Unification of neuronal spikes, seizures, and spreading depression

Uncommon and common roles of inhibitory interneuron and autapse and their cooperations to induce or eliminate epileptiform firing of pyramidal neuron

Different from the common role of inhibitory modulations to suppress firing activities, uncommon roles of inhibitory modulations are observed in recent experiments. For instance, inhibitory autapse can enhance spiking frequency of interneuron, and inhibitory interneuron can enhance spiking of pyramidal neuron to epileptiform firing with high membrane potential and extracellular potassium concentration, presenting possible novel etiology of brain diseases and challenge to excitation-inhibition balance. In the present paper, the uncommon roles, the common roles, and their cooperations are studied in a computation model. Firstly, the inhibitory interneuron with fast instead of slow decay synaptic current plays an uncommon role, and the complex process for the uncommon role is obtained. Compared with slow decay, the fast decay inhibitory synaptic current is strong enough to induce silence with low membrane potential, resulting in long silence and high level of extracellular potassium concentration when firing recovers, initiating positive feedback between firing and potassium concentration to induce the epileptiform firing. Secondly, inhibitory autaptic current with fast rather than slow decay plays an uncommon role to enhance spiking frequency of interneuron. Autaptic current with slow decay causes weak potassium current during downstroke of action potential to induce spike advanced. Finally, different cooperations between the common and uncommon roles of interneuron and autapse are obtained. Especially, fast autapse with great uncommon role can reverse the common role of interneuron, which can induce spiking to the epileptiform firing, and slow autapse with great common role can reverse the uncommon role of interneuron, which can change the epileptiform firing to spiking for the normal state. These findings present explanations to the uncommon roles of inhibitory modulations and multiple feasible measures to modulate the epileptiform firing and brain diseases.

Downmodulation of Potassium Conductances Induces Epileptic Seizures in Cortical Network Models Via Multiple Synergistic Factors

Voltage-gated potassium conductances g K play a critical role not only in normal neural function, but also in many neurological disorders and related therapeutic interventions. In particular, in an important animal model of epileptic seizures, 4-aminopyridine (4-AP) administration is thought to induce seizures by reducing g K in cortex and other brain areas. Interestingly, 4-AP has also been useful in the treatment of neurological disorders such as multiple sclerosis and spinal cord injury, where it is thought to improve action potential propagation in axonal fibers. Here, we examined g K downmodulation in biophysical models of cortical networks that included different neuron types organized in layers, potassium diffusion in interstitial and larger extracellular spaces, and glial buffering. Our findings are fourfold. First, g K downmodulation in pyramidal and fast-spiking inhibitory interneurons led to differential effects, making the latter much more likely to enter depolarization block. Second, both neuron types showed an increase in the duration and amplitude of action potentials, with more pronounced effects in pyramidal neurons. Third, a sufficiently strong g K reduction dramatically increased network synchrony, resulting in seizure-like dynamics. Fourth, we hypothesized that broader action potentials were likely to not only improve their propagation, as in 4-AP therapeutic uses, but also to increase synaptic coupling. Notably, graded-synapses incorporating this effect further amplified network synchronization and seizure-like dynamics. Overall, our findings elucidate different effects that g K downmodulation may have in cortical networks, explaining its potential role in both pathological neural dynamics and therapeutic applications.

Dynamics and conditions for inhibitory synaptic current to induce bursting and spreading depolarization in pyramidal neurons

Enhanced activity of inhibitory neurons, which is often used to suppress behaviors of pyramidal neurons to treat brain diseases, whereas can enhance spiking to a mixed-mode bursting (MMB) in recent experiments on migraine and seizure. The MMB contains a phase with high level of membrane potential/extracellular potassium concentration ([K+]o), which can propagate to form spreading depolarization (SD) wave. Different from the common view that the MMB/SD is often induced by enhanced positive effect or [K+]o, in the present paper, dynamics and conditions for the uncommon MMB/SD evoked by enhanced inhibitory synaptic current are obtained in a theoretical model. Firstly, in addition to the well-known positive threshold across which the common MMB is induced by positive effect, a spiking pyramidal neuron exhibits a novel negative threshold with a low level of [K+]o for the MMB. A long and strong inhibitory stimulation suppresses the spiking to silence phase via a saddle-node bifurcation on an invariant circle at first and then run across the negative threshold, triggering positive feedback to enhance membrane potential and [K+]o to levels high enough, then resulting in the uncommon MMB. Secondly, in a coupling model, enhanced inhibitory effect for enhanced spiking activity of interneuron and conductance of inhibitory synapse, and enhanced spiking activity of pyramidal neuron, are favorable for the uncommon MMB. Then, reducing these activities or parameters present potential measures to prevent the MMB. Finally, in network model, the uncommon MMB of a pyramidal neuron can induce SD wave. The results present a novel theoretical explanation to the uncommon MMB/SD, counterintuitive function of the inhibitory interneuron, and potential measures to treat the diseases.

Modelling the effect of allopregnanolone on the resolution of spike-wave discharges

Childhood absence epilepsy (CAE) is a paediatric generalized epilepsy disorder with a confounding feature of resolving in adolescence in a majority of cases. In this study, we modelled how the small-scale (synapse-level) effect of progesterone metabolite allopregnanolone induces a large-scale (network-level) effect on a thalamocortical circuit associated with this disorder. In particular, our goal was to understand the role of sex steroid hormones in the spontaneous remission of CAE. The conductance-based computational model consisted of single-compartment cortical pyramidal, cortical interneurons, thalamic reticular and thalamocortical relay neurons, each described by a set of ordinary differential equations. Excitatory and inhibitory synapses were mediated by AMPA, GABAa and GABAb receptors. The model was implemented using the NetPyne modelling tool and the NEURON simulator. It was found that the action of allopregnanolone (ALLO) on individual GABAa-receptor mediated synapses can have an ameliorating effect on spike-wave discharges (SWDs) associated with absence seizures. This effect is region-specific and most significant in the thalamus, particularly the synapses between thalamic reticular neurons. The remedying effect of allopregnanolone on SWDs may possibly be true only for individuals that are predisposed to remission due to intrinsic connectivity differences or differences in tonic inhibition. These results are a useful first-step and prescribe directions for further investigation into the role of ALLO together with these differences to distinguish between models for CAE-remitting and non-remitting individuals.

Modeling impairment of ionic regulation with extended Adaptive Exponential integrate-and-fire models

To model the dynamics of neuron membrane excitability many models can be considered, from the most biophysically detailed to the highest level of phenomenological description. Recent works at the single neuron level have shown the importance of taking into account the evolution of slow variables such as ionic concentration. A reduction of such a model to models of the integrate-and-fire family is interesting to then go to large network models. In this paper, we introduce a way to consider the impairment of ionic regulation by adding a third, slow, variable to the adaptive Exponential integrate-and-fire model (AdEx). We then implement and simulate a network including this model. We find that this network was able to generate normal and epileptic discharges. This model should be useful for the design of network simulations of normal and pathological states.

