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. We're gonna look at another individual

topic: One of several that can be merged together to get the axial currents and

then the transmembrane currents. This time let's just look at a local

voltage loop. So, here's my fiber.

I have my red dots, which are just mathematical points.

Not real points in a real fiber, just points for a discussion.

And I have identified four individual points with the letters.

So, this is point A, B, C, D.

You notice the obvious, that these letters go around in a loop.

If I write the voltage for these points I can write the voltage between A and B as

Pi A, potential at A, minus the potential at B.

As we said in a very early segment of the course, the potentials are voltages of all

the points plus the potential field. Every point has a potential, and all those

potentials are voltages measured against a signal, a single common, normally, remote

point. So maybe I have a point way over here, and

I measure the voltage. First I measured here.

Then I measure it there. Then I measure it here.

But I do all these things, without moving my reference point.

So I get all these different potentials, Pi one Pi two, Pi three, Pi four.

And then similarly for the ones inside, and measure the potentials that everyone,

without moving the reference. We'll imagine that has been done.

If I have done that, then the voltage between A and B.

This voltage, I can define as I did before.

Pi A minus Pi B. So what that means is, I take the plus

lead of my voltmeter and put it on A and the minus lead of my voltmeter and put it

on B. And that's the voltage that I get.

If I do that for every different segment in my loop I can get Vab.

Vbc Vcd. V, D, A and go all the way around in a

circle and as you know if you do that with voltages and you go all the way back

around to where you came from, the sum is zero.

Thereby I have this equation, zero is equal to sum of those voltages.

Now you notice something about that process, it was a simple process a

straightforward process. We did it for a set of four points, they

are out here in the middle. And we could do it without reference to

whatever is happening over here on the right, or over here on the left, or

anywhere else along the fiber. That is, we can complete that voltage loop

without having to be concerned about what is happening elsewhere.

This is a little point but a big point. Because, I find if you ask people who

haven't thought about this to start analyzing what happens on tables, they

start writing an equation for every point. Along the fiber, on the inside and the

outside. And it ends up in a horrendous mess.

And that mess is unnecessary. So, we'll just take a simple walk with one

loop, or simple walk along this walkway. We've to, to find our loop, and we'll use

it as we go on to our next segment. Thank you for watching.

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