Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

Abstract

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin-Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio x Na (and x K ), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio x Na (and x K ) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.