorithms. neurolib is designed to be extendable and allows for easy implementation of custom neural mass models, offering a versatile platform for computational neuroscientists for prototyping models, managing large numerical experiments, studying the structure–function relationship of brain networks, and for performing in-silico optimization of whole-brain models. [ABSTRACT FROM AUTHOR]

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 h and reduced the objective function by an average of 13.2% on 3.75 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. [ABSTRACT FROM AUTHOR]

It has been stated that up-down-state (UDS) cortical oscillation levels between excitatory and inhibitory neurons play a fundamental role in brain network construction. Predicting the time series behaviors of neurons in periodic and chaotic regimes can help in improving diseases, higher-order human activities, and memory consolidation. Predicting the time series is usually done by machine learning methods. In paper, the deep bidirectional long short-term memory (DBLSTM) network is employed to predict the time evolution of regular, large-scale UDS oscillations produced by a previously developed neocortical network model. In noisy time-series prediction tasks, we compared the DBLSTM performance with two other variants of deep LSTM networks: standard LSTM, LSTM projected, and gated recurrent unit (GRU) cells. We also applied the classic seasonal autoregressive integrated moving average (SARIMA) time-series prediction method as an additional baseline. The results are justified through qualitative resemblance between the bifurcation diagrams of the actual and predicted outputs and quantitative error analyses of the network performance. The results of extensive simulations showed that the DBLSTM network provides accurate short and long-term predictions in both periodic and chaotic behavioral regimes and offers robust solutions in the presence of the corruption process. [ABSTRACT FROM AUTHOR]

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.

Background: Mathematical modeling and computer simulation are important methods for understanding complex neural systems. The whole-brain network model can help people understand the neurophysiological mechanisms of brain cognition and functional diseases of the brain. Methods: In this study, we constructed a resting-state whole-brain network model (WBNM) by using the Wendling neural mass model as the node and a real structural connectivity matrix as the edge of the network. By analyzing the correlation between the simulated functional connectivity matrix in the resting state and the empirical functional connectivity matrix, an optimal global coupling coefficient was obtained. Then, the waveforms and spectra of simulated EEG signals and four commonly used measures from graph theory and small-world network properties of simulated brain networks under different thresholds were analyzed. Results: The results showed that the correlation coefficient of the functional connectivity matrix of the simulated WBNM and empirical brain networks could reach a maximum value of 0.676 when the global coupling coefficient was set to 20.3. The simulated EEG signals showed rich waveform and frequency-band characteristics. The commonly used graph-theoretical measures and small-world properties of the constructed WBNM were similar to those of empirical brain networks. When the threshold was set to 0.22, the maximum correlation between the simulated WBNM and empirical brain networks was 0.709. Conclusions: The constructed resting-state WBNM is similar to a real brain network to a certain extent and can be used to study the neurophysiological mechanisms of complex brain networks.

A regime of coexistence of asynchronous and clustered dynamics is analysed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based on accurate extensive simulations and complemented by a mean-field description in terms of low-dimensional next generation neural mass models for heterogeneously distributed synaptic couplings. The asynchronous regime is observable at low noise and becomes unstable via a sub-critical Hopf bifurcation at sufficiently large noise. This gives rise to a coexistence region between the asynchronous and the clustered regime. The clustered phase is characterised by population bursts in the γ -range (30–120 Hz), where neurons are split in two equally populated clusters firing in alternation. This clustering behaviour is quite peculiar: despite the global activity being essentially periodic, single neurons display switching between the two clusters due to heterogeneity and/or noise.

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.

A compelling way to disentangle the complexity of the brain is to measure the effects of spatially and temporally synchronized systematic perturbations. In humans, this can be non-invasively achieved by combining transcranial magnetic stimulation (TMS) and electroencephalography (EEG). Spatiotemporally complex and long-lasting TMS-EEG evoked potential (TEP) waveforms are believed to result from recurrent, re-entrant activity that propagates broadly across multiple cortical and subcortical regions, dispersing from and later re-converging on, the primary stimulation site. However, if we loosely understand the TEP of a TMS-stimulated region as the impulse response function of a noisy underdamped harmonic oscillator, then multiple later activity components (waveform peaks) should be expected even for an isolated network node in the complete absence of recurrent inputs. Thus emerges a critically important question for basic and clinical research on human brain dynamics: what parts of the TEP are due to purely local dynamics, what parts are due to reverberant, re-entrant network activity, and how can we distinguish between the two? To disentangle this, we used source-localized TMS-EEG analyses and whole-brain connectome-based computational modelling. Results indicated that recurrent network feedback begins to drive TEP responses from 100 ms post-stimulation, with earlier TEP components being attributable to local reverberatory activity within the stimulated region. Subject-specific estimation of neurophysiological parameters additionally indicated an important role for inhibitory GABAergic neural populations in scaling cortical excitability levels, as reflected in TEP waveform characteristics. The novel discoveries and new software technologies introduced here should be of broad utility in basic and clinical neuroscience research.

