Modeling the Saltatory Conduction in Myelinated Axons by Order Reduction

The saltatory conduction is the way the action potential
is transmitted along a myelinated axon. The potential diffuses along
the myelinated compartments and it is regenerated in the Ranvier
nodes due to the ion channels allowing the flow across the membrane.
For an efficient simulation of populations of neurons, it is important
to use reduced order models both for myelinated compartments
and for Ranvier nodes and to have control over their accuracy and
inner parameters. The paper presents a reduced order model of this
neural system which allows an efficient simulation method for the
saltatory conduction in myelinated axons. This model is obtained
by concatenating reduced order linear models of 1D myelinated
compartments and nonlinear 0D models of Ranvier nodes. The
models for the myelinated compartments are selected from a series of
spatially distributed models developed and hierarchized according to
their modeling errors. The extracted model described by a nonlinear
PDE of hyperbolic type is able to reproduce the saltatory conduction
with acceptable accuracy and takes into account the finite propagation
speed of potential. Finally, this model is again reduced in order to
make it suitable for the inclusion in large-scale neural circuits.

Authors:

• Ruxandra Barbulescu
• Daniel Ioan
• Gabriela Ciuprina

Keywords:

• Saltatory conduction
• action potential
• myelinated compartments
• nonlinear
• Ranvier nodes
• reduced order models
• POD.

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