A Adjusting Parameters for Identifying Features of an Action Potential

[TULC]

The action potential satisfy a 2nd order ODE according to the Hodgkin-Huxley model. See equation (30) of their seminal paper [1]. This equation has no closed form solution, but can be solved numerically.
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[1]. HODGKIN AL, HUXLEY AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952;117(4):500-544. doi:10.1113/jphysiol.1952.sp004764

Thank you, William. That's very useful.

 

[TULC]

Thank you p

Just to recap on this thread:

1. We want to create a frequency modulated audio output following a given curve for presentation to learners with a visual impairment.
2. The given curve is generated by a system of (4) differential equations (ODEs) without an analytical solution.
3. The Desmos website is capable of providing audio output, but it cannot solve differential equations.

One way of overcoming this is to find a (probably piecewise) approximation to the curve and input this into Desmos.

I think a better way is to create an application that can numerically solve ODEs, plot the results and produce an audio output. I have put something together to demonstrate this and it is available at https://avplot.com/#/hodgkin-huxley: an image of the graphical output is shown below. If this is useful, let me know and I will make it a bit smarter and add more functionality as time allows (e.g. the ability to enter arbitrary equations similar to Desmos, change the audio parameters etc). If it is not then it will probably die when the domain renewal comes up, although the (open) source will be available at https://github.com/avplot for as long as GitHub works.

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This is excellent, thank you pbuk! Is it still possible to add the functionalities you mention in your post?

 

[pbuk]

This is excellent, thank you pbuk! Is it still possible to add the functionalities you mention in your post?

Yes in theory: in practice I have very little free time at the moment. What would be the most desireable feature?

 

[WWGD]

To build a formula for a curve - no matter how intricate the curve is - I can always create a formula by adding parameters?
How to add parameters?

Thanks.

Maybe something like Lagrange interpolation. Edit: But then this is likely overfitting, if you want a general model.
I was thinking the curve looked like one of the periods of the Topologist's Sine Curve: f(x)=Sin(1/x); f(0)=0.

 

[TULC]

I understand and appreciate any input. You suggested a couple of things in a previous post including (1) enabling users to enter arbitrary equations similar to Desmos, and (2) changing audio parameters...Both of these suggestions are great, though I would like to learn more. Which audio parameters could we actually adjust in this application?
Regarding this particular sonification: It could be useful to adjust the function such that the users can more easily identify specific features of an action potential. Specifically, it would be helpful to make the undershoot following the fall of the curve a bit more pronounced, e.g., by increasing its amplitude. It would be good to experiment with that particular feature of the curve. Currently, without any visual input, I would not be able to identify that there is an undershoot following the fall of the curve.

 

[pbuk]

You suggested a couple of things in a previous post including (1) enabling users to enter arbitrary equations similar to Desmos

Yes, this could be implemented using the excellent expression parser in math.js.

(2) changing audio parameters...Both of these suggestions are great, though I would like to learn more. Which audio parameters could we actually adjust in this application?

Well the code has these default settings (see https://github.com/avplot/avplot.gi...0bed551481c708dcb9e10/src/avplot/avplot.js#L9)

const defaults = {
  animationDuration: 5000,
  highlightPointRadius: 6,

  maxGain: 0.25,
  valueScale: 1,
  valueOffset: 0,
  // const baseFreq = 440; // A5.
  // const baseFreq = 523.23; // C5.
  baseFrequency: 880, // A6.
  octaveScale: 2,
  octaveOffset: 0,
};

, you can see where I have experimented with different base frequencies for instance. All it needs is a user interface to adjust these (and it would be even easier to build these into a URL e.g. https://avplot.com/#/hodgkin-huxley/settings=baseFreq:440,octaveScale:2 (note this is not implemented and shows a blank screen at the moment).

Regarding this particular sonification: It could be useful to adjust the function such that the users can more easily identify specific features of an action potential. Specifically, it would be helpful to make the undershoot following the fall of the curve a bit more pronounced, e.g., by increasing its amplitude. It would be good to experiment with that particular feature of the curve. Currently, without any visual input, I would not be able to identify that there is an undershoot following the fall of the curve.

Parameters could be introduced to expand the freqency range for e.g. the lower part of the curve which would highlight the detail in this case.