recording total synaptic currents

[bhalterm]

I am trying to produce a synthetic EEG from my model using a formula from (page 1207):
P. Erdi, Z. Huhn, T. Kiss. Hippocampal theta rhythms from a computational perspective:
Code generation, mood regulation and navigation. Neural Networks, 18(9):1202–1211, 2005.

I am running into a problem: first I tried writing a method to sum the synaptic currents of all cells, and then using Vector.record to save the result of the method at each time step. I got an error presumably because Vector.record expects a pointer to a single variable. Then I tried making individual vectors to record each current of each synapse, which worked with a small number of synapses, but runs out of memory in the full model. Is there a way to get the sum of the currents into a single variable at each time step without having to, say, modify fadvance() (which frightens me)?

I also read in the "record current" topic here that mentions using i_membrane of the extracellular mechanism. Would that value include capacitive currents and active membrane currents, as well as synaptic currents? I'll have to ask the people I'm working with if that would be a problem. The extracellular mechanism is way outside my NEURON comfort zone. Is there a gentler introduction to it than the programmer's reference? Does inserting extracellular alter the behavior of the cell, or just provide more variables to record?

[ted]

I am trying to produce a synthetic EEG from my model using a formula

For any situation in which the conductive medium can be regarded as linear, the extracellular potential at any point is the weighted sum of the transmembrane currents of all "neural compartments."

The weights are the transfer impedances between the center of each "neural compartment" and the recording site. If the conductive medium is purely resistive, the weights are transfer resistances. The equation in column 1 of page 1207 of Erdi et al. is valid if (1) the conductivity of the medium is uniform and isotropic (independent of the orientation of current flow in space), and (2) the signal sources are "far away from the boundaries of the medium."

Note that any cell represented as a single compartment will have no effect on the extracellular field.

I am running into a problem: first I tried writing a method to sum the synaptic currents

Just the synaptic currents? There is no situation in which that would produce a valid result. The currents must be the total membrane current in each compartment.

Is there a gentler introduction to it than the programmer's reference?

I'm not aware of one.

Does inserting extracellular alter the behavior of the cell

Only if you change extracellular's parameters from their default values.

There is no need to reinvent the wheel. This has all been worked out already--see
Extracellular stimulation and recording
viewtopic.php?f=28&t=168
and pick up
extracellular_stim_and_rec.zip
which contains two working examples that involve a single model cell. With only a bit of effort that can be generalized to deal with multiple cells.

[bhalterm]

Thanks, this is VERY helpful!
I hope this isn't a stupid question, but why doesn't a single compartment cell affect the extracellular field? Is it an implementation issue, or is there a deeper conceptual reason?

[ted]

Thanks, this is VERY helpful!
I hope this isn't a stupid question, but why doesn't a single compartment cell affect the extracellular field? Is it an implementation issue, or is there a deeper conceptual reason?

It is not a stupid question. It might be a good question for a qualifying exam, perhaps even on someone doing a doctoral defense. Ought to be easy for an engineer, physicist, or biophysicist to answer.

There is a deep reason, which can be expressed simply (as a direct consequence of conservation of current) or with mathematical elegance (the divergence theorem).

Expressed simply: The only way to produce an electrical signal in a conductive medium is for current to flow through that medium. For current to flow through the medium there must be a current source and a current sink, and these must be separated from each other by some nonzero distance. Draw the equivalent circuit of a single compartment model cell as a capacitor in parallel with a "black box," where the latter represents the net ionic membrane current. Label the current through the capacitor as Ic and the current through the black box as Ii. Kirchhoff's current law ("conservation of current") requires that Ic + Ii = 0, so if Ic is directed outward (current source), Ii must be directed inward (current sink).

"OK, so if net ionic current is nonzero, then we have a current source and a current sink, and there should be some effect on extracellular potential."

Yes, if you're talking about a physical cell, with discrete ionic channels, but only in the very near vicinity of each open channel (source and sink are separated because capacitive current flow is distributed over the surface more or less evenly, whereas ionic current flow is restricted to the open channels).

But for a single compartment model, the external ends of the capacitor and black box are (conceptually) both attached to the same point, so there can be no effect on extracellular potential. You need at least two compartments, so that each compartment has its own extracellular node (the point to which its capacitive and ionic circuit elements are connected). The two extracellular nodes must be spatially separated from each other, and there must be a nonzero axial current between the two compartments' internal nodes (the points at which the internal ends of their capacitive and ionic circuit elements are connected).

Expressed with mathematical elegance: start by reading http://en.wikipedia.org/wiki/Divergence_theorem