Transcranial electrical stimulation (tES) is a non-invasive neuromodulatory technique that alters ongoing neural dynamics by injecting an exogenous electrical current through the scalp. Although tES protocols are becoming more common in both clinical and experimental settings, the neurophysiological mechanisms through which tES modulates cortical dynamics are unknown. Most existing tES protocols ignore the potential effect of phasic interactions between endogenous and exogenous currents by stimulating in an open-looped fashion. To better understand the mechanisms of closed-loop tES, we first instantiated a two-column Jansen and Rit model to simulate neuronal dynamics of pyramidal cells and interneurons. An echo-state network (ESN) reservoir computer inverted the dynamics of the model without access to the internal state equations. After inverting the model dynamics, the ESN was used as a closed-loop feedback controller for the neural mass model by predicting the current stimulation input for a desired future output. The ESN was used to predict the endogenous membrane currents of the model from the observable pyramidal cell membrane potentials and then inject current stimulation to destructively interfere with endogenous membrane currents, thereby reducing the energy of the PCs. This simulation approach provides a framework for a model-free closed-loop feedback controller in tES experiments. [ABSTRACT FROM AUTHOR]

Pathological oscillations that have a frequency in the β band are widely recognized to be involved in Parkinson’s disease. Now, we present an adaptive dynamic surface control strategy for suppressing pathological oscillations that exist in the Parkinsonian state. First, the interactions between the subthalamic nucleus and external globus pallidus are fully considered and establish a neural mass model of Parkinson’s disease. Next, by reasonable state transformation, suppressing pathological oscillations can be converted into a tracking control study of a pure-feedback nonlinear system. Moreover, the dynamic surface control technique adopted reduces the dimensionality of the neural network input and effectively eliminates the complexity explosion problem commonly associated with existing methods. By Lyapunov stability analysis, it can be obtained that all the signals of the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the designed control strategy. This work may provide an effective approach to closed-loop deep brain stimulation optimization for the alleviation of the Parkinsonian state. [ABSTRACT FROM AUTHOR]

Temporal nesting of cortical slow oscillations, thalamic spindles, and hippocampal ripples indicates multiregional neuronal interactions required for memory consolidation. However, how the thalamic activity during spindles organizes hippocampal dynamics remains largely undetermined. We analyzed simultaneous recordings of anterodorsal thalamus and CA1 in male mice to determine the contribution of thalamic spindles in cross-regional synchronization. Our results indicated that temporal hippocampo-thalamocortical coupling was more enhanced during slower and longer thalamic spindles. Additionally, spindles occurring closer to slow oscillation trough were more strongly coupled to ripples. We found that the temporal association between CA1 spiking/ripples and thalamic spindles was stronger following spatial exploration compared with baseline sleep. We further developed a hippocampal-thalamocortical model to explain the mechanism underlying the duration and frequency-dependent coupling of thalamic spindles to hippocampal activity. Our findings shed light on our understanding of the functional role of thalamic activity during spindles on multiregional information transfer. [ABSTRACT FROM AUTHOR]

Neural processes are complex and difficult to image. This paper presents a new space-time resolved brain imaging framework, called Neurophysiological Process Imaging (NPI), that identifies neurophysiological processes within cerebral cortex at the macroscopic scale. By fitting uncoupled neural mass models to each electromagnetic source time-series using a novel nonlinear inference method, population averaged membrane potentials and synaptic connection strengths are efficiently and accurately inferred and imaged across the whole cerebral cortex at a resolution afforded by source imaging. The efficiency of the framework enables return of the augmented source imaging results overnight using high performance computing. This suggests it can be used as a practical and novel imaging tool. To demonstrate the framework, it has been applied to resting-state magnetoencephalographic source estimates. The results suggest that endogenous inputs to cingulate, occipital, and inferior frontal cortex are essential modulators of resting-state alpha power. Moreover, endogenous input and inhibitory and excitatory neural populations play varied roles in mediating alpha power in different resting-state sub-networks. The framework can be applied to arbitrary neural mass models and has broad applicability to image neural processes of different brain states.

