Dutch Twist: which way the hierarchy?

[HANS_BLOM2]

[Hans Blom, 961022]

(Rick Marken (961015.1300))

Now we don't have an accurate delimitation of what control systems
are

You might not, but "we" certainly do.

Great to know that you have found an exact delimitation!

a system that strives for constancy of some of its internal
quantities in the face of variations in the outside environment.

Well, sort of. How about "a system that brings a perceptual
representation of some environmental state of affairs to some
constant or varying reference level while protecting it from the
effects of disturbance".

Well, we have a problem here. In some of the physiological control
systems that I teach about, the loop gain is so low (about 3), that
the "reference level" would have an incredibly unintuitive value. If
P is the pressure and R its reference, the closed loop is described
by

  P = 3 * (R - P)

or

  P = R * 3/4

If P is 120 mm Hg, is its reference, i.e. where a control system
would "really" like the pressure to be, 160 mm Hg? You wouldn't be
able to convince any physiologist of that!

A controller can control only in a benign environment, as I have
pointed out frequently.

How is this different from saying, tautologically, "a control system
can only control in an environment in which it can control?"

What's the problem with tautologies? Every true theorem is a
tautology. Logically speaking, distrust statements which are not
tautologies ;-).

But _together_ they [cells] do [control the body].

Oops. Back to square one;-)

It is a truism in physiology -- and I tend to see psychology as the
"higher levels" of physiology -- that all functions of the body have
as their single purpose homeostasis, i.e. the quality of life of the
individual cells. In PCT terminology that would be equivalent to the
statement that the cells' requirements determine the intrinsic
reference levels. And what is, maybe, surprising, is how "passive"
mechanisms are largely used to achieve homeostasis, where "active"
control systems only fine-tune what the passive mechanisms cannot
achieve by themselves, just like in standing the bones do most of the
work (not the physics definition of work). Let me quote from a recent
text of mine on blood, blood gases, hemoglobin, etc.:

The red blood cells, called erythrocytes, are the most numerous [of
the different types of blood cells; in fact, a full one-third of all
the cells of the human body are erythrocytes]. Their major function
is oxygen transport. Hemoglobin (Hb), an iron containing protein
which makes up about 30% of an erytrocyte's volume, easily bonds with
oxygen, forming oxyhemoglobin (HbO2). This is a so-called equilibrium
reaction, because the reaction can proceed in either direction:

     Hb + O2 <--> HbO2 (1.19)

When the oxygen partial pressure in the blood is high (especially in
the blood perfusing the alveoli [i.e. in the lung]), oxyhemoglobin is
formed. When the oxygen partial pressure in the blood is low (in the
systemic peripheral circulation, where the cells consume oxygen,
effectively removing it from the blood), oxyhemoglobin is converted
back into hemoglobin. Figure 1.21 [which, regrettably, I cannot show
here] shows the relationship, which is known as the oxygen
dissociation curve. This mechanism keeps the O2 partial pressure in
the peripheral blood almost constant (40 to 50 mm Hg), although in
hard working muscles it can drop to almost zero. At the normal
systemic venous PO2 of 40 mm Hg, hemoglobin is 75% saturated. Thus,
only 25% of the oxygen has dissociated from hemoglobin and entered
the tissues [after a single passage through the circulatory system].
A very imprecise calculation shows that after 4 passages through the
tissues, all oxygen would have been consumed if oxygen uptake from
the lung would stop. Since the blood circulates in about 1 minute,
this indicates an oxygen reserve in the order of 4 minutes. The
figure also indicates that raising the PO2 above 100 mm Hg will
hardly increase the oxygen content (dissolved plus bound oxygen) of
the blood. [Thus the oxygen dissociation curve mechanism is finely
tuned to the earth's atmosphere and to the anatomy of lung and
airways.]

The oxygen buffering by the oxyhemoglobin is essential. One liter of
blood plasma (without Hb) can contain only 3 ml of O2; one liter of
whole blood, with hemoglobin, can [and normally does] contain about
200 ml O2. [And since we have about 5 l of blood, we carry 1 l of O2
in our blood!] More than 98% of the oxygen in the blood is thus bound
to hemoglobin. Oxygen supply to the cells would be far from adequate
through only dissolved oxygen.

