Viscoelastic Fitzhugh-Nagumo models.

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Modeling

Background:

• The Fitzhugh-Nagumo model is a simplified mathematical representation of neuron action potentials.
• Cardiac electrophysiology involves complex interactions between electrical activity and mechanical properties.
• Understanding the interplay of electrical signals and viscoelasticity is crucial for cardiac modeling.

Purpose of the Study:

• To develop and analyze an extended Fitzhugh-Nagumo model incorporating linear viscoelasticity.
• To investigate the behavior of cardiac fibers under different stimulation conditions.
• To explore the impact of viscoelasticity on action potential propagation and fiber dynamics.

Main Methods:

• Derivation of a generalized Fitzhugh-Nagumo model with linear viscoelasticity.
• Numerical integration of the model equations in one dimension.
• Simulation of a free insulated fiber with an initial action potential.
• Simulation of a clamped fiber under counter-phased electrical stimulation.

Main Results:

• The model qualitatively replicates the physiological contraction and relaxation of cardiac fibers.
• Elastic backreaction significantly influences the system's dynamics.
• Action potential modifications are minimal even under strong electrical stimulation.

Conclusions:

• The extended Fitzhugh-Nagumo model with viscoelasticity provides a valuable framework for studying cardiac electro-mechanical coupling.
• Viscoelastic properties play a crucial role in cardiac fiber behavior, distinct from electrical signal propagation.
• The model's findings align with observed physiological responses in biological samples.