Reduced model and simulation of myelinated axon using eigenfunction expansion and singular perturbation

Area of Science:

• Neuroscience
• Computational Biology
• Mathematical Modeling

Background:

• Myelinated axons are crucial for rapid nerve impulse transmission.
• Action potentials regenerate at unmyelinated nodes of Ranvier, creating non-uniform cable properties.
• Existing compartment models for myelinated axons often lack accuracy or computational efficiency.

Purpose of the Study:

• To develop a more accurate and efficient computational model for myelinated axons.
• To improve the simulation of action potential propagation along nerve fibers.
• To offer an alternative to traditional compartment models.

Main Methods:

• A hybrid modeling approach combining eigenfunction expansion with singular perturbation for myelinated segments.
• Application of different cable equations for myelinated and unmyelinated (nodes of Ranvier) regions.
• Comparison with established finite volume/difference compartment models.

Main Results:

• The proposed hybrid scheme achieves an order of magnitude improvement in accuracy for low-order models.
• Faster convergence rates were observed for the hybrid scheme to reach a desired accuracy.
• Demonstrated superior performance compared to conventional compartment models.

Conclusions:

• The hybrid eigenfunction expansion and singular perturbation method is a highly accurate and efficient alternative for modeling myelinated axons.
• This approach offers significant advantages for simulating nerve impulse propagation.
• Enables the development of more sophisticated computational neuroscience models.