77
solution.
3.3.2.2 Branch-Ortho: Branchwise Orthogonalization
To excise these phantom spikes, we simulate the full model with a suprathreshold
stimulus applied at a location that will allow a spike to propagate throughout the
whole cell; this location should be the soma, a junction point, or the distal end of a
leaf in order to prevent two spikes from occurring on the same branch. Let us denote
the resulting set of snapshots as <S. To isolate the dynamics of branch j we create a
local set £j which is initially the same as <S. The snapshots in £j are then modified by
setting to rest all the values of elements that do not belong to branch j. The final set of
snapshots <S is then the union of the local sets. Hence the snapshots are “orthogonal”
in the sense that only one branch is active in each snapshot. While intuitive, this
technique is a bit naive because it completely isolates branches, effectively throwing
away information about the coupling that occurs at junctions.
An improvement of this method can partially recover this coupling information
by not just generating snapshots of isolated branches, but of connected branches that
form continuous routes throughout the dendritic tree. A route R is defined as a set
of branches in which
• at most one branch is present at each depth in the dendritic tree
• the branch at depth j — 1 is the parent of the branch at depth j.
Hence the dimension of a route, dim(R), is equal to the number of branches it contains,