I am computer science student. I am working on differential equations in neuroscience and came across 1984 paper by Hines on "Efficient computation of branched nerve equations" which describes the branched neuron equation that boils down to the "Hines" matrix. The paper gives the equation for one-dimensional cable, which if I understand correctly is for just one branch of a tree. The equation is
1/(2𝚷a) * 𝜕/𝜕x( ( 𝚷a2 /Ra ) *(𝜕V/𝜕x) ) = Cm 𝜕V/𝜕t + IHH
I am trying to find out the equation that models the entire tree. Also, if possible, could someone tell me where to find the finite difference implicit discretization of this equation along with some sample Initial and Boundary condition values and the constants used to try out this equation solution properly.
Gayatri P K
The basics of how to develop, test, and use models.
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Your answer awaits you in the scientific literature of the 1970s and early 1980s. Rall was an author on some of them, but not all. Tell us what you find.