# Residual current

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Hello everyone

I'm working on a project regarding cochlear implants and tissue conductivity.

For this project, I'd like to express how much current reaches a certain tissue when passing different sorts of other tissues.

Assume an initial current $$I_0$$ passing through $$n$$ different tissues with resistivity $$R_n$$. Assume each tissue has the same volume.

Now, I suppose each time some of the current will reside in the tissue, acting as some sort of capacitor, and some will be passed onto the next tissue? I also assume that current doesn't travel in one direction in a tissue, but is always equally distributed along the tissue volume?

For the sake of having an example, assume an electrode emits a voltage of $$1.0\text{ V}$$, which passes a first tissue with resistivity of $$1\text{ }\Omega\text{m}$$, a second tissue with resistivity of $$0.5\text{ }\Omega\text{m}$$, and a third tissue with resistivity of $$2.0\text{ }\Omega\text{m}$$.

How much current could be passed on theoretically to a tissue further away from the third tissue?

Thanks guys!

Calatinus

Edited by Calatinus
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40 minutes ago, Calatinus said:

Hello everyone

I'm working on a project regarding cochlear implants and tissue conductivity.

For this project, I'd like to express how much current reaches a certain tissue when passing different sorts of other tissues.

Assume an initial current I0 passing through n different tissues with resistivity Rn . Assume each tissue has the same volume.

Now, I suppose each time some of the current will reside in the tissue, acting as some sort of capacitor, and some will be passed onto the next tissue? I also assume that current doesn't travel in one direction in a tissue, but is always equally distributed along the tissue volume?

For the sake of having an example, assume an electrode emits a voltage of 1.0 V , which passes a first tissue with resistivity of 1 Ωm , a second tissue with resistivity of 0.5 Ωm , and a third tissue with resistivity of 2.0 Ωm .

How much current could be passed on theoretically to a tissue further away from the third tissue?

Thanks guys!

Calatinus

You don't say what is causing this current to flow. Do you have two electrodes, and the current flows between the two? If that's the case then if you consider blocks of the intervening tissue, they will be in series and the same current will flow through them all.

Current doesn't reside in conductors. Current is a flow of electric charge, caused by a voltage gradient. A capacitor stores charge, not current.

Are you considering a direct current or an alternating current? Capacitance of a conductor becomes an issue when there is alternating current.

Perhaps if you can provide more details of the scenario it will be easier to make constructive comments.

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4 minutes ago, exchemist said:

You don't say what is causing this current to flow. Do you have two electrodes, and the current flows between the two? If that's the case then if you consider blocks of the intervening tissue, they will be in series and the same current will flow through them all.

Current doesn't reside in conductors. Current is a flow of electric charge, caused by a voltage gradient. A capacitor stores charge, not current.

Are you considering a direct current or an alternating current? Capacitance of a conductor becomes an issue when there is alternating current.

Perhaps if you can provide more details of the scenario it will be easier to make constructive comments.

There are two possible scenarios: monopolar stimulation, where current flows between an electrode in one medium, and an external ground electrode; and bipolar stimulation, where current flows between an electrode in one medium, and another electrode within the same medium.

Cochlear implant electrode stimulations are biphasic, with an anodic phase, and a cathodic phase, as to keep the net tissue charge at 0. So I suppose alternating current?

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31 minutes ago, Calatinus said:

There are two possible scenarios: monopolar stimulation, where current flows between an electrode in one medium, and an external ground electrode; and bipolar stimulation, where current flows between an electrode in one medium, and another electrode within the same medium.

Cochlear implant electrode stimulations are biphasic, with an anodic phase, and a cathodic phase, as to keep the net tissue charge at 0. So I suppose alternating current?

OK. If the current flows between a single implanted electrode and an external ground electrode - effectively the entire skin of the subject, I suppose - then I imagine the current must radiate outward from the implanted electrode. So you will have a current density that drops off with the square of the distance from the electrode, or something like that, i.e. like the way light radiates from a point source.

If on the other hand there are two implanted electrodes, the current will flow through the intervening tissue along a kind of sausage-shaped (or airship-shaped) envelope, the fatness of which will be determined by the electrical resistivity (inverse of conductivity) of the tissue - thinner if the tissue is more conductive, since more of the current can take paths close to a straight line between the electrodes.  There will be a way to calculate the current density at various points between the electrodes, as a function of resistivity of the medium, but I'm afraid don't know it. Maybe someone else here will be able to help.

If the electrodes are transmitting an electrical version of a sound signal (?), then there will indeed be alternating current, but involving a complex mix of frequencies. So the effect of capacitance in the tissues could be fairly hairy to model, it seems to me, as the effect will be frequency-dependent.

I realise all I've been able to do is get the discussion started. We'll have to hope someone more knowledgeable shows up to take it further.

Edited by exchemist

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