Controllability of nonlinear epileptic-seizure spreading dynamics in large-scale subject-specific brain networks

Closed-loop electrical stimulation has become an important alternative to resective surgery for control of pharmacologically-resistant focal epileptic seizures. Seizure spread across large-scale brain networks, rather than its focal onset, is what commonly leads to major disruptions in sensorimotor and cognitive processing, as well as loss-of-consciousness, one of the main impairing aspects of the disorder. Electrical stimulation, triggered by early detection of seizure onset in epileptogenic zones (EZs), has been applied to prevent spread and its subsequent effects. Here, we show how linear feedback seizure-spread controllability in subject-specific (white-matter tractography) Epileptor network models is affected by variations in brain excitability, network coupling strength, control latency and gain, and actuation targets. Feedback control can qualitatively change the nonlinear seizure dynamics, and the paths to seizure termination and spread prevention. Notably, control onset latency is a critical parameter leading to a phase transition in spread controllability. Consequently, the efficacy of EZ-only actuation is limited depending on network excitability, coupling strength, and practical latencies for detection and actuation. Additional feedback-stabilization control of theoretically-derived optimal node subsets in the network are necessary for spread prevention. Finally, we contrast our linear-feedback controllability assessment with other measures based on minimum-energy (Gramian) controllability and nonlinear pulse-perturbation approaches.

Dynamical modeling and analysis of epileptic discharges transition caused by glutamate release with metabolism processes regulation from astrocyte

Glutamate (Glu) is a crucial excitatory neurotransmitter in the central nervous system that transmits brain information by activating excitatory receptors on neuronal membranes. Physiological studies have demonstrated that abnormal Glu metabolism in astrocytes is closely related to the pathogenesis of epilepsy. The astrocyte metabolism processes mainly involve the Glu uptake through astrocyte EAAT2, the Glu-glutamine (Gln) conversion, and the Glu release. However, the relationship between these Glu metabolism processes and epileptic discharges remains unclear. In this paper, we propose a novel neuron-astrocyte model by integrating the dynamical modeling of astrocyte Glu metabolism processes, which include Glu metabolism in astrocytes consisting of the Glu uptake, Glu-Gln conversion, Glu diffusion, and the resulting Glu release as well as Glu-mediated bidirectional communication between neuron and astrocyte. Furthermore, the influences of astrocyte multiple Glu metabolism processes on the Glu release and dynamics transition of neuronal epileptic discharges are verified through numerical experiments and dynamical analyses from various nonlinear dynamics perspectives, such as time series, phase plane trajectories, interspike intervals, and bifurcation diagrams. Our results suggest that the downregulation expression of EAAT2 uptake, the slowdown of the Glu-Gln conversion rate, and excessively elevated Glu equilibrium concentration in astrocytes can cause an increase in Glu released from astrocytes, which results in the aggravation of epileptic seizures. Meanwhile, neuronal epileptic discharge states transition from bursting to mixed-mode spiking and tonic firing induced by the combination of these abnormal metabolism processes. This study provides a theoretical foundation and dynamical analysis methodology for further exploring the dynamics evolution and physiopathological mechanisms of epilepsy.

A multiscale distributed neural computing model database (NCMD) for neuromorphic architecture

Distributed neuromorphic architecture is a promising technique for on-chip processing of multiple tasks. Deploying the constructed model in a distributed neuromorphic system, however, remains time-consuming and challenging due to considerations such as network topology, connection rules, and compatibility with multiple programming languages. We proposed a multiscale distributed neural computing model database (NCMD), which is a framework designed for ARM-based multi-core hardware. Various neural computing components, including ion channels, synapses, and neurons, are encompassed in NCMD. We demonstrated how NCMD constructs and deploys multi-compartmental detailed neuron models as well as spiking neural networks (SNNs) in BrainS, a distributed multi-ARM neuromorphic system. We demonstrated that the electrodiffusive Pinsky-Rinzel (edPR) model developed by NCMD is well-suited for BrainS. All dynamic properties, such as changes in membrane potential and ion concentrations, can be easily explored. In addition, SNNs constructed by NCMD can achieve an accuracy of 86.67% on the test set of the Iris dataset. The proposed NCMD offers an innovative approach to applying BrainS in neuroscience, cognitive decision-making, and artificial intelligence research.

Spontaneous spreading depolarizations originate subcortically in a novel mouse model of familial hemiplegic migraine type 2

The mechanisms of initiation of spreading depolarization (SD) are understudied due to a paucity of disease models with spontaneously occurring events. We here present a novel mouse model of familial hemiplegic migraine type 2 (FHM2), expressing the missense T345A-mutated α2 subunit of the Na+/K+ adenosine triphosphatase pump (Atp1a2T345A). Homozygous Atp1a2T345A mice showed regular spontaneous SDs that exhibit a diurnal rhythm and typically originate from the hippocampus. Heterozygous Atp1a2T345A mice rarely exhibited spontaneous SDs and, for electrically induced SDs, only showed an increased propagation speed, whereas homozygotes showed both increased propagation and decreased threshold. Remarkably, despite hippocampal hyperexcitability, spontaneous SDs in Atp1a2T345A mice were only rarely associated with epileptic behavior, and seizure expression during kindling was decreased. Spontaneous SDs could be prevented by modulation of persistent sodium currents. Hippocampal SDs occurred in the presence of an NMDA-receptor antagonist, but these events did not reach the cortex, suggesting that initiation and propagation of SD depend on different mechanisms in this model.

An electrodiffusive network model with multicompartmental neurons and synaptic connections

Most computational models of neurons assume constant ion concentrations, disregarding the effects of changing ion concentrations on neuronal activity. Among the models that do incorporate ion concentration dynamics, simplifications are often made that sacrifice biophysical consistency, such as neglecting the effects of ionic diffusion on electrical potentials or the effects of electric drift on ion concentrations. A subset of models with ion concentration dynamics, often referred to as electrodiffusive models, account for ion concentration dynamics in a way that ensures a biophysical consistent relationship between ion concentrations, electric charge, and electrical potentials. These models include compartmental single-cell models, geometrically explicit models, and domain-type models, but none that model neuronal network dynamics. To address this gap, we present an electrodiffusive network model with multicompartmental neurons and synaptic connections, which we believe is the first compartmentalized network model to account for intra- and extracellular ion concentration dynamics in a biophysically consistent way. The model comprises an arbitrary number of "units," each divided into three domains representing a neuron, glia, and extracellular space. Each domain is further subdivided into a somatic and dendritic layer. Unlike conventional models which focus primarily on neuronal spiking patterns, our model predicts intra- and extracellular ion concentrations (Na+, K+, Cl-, and Ca2+), electrical potentials, and volume fractions. A unique feature of the model is that it captures ephaptic effects, both electric and ionic. In this paper, we show how this leads to interesting behavior in the network. First, we demonstrate how changing ion concentrations can affect the synaptic strengths. Then, we show how ionic ephaptic coupling can lead to spontaneous firing in neurons that do not receive any synaptic or external input. Lastly, we explore the effects of having glia in the network and demonstrate how a strongly coupled glial syncytium can prevent neuronal depolarization blocks.

