Parameters Analysis of FitzHugh-Nagumo Model for a Reliable Simulation

Abstract : Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model has been one of the most successful neuron / cardiac cell model. It exists many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model. The parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to pride a better simulation environment. The results showed at first that inappropriate time step and integration tolerance in numerical solution of FHN model can give some biased results which would make some publications questionable. Then the thresholds of parameters $\alpha$, $\gamma$ and $\varepsilon$ are presented. $\alpha$ controls the global dynamics of FHN. $\alpha > 0$, the cell is in refractory mode; $\alpha < 0$, the cell is excitable. $\varepsilon$ controls the main morphology of the action potential generated and has a relation with the period ($\mathrm{P} = 3.065 \times \varepsilon^{-0.8275}+4.397$). To show oscillations of relaxation with FHN, $\varepsilon$ should be smaller than $0.0085$. $\gamma$ influences barely AP, it showed linear relationship with the period and duration of action potential. Globally, when $|\alpha| \geq 0.1$, $\varepsilon < 0.0085$, there is no definite threshold for $\gamma$, but smaller values are recommended.
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Binbin Xu, Stéphane Binczak, Sabir Jacquir, Oriol Pont, Hussein Yahia. Parameters Analysis of FitzHugh-Nagumo Model for a Reliable Simulation. 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'14), IEEE Engineering in Medicine and Biology Society, Aug 2014, Chicago, United States. ⟨hal-00998828⟩

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