Modeling the electric field effects on heterogeneous Pinsky-Rinzel neurons under ephaptic transmission

Pinsky-Rinzel (PR) field effect models under ephaptic transmission both in a single neuron and coupling neurons are constructed and studied in this paper. In presence of electric field, the extracellular media have already shown to play a constructive role in neuronal system. Different from the physical synapses, the ephapse is dependent on the conductive property of the extracellular media. Under the ephaptic transmission, the electric field strength, the extracellular media and concentration of extracellular potassium ion has great influence on neuronal firing behavior. In the analysis of heterogeneous coupling neurons, applied the same electric field, the smaller heterogeneity, the stronger synchronicity in coupling neurons and with the concentration of extracellular potassium ion increasing in a certain range, the more synchronous phenomenon is observed. These agree with some epileptic seizure experiments in low calcium solution. It is interesting that for smaller heterogeneous coupling neurons, both the larger negative and positive field may lead to synchronicity and for bigger heterogeneous coupling neurons only the larger negative field can synchronize the neurons.