GABA-Induced Seizure-Like Events Caused by Multi-ionic Interactive Dynamics

Experimental evidence showed that an increase in intracellular chloride concentration [Formula: see text] caused by gamma-aminobutyric acid (GABA) input can promote epileptic firing activity, but the actual mechanisms remain elusive. Here in this theoretical work, we show that influx of chloride and concomitant bicarbonate ion [Formula: see text] efflux upon GABA receptor activation can induce epileptic firing activity by transition of GABA from inhibition to excitation. We analyzed the intrinsic property of neuron firing states as a function of [Formula: see text] We found that as [Formula: see text] increases, the system exhibits a saddle-node bifurcation, above which the neuron exhibits a spectrum of intensive firing, periodic bursting interrupted by depolarization block (DB) state, and eventually a stable DB through a Hopf bifurcation. We demonstrate that only GABA stimuli together with [Formula: see text] efflux can switch GABA's effect to excitation which leads to a series of seizure-like events (SLEs). Exposure to a low [Formula: see text] can drive neurons with high concentrations of [Formula: see text] downward to lower levels of [Formula: see text], during which it could also trigger SLEs depending on the exchange rate with the bath. Our analysis and simulation results show how the competition between GABA stimuli-induced accumulation of [Formula: see text] and [Formula: see text] application-induced decrease of [Formula: see text] regulates the neuron firing activity, which helps to understand the fundamental ionic dynamics of SLE.

Organellular imaging in vivo reveals a depletion of endoplasmic reticular calcium during post-ictal cortical spreading depolarization

During cortical spreading depolarization (CSD), neurons exhibit a dramatic increase in cytosolic calcium, which may be integral to CSD-mediated seizure termination. This calcium increase greatly exceeds that during seizures, suggesting the calcium source may not be solely extracellular. Thus, we sought to determine if the endoplasmic reticulum (ER), the largest intracellular calcium store, is involved. We developed a two-photon calcium imaging paradigm to simultaneously record the cytosol and ER during seizures in awake mice. Paired with direct current recording, we reveal that CSD can manifest as a slow post-ictal cytosolic calcium wave with a concomitant depletion of ER calcium that is spatiotemporally consistent with a calcium-induced calcium release. Importantly, we observed both naturally occurring and electrically induced CSD suppressed post-ictal epileptiform activity. Collectively, this work links ER dynamics to CSD, which serves as an innate process for seizure suppression and a potential mechanism underlying therapeutic electrical stimulation for epilepsy.

The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure

Slow brain rhythms, for example during slow-wave sleep or pathological conditions like seizures and spreading depolarization, can be accompanied by oscillations in extracellular potassium concentration. Such slow brain rhythms typically have a lower frequency than tonic action-potential firing. They are assumed to arise from network-level mechanisms, involving synaptic interactions and delays, or from intrinsically bursting neurons. Neuronal burst generation is commonly attributed to ion channels with slow kinetics. Here, we explore an alternative mechanism generically available to all neurons with class I excitability. It is based on the interplay of fast-spiking voltage dynamics with a one-dimensional slow dynamics of the extracellular potassium concentration, mediated by the activity of the Na+/K+-ATPase. We use bifurcation analysis of the complete system as well as the slow-fast method to reveal that this coupling suffices to generate a hysteresis loop organized around a bistable region that emerges from a saddle-node loop bifurcation-a common feature of class I excitable neurons. Depending on the strength of the Na+/K+-ATPase, bursts are generated from pump-induced shearing the bifurcation structure, spiking is tonic, or cells are silenced via depolarization block. We suggest that transitions between these dynamics can result from disturbances in extracellular potassium regulation, such as glial malfunction or hypoxia affecting the Na+/K+-ATPase activity. The identified minimal mechanistic model outlining the sodium-potassium pump's generic contribution to burst dynamics can, therefore, contribute to a better mechanistic understanding of pathologies such as epilepsy syndromes and, potentially, inform therapeutic strategies.

Focal brain cooling suppresses spreading depolarization and reduces endothelial nitric oxide synthase expression in rats

This study aimed to investigate the effects of focal brain cooling (FBC) on spreading depolarization (SD), which is associated with several neurological disorders. Although it has been studied from various aspects, no medication has been developed that can effectively control SD. As FBC can reduce neuronal damage and promote functional recovery in pathological conditions such as epilepsy, cerebral ischemia, and traumatic brain injury, it may also potentially suppress the onset and progression of SD. We created an experimental rat model of SD by administering 1 M potassium chloride (KCl) to the cortical surface. Changes in neuronal and vascular modalities were evaluated using multimodal recording, which simultaneously recorded brain temperature (BrT), wide range electrocorticogram, and two-dimensional cerebral blood flow. The rats were divided into two groups (cooling [CL] and non-cooling [NC]). Warm or cold saline was perfused on the surface of one hemisphere to maintain BrT at 37°C or 15°C in the NC and CL groups, respectively. Western blot analysis was performed to determine the effects of FBC on endothelial nitric oxide synthase (eNOS) expression. In the NC group, KCl administration triggered repetitive SDs (mean frequency = 11.57/h). In the CL group, FBC increased the duration of all KCl-induced events and gradually reduced their frequency. Additionally, eNOS expression decreased in the cooled brain regions compared to the non-cooled contralateral hemisphere. The results obtained by multimodal recording suggest that FBC suppresses SD and decreases eNOS expression. This study may contribute to developing new treatments for SD and related neurological disorders.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Dynamical modulation of hypersynchronous seizure onset with transcranial magneto-acoustic stimulation in a hippocampal computational model

