[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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