### Instabilities in ephaptic coupling

Posted:

**Wed May 31, 2017 8:11 am**Dear all,

I am simulating ephaptic coupling between two unmyelinated axons (the simplest case I could use) by calculating the external potential from the membrane currents at each time step, with

phi(x) = (1/4*pi*sigma) * sum[over the nodes](I(node) / dist(x, node)), (so, the typical for LFPs if I am not mistaken)

and using this potential as a stimulation for the axons. (Too obvious to be said, but with this formula 1st axon's currents stimulate the 2nd axon and viceversa).

I stimulate only the 1st axon with a current injection in the middle. So far, so good.

The problem comes when I use a resistive medium (e.g. sigma = 10^-3 S/m). In many cases the simulation is unstable. I have some figures showing the instabilities in this Dropbox folder:

https://www.dropbox.com/sh/0g2ywxga32o0 ... -sWJa?dl=0

Instabilities appear at the current injection point and in the boundaries, so I guessed that the instabilities were due to very rapid variations in x of phi. Then I applied a low-pass filter (Butterworth) to phi(x) (x domain instead of time domain... just to clarify) to eliminate high spatial frequencies. But almost no matter what the cut-off frequency is, I always get instabilities (cases for different filters are also shown in the figures). Decreasing the frequency only delays the apparison of the instability. I have observed that when applying the filter, unstable growth appears in the left boundary and propagates to the right. It looks like some cumulative effect of phi on the membranes which overrides any ioninc channels.

It is also worh noting that some components of the instabilities (I think it is the high-frequency ones) change sign at every time step.

Maybe by having a look may you see what I am doing wrong? If you could give me a clue on that, it would be much appreciated.

Note: I would need to use this approach for ephaptic coupling instead of the linear model you use in your examples, if at all possible. I saw that in a post in this thread*1 you mentioned the possibility of instabilities if coupling NEURON to a Poison solver. Is this one of the instabilities you meant?

*1: viewtopic.php?f=12&t=3199&p=13395&hilit=ephaptic#p13395

All the best,

Miguel

I am simulating ephaptic coupling between two unmyelinated axons (the simplest case I could use) by calculating the external potential from the membrane currents at each time step, with

phi(x) = (1/4*pi*sigma) * sum[over the nodes](I(node) / dist(x, node)), (so, the typical for LFPs if I am not mistaken)

and using this potential as a stimulation for the axons. (Too obvious to be said, but with this formula 1st axon's currents stimulate the 2nd axon and viceversa).

I stimulate only the 1st axon with a current injection in the middle. So far, so good.

The problem comes when I use a resistive medium (e.g. sigma = 10^-3 S/m). In many cases the simulation is unstable. I have some figures showing the instabilities in this Dropbox folder:

https://www.dropbox.com/sh/0g2ywxga32o0 ... -sWJa?dl=0

Instabilities appear at the current injection point and in the boundaries, so I guessed that the instabilities were due to very rapid variations in x of phi. Then I applied a low-pass filter (Butterworth) to phi(x) (x domain instead of time domain... just to clarify) to eliminate high spatial frequencies. But almost no matter what the cut-off frequency is, I always get instabilities (cases for different filters are also shown in the figures). Decreasing the frequency only delays the apparison of the instability. I have observed that when applying the filter, unstable growth appears in the left boundary and propagates to the right. It looks like some cumulative effect of phi on the membranes which overrides any ioninc channels.

It is also worh noting that some components of the instabilities (I think it is the high-frequency ones) change sign at every time step.

Maybe by having a look may you see what I am doing wrong? If you could give me a clue on that, it would be much appreciated.

Note: I would need to use this approach for ephaptic coupling instead of the linear model you use in your examples, if at all possible. I saw that in a post in this thread*1 you mentioned the possibility of instabilities if coupling NEURON to a Poison solver. Is this one of the instabilities you meant?

*1: viewtopic.php?f=12&t=3199&p=13395&hilit=ephaptic#p13395

All the best,

Miguel