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### Decompose LFP into components

Posted: **Tue Sep 10, 2019 7:16 pm**

by **breakwave922**

I have a network model consisting of thousands of neurons, and I calculated LFP using 'xtra' . In this way, the calculation of LFP is based on the recording of i_membrane (transmembrane current). But now, I want to decompose the LFP into components reflecting different types of sources. For instance, I want to know the contribution of opto-channel current that I built on my cell to the LFP. Is there any method that I can calculate this?

What I plan to do is, record certain channel current, and replace the transmembrane currents with it in the equation for calculating LFP, and the result will be the contribution to LFP from this current source. Is this the correct way to do?

Thanks in advance.

### Re: Decompose LFP into components

Posted: **Wed Sep 11, 2019 12:07 pm**

by **ted**

Assuming that one or more cells are embedded in a conductive medium that is linear, the potential Vi at any point i in the medium is

where the index j ranges over all compartments in the model, Im_j is the total (i.e. ionic + capacitive) transmembrane current for compartment j, Zx_j is the transfer impedance between i and j. Note that Vi and Im_j are the Fourier (or Laplace) transforms of the corresponding time domain variables vi_j and im_j.

If the medium is nondispersive (can be treated as purely resistive), the formula can be simplified to

where Rx_j is the transfer resistance between i and j.

For any particular component x of membrane current it is possible to calculate the contribution of that component to vi

### Re: Decompose LFP into components

Posted: **Thu Sep 12, 2019 12:24 pm**

by **breakwave922**

Thanks, Ted. I guess it is clearer to me now.

I'm wondering, if the channel current is implemented as point process mechanism, I can simply use the distance between the position of the channel and the electrode to calculate contributed LFP. However, if the channel current is implemented as distributed(density) mechanism, how can I calculate the distance to the electrode to calculate contributed LFP, as the channel is distributed all over the compartment.

### Re: Decompose LFP into components

Posted: **Fri Sep 13, 2019 10:50 am**

by **ted**

At large distances (more than about 10 x segment length) it is reasonable to treat the segment as a point source of current located at the segment center. A more fastidious approach is to treat each segment as a line source with the same length as the segment, centered at the location of the segment center, and oriented parallel to the line that joins the segment ends. Segment orientation and center location can be calculated by treating the section's pt3d data as piecewise linear functions of range. The mathematical basis of the line source approximation has been published more than once, e.g. ModelDB entry 84589.

### Re: Decompose LFP into components

Posted: **Fri Sep 13, 2019 6:27 pm**

by **breakwave922**

Thanks Ted.

Another question I forgot to discuss with you was, if I calculate single channel current's (implemented as point-process) contribution to LFP, according to what you suggested, I can obtain it by using this channel's current weighted it by distance and medium conductivity. I'm wondering in this way, do I only consider the channel current flow into the cell? But how about the current flow out of the cell thru passive channel? If I only consider the current flow in at certain point to calculate it's contribution to LFP, is it correct?

### Re: Decompose LFP into components

Posted: **Sat Sep 14, 2019 11:17 am**

by **ted**

breakwave922 wrote: ↑Fri Sep 13, 2019 6:27 pm

if I calculate single channel current's (implemented as point-process) contribution to LFP

As a point process? What does point process have to do with anything? Most voltage-gated channels are implemented as density mechanisms. The currents they generate have units of mA/cm2 and must be multiplied by segment area and a scale factor to convert to mA or nA.

do I only consider the channel current flow into the cell? But how about the current flow out of the cell thru passive channel?

Look, if you're interested in the contribution of some channel X to LFP, then calculate the LFP that would be produced by the current that flows through the X channel, regardless of whether that current flows in or out of the cell. If the cell also has some other channel Y, then the current that flows through channel Y is the current that flows through channel Y, and it makes its own, separate contribution to the LFP.