Bruce's BLINK program

[From Bill Powers (950503.0740 MDT)]

Bruce Abbott (950502 etc) --

OK, I finally got around to your eyeblink program. A nice, tidy job.

I didn't notice any place in it for a disturbance of eye dryness. This
could be introduced easily as a perturbation in k2 (or is it k1) -- the
evaporation rate. A puff of air would shoot the evaporation rate upward.
A mild flow of air would increase it, reducing the time between blinks
but not causing an immediate blink.

I'm a little puzzled by the way the "perceived corneal intensity" pc
jumps upward before it starts downward again. As near as I can figure it
out, what happens is that the corneal exposure starts increasing as if
there had been a switch from K1 to K2, so the now-unstable second-level
system starts to oscillate at a high frequency. The oscillation goes to
its maximum, dives down toward zero, and then the constant switches back
to K1 (or the other way if I've got them backward). I did a plot with
time := time + 5*dt to stretch out the trace, and also plotted "expose"
instead of the reference signal. It seems that pc rises rapidly to its
peak, and _then_ the exposure starts to decrease.

The second-level system is set up nominally like a control system, but
the gain is so high when the "wet rate" constant is in effect that it's
actually unstable and spontaneously oscillates. As soon as the gain
switches to "evap rate" the oscillations stop. If you reduce the wet
rate constant to about 0.01, you'll see the whole system oscillating in
a sine wave; lower than that, and it stops oscillating.

This isn't a criticism; actually this is a quite plausible model for the
eye-blink system with only a few details to clean up. There may be other
models that would also work, but this one has the nice feature that it
uses an existing eyelid position control system, which can still be used
to squint or close the eyes, but adds another level that produces blinks
in a way that has minimal effects on vision while keeping the eye
moistened. The gain change that occurs is perfectly natural and
expresses physical facts. And I do believe that the model predicts a
phenomenon that the classical-conditioning approach wouldn't predict: an
increase in blink rate with air velocity, which leads naturally into the
"blink reflex" for a sudden intense flow of air.

Another possibility for the controlled variable is corneal temperature.
The "drying" of the cornea is a fuzzy concept, because drying alone
shouldn't have any direct sensory effects, particular very rapid ones.
But drying means lowering of temperature, and a blink can quickly
restore temperature both from contact with the eyelid itself and from
washing warm fluid over the cornea. A sudden blast of air would lead to
very rapid cooling and an instant blink, while slow air flows would lead
to slower cooling and a lower blink rate. This would lead to the same
predictions as above, plus one more new prediction: that a flow of moist
or warm air against the eye would produce a lower blink rate than the
same flow of cool or dry air. Actually, I suppose that the critical
effect would come from relative humidity, which determines the net
evaporation rate and hence the cooling effect.

So we have several possibilities for a controlled variable, one that
might even be measurable by direct or indirect means. Infrared
measurements might be able to pick up changes in corneal temperature, or
brave volunteers might even allow tiny fast temperature probes to be in
contact with the cornea. This would be ideal, because then we could
directly measure all the variables external to the control loop and
wouldn't have to guess at any of them.

This is obviously a rather large experiment -- do you want to launch it,
with grant proposals and everything? I do hope we can start up the rat
experiment pretty soon -- they aren't getting any younger.

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Best,

Bill P.