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

So hello again, this is Roger Cobar. Week five, segment eleven.

It's useful here to do a problem session that's about getting exhale and membrane

currents from a set of transmembrane potentials.

You're going to be amazed at how easy this is.

Here is our problem. We have a list that goes along the x axis

and for each different x value, so list, the sites along the x axis for each of our

x values, We have a corresponding transmembrane

potential, the Vm. Now I have listed these Vms as values of

Vm relative to the baseline. You could have them listed absolute, it

isn't going to matter. First question is, what is the sign of the

intrasailor axial current in each interval along the way?

So the answer can be positive, negative, or zero.

And the second question is, that each of the sites, one to five, that is not at the

ends, but all of the interior sites, What is the sign of the transmemberinng

current? It can plus, minus, or zero.

So I can tell you, it is very useful here, mentally, to begin by drawing a sketch And

if we do that, in this case, we'd say what we have as it goes like this.

These are the Vm values as a function of distance.

Here's our distance axis, here's our Vm axis.

So I can look at that. I don't have to compute anything.

I can look at that and say, it's like this.

This is where my currents are going. They're going nowhere in this segment

right here. The axial currents, there are none.

They're coming downhill in this segment over here.

For this direction, I'd say they're like that,

So they're all minus. In the third part, the part over here on

the right hand side, I'd say, these currents are all going this way,

throughout this segment. They're going to the right.

That is, as soon as you see the Vm curve, you know which way the currents are

flowing. They flow downhill.

I won't put in actual signs or numbers, but you can substitute them easily from

the numbers on the list. I hope you'll do that.

In this second part of the equa- of this question, it asks, what is the sign of the

transmembrane current? It can be plus or minus or zero.

Let's again do the question graphically. It's really easier that way.

I'll make my plot once again. So here's the plot.

Here's Vm as a function of distance. Distance this way, Vm that way.

And I say, where is their transmembrane current?

So the way I want to do this is first, I want to find the axial current.

That's how the derivation went and that's what I wanna do again.

So let me draw the axial current. No axial current, here.

Over in the next part, I have trans, I have axial current that's flowing to the

left. After I get to this peak, I have axial

current that's flowing to the right. If I look at this, I know right away where

the sources and sinks are. Right here, we have IM is positive.

Because current flows into this junction, Flowing in from the right,

There's no current to the left, so it has to be outward.

Peer, I have IM negative. And I know that because I have current

flowing away to the right, I have current flowing, I have axial current flowing away

to the right, I have axial current flowing away to the left.

So my transmembrane current just has to be pouring in here.

Just as it's going out there, it has to be pouring in here so that it can divide on

the left side and the right side and all the currents, loops, can work as they

should. Once again, I won't put in plus, minus and

zero, or compute numbers, I'll leave this up to you, but I hope that you will do so.

Thanks for watching. And we'll move on now to a review of the

week that we've just completed. Here's a picture of the Duke University

clock tower. Which is a famous campus landmark.

You see the clock up there, on the top of the tower.

I think at one time the clock was really, had a lot of functional value.

People referred to the clock to tell the time.

But nowadays wristwatches are so inexpensive, and so many people tell the

time from their cellphone, or some other way, the clock serves mainly as a

decoration. An interesting campus story is that one

time some undergraduate students, who were experts in climbing, climbed up that tower

to the clock. And put some big fancy gloves on each of

the hands. Sort of Mickey Mouse type hands.

And it went around like that for a few days.

Until the campus administration asked the students if they would please come back

and take them off. And so they did.

Thank you for watching.

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