[time-nuts] simulation of interconnected clocks
Jim Lux
jimlux at earthlink.net
Sat Nov 30 09:31:01 EST 2013
Recently, I've been looking at the variations of some human clocks which
are millenia old: Galileo used his pulse as a timer for his famous "roll
balls down a ramp" experimenet". I thought that some time-nuts might be
interested in working with a clock that's a bit different than one
depending on atomic vibrations, or motion within a crystal lattice.
In particular, modeling the behavior of the heart beats, or more
properly, determining the model parameters given a (noisy) data set.
It is well known that one's heart rate goes up and down as you breath
(up when you breath in, down when you breath out). The magnitude of the
Respiratory Sinus Arrhythmia (RSA) is about 10-15 beats/minute, so it's
a pretty big factor. The attached picture is data from an optical
plethysmograph sensor for heart rate, the estimated beat/beat interval,
and the motion of the chest wall measured by a radar. The heart rate
varies between the low 70s and the high 80s in this example from which
I'm going to guess the subject was sitting quietly breathing fairly
deeply (for reasons explained below).
What's interesting is how this comes about: There's basically the
oscillator of the heart (the SinoAtrial Node) which has a 1/f
characteristic like most oscillators. But effectively, this oscillator
is a VCO, and is driven by two sources: one is related to the blood
pressure (if the pressure drops, the rate increases); the other is
driven by the master oscillator that drives respiration. It turns out
that even if you don't breath (hold your breath, or be unlucky enough to
be hit by a curare tipped dart in the jungle), your heart rate still
cycles up and down. (or if you're a lab animal that has had the nerves
cut or blocked by drugs) The respiration oscillator is driven mostly by
the CO2 content (high CO2 -> rapid breathing, low CO2 -> less rapid).
There's been research on this since the middle of the 19th century, at
least. There's a great paper out there by Hirsch and Bishop (1981) that
measured the RSA amplitude vs depth of breathing and also vs rate of
breathing, and not so surprising, there's a fairly simple low pass
filter function that relates the two. Below a certain respiratory corner
frequency, the RSA amplitude is basically constant, and above that
corner, the RSA amplitude falls off at about 20 dB/decade, although
different individuals have a different slope (which is interesting).
The corner frequency (and below corner RSA amplitude) seem to be related
to tidal volume (how much air goes in and out with each breath).
Hirsch and Bishop's paper is linked from pubmed:
http://www.ncbi.nlm.nih.gov/pubmed/7315987
So there's a whole lot of interesting work ahead on developing models
for these coupled oscillators. I'm interested in things like "how
stable are the filter parameters over time", and, of course, "are there
computationally efficient algorithms to do the model estimation".
And, relevant to our recent discussion, given model parameters, can I
build a simple simulator (e.g. fitting in an Arduino to drive a
mechanical target)
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