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help with distributed HH simulation

Ulf Andrick ura at strix.cluster.sub.org
Sun Sep 12 19:12:51 EST 1993

In <1993Sep8.200728.16169 at news.arc.nasa.gov> Bruce Parnas (brp at neuron.arc.nasa.gov) writes:

: As the subject says, I'm working on a distributed HH simulation.  Multi-compartment,
: each one HH in nature (I'm not fond of the HH model, mind you, but I have to do this).

: Here's the problem:

: I'm coupling compartments passively, i.e. I(k) = {v(k-1) - v(k+1)}/axial_res.

I think it's better to take the difference between neighbouring
compartments. Otherwise the effective axial resistence is only half of
what one would expect. In a clear-cut circuit, the axial resistence is a
resistor between the points where you measure/calculate your potentials.

: If I compute the HH model per unit area (the way the parameters are given in the
: original paper), the input between compartments is too small to cause propagation.

I think you shouldn't do that. Remember that an axon is a tube. A long 
thin tube and a wide short one have different electrical properties, 
though their surface areas might be equal. If you increase the 
length linearly, the leakage and axial resitences and the capacity of 
a compartment will grow linearly as well. But if you change the 
diameter, then you have to consider that the axial resistence is 
inversely proportional to the square of the diameter, while the other 
parameters still increase proportionally.

So, you should determine

- what axon length you want to simulate
- what the axon diameter is
- how the single parameters are related to the geometry
- and how many compartments you have

and set the parameters of the compartments appropriately.

This way, it should be possible to tailor a reasonable simulation if
your algorithms work properly.

: If I normalize to the area, then Cm is ver small, 1/Cm is large and the input from
: neighboring compartments is too large and the thing goes unstable, even for very
: small timesteps.

: In the first case, it works ok if i reduce axial_res by about 10,000
: In the second case, I have to increase it by about 3000.

: Neither of these scale factors is justifiable.  

I think it's not justifiable to change the axial resistence alone
(at least if you still want to be close to the squid axon).
Keep the geometry of the real object in mind.

: Anybody have any suggestions for what might be going on here?  Or a different
: way of coupling the compartments?

A different way of coupling would be a sacrilege to the HH 
model :-)

: btw, i've run this code for a point HH model, and it works just fine. It's the
: compartmental coupling that's causing the problems here.

Ulf Andrick
ura at strix.cluster.sub.org

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