Mathematically modeling action potentials in myelinated neurons to examine the role of myelin, ion channel density, and myelinated lengths on conduction

Abstract

Since the seminal work of Hodgkin and Huxley, which quantitatively described the propagation of electrical signals through neurons, there has been much investigation into the electrical and geometrical properties of neurons and how they affect conduction velocity along a neuron’s length. To study human neuron behaviors, mathematical models have expanded upon Hodgkin and Huxley’s models to incorporate the effects of neurons that are myelinated by modeling myelinated portions of neurons as passive cables.Here, we present a developed mathematical model that discretizes a myelinated axon length and finely allows for control over a number of important electrical and geometrical properties. Using this model, we present and compare how myelin, inter-node length, and ion channel density affect conduction velocity in two different lengths of axons. We confirm that myelination, internode-length, and ion channel density correlate positively with conduction velocity, and propose potential mechanisms of this effect at lower node length and inter-node length values.