"HARRY R. ERWIN" <herwin at osf1.gmu.edu> writes:
> Spent the weekend working through Koch and Segev. Didn't help
> that much for the presynaptic side. Mascagni's chapter on
> numerical methods was extremely interesting--it confirmed some
> suspicions I had about the stiffness of compartmental models.
> Unfortunately, compartmental models result in extremely large
> connectivity matrices--the one I'm using in a massively
> simplified model of a piece of the olfactory bulb is
> 608x608--pretty much ruling out implicit methods. To avoid
> stability problems with explicit schemes, I have to reduce both
> time stepsize and spatial stepsize, driving me towards even
> larger connectivity matrices. Now I see why Freeman uses
> Katchalsky Networks.
Fortunately for all of us doing compartmental modeling, Michael Hines
worked out, a few years back, an efficient implicit integration method
for tree structures. It's stable and first order in the number of
compartments -- altogether very nice. It is incorporated in his
Neuron simulator and several other biophysically realistic simulators,
and is described in the paper, "Efficient computation of branched
nerve equations", M. Hines, Int J Bio-Med Comp 15:69-76 (1984).
In the words of Christof Koch: "Euler is evil!"