Hypersynchronous (HYP) seizure onset is one of the frequently observed seizure-onset patterns in temporal lobe epileptic animals and patients, often accompanied by hippocampal sclerosis. However, the exact mechanisms and ion dynamics of the transition to HYP seizures remain unclear. Transcranial magneto-acoustic stimulation (TMAS) has recently been proposed as a novel non-invasive brain therapy method to modulate neurological disorders. Therefore, we propose a biophysical computational hippocampal network model to explore the evolution of HYP seizure caused by changes in crucial physiological parameters and design an effective TMAS strategy to modulate HYP seizure onset. We find that the cooperative effects of abnormal glial uptake strength of potassium and excessive bath potassium concentration could produce multiple discharge patterns and result in transitions from the normal state to the HYP seizure state and ultimately to the depolarization block state. Moreover, we find that the pyramidal neuron and the PV+ interneuron in HYP seizure-onset state exhibit saddle-node-on-invariant-circle/saddle homoclinic (SH) and saddle-node/SH at onset/offset bifurcation pairs, respectively. Furthermore, the response of neuronal activities to TMAS of different ultrasonic waveforms revealed that lower sine wave stimulation can increase the latency of HYP seizures and even completely suppress seizures. More importantly, we propose an ultrasonic parameter area that not only effectively regulates epileptic rhythms but also is within the safety limits of ultrasound neuromodulation therapy. Our results may offer a more comprehensive understanding of the mechanisms of HYP seizure and provide a theoretical basis for the application of TMAS in treating specific types of seizures.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

Finite-element modeling of neuromodulation via controlled delivery of potassium ions using conductive polymer-coated microelectrodes

Objective. The controlled delivery of potassium is an interesting neuromodulation modality, being potassium ions involved in shaping neuron excitability, synaptic transmission, network synchronization, and playing a key role in pathological conditions like epilepsy and spreading depression. Despite many successful examples of pre-clinical devices able to influence the extracellular potassium concentration, computational frameworks capturing the corresponding impact on neuronal activity are still missing.Approach. We present a finite-element model describing a PEDOT:PSS-coated microelectrode (herein, simplyionic actuator) able to release potassium and thus modulate the activity of a cortical neuron in anin-vitro-like setting. The dynamics of ions in the ionic actuator, the neural membrane, and the cellular fluids are solved self-consistently.Main results. We showcase the capability of the model to describe on a physical basis the modulation of the intrinsic excitability of the cell and of the synaptic transmission following the electro-ionic stimulation produced by the actuator. We consider three case studies for the ionic actuator with different levels of selectivity to potassium: ideal selectivity, no selectivity, and selectivity achieved by embedding ionophores in the polymer.Significance. This work is the first step toward a comprehensive computational framework aimed to investigate novel neuromodulation devices targeting specific ionic species, as well as to optimize their design and performance, in terms of the induced modulation of neural activity.

How neuronal morphology impacts the synchronisation state of neuronal networks

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Astrocytes as critical players of the fine balance between inhibition and excitation in the brain: spreading depolarization as a mechanism to curb epileptic activity

Spreading depolarizations (SD) are slow waves of complete depolarization of brain tissue followed by neuronal silencing that may play a role in seizure termination. Even though SD was first discovered in the context of epilepsy research, the link between SD and epileptic activity remains understudied. Both seizures and SD share fundamental pathophysiological features, and recent evidence highlights the frequent occurrence of SD in experimental seizure models. Human data on co-occurring seizures and SD are limited but suggestive. This mini-review addresses possible roles of SD during epileptiform activity, shedding light on SD as a potential mechanism for terminating epileptiform activity. A common denominator for many forms of epilepsy is reactive astrogliosis, a process characterized by morphological and functional changes to astrocytes. Data suggest that SD mechanisms are potentially perturbed in reactive astrogliosis and we propose that this may affect seizure pathophysiology.

Cellular communication among smooth muscle cells: The role of membrane potential via connexins

Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example. Understanding the mechanism of this non-action potential communication is critical in many cases, like synchronization of cellular activity, under normal and pathological conditions. In this paper, we employ a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model. This is achieved by considering different diffusion coefficients and incorporating nonlinear interface conditions. Subsequently, the homogenized macroscopic model is used to investigate communication in multi-cellular tissues. Our computational simulations reveal that the membrane potential of syncytia, formed by interconnected cells via connexins, plays a crucial role in propagating oscillations from one region to another, providing an effective means for fast cellular communication. Statement of Significance: In this study, we investigated cellular communication and ion transport in vascular smooth muscle cells, shedding light on their mechanisms under normal and abnormal conditions. Our research highlights the potential of mathematical models in understanding complex biological systems. We developed effective macroscale electro-neutral bi-domain ion transport models and examined their behavior in response to different stimuli. Our findings revealed the crucial role of connexinmediated membrane potential changes and demonstrated the effectiveness of cellular communication through syncytium membranes. Despite some limitations, our study provides valuable insights into these processes and emphasizes the importance of mathematical modeling in unraveling the complexities of cellular communication and ion transport.

Can in vitro studies aid in the development and use of antiseizure therapies? A report of the ILAE/AES Joint Translational Task Force

In vitro preparations (defined here as cultured cells, brain slices, and isolated whole brains) offer a variety of approaches to modeling various aspects of seizures and epilepsy. Such models are particularly amenable to the application of anti-seizure compounds, and consequently are a valuable tool to screen the mechanisms of epileptiform activity, mode of action of known anti-seizure medications (ASMs), and the potential efficacy of putative new anti-seizure compounds. Despite these applications, all disease models are a simplification of reality and are therefore subject to limitations. In this review, we summarize the main types of in vitro models that can be used in epilepsy research, describing key methodologies as well as notable advantages and disadvantages of each. We argue that a well-designed battery of in vitro models can form an effective and potentially high-throughput screening platform to predict the clinical usefulness of ASMs, and that in vitro models are particularly useful for interrogating mechanisms of ASMs. To conclude, we offer several key recommendations that maximize the potential value of in vitro models in ASM screening. This includes the use of multiple in vitro tests that can complement each other, carefully combined with in vivo studies, the use of tissues from chronically epileptic (rather than naïve wild-type) animals, and the integration of human cell/tissue-derived preparations.

Clarifying the composition of the ATP consumption factors required for maintaining ion homeostasis in mouse rod photoreceptors

To date, no effective treatment has been established for photoreceptor loss due to energy imbalances, but numerous therapeutic approaches have reported some success in slowing photoreceptor degeneration by downregulating energy demand. However, the detailed mechanisms remain unclear. This study aimed to clarify the composition of ATP consumption factors in photoreceptors in darkness and in light. We introduced mathematical formulas for ionic current activities combined with a phototransduction model to form a new mathematical model for estimating the energy expenditure of each ionic current. The proposed model included various ionic currents identified in mouse rods using a gene expression database incorporating an available electrophysiological recording of each specific gene. ATP was mainly consumed by Na+/K+-ATPase and plasma membrane Ca2+-ATPase pumps to remove excess Na+ and Ca2+. The rod consumed 7 [Formula: see text] 107 molecules of ATP s-1, where 65% was used to remove ions from the cyclic nucleotide-gated channel and 20% from the hyperpolarization-activated current in darkness. Increased light intensity raised the energy requirements of the complex phototransduction cascade mechanisms. Nevertheless, the overall energy consumption was less than that in darkness due to the significant reduction in ATPase activities, where the hyperpolarization-activated current proportion increased to 83%. A better understanding of energy demand/supply may provide an effective tool for investigating retinal pathophysiological changes and analyzing novel therapeutic treatments related to the energy consumption of photoreceptors.

