Parameters analysis of FitzHugh-Nagumo model for a reliable simulation

Area of Science:

• Computational neuroscience
• Biophysics
• Nonlinear dynamics

Background:

• The FitzHugh-Nagumo (FHN) model is a simplified yet powerful tool for studying neuron and cardiac cell dynamics, derived from the Hodgkin-Huxley model.
• Numerous variations exist, but biased parameter conditions can lead to questionable simulation results.

Purpose of the Study:

• To determine critical parameter thresholds for a common FHN model variant.
• To establish a reliable simulation environment for FHN models.

Main Methods:

• Investigated the impact of numerical solution parameters (time step, integration tolerance) on FHN model outputs.
• Identified and presented threshold values for key FHN model parameters: α, γ, and ε.

Main Results:

• Inappropriate numerical settings can yield biased FHN model results, potentially compromising published findings.
• Parameter α dictates global dynamics (refractory vs. excitable states).
• Parameter ε influences action potential morphology and period (P = 3.065 × αα,γ(-0.8275)+ 4.397), requiring ε < 0.0085 for relaxation oscillations.
• Parameter γ shows a linear relationship with action potential period and duration, with smaller values recommended.

Conclusions:

• Establishing parameter thresholds is crucial for accurate FHN model simulations.
• The study provides essential guidelines for researchers using FHN models, ensuring the validity of their findings.