Alzheimer’s disease (AD) is a degenerative brain disease, and the condition is difficult to assess. In the past, numerous brain dynamics models have made remarkable contributions to neuroscience and the brain from the microcosmic to the macroscopic scale. Recently, large-scale brain dynamics models have been developed based on dual-driven multimodal neuroimaging data and neurodynamics theory. These models bridge the gap between anatomical structure and functional dynamics and have played an important role in assisting the understanding of the brain mechanism. Large-scale brain dynamics have been widely used to explain how macroscale neuroimaging biomarkers emerge from potential neuronal population level disturbances associated with AD. In this review, we describe this emerging approach to studying AD that utilizes a biophysically large-scale brain dynamics model. In particular, we focus on the application of the model to AD and discuss important directions for the future development and analysis of AD models. This will facilitate the development of virtual brain models in the field of AD diagnosis and treatment and add new opportunities for advancing clinical neuroscience.

As a newly emerging field, connectomics has greatly advanced our understanding of the wiring diagram and organizational features of the human brain. Generative modeling-based connectome analysis, in particular, plays a vital role in deciphering the neural mechanisms of cognitive functions in health and dysfunction in diseases. Here we review the foundation and development of major generative modeling approaches for functional magnetic resonance imaging (fMRI) and survey their applications to cognitive or clinical neuroscience problems. We argue that conventional structural and functional connectivity (FC) analysis alone is not sufficient to reveal the complex circuit interactions underlying observed neuroimaging data and should be supplemented with generative modelingbased effective connectivity and simulation, a fruitful practice that we term "mechanistic connectome." The transformation from descriptive connectome to mechanistic connectome will open up promising avenues to gain mechanistic insights into the delicate operating principles of the human brain and their potential impairments in diseases, which facilitates the development of effective personalized treatments to curb neurological and psychiatric disorders. [ABSTRACT FROM AUTHOR]

We propose that to fully understand biological mechanisms underlying pathological brain activity with transitions (e.g., into and out of seizures), wide-bandwidth electrophysiological recordings are important. We demonstrate the importance of ultraslow potential shifts and infraslow oscillations for reliable tracking of synaptic physiology, within a neural mass model, from brain recordings that undergo pathological phase transitions. We use wide-bandwidth data (direct current (DC) to high-frequency activity), recorded using epidural and penetrating graphene micro-transistor arrays in a rodent model of acute seizures. Using this technological approach, we capture the dynamics of infraslow changes that contribute to seizure initiation (active pre-seizure DC shifts) and progression (passive DC shifts). By employing a continuous-discrete unscented Kalman filter, we track biological mechanisms from full-bandwidth data with and without active pre-seizure DC shifts during paroxysmal transitions. We then apply the same methodological approach for tracking the same parameters after application of high-pass-filtering >0.3Hz to both data sets. This approach reveals that ultraslow potential shifts play a fundamental role in the transition to seizure, and the use of high- pass-filtered data results in the loss of key information in regard to seizure onset and termination dynamics. [ABSTRACT FROM AUTHOR]

Our investigation delves into the intricate dynamical properties of a network of coupled neural oscillators, each comprising identical Jansen–Rit masses. The connections between these nodes follow the renowned Watts–Strogatz topology. Every node receives inputs from two primary sources: external and internal inputs derived from its neighboring nodes' outputs. In this paper, we aim to explore the consequences of changing these two inputs and analyze the results generated. To begin with, we analyzed the model using the mean-field approximation, assuming identical outputs across all nodes due to identical internal and external inputs. Subsequently, we relaxed this assumption, and a more detailed analysis of both states is discussed. As a result of the mean-field approach, we observed that there was no phase transition, despite apparent changes in behavior. However, the relaxation of the mean-field assumption led to the occurrence of the first (discontinuous) and second (continuous) phase transitions. Moreover, our findings indicate that by relaxing the mean-field assumption in our analysis of the single Jansen–Rit neural mass model, theta waves can be generated. Our study provides a comprehensive examination of various observed behaviors by the model, including transitions between synchrony and asynchrony. Additionally, our work highlights the potential contribution of external and internal inputs in studying phase transition and synchronization of neural mass models. Overall, our investigation sheds light on the intricate dynamics of coupled neural oscillators and their sensitivity to varying inputs. • The analysis of oscillatory behavior in a coupled nonlinear system is considered. • The change of coupling term and external input results in a transition to different dynamical states. • The first (discontinuous) and second (continuous) phase transitions result from relaxing the mean-field assumption. • Theta waves can be generated by relaxing the mean-field assumption in a single Jansen–Rit neural mass model, which has not been previously observed in a single Jansen–Rit neural mass analysis. [ABSTRACT FROM AUTHOR]

