Reduced order models of myelinated axonal compartments

Area of Science:

• Computational neuroscience
• Biophysics
• Mathematical modeling

Background:

• Myelinated axons are crucial for rapid nerve impulse transmission.
• Accurate computational models are needed for simulating neuronal behavior.
• Existing models may lack efficiency for large-scale neural network simulations.

Purpose of the Study:

• To develop and analyze a hierarchy of computational models for myelinated axonal compartments.
• To identify the most computationally efficient model for order reduction.
• To establish a procedure for creating simplified models with controlled accuracy.

Main Methods:

• Systematic analysis of 2.5D ElectroQuasi-Static (EQS), 1D Transmission Line (TL), and 0D lumped parameter models.
• Application of analytical and numerical approaches.
• Development of an error estimator for model accuracy assessment.
• Order reduction using vector fitting techniques.

Main Results:

• The analytical 1D TL model demonstrated the highest computational efficiency with accuracy below 0.1%.
• Order reduction via vector fitting yielded a finite model with a relative difference of 10^-4 at order 5.
• Coupling reduced linear myelinated compartment models with nonlinear models of neuronal components allows for global reduced models.

Conclusions:

• The proposed method facilitates the creation of low-order, accurate models for myelinated axons.
• These reduced models are essential for efficient simulation of large-scale neuronal systems.
• This work represents a significant step towards controlled-accuracy simulations of neural systems.