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

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

Hello again.

This is Roger Coke Barr for the Bioelectricity Course.

We're in week four and this is segment nine and here we want to review

the changes that occur in the values of all of the state variables.

Changes in n, m and h, and changes in vm.

Let's look at this process as a whole without so much detail to any one part.

If we say we're going to change vm from one moment to the next moment.

How will we do that?

With saying again what we've said already.

What we will do is first we will compute dvm

according to this equation dvm is dt times

the membrane current minus the ionic current divided by cn.

We've discussed this above.

Once we find dvm we'll get a new value for vm, new value for

vm by taking the old value and adding the change.

In that fashion, we'll have moved from our starting time

to a new time which here is designated time number one.

Let's look and see where the values came from that allowed us to make this shift.

im in our case is the stimulus current so

we know it from because it is given to us and

in every situation it will come from some outside effect.

The ionic current, ion is some of

the ionic currents comes about and adding them up individually,

so we use this equation to get the Ionic Crust.

Cm of course is a custom for our tissue.

Now if we back up again and we say well,

the ionic is the sum of ina and ik and il, where do they come from?

Well they come from n, m, and h, as well as vm.

So those values all go in there.

So we use all of the values, values for

all of the state variables in getting to a new value for vm.

Now let's look at where we are as far as getting new values for n, m, and h.

We do each one by the same pattern.

We will get a value for d and

dt using the process d and

dt = alpha n(1-n)- beta n times n.

Then we will say n [1] = n.

That is to say,

the old value of n, + dn.

We can do the same thing for m and for h.

But now look and let's see where these values come from.

Here we're changing n, m, and h.

Based on the equation that we have, alpha n, beta n, as well as the old value.

And where do we get the alphas and the betas?

We get the alphas and the betas because we know vm.

vm goes over here into the alpha formula.

We were discussing that above.

And then the alpha formula,

the result comes down here to the value of alpha, that's used for d and dt.

So in getting new values of n, m and

h we have to know the value of the other state variable, vm.

There's a certain of asymmetry here.

We have to know the value of vm to get new values of n,m and h.

And we have to know the value of n,m and h to get a new value for vm.

It's an interwoven process, but it works.

And it's amazingly,

amazingly powerful both in the real tissue and in the calculation,

but it's also complicated and

there are little cracks here and there where one can make an error.

So to conclude this segment, I put in the picture of the sidewalk with cracks.

Not to say that you'll slip between the cracks, either on the sidewalk or

the calculation, but you do have to be careful to step over.

Thank you for watching this segment, I will see you in the next one.