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

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En provenance du cours de 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.

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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 Coke Barr for the

Bioelectricity course, Week number five, and we're doing the week

in review in segment twelve. We begin this week with the realization

that we needed to know the membrane current, we needed it because it's the

starting term in our equation im equals ic plus Iion. So we set out to get a value

for im and to get this from the set of vm's up and down our structure.

In order to find the membrane current, we have to know what the structure is.

We chose in particular the core conductor model, for a simple, uniform, cylindrical

fiber. What we found was that at a home site,

that is to say, in a particular site on the fiber.

The membrane current depends on the pattern of vm in that neighborhood that is

to say, all around our site. And especially, it depends on the second

spatial derivative of vm, a fact that seemed obvious in retrospect, but was no

means obvious before we did the derivation.

We found finally, that even though IM is equal to the capacity of current plus the

Iionic current, The membrane current could be found, and

was found, without the need of any calculations of either the Iionic current

or the capacity current. So I posed the question is that really

true?" Even the llamas were sceptical. But yes, it is really true.

And I thought you just probably doubted that llamas really lived in the wild in

North Carolina, yes really they do, there's a picture of one of them.

So taking the week as a whole, It hasn't been technically extremely

complicated but there have been a series of individual small items that had to be

put together. We needed to know the membrane current.

We needed to have a structure. We found that the membrane current depends

on the pattern in the neighborhood, Notice that says you don't find IM by VM at the

same place. You find it by the pattern of VMs in the

neighborhood and especially the second spatial derivative.

But, the good news is, the membrane current can be found without need for any

calculations of either the ionic current, or the capacity current.

So we're in a bright spot now. We have all the components of our train

system. We have the engine, we know about

channels, we have the track. We can put them all together and watch our

trains go someplace. In the next week's work, that's exactly

what we will do. Thank you for watching.

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