...

Blood carbon dioxide is also buffered. Although erythrocytes buffer
some CO2, the major mechanism is very different. Carbon dioxide and
water form carbonic acid, which partly ionizes

     CO2 + H2O <--> H2CO3 <--> H+ + HCO3- (1.26)

These are equilibrium reactions as well. If the CO2 partial pressure
in the blood rises, the reaction proceeds from left to right,
producing more carbonic acid, which splits into a hydrogen ion and a
bicarbonate ion. When the hydrogen ion concentration rises, the
reaction proceeds to the left, resulting in the production of CO2.
This mechanism keeps the CO2 partial pressure in the blood almost
constant. In systemic arterial blood, about 90% of the carbon dioxide
is in the form of bicarbonate. The same mechanism also controls the
body's acid-base balance (the acidity of the blood, i.e its pH, is
determined by the H+ concentration). Both too acidic (low pH) and too
alkaline (high pH) cell environments are prevented by the above
equilibrium reaction.

Several other chemical reactions modify these basic oxygen and carbon
dioxide dissociation processes. Their combined effect is the extra
facilitation of oxygen uptake and carbon dioxide release in the lung
and oxygen release and carbon dioxide uptake in the tissues.

In addition to these "passive" chemical reactions, internal control
systems adjust respiration in accordance with the needs of the
tissues. Although [respiratory] minute volume [i.e. the volume of air
that we in- and expire every minute] is increased by a decrease in
arterial PO2, this only happens when the decrease is large. Even a
slight increase of arterial PCO2, however, is rapidly compensated
for. The stimulus for this reflex [you might want to say this
differently; this is how a physiologist would express it] is not the
increased PCO2 itself, but the concomitant increase in H+
concentration in the arterial blood and in the brain. During moderate
exercise, blood gas concentrations and pH remain unchanged, because
ventilation increases in exact proportion to metabolism. During very
strenuous exercise, full compensation is not possible anymore.

What controls and what is controlled may be mostly a matter of what
we consider, at any moment, "the (control) system under
consideration".

If you ever learn what control is (after 6 years of watching your
resistance to understanding anything about PCT I'm not holding my
breath), you will see that this statement is not true. See "The
asymmetry of control" in LCS II.

So pray tell me, in the above example of control (is it that?) of
oxygen and carbon dioxide partial pressures in our blood, what
controls what, and especially what decides the reference levels. That
is, how is the hierarchy organized?

Greetings,

Hans

[Bill_Powers1]

[From Bill Powers (961022.1100 MDT)]

Hans Blom, 961022 --

It is a truism in physiology -- and I tend to see psychology as the
"higher levels" of physiology -- that all functions of the body have
as their single purpose homeostasis, i.e. the quality of life of the
individual cells.

I would say that all functions of the body have as their purpose whatever
reference level the associated control systems (if any) have for the
variables they control. I don't understand why you want to introduce a
sweeping and untestable generalization like that. I can't think of any
justification for saying that cells control for "quality of life." I don't
think they can perceived such a thing, nor that they control a variable that
indicates "quality of life." Aren't you being a bit anthropomorphic? Is an
erythrocyte really concerned with "quality of life?"

Your discussion of blood gases etc. was quite interesting, although the
mechanisms you describe have been known for some time. In particular, I
learned long ago that O2 partial pressure is not a primary controlled
variable, CO2 partial pressure (or more precisely, H+ ion concentration, as
you say) being much more closely regulated. Since O2 and C02 are normally
inversely related, it makes sense that only one of them would be regulated;
to try to regulate both independently would lead to conflict. Under unusual
conditions (high altitude, artificially-maintained low CO2 ambient
concentrations) the increased losses of CO2 can slow breathing to the point
of oxygen starvation, at least before the whole system readjusts to the new
conditions.

