The name is absent



113

With this partition in place, it is necessary to reorder the branches in the strong
and weak parts. This means that we assign local branch indices according to decreas-
ing dendritic depth with respect to a specific reference point. For the strong part
the soma is the reference point, and for the weak system it is the transition point
xτ- This reordering allows for construction of a coupled “Hines” matrix for which
Gaussian Elimination can efficiently be used. As a consequence of the reordering, the
transition point
lies at the proximal end of branch βw = Bw in the local ordering of
the weak part, but
lies at the distal end of branch βs ∈ [1, Bs]. Thus the absolute
voltages for the strong and weak parts of branch
in the local indexing are denoted
by
s,s and w,w> and the radii of these components are denoted by s,s and apw>w.

The boundary conditions, initial conditions, and soma conditions for the strong-
weak model are the same as those given in (2.19)-(2.26), but we must include condi-
tions at the transition point to account for the strong-weak coupling. The voltage at
the transition point
is given by

Vτ(t) = Vρsts(xτ,t) = Vρwtiυ(xτ,t), Vτ(t) = Vτ(t)-Vt- (4.18)

We assume that the dendritic radii are not discontinuous in space, and thus continuity
of current at the transition point requires

xs,s(xτ,t) = ∂xυ0wrw(xτ,t).

(4.19)




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