A neural mass model based on single cell dynamics to model pathophysiology

Multi-scale modelling of the epileptic brain: advantages of computational therapy exploration

Objective: Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details.Approach: Here, we review various types of computational model of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail.Main results: A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioural observations.Significance: With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.

A mean-field model of glutamate and GABA synaptic dynamics for functional MRS

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

Scaling of Network Excitability and Inhibition may Contribute to the Septotemporal Differentiation of Sharp Waves-Ripples in Rat Hippocampus In Vitro

The functional organization of the hippocampus along its longitudinal (septotemporal or dorsoventral) axis is conspicuously heterogeneous. This functional diversification includes the activity of sharp wave and ripples (SPW-Rs), a complex intrinsic network pattern involved in memory consolidation. In this study, using transverse slices from the ventral and the dorsal rat hippocampus and recordings of CA1 field potentials we studied the development of SPW-Rs and possible changes in local network excitability and inhibition, during in vitro maintenance of the hippocampal tissue. We found that SPW-Rs develop gradually in terms of magnitude and rate of occurrence in the ventral hippocampus. On the contrary, neither the magnitude nor the rate of occurrence significantly changed in dorsal hippocampal slices during their in vitro maintenance. The development of SPW-Rs was accompanied by an increase in local network excitability more in the ventral than in the dorsal hippocampus, and an increase in local network inhibition in the ventral hippocampus only. Furthermore, the amplitude of SPWs positively correlated with the level of maximum excitation of the local neuronal network in both segments of the hippocampus, and the local network excitability and inhibition in the ventral but not the dorsal hippocampus. Blockade of α5 subunit-containing GABA_A receptor by L-655,708 significantly reduced the rate of occurrence of SPWs and enhanced the probability of their generation in the form of clusters in the ventral hippocampus without affecting activity in the dorsal hippocampus. The present evidence suggests that a dynamic upregulation of excitation and inhibition in the local neuronal network may significantly contribute to the generation of SPW-Rs, particularly in the ventral hippocampus.

A novel neural computational model of generalized periodic discharges in acute hepatic encephalopathy

Acute hepatic encephalopathy (AHE) due to acute liver failure is a common form of delirium, a state of confusion, impaired attention, and decreased arousal. The electroencephalogram (EEG) in AHE often exhibits a striking abnormal pattern of brain activity, which epileptiform discharges repeat in a regular repeating pattern. This pattern is known as generalized periodic discharges, or triphasic-waves (TPWs). While much is known about the neurophysiological mechanisms underlying AHE, how these mechanisms relate to TPWs is poorly understood. In order to develop hypotheses how TPWs arise, our work builds a computational model of AHE (AHE-CM), based on three modifications of the well-studied Liley model which emulate mechanisms believed central to brain dysfunction in AHE: increased neuronal excitability, impaired synaptic transmission, and enhanced postsynaptic inhibition. To relate our AHE-CM to clinical EEG data from patients with AHE, we design a model parameter optimization method based on particle filtering (PF-POM). Based on results from 7 AHE patients, we find that the proposed AHE-CM not only performs well in reproducing important aspects of the EEG, namely the periodicity of triphasic waves (TPWs), but is also helpful in suggesting mechanisms underlying variation in EEG patterns seen in AHE. In particular, our model helps explain what conditions lead to increased frequency of TPWs. In this way, our model represents a starting point for exploring the underlying mechanisms of brain dynamics in delirium by relating microscopic mechanisms to EEG patterns.

The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population's activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.

Macroscopic neural mass model constructed from a current-based network model of spiking neurons

Neural mass models (NMMs) are efficient frameworks for describing macroscopic cortical dynamics including electroencephalogram and magnetoencephalogram signals. Originally, these models were formulated on an empirical basis of synaptic dynamics with relatively long time constants. By clarifying the relations between NMMs and the dynamics of microscopic structures such as neurons and synapses, we can better understand cortical and neural mechanisms from a multi-scale perspective. In a previous study, the NMMs were analytically derived by averaging the equations of synaptic dynamics over the neurons in the population and further averaging the equations of the membrane-potential dynamics. However, the averaging of synaptic current assumes that the neuron membrane potentials are nearly time invariant and that they remain at sub-threshold levels to retain the conductance-based model. This approximation limits the NMM to the non-firing state. In the present study, we newly propose a derivation of a NMM by alternatively approximating the synaptic current which is assumed to be independent of the membrane potential, thus adopting a current-based model. Our proposed model releases the constraint of the nearly constant membrane potential. We confirm that the obtained model is reducible to the previous model in the non-firing situation and that it reproduces the temporal mean values and relative power spectrum densities of the average membrane potentials for the spiking neurons. It is further ensured that the existing NMM properly models the averaged dynamics over individual neurons even if they are spiking in the populations.

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

Sleep plays a pivotal role for the consolidation of memory. While REM sleep had originally been the focus of research due to its similarity with wakefulness, more recent studies suggest that different sleep stages are responsible for the consolidation of different types of memory. To better understand the changes in neuronal dynamics between the different sleep stages, neural mass models are a valuable tool, as they relate directly to the large-scale dynamics measured by an EEG. Here, we present a model of the sleeping thalamocortical system. We first show that the isolated thalamic submodule is able to generate different oscillatory behavior found in vivo. Furthermore, the full thalamocortical model reproduces the EEG of sleep stages N2 and N3 and preserves the temporal relationship between cortical K-complexes/slow oscillations and thalamic sleep spindles. A comparison with event related potential data from a recent sleep study in humans demonstrates its possible application in predicting the outcome of external stimulation on EEG rhythms. Our study shows, that a neural mass model incorporating few key mechanisms is sufficient to reproduce the complex brain dynamics observed during sleep.

Suppressing epileptic activity in a neural mass model using a closed-loop proportional-integral controller

Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. However, there are currently no analytical approaches to determine the stimulation parameters for effective and safe treatment protocols. Proportional-integral (PI) control is the most extensively used closed-loop control scheme in the field of control engineering because of its simple implementation and perfect performance. In this study, we took Jansen's neural mass model (NMM) as a test bed to develop a PI-type closed-loop controller for suppressing epileptic activity. A graphical stability analysis method was employed to determine the stabilizing region of the PI controller in the control parameter space, which provided a theoretical guideline for the choice of the PI control parameters. Furthermore, we established the relationship between the parameters of the PI controller and the parameters of the NMM in the form of a stabilizing region, which provided insights into the mechanisms that may suppress epileptic activity in the NMM. The simulation results demonstrated the validity and effectiveness of the proposed closed-loop PI control scheme.

Animal models of monogenic migraine

Migraine is a highly prevalent and disabling neurological disorder with a strong genetic component. Rare monogenic forms of migraine, or syndromes in which migraine frequently occurs, help scientists to unravel pathogenetic mechanisms of migraine and its comorbidities. Transgenic mouse models for rare monogenic mutations causing familial hemiplegic migraine (FHM), cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL), and familial advanced sleep-phase syndrome (FASPS), have been created. Here, we review the current state of research using these mutant mice. We also discuss how currently available experimental approaches, including epigenetic studies, biomolecular analysis and optogenetic technologies, can be used for characterization of migraine genes to further unravel the functional and molecular pathways involved in migraine.