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 onedimensional 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.
With Regards
Gayatri P K
Equation that models the entire tree

 Site Admin
 Posts: 5303
 Joined: Wed May 18, 2005 4:50 pm
 Location: Yale University School of Medicine
 Contact:
Re: Equation that models the entire tree
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.