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.

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.

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

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.

One of the early markers of minimal hepatic encephalopathy (MHE) is the disruption of alpha rhythm observed in electroencephalogram (EEG) signals. However, the underlying mechanisms responsible for this occurrence remain poorly understood. To address this gap, we develop a novel biophysical model MHE-AWD-NCM, encompassing the communication dynamics between a cortical neuron population (CNP) and an astrocyte population (AP), aimed at investigating the relationship between alpha wave disturbance (AWD) and mechanistical principles, specifically concerning astrocyte-neuronal communication in the context of MHE. In addition, we introduce the concepts of peak power density and peak frequency within the alpha band as quantitative measures of AWD. Our model faithfully reproduces the characteristic EEG phenomenology during MHE and shows how impairments of communication between CNP and AP could promote AWD. The results suggest that the disruptions in feedback neurotransmission from AP to CNP, along with the inhibition of GABA uptake by AP from the extracellular space, contribute to the observed AWD. Moreover, we found that the variation of external excitatory stimuli on CNP may play a key role in AWD in MHE. Finally, the sensitivity analysis is also performed to assess the relative significance of above factors in influencing AWD. Our findings align with the physiological observations and provide a more comprehensive understanding of the complex interplay of astrocyte-neuronal communication that underlies the AWD observed in MHE, which potentially may help to explore the targeted therapeutic interventions for the early stage of hepatic encephalopathy.

Task-free brain activity affords unique insight into the functional structure of brain network dynamics and is a strong marker of individual differences. In this work, we present an algorithmic optimization framework that makes it possible to directly invert and parameterize brain-wide dynamical-systems models involving hundreds of interacting brain areas, from single-subject time-series recordings. This technique provides a powerful neurocomputational tool for interrogating mechanisms underlying individual brain dynamics (\"precision brain models\") and making quantitative predictions. We extensively validate the models\' performance in forecasting future brain activity and predicting individual variability in key M/EEG markers. Lastly, we demonstrate the power of our technique in resolving individual differences in the generation of alpha and beta-frequency oscillations. We characterize subjects based upon model attractor topology and a dynamical-systems mechanism by which these topologies generate individual variation in the expression of alpha vs. beta rhythms. We trace these phenomena back to global variation in excitation-inhibition balance, highlighting the explanatory power of our framework in generating mechanistic insights.

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.

Metabolic limitations within the brain frequently arise in the context of aging and disease. As the largest consumers of energy within the brain, ion pumps that maintain the neuronal membrane potential are the most affected when energy supply becomes limited. To characterize the effects of such limitations, we analyze the ion gradients present in a conductance-based (Morris-Lecar) neural mass model. We show the existence and locations of Neimark-Sacker and period-doubling bifurcations in the sodium, calcium, and potassium reversal potentials and demonstrate that these bifurcations form physiologically relevant bounds of ion gradient variability. Within these bounds, we show how depolarization of the gradients causes decreased neural activity. We also show that the depolarization of ion gradients decreases inter-regional coherence, causing a shift in the critical point at which the coupling occurs and thereby inducing loss of synchrony between regions. In this way, we show that the Larter-Breakspear model captures ion gradient variability present at the microscale level and propagates these changes to the macroscale effects such as those observed in human neuroimaging studies.

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.

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.