SUMMARYPurpose: The aim of this work is to study, by means of computational simulations, the induction and sustaining of nonsynaptic epileptiform activity. Methods: The computational model consists of a network of cellular bodies of neurons and glial cells connected to a three-dimensional (3D) network of juxtaposed extracellular compartments. The extracellular electrodiffusion calculation was used to simulate the extracellular potential. Each cellular body was represented in terms of the transmembrane ionic transports (Na + /K + pumps, ionic channels, and cotransport mechanisms), the intercellular electrodiffusion through gap-junctions, and the neuronal interaction by electric field and the variation of cellular volume. Results: The computational model allows simulating the nonsynaptic epileptiform activity and the extracellular potential captured the main feature of the experimental measurements. The simulations of the concomitant ionic fluxes and concentrations can be used to propose the basic mechanisms involved in the induction and sustaining of the activities. Discussion: The simulations suggest: The bursting induction is mediated by the Cl ) Nernst potential overcoming the transmembrane potential in response to the extracellular [K + ] increase. The burst onset is characterized by a critical point defined by the instant when the Na + influx through its permeable ionic channels overcomes the Na + / K + pump electrogenic current. The burst finalization is defined by another critical point, when the electrogenic current of the Na + /K + pump overcomes its influx through the channels.

Computational modeling of spreading depression (SD) has been used increasingly to study the different mechanisms that are involved in this phenomenon. One of them that is still under discussion involves the mechanisms that originate the extracellular electrical field responsible for the dc potential shift. The main goal of this paper is to present a mathematical derivation for the extracellular electric field that is incorporated in a SD model that has the basic structure of Tuckwell and Miura's model, but with the ionic variations calculated electrochemically. Electrodiffusion equations were used to describe the ionic movement of the four ions Na+, K+, Cl-, and Ca2+. These are mutually coupled by the electric field within the extracellular space (ECS). The results from the simulations show that the model is able to calculate the effect of the ionic changes along the ECS on the electric field, and to reproduce the SD in respect to the most important features that characterize the phenomenon experimentally in the retina or hippocampus. It is suggested that the extracellular negative field-potential shift during SD is due to an electrical field generated by a Goldman-Hodgkin-Katz equation acting within the ECS.

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Structural rearrangement of the dentate gyrus has been described as the underlying cause of many types of epilepsies, particularly temporal lobe epilepsy. It is said to occur when aberrant connections are established in the damaged hippocampus, as described in human epilepsy and experimental models. Computer modelling of the dentate gyrus circuitry and the corresponding structural changes has been used to understand how abnormal mossy fibre sprouting can subserve seizure generation observed in experimental models when epileptogenesis is induced by status epilepticus. The model follows the McCulloch-Pitts formalism including the representation of the nonsynaptic mechanisms. The neuronal network comprised granule cells, mossy cells, and interneurons. The compensation theory and the Hebbian and anti-Hebbian rules were used to describe the structural rearrangement including the effects of the nonsynaptic mechanisms on the neuronal activity. The simulations were based on neuroanatomic data and on the connectivity pattern between the cells represented. The results suggest that there is a joint action of the compensation theory and Hebbian rules during the inflammatory process that accompanies the status epilepticus. The structural rearrangement simulated for the dentate gyrus circuitry promotes speculation about the formation of the abnormal mossy fiber sprouting and its role in epileptic seizures.

The important role of cation-chloride co-transporters in epilepsy is being supported by an increasing number of investigations. However, enormous complexity is involved since the action of these co-transporters has effects on the ionic homeostasis influencing directly the neuronal excitability and the tissue propensity to sustain seizure. To unravel the complex mechanisms involving the co-transporters action during seizure, this paper shows simulations of non-synaptic epileptiform activity and the effect of the blockage of the two different types of cation-chloride co-transporters present in the brain: Na, K and 2Cl co-transporter (NKCC) and K and Cl co-transporter (KCC). The simulations were performed with an electrochemical model representing the non-synaptic structure of the granule cell layer of the dentate gyrus (DG) of the rat hippocampus. The simulations suggest: (i) the potassium clearance is based on the systemic interplay between the Na/K pump and the NKCC co-transporters; (ii) the simultaneous blockage of the NKCC of the neurons and KCC of glial cells acts efficiently suppressing the epileptiform activities; and (iii) the simulations show that depending on the combined blockage of the co-transporters, the epileptiform activities may be suppressed or enhanced.

In the study of the spreading depression (SD) wave phenomenon and its dynamics, it is necessary to describe the ionic movements along the extracellular space, as well as between this and the intracellular space. In both cases, the ionic movement includes a double coupling involving the concentration and the potential gradients and hence must be described by electrodiffusion mechanisms. Based on this, the effects of the ionic composition on the characteristics of the wave propagation can be predicted. The influence of varying extracellular sodium and chloride concentrations on the velocity of propagation of the SD wave was investigated by simulation. The results achieved are close to the experimental measurement from the literature. These findings suggest the potentiality of the model proposed in supporting the interpretation of experimental data in neuronal tissues, particularly the SD.