some questions about extracellular stimulation and recording

[luckychild]

Hi all,
I have just begun to learn to use NEURON and read the Extracellular Stimulation and Recording program downloaded from http://www.neuron.yale.edu/ftp/ted/neur ... nd_rec.zip
. Now I have six very primary questions:
1 nesg is decided by d_lambda rule. In other words nesg=int((L/(0.1*lambda_f(100))+0.9)/2)*2+1. Could you please tell me how to derive this equation?
2 lambda_f=(1/2)square(d/(pi*f*Ra*Cm)). Where does this equation come from?
3 In calcrxc.hoc, the resistance outside the sphere electrode with radius r0 can be calculated as follows.

A conductive sphere of radius r0 is suspended in an infinite
volume of solution that has resistivity rho [ohm cm]. Ignoring
electrochemical effects at the electrode|solution interface,
what is the resistance between the surface of the sphere and
an infinitely distant ground electrode?

The surface area of a sphere with radius r is 4 PI r^2.
The resistance of a shell with thickness dr is
rho dr / 4 PI r^2
and the resistance is therefore
inf
INTEGRAL rho dr / 4 PI r^2
r0
inf
= - rho / 4 PI r | = rho / 4 PI r0
r0

Therefore the resistance between r1 and r0 should be

r1
INTEGRAL rho dr / (4 PI r^2)
r0
r1
=( - rho / 4 PI r |) = -rho / (4 PI r1)+rho /( 4 PI r0)
r0
where r1 is the distance from the center of the electrode.
so,why

to a first approximation, a monopolar stimulating electrode
that delivers current I produces a field in which potential V
is given by
V = I rho / (4 PI r)
where r is the distance from the center of the electrode

4 The statement “for(x) ……â€

[ted]

You actually read the notes in the code, thought about them, and asked quite appropriate
questions. Excellent!

1 nesg is decided by d_lambda rule. In other words nesg=int((L/(0.1*lambda_f(100))+0.9)/2)*2+1. Could you please tell me how to derive this equation?

It is just a formula that finds the smallest odd number nseg such that L/nseg is <=
0.1 * AC length constant at 100 Hz.

2 lambda_f=(1/2)square(d/(pi*f*Ra*Cm)). Where does this equation come from?

Correction: the formula is
lambda_f=(1/2)sqrt(d/(pi*f*Ra*Cm))
where sqrt means "square root".
This comes straight from the solution to the cable equation. The formula is presented in
Hines, M.L. and Carnevale, N.T. NEURON: a tool for neuroscientists.
The Neuroscientist 7:123-135, 2001. Preprint available from
http://www.neuron.yale.edu/neuron/paper ... e_rev1.pdf
The derivation is presented here:
http://www.neuron.yale.edu/neuron/paper ... a_rev2.pdf

3 In calcrxc.hoc, the resistance outside the sphere electrode with radius r0

rho / (4 PI r)
is the resistance that you would measure if you placed a spherical electrode of radius r
in an infinite conductive medium with resistivity rho, and attached your ohmmeter's
electrodes to the sphere and the "container of the infinite conductive medium." Therefore
I * rho / (4 PI r) is the voltage drop that would be induced by attaching one terminal of
a current source I to the spherical electrode, and attaching the other terminal to the
"container of the infinite conductive medium."

4 The statement “for(x) ……â€

[luckychild]

Thank you very much. Your answer is very useful for my farther learning.
However there is still confusing about the meaning about variable r
As you mentioned

rho / (4 PI r)
is the resistance that you would measure if you placed a spherical electrode of radius r
in an infinite conductive medium with resistivity rho, and attached your ohmmeter's
electrodes to the sphere and the "container of the infinite conductive medium."

So r is the radius of the spherical electrode.
However, in the note of calcrxc.hoc,

V = I rho / 4 PI r
where r is the distance from the center of the electrode.

therefore

The extracellular potential at location x produced by electrode
1 is
V1 = I rho / 4 PI r1
where r1 is the distance from electrode 1 to x. This distance is
r1 = sqrt( ((x-0.5)*L) + 0.5*b)^2 + c^2 )

and

Likewise the potential at x produced by electrode 2 is
V2 = -I rho / 4 PI r2
where r2 is the distance from electrode 2 to x, i.e.
r2 = sqrt( ((x-0.5)*L) - 0.5*b)^2 + c^2 )

Here, r r1 and r2 are the distances from electrode to x. and the radius of electrode does not appear.
I suppose the distances is not equal to the radius of electrode.
what do you think?
thank you!

[ted]

in the note of calcrxc.hoc,

in the statement

where r1 is the distance from electrode 1 to x

r1 is to be understood as the distance from the center of the electrode to x

[luckychild]

rho / (4 PI r)
is the resistance that you would measure if you placed a spherical electrode of radius r in an infinite conductive medium with resistivity rho, and attached your ohmmeter's electrodes to the sphere and he "container of the infinite conductive medium."

Thus, since rho / (4 PI r1) is the resistance between an infinite electrode and a spherical electrode of radius r1,

r1 is to be understood as the distance from the center of the electrode to x

the question is, according to the note of calcrxc.hoc , rho / (4 PI r1) is

the transfer resistances between bipolar extracellular timulating|recording electrode(s) and a model neuron .

but r1 is still the distance between the center of the electrode and a model neuron at x .
Thank you for your patient explaination again!

[luckychild]

I have made a misunderstanding about the meaning of the “transfer resistanceâ€

[ted]

You're getting this all mixed up.

"Transfer resistance between A and B" is not the "resistance between A and B",
nor is it the resistance from either A or B to ground.

It is the voltage that is produced at B by injecting a unit current at A.
It is also the voltage that is produced at A by injecting a unit current at B.

Transfer resistance can be used to describe the coupling between two points in a
conductive medium as long as the conductive medium obeys Ohm's law, i.e. the
relationship beween applied current is a simple instantaneous proportionality.
Most studies of field effects assume that the medium is ohmic.

If the medium has capacitive or inductive properties, it may be necessary to take those
into account, and one then describes the coupling between A and B in terms of a
transfer impedance.

[luckychild]

I get it!　Thank you very much!