Biological restraint on the Izhikevich neuron model essential for seizure modeling

Izhikevich model of a neuron allows for simulation of spiking pattern that mimics known biological subtypes. When a current within a range typical for biological experiments is injected into the cell the firing pattern produced in the simulation is close to that observed biologically. However, once these neurons are embedded into a network, the level of depolarization is controlled only by the synaptic depolarization received by the simulated connections. Under these conditions there is no limit on the maximum firing rate produced by any of the neurons. Here we introduce a modification of the Izhikevich model to restrict the firing rate. We demonstrate how this modification affects the overall network activity using a simple artificial neural network. The proposed restraint on the Izhikevich model is particularly important for larger scale simulations or when the frequency dependent short-term plasticity is used in the network. Although maximum firing rates are most likely exceeded in simulations of seizure-like activity we show that restriction of neuronal firing frequencies impacts even small networks with moderate levels of activity.