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### Axial currents at branch points

Posted: Thu May 06, 2021 5:52 am
Hello,

I've been going through NEURON documentation and source code but the handling of axial current and the notion of breakpoint at branch points (mentionned in post "recording axial current") still remain really confusing for me.

Is there any difference between the handling of the axial current flowing between the segments of a single section and the one flowing between segments of two differents sections ?

Since in the Mathematical Basis of neuron it is said that in the particular case of a section with segments of equal size, the equation for axial current corresponds to the difference of potential with neighbors segments multiplied by the coefficient d/(4*ra*dx²) -> (in units of S/cm² if multiplied by 10^4) , I thought that it might be the equation used for currents between segments in a section. However when looking in the source code it looks like all coefficients for axial currents are based the on the calculation of Ri,j and the area of parent/child node (to convert in density of current).

### Re: Axial currents at branch points

Posted: Thu May 06, 2021 11:42 am
the notion of breakpoint at branch points (mentionned in post "recording axial current") still remain really confusing for me
To me the most confusing thing is that the word "breakpoint" doesn't appear anywhere in the discussion thread titled recording axial current viewtopic.php?f=15&t=2942. Or maybe you're referring to a different discussion thread?
Is there any difference between the handling of the axial current flowing between the segments of a single section and the one flowing between segments of two differents sections ?
Kirchhoff's current and voltage laws apply to both cases.
Since in the Mathematical Basis of neuron it is said that
Can you please provide a more specific citation (title of source, page number, equation number) so I can be sure that I am looking at the same description that you are seeing?

### Re: Axial currents at branch points

Posted: Fri May 07, 2021 8:42 am
Sorry for the mistake I mixep up breakpoint and "breaks down at branch points". It's the notion of axial current breaking down at branch points that I didn't really understand and more specifically what are the changes on the current.

The equations I was referring to are the ones from the section "3.1 The cable equation" in the Mathemical Basis 1. I was mainly talking about the Equation (2) and the two following equations that come from that latter.

### Re: Axial currents at branch points

Posted: Fri May 07, 2021 12:02 pm
It's the notion of axial current breaking down at branch points that I didn't really understand
The originator of the discussion thread to which you refer was "trying to measure the axial current between every segment in an object." Presumably that person's aim was to determine the current that flows between adjacent segments. In an unbranched string of sections the axial current that exits the last segment of the parent section must equal the axial current that enters the first segment of the child section. But at a branch point there will be two or more children. This means the notion of "axial current between adjacent segments" is no longer useful because the axial current that exits the last segment of the parent section will in general NOT be equal to the axial current that enters the first segment of any of the children.
The equations I was referring to are the ones from the section "3.1 The cable equation" in the Mathemical Basis
I'm sorry. I am unaware of any NEURON-related publication with the title "The Mathematical Basis." Could you please be more specific about where you found it?

### Re: Axial currents at branch points

Posted: Mon May 10, 2021 5:56 am
Thank you for the explanation it helped.

The related documentaion is the one at the following link : https://www.neuron.yale.edu/neuron/stat ... /nc3p1.htm, sorry for the inconvenience.