A simple model of epileptic seizure propagation: Potassium diffusion versus axo-dendritic spread

Temperature effects on neuronal synchronization in seizures

We present a computational model of networked neurons developed to study the effect of temperature on neuronal synchronization in the brain in association with seizures. The network consists of a set of chaotic bursting neurons surrounding a core tonic neuron in a square lattice with periodic boundary conditions. Each neuron is reciprocally coupled to its four nearest neighbors via temperature dependent gap junctions. Incorporating temperature in the gap junctions makes the coupling stronger when temperature rises, resulting in higher likelihood for synchrony in the network. Raising the temperature eventually makes the network elicit waves of synchronization in circular ripples that propagate from the center outwardly. We suggest this process as a possible underlying mechanism for seizures induced by elevated brain temperatures.

An exploratory computational analysis in mice brain networks of widespread epileptic seizure onset locations along with potential strategies for effective intervention and propagation control

Mean-field models have been developed to replicate key features of epileptic seizure dynamics. However, the precise mechanisms and the role of the brain area responsible for seizure onset and propagation remain incompletely understood. In this study, we employ computational methods within The Virtual Brain framework and the Epileptor model to explore how the location and connectivity of an Epileptogenic Zone (EZ) in a mouse brain are related to focal seizures (seizures that start in one brain area and may or may not remain localized), with a specific focus on the hippocampal region known for its association with epileptic seizures. We then devise computational strategies to confine seizures (prevent widespread propagation), simulating medical-like treatments such as tissue resection and the application of an anti-seizure drugs or neurostimulation to suppress hyperexcitability. Through selectively removing (blocking) specific connections informed by the structural connectome and graph network measurements or by locally reducing outgoing connection weights of EZ areas, we demonstrate that seizures can be kept constrained around the EZ region. We successfully identified the minimal connections necessary to prevent widespread seizures, with a particular focus on minimizing surgical or medical intervention while simultaneously preserving the original structural connectivity and maximizing brain functionality.

Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models

When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena.

High Levels of Extracellular Potassium Can Delay Myxoma Virus Replication by Preventing Release of Virions from the Endosomes

Potassium (K+) is one of the most abundant cations in the human body. Under normal conditions, the vast majority of K+ is found within cells, and the extracellular [K+] is tightly regulated to within 3.0 to 5.0 mM. However, it has recently been shown that high levels of localized necrosis can increase the extracellular concentration of K+ to above 50 mM. This raises the possibility that elevated extracellular K+ might influence a variety of biological processes that occur within regions of necrotic tissue. For example, K+ has been shown to play a central role in the replication cycles of numerous viral families, and in cases of lytic infection, localized regions containing large numbers of necrotic cells can be formed. Here, we show that the replication of the model poxvirus myxoma virus (MYXV) is delayed by elevated levels of extracellular K+. These increased K+ concentrations alter the cellular endocytic pathway, leading to increased phagocytosis but a loss of endosomal/lysosomal segregation. This slows the release of myxoma virus particles from the endosomes, resulting in delays in genome synthesis and infectious particle formation as well as reduced viral spread. Additionally, mathematical modeling predicts that the extracellular K+ concentrations required to impact myxoma virus replication can be reached in viral lesions under a variety of conditions. Taken together, these data suggest that the extracellular [K+] plays a role in determining the outcomes of myxoma infection and that this effect could be physiologically relevant during pathogenic infection. IMPORTANCE Intracellular K+ homeostasis has been shown to play a major role in the replication of numerous viral families. However, the potential impact of altered extracellular K+ concentrations is less well understood. Our work demonstrates that increased concentrations of extracellular K+ can delay the replication cycle of the model poxvirus MYXV by inhibiting virion release from the endosomes. Additionally, mathematical modeling predicts that the levels of extracellular K+ required to impact MYXV replication can likely be reached during pathogenic infection. These results suggest that localized viral infection can alter K+ homeostasis and that these alterations might directly affect viral pathogenesis.

Theta waves, neural spikes and seizures can propagate by ephaptic coupling in vivo

Electric field coupling has been shown to be responsible for non-synaptic neural activity propagation in hippocampal slices and cortical slices. Epileptiform and slow-wave sleep activity can propagate by electric field coupling without using synaptic connections at speeds of ~0.1 m/s in vitro. However, the characteristics of the events that can propagate using electric field coupling through a volume conductor in vivo have not been studied. Thus, we tested the hypothesis that various types of neural signals such as interictal spikes, theta waves and seizures could propagate in vivo across a transection in the hippocampus. We induced epileptiform activity in 4 rats under anesthesia by injecting 4-aminopyridine in the temporal region of the hippocampus, four recording electrodes were inserted along the longitudinal axis of the hippocampus. A transection was made between the electrodes to study the propagation of the neural activity. Although 54% of the interictal spikes could propagate through the cut, only those spikes with a high amplitude and short duration had a high probability to do so. 70% of seizure events could propagate through the cut but parameters distinguishing between propagating and non-propagating seizure events could not be identified. Theta activity was also observed to propagate at a mean speed of 0.16 ± 0.12 m/s in the characteristic range of propagation using electric field coupling through the transection. The electric field volume conduction mechanism was confirmed by showing that propagation was blocked by placing a dielectric layer within the cut. The speed of propagation was not affected by the transection thereby providing further evidence that various types of neural signals including activity in the theta range can propagate by electric field coupling in-vivo.

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.

In Vitro and In Vivo Study of the Short-Term Vasomotor Response during Epileptic Seizures

Epilepsy remains one of the most common brain disorders, and the different types of epilepsy encompass a wide variety of physiological manifestations. Clinical and preclinical findings indicate that cerebral blood flow is usually focally increased at seizure onset, shortly after the beginning of ictal events. Nevertheless, many questions remain about the relationship between vasomotor changes in the epileptic foci and the epileptic behavior of neurons and astrocytes. To study this relationship, we performed a series of in vitro and in vivo experiments using the 4-aminopyridine model of epileptic seizures. It was found that in vitro pathological synchronization of neurons and the depolarization of astrocytes is accompanied by rapid short-term vasoconstriction, while in vivo vasodilation during the seizure prevails. We suggest that vasomotor activity during epileptic seizures is a correlate of the complex, self-sustained response that includes neuronal and astrocytic oscillations, and that underlies the clinical presentation of epilepsy.