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

We propose that to fully understand biological mechanisms underlying pathological brain activity with transitions (e.g., into and out of seizures), wide-bandwidth electrophysiological recordings are important. We demonstrate the importance of ultraslow potential shifts and infraslow oscillations for reliable tracking of synaptic physiology, within a neural mass model, from brain recordings that undergo pathological phase transitions. We use wide-bandwidth data (direct current (DC) to high-frequency activity), recorded using epidural and penetrating graphene micro-transistor arrays in a rodent model of acute seizures. Using this technological approach, we capture the dynamics of infraslow changes that contribute to seizure initiation (active pre-seizure DC shifts) and progression (passive DC shifts). By employing a continuous–discrete unscented Kalman filter, we track biological mechanisms from full-bandwidth data with and without active pre-seizure DC shifts during paroxysmal transitions. We then apply the same methodological approach for tracking the same parameters after application of high-pass-filtering >0.3Hz to both data sets. This approach reveals that ultraslow potential shifts play a fundamental role in the transition to seizure, and the use of high-pass-filtered data results in the loss of key information in regard to seizure onset and termination dynamics.

There is substantial evidence that neuromodulatory systems critically influence brain state dynamics; however, most work has been purely descriptive. Here, we quantify, using data combining local inactivation of the basal forebrain with simultaneous measurement of resting-state fMRI activity in the macaque, the causal role of long-range cholinergic input to the stabilization of brain states in the cerebral cortex. Local inactivation of the nucleus basalis of Meynert (nbM) leads to a decrease in the energy barriers required for an fMRI state transition in cortical ongoing activity. Moreover, the inactivation of particular nbM sub-regions predominantly affects information transfer in cortical regions known to receive direct anatomical projections. We demonstrate these results in a simple neurodynamical model of cholinergic impact on neuronal firing rates and slow hyperpolarizing adaptation currents. We conclude that the cholinergic system plays a critical role in stabilizing macroscale brain state dynamics. [Display omitted] • ACh inhibition impairs brain state transitions while preserving correlations • ACh inhibition leads to flattened energy barriers between brain state attractors • ACh inactivation decreases information flow between targeted cortical regions • Cholinergic model of firing rates and adaptation currents reproduces findings Taylor et al. found that the cholinergic system is important for stabilizing brain state dynamics, which builds upon a body of work emphasizing the importance of the ascending arousal system in modulating global brain state reconfigurations. [ABSTRACT FROM AUTHOR]

Sleep manifests itself by the spontaneous emergence of characteristic oscillatory rhythms, which often time-lock and are implicated in memory formation. Here, we analyze a neural mass model of the thalamocortical loop in which the cortical node can generate slow oscillations (approximately 1 Hz) while its thalamic component can generate fast sleep spindles of σ-band activity (12–15 Hz). We study the dynamics for different coupling strengths between the thalamic and cortical nodes, for different conductance values of the thalamic node's potassium leak and hyperpolarization-activated cation-nonselective currents, and for different parameter regimes of the cortical node. The latter are listed as follows: (1) a low activity (DOWN) state with noise-induced, transient excursions into a high activity (UP) state, (2) an adaptation induced slow oscillation limit cycle with alternating UP and DOWN states, and (3) a high activity (UP) state with noise-induced, transient excursions into the low activity (DOWN) state. During UP states, thalamic spindling is abolished or reduced. During DOWN states, the thalamic node generates sleep spindles, which in turn can cause DOWN to UP transitions in the cortical node. Consequently, this leads to spindle-induced UP state transitions in parameter regime (1), thalamic spindles induced in some but not all DOWN states in regime (2), and thalamic spindles following UP to DOWN transitions in regime (3). The spindle-induced σ-band activity in the cortical node, however, is typically the strongest during the UP state, which follows a DOWN state "window of opportunity" for spindling. When the cortical node is parametrized in regime (3), the model well explains the interactions between slow oscillations and sleep spindles observed experimentally during Non-Rapid Eye Movement sleep. The model is computationally efficient and can be integrated into large-scale modeling frameworks to study spatial aspects like sleep wave propagation. [ABSTRACT FROM AUTHOR]

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—in which 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. [ABSTRACT FROM AUTHOR]

