114
Now we discretize the neuron in space, which yields Ns and Nw compartments in
the strong and weak parts, respectively, as well as the transition compartment, for
a total of N = Ns + Nw + 1 compartments. This implies that the strong and weak
voltage vectors are
vs∈Rjv∙s, v,λ, ∈ R∕v,".
To construct the coupled “Hines” matrix properly we will need the local indices
of the compartments adjacent to the transition compartment. These local indices are
denoted by Nw and Np for the adjacent strong and weak compartments, respectively.
Using these local indices, the voltage of the adjacent weak compartment is denoted
by v^w, and the voltage of the adjacent strong compartment is denoted by vfr. The
voltage of the transition compartment is denoted as before as vʃ.
Discretizing (4.19) yields
where Nx is the compartment length for branch bp- Using the continuity of potential
condition of (4.18) we solve for vτ:
v^τ — vτ
Nx
vτ~vww'
Nx
vτ = V⅛∙ + ⅛^4
τ 2 s 2 w
Now we are ready to apply the generalized cable equation’s second-derivative oper-
ator. We can use our previously derived results (see Appendix A) for all compartments