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.

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Hodgkin-Huxley Membrane Models

This week we will examine the Hodgkin-Huxley model, the Nobel-prize winning set of ideas describing how membranes generate action potentials by sequentially allowing ions of sodium and potassium to flow. The learning objectives for this week are: (1) Describe the purpose of each of the 4 model levels 1. alpha/beta, 2. probabilities, 3. ionic currents and 4. trans-membrane voltage; (2) Estimate changes in each probability over a small interval $$\Delta t$$; (3) Compute the ionic current of potassium, sodium, and chloride from the state variables; (4) Estimate the change in trans-membrane potential over a short interval $$\Delta t$$; (5) State which ionic current is dominant during different phases of the action potential -- excitation, plateau, recovery.

- 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. This is Week four, segment number eleven.

And, I thought it would be good here to have a bit of a problem session.

Suppose we consider this question. We begin with the standard conditions, the

tissue is active. At the moment, the state variables are

those of set one, so there is no stimulus. Here are our questions.

What is Vm after one time step if each time step is 50 marker seconds?

What are n, m, and h after one time step? And then, what is Vm after two time steps?

Question A, this is very similar to the question, may be the same as the question

asked in the previous problem session. So, I'm sure you can work it out and get

Vm1, so go ahead please and read that back or get it again and write down what Vm1 is

equal to. N, m, and h were not done before, but a

earlier lecture outlined the algorithm. Follow those steps and get n1, m1, and h1.

You will have to evaluate the alphas and betas, all six of them, in order to get dN

/ dt, dM / dt, and dH/dt. Now, here's the tricky part of this

question. What is Vm after two time steps?

So, it is tempting, very tempting to just do the force calculation again.

So, I write down, do part A again with a question mark.

And the answer is, well, no. Not quite.

So, I'll make a note, not quite. To go from Vm1 to Vm2, go from Vm1.

To Vm2. You need use n1, n1, and h1.

That is to say, not the original values of n, m and h, but the new values of n, m,

and h. And if you do that, you should be able to

get it just fine. Let me say another word here just about

the synchronization of all these calculiza, calculations.

You will find, I believe that if you start off with Vm, start off with Vm, n, m, and

h, and use this set of values to get Vm1. And use start with these values, get Vm1.

Start with these same values, get n1, m1, and h1.

Your life will work out a lot better than if you do the following algorithm starting

with Vm, n, m, and h to get Vm1, and then use Vm1 to get n1, m1, h1.

Cuz if you start with these original values, get a new Vm, then you might use

that new Vm to get new values for n, m, and h.

So, I'm suggesting to you that you not do that, because if you do, you'll get very

confused. This is just what comes from what.

Your program will have errors in it or calculations will have errors in it.

You'll get all confused in trying to figure out what came from what.

Just keep it simple. Let everything new come from the set, drom

this set. Don't intermix changes in one thing with

changes in the other. I think you'll find that works out a whole

lot better in the long term. Thank you for watching.

I'll see you in the next week's work.

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