Mechanisms underlying pathological cortical bursts during metabolic depletion

Cortical activity depends upon a continuous supply of oxygen and other metabolic resources. Perinatal disruption of oxygen availability is a common clinical scenario in neonatal intensive care units, and a leading cause of lifelong disability. Pathological patterns of brain activity including burst suppression and seizures are a hallmark of the recovery period, yet the mechanisms by which these patterns arise remain poorly understood. Here, we use computational modeling of coupled metabolic-neuronal activity to explore the mechanisms by which oxygen depletion generates pathological brain activity. We find that restricting oxygen supply drives transitions from normal activity to several pathological activity patterns (isoelectric, burst suppression, and seizures), depending on the potassium supply. Trajectories through parameter space track key features of clinical electrophysiology recordings and reveal how infants with good recovery outcomes track toward normal parameter values, whereas the parameter values for infants with poor outcomes dwell around the pathological values. These findings open avenues for studying and monitoring the metabolically challenged infant brain, and deepen our understanding of the link between neuronal and metabolic activity.

Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow

Recent studies have linked spreading depolarization (SD, an electro-chemical wave in the brain following stroke, migraine, traumatic brain injury, and more) with increase in cerebrospinal fluid (CSF) flow through the perivascular spaces (PVSs, annular channels lining the brain vasculature). We develop a novel computational model that couples SD and CSF flow. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change in cross-sectional area, pressure, and volume flow rate through the PVSs. The coupling is modelled using an empirical relationship between the excess potassium ion concentration in the extracellular space following SD and the vessel radius. We find that the CSF volumetric flow rate depends intricately on the length and width of the PVS, as well as the vessel radius and the angle of incidence of the SD wave. We derive analytical expressions for pressure and volumetric flow rates of CSF through the PVS for a given SD wave and quantify CSF flow variations when two SD waves collide. Our numerical approach is very general and could be extended in the future to obtain novel, quantitative insights into how CSF flow in the brain couples with slow waves, functional hyperemia, seizures, or externally applied neural stimulations.

A cold and quiet brain: mechanisms of insect CNS arrest at low temperatures

Exposure to cold causes insects to enter a chill coma at species-specific temperatures and such temperature sensitivity contributes to geographic distribution and phenology. Coma results from abrupt spreading depolarization (SD) of neural tissue in the integrative centers of the CNS. SD abolishes neuronal signaling and the operation of neural circuits, like an off switch for the CNS. Turning off the CNS by allowing ion gradients to collapse will conserve energy and may offset negative consequences of temporary immobility. SD is modified by prior experience via rapid cold hardening (RCH) or cold acclimation which alter properties of K_v channels, Na⁺/K⁺-ATPase and Na⁺/K⁺/2Cl^- cotransporter. The stress hormone octopamine mediates RCH. Future progress depends on developing a more complete understanding of ion homeostasis in and of the insect CNS.

Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by NaV1.1/SCN1A mutations

Na_V1.1 (SCN1A) is a voltage-gated sodium channel mainly expressed in GABAergic neurons. Loss of function mutations of Na_V1.1 lead to epileptic disorders, while gain of function mutations cause a migraine in which cortical spreading depolarizations (CSDs) are involved. It is still debated how these opposite effects initiate two different manifestations of neuronal hyperactivity: epileptic seizures and CSD. To investigate this question, we previously built a conductance-based model of two neurons (GABAergic and pyramidal), with dynamic ion concentrations (Lemaire et al. in PLoS Comput Biol 17(7):e1009239, 2021. https://doi.org/10.1371/journal.pcbi.1009239 ). When implementing either Na_V1.1 migraine or epileptogenic mutations, ion concentration modifications acted as slow processes driving the system to the corresponding pathological firing regime. However, the large dimensionality of the model complicated the exploitation of its implicit multi-timescale structure. Here, we substantially simplify our biophysical model to a minimal version more suitable for bifurcation analysis. The explicit timescale separation allows us to apply slow-fast theory, where slow variables are treated as parameters in the fast singular limit. In this setting, we reproduce both pathological transitions as dynamic bifurcations in the full system. In the epilepsy condition, we shift the spike-terminating bifurcation to lower inputs for the GABAergic neuron, to model an increased susceptibility to depolarization block. The resulting failure of synaptic inhibition triggers hyperactivity of the pyramidal neuron. In the migraine scenario, spiking-induced release of potassium leads to the abrupt increase of the extracellular potassium concentration. This causes a dynamic spike-terminating bifurcation of both neurons, which we interpret as CSD initiation.

From phenomenological to biophysical models of seizures

Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.

Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets

The perineuronal nets (PNNs) are sugar coated protein structures that encapsulate certain neurons in the brain, such as parvalbumin positive (PV) inhibitory neurons. As PNNs are theorized to act as a barrier to ion transport, they may effectively increase the membrane charge-separation distance, thereby affecting the membrane capacitance. Tewari et al. (2018) found that degradation of PNNs induced a 25%-50% increase in membrane capacitance [Formula: see text] and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in [Formula: see text] affects the firing rate in a selection of computational neuron models, ranging in complexity from a single compartment Hodgkin-Huxley model to morphologically detailed PV-neuron models. In all models, an increased [Formula: see text] lead to reduced firing, but the experimentally reported increase in [Formula: see text] was not alone sufficient to explain the experimentally reported reduction in firing rate. We therefore hypothesized that PNN degradation in the experiments affected not only [Formula: see text], but also ionic reversal potentials and ion channel conductances. In simulations, we explored how various model parameters affected the firing rate of the model neurons, and identified which parameter variations in addition to [Formula: see text] that are most likely candidates for explaining the experimentally reported reduction in firing rate.

The ATP1A2 Mutation Associated with Hemiplegic Migraines: Case Report and Literature Review

Familial hemiplegic migraine type 2 is a premonitory subtype of migraine caused by an ATP1A2 gene mutation. It is an autosomal dominant genetic disease. Here, we report a 51-year-old woman who had a migraine attack due to a pathogenic ATP1A2 gene mutation. With frequent attacks, the patient developed complete left hemiplegia, a confusion of consciousness and partial seizures. Magnetic resonance imaging showed extensive angiogenic edema in the right cerebral hemisphere. In this article, we review the latest literature and try to explain the above symptoms in our patient with cortical spreading depression (CSD) and ATP1A2 gene mutations.

