Is there a mathematical function giving an approximation to human breathing over time?

I want to animate something with the same frequency that a human breathes in and out, something like the Apple Macbook power light when it is in sleep mode.

So basically an ease in ease out function over time, but that has a curve that approximates the way a human breathes.

Edit: I just need the algorithm as a function of time, don't care which language.

http://www.normalbreathing.com/d/etco2-capnography.php

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Why don't you record yourself with a microphone ? – Alexandre C. Dec 1 '11 at 20:51
Respiratory rate? – Jesse Dec 1 '11 at 20:52
@AlexandreC because I want a mathematical function which approximates the breath – justinhj Dec 1 '11 at 20:55
@Jesse doesn't answer my question at all – justinhj Dec 1 '11 at 20:56
Here's the relevant patent, for what it's worth. freepatentsonline.com/6658577.html – Harry Stern Dec 2 '11 at 0:04

Your curves look like they could be approximated by exponentials. The first could be $1-\exp (\lambda_1 t)$ for $0<t<3$, $\exp (\lambda_2 (t-3)t)$ for $3<t<5$ then repeat. Choose the $\lambda$s to make it look right. For the hyperventilation, change the range of $t$s appropriately. The easiest way to set the $\lambda$s is to look for the $\frac{1}{e}$ point, where the signal is about $0.37$ of the final value and set $\lambda$ to the inverse of that time.

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Just a search on google images:

If you like the first one, a lot of functions could look like that. For example, get partly cos(t)^3 and partly flat. Of course, with coefficients to adjust it.

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Now that I look at it more closely, it looks odd. I mean, the Ideal pattern is 3 breaths/min? Never the less, the shape completely makes sense – Shahbaz Dec 1 '11 at 20:58
does not look right. why would breathing be more sinusoidal when breathing quickly...? – vidstige Sep 18 '15 at 9:06
Sinusoidal is essentially "inhale fast, short pause, exhale fast, short pause". This is a mechanical system, so pauses and smoothness are unavoidable. Looks right to me. – Shahbaz Sep 18 '15 at 13:02
I guess my main objective is the shape of the function for breathing normally is fundamentally different from breathng "in the sick". I suspect actually measuring the chest move would be much more asymetric. It's a good start though! – vidstige Sep 18 '15 at 21:58