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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Duke University

24 ratings

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. <p>The learning objectives for this week are:</p><ul><li>Select the characteristics that distinguish core-conductor from other models.</li><li>Identify the differences between axial and trans-membrane currents</li><li>Given a list of trans-membrane potentials, decide where axial andtrans-menbrane currents can be found.</li><li>Compute axial currents in multiple fiber sigments from trans-membrane potentials and fiber parameters</li><li>Compute membrane currents at multiple sites from trans-mebrane potentials</li></ul>

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

Biomedical Engineering, Pediatrics

Hello. This is Roger Coke Barr for the Bioelectricity course. We're in Week five and this is Lecture number four. We're going to begin talking about some of the features of a one-day cable. It's called one-day because the spatial change all occurs along the x-axis. Let's just talk about the dimensions of our cable. So, if we think about this cable along one axis, we'll call that axis x. At different times, people sometimes call X. Let's say that our fiber has only three important geometrical dimensions. It has a radius, Call that a. It has the radius to an outer structure that is to say, the limit of where currents can be conducted. We'll call that b. And here, we are assuming that b is very large indeed. There is a limit, but it's, it's a big number. And then finally, we are on some occasions concerned with the length of the fiber. So, if it goes from here to here, we'll call that distance l. But more often, we subdivide our cable into segments and where it's subdivided into segments, we'll think of each segment, We subdivide into segments. Let's say, each segment has a length delta x Along axis x, there are currents.

There's an intracellular current. I'll call that Ii.. And when the intracellular current is positive, that means it's going in the same direction as x. There's an extracellular current.

Sometimes called the interstitial current. But here are es so that it is easily distinguished from the number zero, e for extracellualar and when there is extracellular current, it likewise falls in the direction of x. It's important to realize that, that is a restriction because the extracellular volume is very large. So, in general, currents outside the fiber can flow on all sorts of pathways. Right now, we are forcing our extracellular current to just flow in the x direction alone.

Then, there is membrane current. Membrane current flows across the boundary. You're familiar with that, because we've talked about it so much in various other connections. When the membrane current is positive, we'll say that it's flowing from the inside to the outside. One-day uniform cable model has resistance that's specified in various fashions. So, we consider the bulk conductivity of the interior is row i The bulk conductivity of the extracellular is row E. These are the conductivities in ohm centimeters. And we were talking way back there about seawater and how it is in the range of 25 ohm centimeters. That's what we're talking about here with row i and row e. Often, the bulk resistivity, as it is called, is transformed into another form called ri An ri is row i divided by the cross-sectional area. So here, that would be row i divided by ia squared. It's done that way because now ri can be converted to the resistance r The intracellular side can be equal to ri times delta x That is to say, people create this entity, ri, so that some of the calculation that otherwise would be necessary, row i delta x over pi a squared.

This is already done in advance. A similar thing is done for row e uwing the radius b, but often, then re is rather small.

This model of a fiber, where there's one dimension, we've called it x Currents along the fiber, intracellular, extracellular, they bring current crossing over. This is called the core conductor model. It's a simple model, but it was not made up by somebody in kindergarten. It is a model that was created or at least perfected by Lord Kelvin in England. This is the Kelvin for whom the units degrees Kelvin is named. Kelvin made use of the core conductor model because he was a member of the scientific establishment in England. When at huge cost a cable is laid from one side of the Atlantic to the other and the cable failed. It did not work. So, a scientific committee or a review committee was put together. Kelvin was a member of the committee to figure out what had happened. And in the course of doing that work, the work on the transatlantic cable, the mathematical model that was frequently used came to be called the core conductor model because in that connection this. This cylinder was a physical cable that went from England to the United States. Of course, we have adapted that work into an entirely different context. But the basic idea is much the same. In our case, we're thinking perhaps of a nerve axon that is possibly cylindrical. It's within a salt solution that surrounds it. So, although much smaller and not going nearly as far, it is fundamentally similar in the currents that it carries to the transatlantic cable that was studied by Calvin and thus, we use the core conductor model here, just as he did there. Thank you for watching. I'll see you at the next segment.

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