Report cable

Overview

Begin with a brief history of the cable equation, starting with Lord Kelvin, whose

interest was on telegraphs, not neurons, then the idea of connecting it to the heat

equation by Hoorweg, then extending it to neuronal transmission by Hermann, Cre-

mer, Cole, Hodgkin, and several others. Comment on how experimental data helped

assess the pros and cons of the cable theory. What you find in Wikipedia or other

online resources may be inspirational but will not suffice.

Write your derivation of the mathematical form of the cable equation. Again, you can

use any aids that you wish, but ultimately what you turn in as your writing should

be your own elaboration. In the era of A.I., personal elaboration is more important

than ever.

Using either the Matlab code that you can find in the notes in Canvas, or any other

solver that you may wish to implement (or if you download it, cite the source) solve

numerically the cable equation. The purpose of doing so is to deepen your under-

standing of the model. The instructions on what to do are in Exercise 2 and 3 at the

end of Chapter 2 of the book draft (page 28).

Use the results of your simulations in the previous part to explain the shortcomings of

the cable equation as a model for the transmission of signal in the brain. In this last

part you may include references to considerations and experiments that eventually

led to the Hodgkin-Huxley more realistic model of action potential transmission.

IMPORTANT: You can use any sources that you wish, as long as you cite them and, more

importantly, what you write is your own elaboration that you can explain in detail