Date of Award

12-2025

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Committee Chair(s)

Zilong Song (Committee Chair)

Committee

Zilong Song

Committee

Erin Beckman

Committee

Luis Gordillo

Abstract

Neurons in humans and other species transmit information by sending electric signals via axons. This process relies on the generation and propagation of action potentials—rapid changes in the membrane potential of the axon. Understanding the mechanisms of action potentials, including how they are generated and influenced by the axon geometry and material parameters, is crucial for gaining insight into neurological diseases such as Alzheimer’s and Multiple Sclerosis (diseases highly correlated to demyelination). In this work, we review and summarize mathematical models for signal transmission–including the classical Hodgkin-Huxley model, the Single Cable (SC) model, and the Double Cable (DC) model. We adopt the finite-difference method to numerically solve these models. We focus on the differences between the SC and DC models based on existing parameters for a rat axon, e.g., the conduction velocity, the voltage profiles, the signal decay etc. We also apply the model with modified parameters based on semiconductor nanomembrane tubes, used to resemble a natural myelin sheath. Finally, we provide a parameter sensitivity analysis of other key parameters (particularly the myelin capacitance and paranodal resistance) that affect the conduction velocity and voltage dynamics of myelinated axons.

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