Nerves, the heart, and the brain are electrical. How do these things work? This course presents fundamental principles, described quantitatively.

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From the course by Duke University

Bioelectricity: A Quantitative Approach

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Nerves, the heart, and the brain are electrical. How do these things work? This course presents fundamental principles, described quantitatively.

From the lesson

Axial and Membrane Current in the Core-Conductor Model

This week we will examine axial and transmembrane currents within and around the tissue structure: including how these currents are determined by transmembrane voltages from site to site within the tissue, at each moment. The learning objectives for this week are: (1) Select the characteristics that distinguish core-conductor from other models; (2) Identify the differences between axial and trans-membrane currents; (3) Given a list of trans-membrane potentials, decide where axial andtrans-menbrane currents can be found; (4) Compute axial currents in multiple fiber segments from trans-membrane potentials and fiber parameters; (5) Compute membrane currents at multiple sites from trans-mebrane potentials.

- Dr. Roger BarrAnderson-Rupp Professor of Biomedical Engineering and Associate Professor of Pediatrics

Biomedical Engineering, Pediatrics

Hello again. This is Roger Coke Barr for the

bioelectricity course. And we're in week five about the track,

laying the track, and we're at segment number five.

Now. This is not going to be a long segment, in

fact, it seems so obvious right at first. But let's talk about segmenting the one

day model. Here we have a one day fiber.

We want to compute what is happening in our fiber from place to place.

It gets to be a little bit complicated. And the reason its a little bit

complicated, is we have to compute currents going in more than one direction.

We have to compute currents that are going in and out of the fiber, I'll signify that

by this blue arrow, and we have to compute currents that are going along the fiber.

Might say we have to compute currents in X and in Y.

As we do that, it's helpful in many cases to think of the fiber as broken up into

segments. Now, this breaking up,

Doesn't mean that the fiber is literally broken up.

It means that for purposes of doing a calculation, we are imagining that the

fiber is broken up into different segments.

And I mark the center of the fiber at each successive segment with a red dot.

So we'd say. The segment here near the middle, how far,

how big is this segment? So maybe this is delta X of 100

micrometers. It'll certainly be less than a millimeter.

It might be less than 100 micrometers but that gives you an idea of how long the

segments are. As soon as we have broken the fiber up

into segments, then we can calculate the membrane resistance.

For the currents going out of the wall of this segment, we can calculate a membrane

capacitance. For currents going out of the wall of this

segment. And most importantly, we can have a single

value of vm that we assume is present. Throughout this entire segment, so the

core assumption of what we are doing if we, we are saying, well across the length

of this segment, here I'll make a line here; we're saying well, across the length

of this segment the membrane voltage, the trans membrane voltage is equal to a

constant. You remember the discussion of a membrane

patch. I think this was back in week two.

In the discussion of a patch, it said that the idea of a patch was that a patch be

big enough that all the different channels and pumps are represented in proportion to

their true numbers. And on the other hand, the definition of a

patch was that it be small enough that we could assume, to good accuracy, that there

was no variation in the transmembrane potential across the patch.

So here, the crucial assumption is that VM is equal to a constant at whatever spacing

we assume. Now that's a checkable assumption.

And I can tell you that a hundred microns is gonna tend to be on the big side, but

it might work. As you get much more than that, things

will not work. And the assumption is a bad assumption.

And the calculation will run into trouble. On the other hand, if you make the patch

size too small, then the amount of calculation grows large and the stability,

numerical stability, of the calculation may come into doubt.

Depending on how you do it. So, there's an art to choosing these

segment's lengths. On the other hand, the fact that you take

a long fiber and divide it into segments is common practice and very, very useful

and we will do that here. So, once again, the membrane itself is

continuous. The division into patches, is something we

put on it, for our own utility as we proceed to do analysis.

It's a part of building the track. Part of the way that we do it.

You might say, in a very loose sense, it's like putting down the cross ties on the

railroad before you actually put down the rails.

You have to put down the cross ties so that you have a way to support the rails.

Here we have to create the segments as a way to support our calculation.

So here, well, is a nice picture of one of the dormitories on the Duke campus.

You could say these people have built these walls as a way to support the

residents inside the camp-, inside the dormitory, who are then inside the

university. In the same way, we segment our fiber as a

way to support our calculation and find out what the fiber as a whole is doing.

Thank you for watching. We'll see you in the next segment.

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