Thermal effects on neurons during stimulation of the brain

All electric and magnetic stimulation of the brain deposits thermal energy in the brain. This occurs through either Joule heating of the conductors carrying current through electrodes and magnetic coils, or through dissipation of energy in the conductive brain.Objective.Although electrical interaction with brain tissue is inseparable from thermal effects when electrodes are used, magnetic induction enables us to separate Joule heating from induction effects by contrasting AC and DC driving of magnetic coils using the same energy deposition within the conductors. Since mammalian cortical neurons have no known sensitivity to static magnetic fields, and if there is no evidence of effect on spike timing to oscillating magnetic fields, we can presume that the induced electrical currents within the brain are below the molecular shot noise where any interaction with tissue is purely thermal.Approach.In this study, we examined a range of frequencies produced from micromagnetic coils operating below the molecular shot noise threshold for electrical interaction with single neurons.Main results.We found that small temperature increases and decreases of 1∘C caused consistent transient suppression and excitation of neurons during temperature change. Numerical modeling of the biophysics demonstrated that the Na-K pump, and to a lesser extent the Nernst potential, could account for these transient effects. Such effects are dependent upon compartmental ion fluxes and the rate of temperature change.Significance.A new bifurcation is described in the model dynamics that accounts for the transient suppression and excitation; in addition, we note the remarkable similarity of this bifurcation's rate dependency with other thermal rate-dependent tipping points in planetary warming dynamics. These experimental and theoretical findings demonstrate that stimulation of the brain must take into account small thermal effects that are ubiquitously present in electrical and magnetic stimulation. More sophisticated models of electrical current interaction with neurons combined with thermal effects will lead to more accurate modulation of neuronal activity.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Focal seizures are organized by feedback between neural activity and ion concentration changes

Human and animal EEG data demonstrate that focal seizures start with low-voltage fast activity, evolve into rhythmic burst discharges and are followed by a period of suppressed background activity. This suggests that processes with dynamics in the range of tens of seconds govern focal seizure evolution. We investigate the processes associated with seizure dynamics by complementing the Hodgkin-Huxley mathematical model with the physical laws that dictate ion movement and maintain ionic gradients. Our biophysically realistic computational model closely replicates the electrographic pattern of a typical human focal seizure characterized by low voltage fast activity onset, tonic phase, clonic phase and postictal suppression. Our study demonstrates, for the first time in silico, the potential mechanism of seizure initiation by inhibitory interneurons via the initial build-up of extracellular K+ due to intense interneuronal spiking. The model also identifies ionic mechanisms that may underlie a key feature in seizure dynamics, i.e., progressive slowing down of ictal discharges towards the end of seizure. Our model prediction of specific scaling of inter-burst intervals is confirmed by seizure data recorded in the whole guinea pig brain in vitro and in humans, suggesting that the observed termination pattern may hold across different species. Our results emphasize ionic dynamics as elementary processes behind seizure generation and indicate targets for new therapeutic strategies.

Mapping spreading depolarisations after traumatic brain injury: a pilot clinical study protocol

INTRODUCTION

Cortical spreading depolarisation (CSD) is characterised by a near-complete loss of the ionic membrane potential of cortical neurons and glia propagating across the cerebral cortex, which generates a transient suppression of spontaneous neuronal activity. CSDs have become a recognised phenomenon that imparts ongoing secondary insults after brain injury. Studies delineating CSD generation and propagation in humans after traumatic brain injury (TBI) are lacking. Therefore, this study aims to determine the feasibility of using a multistrip electrode array to identify CSDs and characterise their propagation in space and time after TBI.

METHODS AND ANALYSIS

This pilot, prospective observational study will enrol patients with TBI requiring therapeutic craniotomy or craniectomy. Subdural electrodes will be placed for continuous electrocorticography monitoring for seizures and CSDs as a research procedure, with surrogate informed consent obtained preoperatively. The propagation of CSDs relative to structural brain pathology will be mapped using reconstructed CT and electrophysiological cross-correlations. The novel use of multiple subdural strip electrodes in conjunction with brain morphometric segmentation is hypothesised to provide sufficient spatial information to characterise CSD propagation across the cerebral cortex and identify cortical foci giving rise to CSDs.

ETHICS AND DISSEMINATION

Ethical approval for the study was obtained from the Hennepin Healthcare Research Institute's ethics committee, HSR 17-4400, 25 October 2017 to present. Study findings will be submitted for publication in peer-reviewed journals and presented at scientific conferences.

TRIAL REGISTRATION NUMBER

NCT03321370.

Multiscale Computer Modeling of Spreading Depolarization in Brain Slices

Spreading depolarization (SD) is a slow-moving wave of neuronal depolarization accompanied by a breakdown of ion concentration homeostasis, followed by long periods of neuronal silence (spreading depression), and is associated with several neurologic conditions. We developed multiscale (ions to tissue slice) computer models of SD in brain slices using the NEURON simulator: 36,000 neurons (two voltage-gated ion channels; three leak channels; three ion exchangers/pumps) in the extracellular space (ECS) of a slice (1 mm sides, varying thicknesses) with ion (K+, Cl-, Na+) and O2 diffusion and equilibration with a surrounding bath. Glia and neurons cleared K+ from the ECS via Na+/K+ pumps. SD propagated through the slices at realistic speeds of 2-4 mm/min, which increased by as much as 50% in models incorporating the effects of hypoxia or propionate. In both cases, the speedup was mediated principally by ECS shrinkage. Our model allows us to make testable predictions, including the following: (1) SD can be inhibited by enlarging ECS volume; (2) SD velocity will be greater in areas with greater neuronal density, total neuronal volume, or larger/more dendrites; (3) SD is all-or-none: initiating K+ bolus properties have little impact on SD speed; (4) Slice thickness influences SD because of relative hypoxia in the slice core, exacerbated by SD in a pathologic cycle; and (5) SD and high neuronal spike rates will be observed in the core of the slice. Cells in the periphery of the slice near an oxygenated bath will resist SD.

Simulating epileptic seizures using the bidomain model

Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain's activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.

Biophysical Model: A Promising Method in the Study of the Mechanism of Propofol: A Narrative Review

The physiological and neuroregulatory mechanism of propofol is largely based on very limited knowledge. It is one of the important puzzling issues in anesthesiology and is of great value in both scientific and clinical fields. It is acknowledged that neural networks which are comprised of a number of neural circuits might be involved in the anesthetic mechanism. However, the mechanism of this hypothesis needs to be further elucidated. With the progress of artificial intelligence, it is more likely to solve this problem through using artificial neural networks to perform temporal waveform data analysis and to construct biophysical computational models. This review focuses on current knowledge regarding the anesthetic mechanism of propofol, an intravenous general anesthetic, by constructing biophysical computational models.

Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits

Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.