From the low loop gains you are measuring, around 3, I would guess that what

you are taking to be the controlled variable is only related to a true
controlled variable. It's possible that the control system actually has such
a low gain, but before I believed such a conclusion I would look for
alternative definitions of the controlled variable, and try to identify the
actual sensors involved. Also, these control processes do not take place in
isolation; there is a rather large set of interacting systems which control
multiple variables and the reference levels of all homeostatic systems are
subject to variation by higher systems (see Myrsovski, "Rheostasis"). A
variation in the reference signal that is related to the disturbance you're
using would obviously result in a spurious measure of loop gain.

The biggest problem in indentifying physiological control systems is that
the measures which are most convenient to obtain (like partial pressures)
are not necessarily directly related to the variables that are under
control. I ran into this in working on the Little Man control systems. It's
been assumed that because the tendon reflex responds to stretching of the
tendons that the tendon reflex should resist forces applied to a limb. When
you measure the resistance of this control system to applied forces that
change the stretch of a tendon, however, you come up with very low loop
gains, like 3 to 7. Actually, the number should have been much less than
that, closer to 0, but most work is done with single-muscle preparations so
the real picture is hard to see.

When I modeled the combined tendon and stretch reflexes, I found that the
tendon loop had to have a loop gain of about -200 to make the model behave
realistically. This reflex is not a position-control system, but a force
control system. If there is a constant reference level for force, then
disturbances which move the limb and tend to stretch the tendon are resisted
not in terms of position but in terms of applied force. If you disturb a
limb, the tendon may tend to stretch, but the feedback loop immediately
changes the muscle tension in the direction that maintains the original
stretch of the tendon; the effect of the feedback is to make the limb MORE
compliant to external forces, not less. In fact, the main effect is to
reduce the apparent moment of inertia of the limb close to zero in
comparison with its passive moment of inertia. The stretch reflex, which
includes the tendon reflex in its output function, thus sees a limb with an
apparent mass that is much less than the actual mass, and this greatly
simplifies the problem of stabilization. The natural frequency of the
physical system is raised, making the effects of position disturbances more
nearly proportional to the disturbances. This is the main reason that so
little had to be done to stabilize the model.

In evaluating a possible control system, one of the points you have to keep
in mind is that the control system may be sensing the controlled variable at
one place, while you (even if you have guessed right as to what it is) may
be measuring it in another place and disturbing it in still another place.
Suppose you decided to test for body temperature control by measuring the
temperature on the skin of the abdomen, while raising or lowering the
ambient air temperature. You would measure a rather low loop gain, and might
find that the control was quite uncertain. However, if you were to measure
the temperature of the blood in the hypothalamus or in the carotid artery,
you would find a far higher loop gain as well as much less noisy control.
The reason is that the temperature sensors are in the hypothalamus, and what
they measure is the temperature of the blood flowing to the brain.

Also, you have to be aware that the control action and int3ervening passive
effects are reducing the magnitude of the effect of the disturbance, so if
you measure the disturbance at the source, you will not see its actual
effect on the controlled variable. By measuring the ambient air temperature,
you fail to take into account the compensating effects of sweating or
shivering on the heat losses and gains at the point where you're measuring
the temperature on the abdomen. You have to calculate the loop gain from the
effects after the compensation has taken place.

I'm sure you're aware of all this; I mention it only so point out the
general pitfalls involved in trying to identify physiological control
systems. From what I've seen of the literature, these pitfalls are not
generally taken into account.

Natural buffering does make the control task easier, to be sure. Mainly it
reduces the effect of transient disturbances, in effect putting a low-pass
filter in series with them. Buffering, however, is of little use in the long
term; energy stores in the bloodstream, whether from oxygen or glucose, must
in the long run be replaced at the same rate at which they are depleted.
It's possible that many traditional studies have under-measured loop gain
simply because they didn't wait long enough to see the effect of a
protracted constant disturbance. This would be particularly true if the
experimenter thought of a "disturbance" as a brief event.

All in all, I would be most comfortable with measuring loop gains after
having found the sensors that monitor the controlled variable. If the sum of
all equivalent sensory signals (or an estimate based on measures of a few of
them) is defined as the real controlled variable, and if the effects of
disturbances on the real controlled variable are measured with the loop
broken (when possible), the calculation of loop gain will be as accurate as
possible.

Best,

Bill P.