Synchronization regimes in the ring of rodent hippocampal neurons at limbic epilepsy

Abstract

This study aims to consider an ensemble of hippocampal neurons coupled in a ring, which may be responsible for generation of the primary rhythm at limbic epilepsy. Methods. Model equations were solved numerically. To determine the areas of oscillatory and excitable regime existance for a single neuron, the bifurcation analysis for the leakadge conductivity parameter was performed. The coupling delays was not implemented directly, instead, inertia in the synapse was introduced. To determine the stability of generation some couplings were removed and parameter detunig was introduced. Results. In the single neuron model the bistability region was detected, in which a stable focus coexhists with a limit cycle. Two main synchronous regimes were detected. The first regime inherits frequency of individual oscillator, with a relatively small phase shift between oscillators in the ring. The frequency of the second regime depends on the number of neurons in the ring, with the phase shift between neighbor oscillators being equal to ratio of oscillation period and number of neurons. This second regime can occur both for the parameters corresponding to bistabler regime in the individual neuron and for the parameters at which the only existing attractor is stable focus. The second synchronous regime is preserved for parameter detuning of 2% from their absolute values. Conclusion. It was shown that in the mathematical model of the ring of hippocampal neurons, where all the main significant currents are taken into account for individual neurons, and their parameters can vary, there is an oscillatory mode, the frequency of which is determined by the length of the ring and synaptic conductivity, rather than by the parameters individual neuron. In this case, a small change in synaptic conductivity can lead to a sharp (2–7 times) change in the generation frequency.

Keywords

• hodgkin–huxley model
• neural networks
• collective dynamics
• hippocampus
• pyramidal neuron
• epilepsy