Action Potentials Are Critical for the Propagation of Focally Elicited Spreading Depolarizations

Spreading depolarizations (SDs) of gray matter occur in the brain in different pathologic conditions, and cause varying degrees of tissue damage depending on the extent of metabolic burden on the tissue. As might be expected for such large depolarizations, neurons exhibit bursts of action potentials (APs) as the wave propagates. However, the specific role of APs in SD propagation is unclear. This is potentially consequential, since sodium channel modulation has not been considered as a therapeutic target for SD-associated disorders, because of ambiguous experimental evidence. Using whole-cell electrophysiology and single-photon imaging in acute cortical slices from male C57Bl6 mice, we tested the effects of AP blockade on SDs generated by two widely used induction paradigms. We found that AP blockade using tetrodotoxin (TTX) restricted propagation of focally induced SDs, and significantly reduced the amplitude of neuronal depolarization, as well as its Ca2+ load. TTX also abolished the suppression of spontaneous synaptic activity that is a hallmark of focally induced SD. In contrast, TTX did not affect the propagation of SD induced by global superfusion of high [K+]e containing artificial CSF (ACSF). Thus, we show that voltage-gated sodium channel (Nav)-mediated neuronal AP bursts are critical for the propagation and downstream effects of focally induced SD but are less important when the ionic balance of the extracellular space is already compromised. In doing so we corroborate the notion that two different SD induction paradigms, each relevant to different clinical situations, vary significantly in their characteristics and potentially their response to treatment.SIGNIFICANCE STATEMENT Our findings suggest that voltage-gated sodium channel (Nav) channels have a critical role in the propagation and downstream neural effects of focally induced spreading depolarization (SD). As SDs are likely induced focally in many disease conditions, these studies support sodium channel modulation, a previously underappreciated therapeutic option in SD-associated disorders, as a viable approach.

Validating a Computational Framework for Ionic Electrodiffusion with Cortical Spreading Depression as a Case Study

Cortical spreading depression (CSD) is a wave of pronounced depolarization of brain tissue accompanied by substantial shifts in ionic concentrations and cellular swelling. Here, we validate a computational framework for modeling electrical potentials, ionic movement, and cellular swelling in brain tissue during CSD. We consider different model variations representing wild-type (WT) or knock-out/knock-down mice and systematically compare the numerical results with reports from a selection of experimental studies. We find that the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular K+ concentration as well as a pronounced shrinkage of extracellular space (ECS) are well in line with what has previously been observed experimentally. Further, we assess how key model parameters including cellular diffusivity, structural ratios, membrane water and/or K+ permeabilities affect the set of CSD characteristics.

The Relationship Between Seizures and Spreading Depolarizations in Patients with Severe Traumatic Brain Injury

BACKGROUND

Both seizures and spreading depolarizations (SDs) are commonly detected using electrocorticography (ECoG) after severe traumatic brain injury (TBI). A close relationship between seizures and SDs has been described, but the implications of detecting either or both remain unclear. We sought to characterize the relationship between these two phenomena and their clinical significance.

METHODS

We performed a post hoc analysis of a prospective observational clinical study of patients with severe TBI requiring neurosurgery at five academic neurotrauma centers. A subdural electrode array was placed intraoperatively and ECoG was recorded during intensive care. SDs, seizures, and high-frequency background characteristics were quantified offline using published standards and terminology. The primary outcome was the Glasgow Outcome Scale-Extended score at 6 months post injury.

RESULTS

There were 138 patients with valid ECoG recordings; the mean age was 47 ± 19 years, and 104 (75%) were men. Overall, 2,219 ECoG-detected seizures occurred in 38 of 138 (28%) patients in a bimodal pattern, with peak incidences at 1.7-1.8 days and 3.8-4.0 days post injury. Seizures detected on scalp electroencephalography (EEG) were diagnosed by standard clinical care in only 18 of 138 (13%). Of 15 patients with ECoG-detected seizures and contemporaneous scalp EEG, seven (47%) had no definite scalp EEG correlate. ECoG-detected seizures were significantly associated with the severity and number of SDs, which occurred in 83 of 138 (60%) of patients. Temporal interactions were observed in 17 of 24 (70.8%) patients with both ECoG-detected seizures and SDs. After controlling for known prognostic covariates and the presence of SDs, seizures detected on either ECoG or scalp EEG did not have an independent association with 6-month functional outcome but portended worse outcome among those with clustered or isoelectric SDs.

CONCLUSIONS

In patients with severe TBI requiring neurosurgery, seizures were half as common as SDs. Seizures would have gone undetected without ECoG monitoring in 20% of patients. Although seizures alone did not influence 6-month functional outcomes in this cohort, they were independently associated with electrographic worsening and a lack of motor improvement following surgery. Temporal interactions between ECoG-detected seizures and SDs were common and held prognostic implications. Together, seizures and SDs may occur along a dynamic continuum of factors critical to the development of secondary brain injury. ECoG provides information integral to the clinical management of patients with TBI.

Personality traits as a risk factor for postpartum depression: A systematic review and meta-analysis

BACKGROUND

Certain personality traits increase vulnerability to depression, but the evidence linking personality and postpartum depression (PPD) is less robust. This systematic review aimed to identify personality traits that increase the risk of PPD.

METHODS

We systematically reviewed studies retrieved from PubMed/Medline, PsycINFO, Scopus, CINAHL, and Cochrane, following the PRISMA guidelines for reporting. We carried out a meta-analysis on the association between neuroticism and PPD.

RESULTS

A total of 34 studies were analyzed. Of these, 31 considered at least one trait associated with PPD; 10 studies considered at least one trait not associated with PPD. The meta-analysis included 13 studies, concluding that neuroticism was associated with PPD (OR: 1.37; 95%CI: 1.22-1.53; p<0.001).

LIMITATIONS

Study design and approach to personality assessment influence results. Prospective longitudinal studies of persons with no prior history of mood disorder would provide stronger evidence about whether particular personality traits predict PPD. Most studies reviewed used self-report measures to assess personality. Study design and approach to personality assessment influence results, and indications of publication bias were found.

CONCLUSIONS

Neuroticism is the personality trait most widely studied in relation to PPD. Our meta-analysis found this trait is strongly related with PPD. Moreover, vulnerable personality style and trait anxiety are also associated with PPD. Screening for these traits might help identify women at risk, improving prevention, early detection, and possibly treatment.

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations’ interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront’s propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID’s speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na⁺/K⁺ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

During an epileptic seizure, neuronal excitation spreads across the brain tissue and is accompanied by significant changes in ionic concentrations. Ictal discharge front spreads at low speeds, less than 1 mm/s. Mechanisms underlying this phenomenon are not yet well understood. We study these mechanisms using electrophysiological recordings in brain slices and computer simulations. Our detailed biophysical model describing neuronal populations’ interaction, spatial propagation, and ionic dynamics reproduces the generation and propagation of spontaneously repeating ictal discharges. The simulations are consistent with our recordings of the electrical activity and the extracellular potassium ion concentration. We distinguished between the two alternative mechanisms of the ictal wavefront propagation: (i) the diffusion of potassium ions released from excited neurons, which depolarizes distant neurons and thus supports excitation, and (ii) the axonal spread of excitation followed by the local extracellular potassium ion accumulation that supports the excitation. Our simulations provide evidence in favor of the latter mechanism. Our experiment-based modeling contributes to a mathematical description of brain tissue functioning and potentially contributes to developing new treatments against epilepsy.

