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

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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.

从本节课中

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 in discussing this whole situation in a more systematic

way, the discussion is basically divided into two parts.

In the first group of lectures, there is a discussion of,

in a sense, how you set up the analysis.

And then in the last group of lectures, 8 through 12,

is a discussion of how you really analyze the situation.

Let us now begin thinking about the problem for a moment, as a quantitative

problem, and let's think about it in terms of the basic membrane equation.

After all, the goal of the track is to support the train and the goal of

the analysis here for bioelectricity, is to show how currents flowing down

the interior of the fiber, will stimulate the fiber and cause an action potential

further on down the nerve from where it has been stimulated so far.

Basic membrane equation that applies to any point along the nerve, is this one.

We have seen this equation before.

The total membrane current is I m, and it can be subdivided into two parts.

The capacitative current, and the ionic current.

Earlier in the course, I believe that was in section 2,

we were talking about the capacitative current.

Cm equals dvmdt.

It's the charging and the discharging of the membrane.

Just more recently been, we've been talking about the ionic current.

The ionic current is what is determined for us by the Hodgkin Huxman model.

Now you could say that the way you get Im is by adding capacity of an ionic current.

But that's not the way it is.

Instead you turn things around and you first find

m from knowing about the structure and the track.

Then from Im, you look forward to find the other quantities.

Up until now, we've always assigned the membrane current Im equal to 0.

That's because we have always been considering one patch in isolation.

That is to say we've always been doing that when,

when we have been analyzing memory in currents of the Hodgkin Huxman model.

However, if we think now of a cable or a set of cells

as being more than one patch, each one has an effect on the others.

And in particular, the effect that one has one the next,

is expressed to that next patch by changes in Im.

That's what we've got to figure out.

Just restating that, so that the big picture is fully in line.

Up until now, we've never worried about the tissue structure.

A patch was an independent patch wherever it was.

Now we're looking at the patch's interaction with its neighbors.

We have to know what the structure is, say it's a cylindrical structure for

example, so as to know what the neighbors of a given patch actually are.

And as soon as we know those neighbors, we can figure out the membrane current

created on a patch by the neighboring patches.

And that membrane current is what will stimulate the new patch.

Well those ideas sort of turn everything around backwards.

It takes a little while for it to settle down.

So while those are settling down,

here's some nice looking Duke Campus flowers to consider.

Thank you for listening and

watching, and, I'll talk to you again in the next lecture.