## Reverse Recruitment problem, i_membrane problems?

Anything that doesn't fit elsewhere.
JimH
Posts: 54
Joined: Tue Apr 10, 2007 3:36 pm
Location: Duke University

### Reverse Recruitment problem, i_membrane problems?

Hello all,

I'm trying to reproduce a common observation that a larger neuron tends to get activated at a lower current threshold, via extracellular stimulation, than a smaller neuron. Unfortunately I am working with magical neurons that the opposite seems to be the case. Doubting my results and magical neuron, I'm stuck trying to figure out why I am observing the difference from expected results.

Working through the logic, it seems that for a given extracellular current, the the applied extracellular voltage would be the same regardless of the diameter of the neurons (assuming the membrane potential on the surface of a small ring patch is equal to the potential at the center of that ring). In this regard, it seems that it should be the change in resistance by changing diameter that would cause different current densities and thus different levels of excitability for a given extracellular potential.

Along these same lines, if a neuron is more likely to be excited at a given level, I would think the current density would need to be higher at that level than the current density of a less excitable neuron. When examining i_membrane for a completely passive neuron this doesn't seem to be the case, the larger diameter neuron has a smaller current density (except for at stimulus onset due to capacitive currents).

Thoughts on why the current density might be lower for a larger neuron? How exactly is i_membrane calculated, or rather the component that comes from the the extracellular potential? It would seem to be dependent on the difference in extracellular potential between a node of interest and neighboring nodes, and the resistance in between. As the diameter increases this would cause a decrease in axial resistance, and an increase in "injected current" from the applied voltage.

Thanks.

JimH
Posts: 54
Joined: Tue Apr 10, 2007 3:36 pm
Location: Duke University
A small problem that I found, which if you read the documentation it mentions, is that for x = 0 and x = 1, the nodes have no area. I've changed my stimulation code so that when I am going through a section and for every x in that section, I have the following code:

for (x) {
if(x != 0 && x != 1){
//run code that applies extracellular stimulation
}
}

I'm not sure yet that this fixes my problem but it does allow me now to record from i_membrane at every point that I apply stimulation (this is also mentioned in the extracellular documentation), and my recorded applied extracellular potential now matches that which I calculate.

ted
Posts: 5770
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:
for (x, 0) stmt
evaluates stmt at all nodes except 0 and 1.
See documentation of "for" in the Programmer's Reference,
specifically the
for (var, expr) stmt
form
http://www.neuron.yale.edu/neuron/stati ... r.html#for

Extracellular stimulation has been a topic of much experimental and theoretical literature, a
good deal of which is unfortunately not read or referenced in this brave new world of
digital media. Here's an interesting and pertinent book that can be had for the effort of
Bioelectromagnetism by Malmivuo and Plonsey (1993)
http://butler.cc.tut.fi/~malmivuo/bem/bembook/
or simply browsed on line--e.g. the particularly relevant chapter 21.
The "Info" link at their URL even includes a list of errata.

JimH
Posts: 54
Joined: Tue Apr 10, 2007 3:36 pm
Location: Duke University
I had been trying to implement some of the features of McNeal 1976, the first extracellular stimulation paper in the field.

My model was occasionally suggesting inverse recruitment (larger fibers getting recruited first), although the majority of the time smaller diameter fibers had lower thresholds. The thresholds I had computed were also much, much lower than what the McNeal paper, and others had published (not saying that they were necessarily the most accurate, but the same model implemented in Neuron was not yielding the same results). I switched to specifying equivalent intracellular currents and the model now shows inverse recruitment and values that are close to the McNeal paper.

I've attached some code, as it is very likely that I had made a mistake in model implementation when using the extracellular mechanism (this is the old code). As I mentioned in a previous post, I recorded the extracellular potential and it matched my expectation.

Code: Select all

``````	zL = 0 //z length
segs = 0
sect = 0
forsec axon{
sect = sect + 1
insert extracellular
for (x) {
if(x != 0 && x != 1){
s = new Vector(4,1)
xN = rP*cos(thetaP)
yN = rP*sin(thetaP)
zN = zP + x*L + zL //zP => starting location of axon
dist = (xN^2+yN^2+zN^2)^.5
distVec.x[segs] = dist
areaVec.x[segs] = area(x)*1e-8
LVec.x[segs] = L
R = rho_ext/(4*PI*dist)
vCalcVec.x[segs] = ivec.x*R/1000
s.x = ivec.x*R/1000
s.x = ivec.x*R/1000
s.x = ivec.x*R/1000
s.x = ivec.x*R/1000
s.play(&e_extracellular(x),tvec)
stims.append(s)
tempRecVec = new Vector()
memIVec = new Vector()
if(recVm == 1){
tempRecVec.record(&v(x))		//Record potential across membrane
}else{
tempRecVec.record(&vext(x))	//Record extracellular applied voltage
}
memIVec.record(&i_membrane(x))
IList.append(memIVec)
rec.append(tempRecVec)
segs = segs+1
}
}
zL = zL + L
}``````

ted