A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level

The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K⁺ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K⁺ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K⁺ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.

Spatio-temporal spike dynamics predict surgical outcome in adult focal epilepsy

OBJECTIVE

We hypothesized that spatio-temporal dynamics of interictal spikes reflect the extent and stability of epileptic sources and determine surgical outcome.

METHODS

We studied 30 consecutive patients (14 good outcome). Spikes were detected in prolonged stereo-electroencephalography recordings. We quantified the spatio-temporal dynamics of spikes using the variance of the spike rate, line length and skewness of the spike distribution, and related these features to outcome. We built a logistic regression model, and compared its performance to traditional markers.

RESULTS

Good outcome patients had more dominant and stable sources than poor outcome patients as expressed by a higher variance of spike rates, a lower variance of line length, and a lower variance of positive skewness (ps < 0.05). The outcome was correctly predicted in 80% of patients. This was better or non-inferior to predictions based on a focal lesion (p = 0.016), focal seizure-onset zone, or complete resection (ps > 0.05). In the five patients where traditional markers failed, spike distribution predicted the outcome correctly. The best results were achieved by 18-h periods or longer.

CONCLUSIONS

Analysis of spike dynamics shows that surgery outcome depends on strong, single and stable sources.

SIGNIFICANCE

Our quantitative method has the potential to be a reliable predictor of surgical outcome.

Analyses of HH and GHK equations with another perspective: Can ion adsorption also govern trans-membrane potential?

Two mathematically distinct physiological concepts, the Goldman-Hodgkin-Katz eq. (GHK eq.) and the Hodgkin-Huxley model (HH model) were successfully associated with each other in a prior work. The previous work was performed on the following premises (i) The membrane potential is generated by ion adsorption, as opposed to the classical ion transport mechanisms, (ii) The living cell is a thermodynamically real system rather than an ideal system, and (iii) The conductance employed in the HH model is replaced by the ion activity coefficient, which is weighted with the role of conductance. Consequently, the GHK eq. was mathematically associated with the HH model through the intermediary of Boltzmann ion distribution and mass action law. To verify if our theoretical formularization could afford a physiologically, physically and chemically viable model, we performed computational analysis using the formulae (quantitative correlations between various variables) we derived in the previous work. The computational results obtained through associating the GHK eq. with the HH model validated our model and its predictions. This outcome suggests that the current prevailing physiological concepts could be expanded further, to incorporate the newly proposed mechanisms. That is, GHK eq. and HH model could be interpreted via another set of founding principles that incorporate the ubiquitous phenomena of ion-adsorption.

Kcnq2/Kv7.2 controls the threshold and bi-hemispheric symmetry of cortical spreading depolarization

Spreading depolarization is a slowly propagating wave of massive cellular depolarization associated with acute brain injury and migraine aura. Genetic studies link depolarizing molecular defects in Ca2+ flux, Na+ current in interneurons, and glial Na+-K+ ATPase with spreading depolarization susceptibility, emphasizing the important roles of synaptic activity and extracellular ionic homeostasis in determining spreading depolarization threshold. In contrast, although gene mutations in voltage-gated potassium ion channels that shape intrinsic membrane excitability are frequently associated with epilepsy susceptibility, it is not known whether epileptogenic mutations that regulate membrane repolarization also modify spreading depolarization threshold and propagation. Here we report that the Kcnq2/Kv7.2 potassium channel subunit, frequently mutated in developmental epilepsy, is a spreading depolarization modulatory gene with significant control over the seizure-spreading depolarization transition threshold, bi-hemispheric cortical expression, and diurnal temporal susceptibility. Chronic DC-band cortical EEG recording from behaving conditional Kcnq2 deletion mice (Emx1cre/+::Kcnq2flox/flox) revealed spontaneous cortical seizures and spreading depolarization. In contrast to the related potassium channel deficient model, Kv1.1-KO mice, spontaneous cortical spreading depolarizations in Kcnq2 cKO mice are tightly coupled to the terminal phase of seizures, arise bilaterally, and are observed predominantly during the dark phase. Administration of the non-selective Kv7.2 inhibitor XE991 to Kv1.1-KO mice partly reproduced the Kcnq2 cKO-like spreading depolarization phenotype (tight seizure coupling and bilateral symmetry) in these mice, indicating that Kv7.2 currents can directly and actively modulate spreading depolarization properties. In vitro brain slice studies confirmed that Kcnq2/Kv7.2 depletion or pharmacological inhibition intrinsically lowers the cortical spreading depolarization threshold, whereas pharmacological Kv7.2 activators elevate the threshold to multiple depolarizing and hypometabolic spreading depolarization triggers. Together these results identify Kcnq2/Kv7.2 as a distinctive spreading depolarization regulatory gene, and point to spreading depolarization as a potentially significant pathophysiological component of KCNQ2-linked epileptic encephalopathy syndromes. Our results also implicate KCNQ2/Kv7.2 channel activation as a potential adjunctive therapeutic target to inhibit spreading depolarization incidence.

A dynamics model of neuron-astrocyte network accounting for febrile seizures

Febrile seizure (FS) is a full-body convulsion caused by a high body temperature that affect young kids, however, how these most common of human seizures are generated by fever has not been known. One common observation is that cortical neurons become overexcited with abnormal running of sodium and potassium ions cross membrane in raised body temperature condition, Considering that astrocyte Kir4.1 channel play a critical role in maintaining extracellular homeostasis of ionic concentrations and electrochemical potentials of neurons by fast depletion of extracellular potassium ions, we examined here the potential role of temperature-dependent Kir4.1 channel in astrocytes in causing FS. We first built up a temperature-dependent computational model of the Kir4.1 channel in astrocytes and validated with experiments. We have then built up a neuron-astrocyte network and examine the role of the Kir4.1 channel in modulating neuronal firing dynamics as temperature increase. The numerical experiment demonstrated that the Kir4.1 channel function optimally in the body temperature around 37 °C in cleaning 'excessive' extracellular potassium ions during neuronal firing process, however, higher temperature deteriorates its cleaning function, while lower temperature slows down its cleaning efficiency. With the increase of temperature, neurons go through different stages of spiking dynamics from spontaneous slow oscillations, to tonic spiking, fast bursting oscillations, and eventually epileptic bursting. Thus, our study may provide a potential new mechanism that febrile seizures may be happened due to temperature-dependent functional disorders of Kir4.1 channel in astrocytes.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-021-09706-w.