Combining the neural mass model and Hodgkin–Huxley formalism: Neuronal dynamics modelling

Epilepsy is a neurological disorder that affects the nervous system and is characterized by recurrent seizures. Experimental data shows that increase in the extracellular potassium concentration can support the generation of seizures and that the T-type calcium channel antagonists can be effective as anti-epileptic drugs. To investigate these two phenomena in detail, we combine microscopic level modelling using Hodgkin–Huxley formalism and a macroscopic level approach using a neural mass model. The microscopic level approach describes the initiation of action potentials in individual neurons using conductance-based model. The macroscopic (neural mass model) approach is a low-dimensional phenomenological model that describes the activity of a large population of neurons. The neural mass model replicated the interactions between inhibitory and excitatory neuronal populations by using a sigmoidal function that converts neuronal postsynaptic potential into the average spiking rate of a given population. This sigmoidal function links two levels of modelling: microscopic and macroscopic. Our results are in agreement with experimental data and show that an increase in the extracellular potassium concentration or an increase in the T-type calcium conductance can cause brain network transitions from normal background to pathological seizure-like dynamics. In addition, the results show that these transitions only happen for a limited range of network parameters and that the slow-inhibitory synaptic gain has a stronger effect on network dynamics during transitions than the fast-inhibitory synaptic gain.