The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus

Experiments on hippocampal slices have recorded that a novel pattern of epileptic seizures with alternating excitatory and inhibitory activities in the CA1 region can be induced by an elevated potassium ion (K⁺) concentration in the extracellular space between neurons and astrocytes (ECS-NA). To explore the intrinsic effects of the factors (such as glial K⁺ uptake, Na⁺–K⁺-ATPase, the K⁺ concentration of the bath solution, and K⁺ lateral diffusion) influencing K⁺ concentration in the ECS-NA on the epileptic seizures recorded in previous experiments, we present a coupled model composed of excitatory and inhibitory neurons and glia in the CA1 region. Bifurcation diagrams showing the glial K⁺ uptake strength with either the Na⁺–K⁺-ATPase pump strength or the bath solution K⁺ concentration are obtained for neural epileptic seizures. The K⁺ lateral diffusion leads to epileptic seizure in neurons only when the synaptic conductance values of the excitatory and inhibitory neurons are within an appropriate range. Finally, we propose an energy factor to measure the metabolic demand during neuron firing, and the results show that different energy demands for the normal discharges and the pathological epileptic seizures of the coupled neurons.