Epilepsy is a neurological disorder resulting from a sudden development of synchronous firing in a massive group of neurons. For the particularity of the epilepsy, a neural mass model (NMM) is commonly utilized to understand and simulate the mechanism and evolution of the epilepsy. In this paper, based on a multi-coupling NMM and real EEGs of an epileptic mouse, a computational epileptic model is established to simulate the abnormal discharges of a mouse during seizures. Thus, rather than make animal experiments directly, numerical tests can be performed first. It reduces risks and helps improve the closed-loop neuromodulation. In addition, considering that no epileptic model can be utilized for neuromodulation in clinic, and even if a model exists, it still cannot describe the dynamics of the epilepsy faithfully, a scalable observer bandwidth and phase leading active disturbance rejection control (SOB-PLADRC) is proposed. Accordingly, a timelier and more accurate total disturbance estimation can be obtained by a scalable observer bandwidth and phase leading extended state observer, and an expected closed-loop neuromodulation can be realized without an accurate epileptic model. Numerical simulations based on the established model also show that the SOB-PLADRC suppresses seizures best among the PI and other active disturbance rejection approaches. More powerful disturbance rejection ability and more satisfactory closed-loop neuromodulation make the SOB-PLADRC more promising in the seizure control. [ABSTRACT FROM AUTHOR]

Sleep manifests itself by the spontaneous emergence of characteristic oscillatory rhythms, which often time-lock and are implicated in memory formation. Here, we analyze a neural mass model of the thalamocortical loop in which the cortical node can generate slow oscillations (approximately 1 Hz) while its thalamic component can generate fast sleep spindles of σ-band activity (12–15 Hz). We study the dynamics for different coupling strengths between the thalamic and cortical nodes, for different conductance values of the thalamic node's potassium leak and hyperpolarization-activated cation-nonselective currents, and for different parameter regimes of the cortical node. The latter are listed as follows: (1) a low activity (DOWN) state with noise-induced, transient excursions into a high activity (UP) state, (2) an adaptation induced slow oscillation limit cycle with alternating UP and DOWN states, and (3) a high activity (UP) state with noise-induced, transient excursions into the low activity (DOWN) state. During UP states, thalamic spindling is abolished or reduced. During DOWN states, the thalamic node generates sleep spindles, which in turn can cause DOWN to UP transitions in the cortical node. Consequently, this leads to spindle-induced UP state transitions in parameter regime (1), thalamic spindles induced in some but not all DOWN states in regime (2), and thalamic spindles following UP to DOWN transitions in regime (3). The spindle-induced σ-band activity in the cortical node, however, is typically the strongest during the UP state, which follows a DOWN state “window of opportunity” for spindling. When the cortical node is parametrized in regime (3), the model well explains the interactions between slow oscillations and sleep spindles observed experimentally during Non-Rapid Eye Movement sleep. The model is computationally efficient and can be integrated into large-scale modeling frameworks to study spatial aspects like sleep wave propagation.

Background: Neuronal- and circuit-level abnormalities of excitation and inhibition are shown to be associated with tau and amyloid-beta (Aβ) in preclinical models of Alzheimer’s disease (AD). These relationships remain poorly understood in patients with AD. Methods: Using empirical spectra from magnetoencephalography and computational modeling (neural mass model), we examined excitatory and inhibitory parameters of neuronal subpopulations and investigated their specific associations to regional tau and Aβ, measured by positron emission tomography, in patients with AD. Results: Patients with AD showed abnormal excitatory and inhibitory time-constants and neural gains compared to age-matched controls. Increased excitatory time-constants distinctly correlated with higher tau depositions while increased inhibitory time-constants distinctly correlated with higher Aβ depositions. Conclusions: Our results provide critical insights about potential mechanistic links between abnormal neural oscillations and cellular correlates of impaired excitatory and inhibitory synaptic functions associated with tau and Aβ in patients with AD. Funding: This study was supported by the National Institutes of Health grants: K08AG058749 (KGR), F32AG050434-01A1 (KGR), K23 AG038357 (KAV), P50 AG023501, P01 AG19724 (BLM), P50-AG023501 (BLM and GDR), R01 AG045611 (GDR); AG034570, AG062542 (WJ); NS100440 (SSN), DC176960 (SSN), DC017091 (SSN), AG062196 (SSN); a grant from John Douglas French Alzheimer’s Foundation (KAV); grants from Larry L. Hillblom Foundation: 2015-A-034-FEL (KGR), 2019-A-013-SUP (KGR); grants from the Alzheimer’s Association: AARG-21-849773 (KGR); PCTRB-13-288476 (KAV), and made possible by Part the CloudTM (ETAC-09-133596); a grant from Tau Consortium (GDR and WJJ), and a gift from the S. D. Bechtel Jr. Foundation.

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—in which 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.