Dear Scott,

I guess I will have to give up on my request that
you review a quantative-predictive model for
the behavior of the natural eye.

Here is the work to establish whether the
natural eye is an "open-loop" system
or a highly sophisticated control system.

As I suggested, to one group of scientists,
it is intuitively obvious that the natural
eye is a control-system, and must therefore
have a "transfer-function".

Scott, as a friend and author,
I would be curious about you comments.

One OD requested that we "AGREE".  I propsed that
we first all agree that the natural eye is
a sophisticated control system -- or not.

I we can not agree on fundamental principles,
then obviously we will never agree on anything else.

The is an arguement about fundamentals.

Best,

Otis

Engineer

______________________

                PAPER 24

              By Otis Brown

     PHYSIOLOGICAL MODELING OF THE NATURAL EYE'S FOCAL BEHAVIOR

    A NEW PARADIGM FOR A SOPHISTICATED OPTICAL CONTROL SYSTEM

    The formulation of a problem is often far more essential than
its solution, which may be a matter of mathematical or
experimental skill.  To raise new questions, new possibilities, to
regard old problems from a new angle, requires creative
imagination and marks real advances in science.

                    Albert Einstein

      COMPARING TWO CONCEPTS OF THE EYE'S BEHAVIOR

    This work is intended to clarify the fundamental behavior
characteristic of the natural eye.

    The two theories involved are derived from "Treatise on
Physiological Optics" written by Dr.  Herman Helmholtz in 1864.
Although an excellent optical theory, the Helmholtz theory is not
clear about the fundamental behavior characteristic of the normal
eye, as to whether the eye is absolutely passive or dynamic in its
fundamental behavior characteristic.

    The data available in the 1860's was not sufficiently
accurate to resolve the question.  In the 1990's we should be able
to resolve the question by concentrating on two concepts; a
Helmholtz-passive and a Helmholtz-dynamic model.  Clearly all
normal eyes, at least, behave one way or the other.

   EXCESSIVE CONCENTRATION IN MODELING THE "DEFECTIVE" EYE

    There has been an immense concentration on the defective eye
and correspondingly little interest in establishing the
fundamental behavior characteristic of the normal eye.

    The tendency is to clarify refractive states of the natural
eye as "errors" or faults of some type.

    Dr.  Francis Young, over a period of thirty years, has been
able to establish the fact that the normal eye tracks its average
visual environment with 0.97 as the correlation coefficient.  When
you make a slight shift in the eye's average visual environment,
the natural eye makes a corresponding focal state shift by the
same quantitative amount.  There are many other indications that,
whenever the natural eye is correctly tested, it will always show
this fundamental "tracking", focal-control behavior
characteristic.

    An analog computer presented in this paper to a prototype
this characteristic of a sophisticated eye.  Later papers will
further detail the concept that develops from this type of
analysis of the normal eye's behavior.  Detailed predictions of
the model, and correspondence with the experimental data will be
demonstrated.

        ESTABLISHING A MATHEMATICAL MODEL

    The eye is known to be a complex of feedback control
elements.  The subject of nearsightedness (a negative refractive
state of the eye) suggests the question, "How does the normal eye
control its long-term growth?".

    Work done by Dr.  Lawrence Stark (1) and others has shown
that short- term focus (accommodation-system) is by feedback
control.

    The process by which the eye grows and controls its
refractive-status is a dynamic (closed loop) system.  After
initial review we found that it is impossible to model the normal
eye's long-term focusing ability in terms of a heredity (passive
and open-loop) system.

    We shall establish a working-model for the long-term growth
of the eye.

    Stability is not a problem, and our choice shall be a first
order control-system.  The transfer function (developed from
electrical and control theory engineering) will accurately
represent the eye's feedback-controlled growth.  (Below) (2)

            1 / (TAU  s + 1 )

    The input to this function is the average value of
accommodation of the eye.  The equation is implemented by the
operational amplifier.    (Figure 1)

    When we build a model we must choose the independent variable
and the controlled variable.  For the sake of simplicity, we will
choose to build a model in which the long-term focal state of the
eye is the controlled variable.  (Figures 2 and 3)

    The author's preliminary estimate (after exhaustive review of
the relevant experimental data) that the normal eye's time-constant
is approximately three months.    This parameter is a function of
the youthfulness of the individual.  (3) Thus, for a child or
adolescent, the time-constant is estimated at three to four
months, while in an adult, this parameter is more likely to be on
the order of five months.  (A direct test for the normal eye's
time-constant will cause a change of focal state in the normal
eye, since a sharp negative-delta must be made in the
accommodation system for this test.)

    Two additional elements must be included to make our model
accurately represent the major facts known about the eye's
long-term behavior:

1.  The eye has an offset of about 1.5 diopters.  This fact is
   represented by applying a DC offset to the operational
   amplifier.    (This offset is a characteristic of all natural
   eyes.) (Figure 4)

2.  In our mechanical model of the eye, the fact that the
   short-term focus controls the long-term focus will
   occasionally produce a normal but negative (blurred) focal
   state for the eye -- if the eye is maintained in a severely
   confined visual environment for a long period of time.  In
   our electrical model, this is represented by a diode which
   inhibits proper feedback for control of the eye's focus.
   (Figure 4)

    Time scaling is accomplished by the 5,000 micro-farad
capacitor and the 10,000 ohm resistor.    The time relation chosen
is one minute equals one year.    Thus, the time-constant of the
computer is 20 seconds real time, or four months simulated time.

    The offset (DC voltage) applied to the second operational
amplifier causes a +1.5 volt offset (relative to the accommodation
system) at the output of the operational amplifier.  This
represents the +1.5 diopter (average) offset that is observed for
the normal primate eye.  For instance, if the eye has a
steady-state environment of -0.8 diopters, the typical refractive
state will be +0.7 diopters.

    This completes the construction of the eye's long-term
behavior computer.  Space does not permit a more extensive
discussion of the computer's development.  It is the survivor of
many less accurate models.

    Initially, it was found impossible to model the eye's
ordinary growth in terms of a Helmholtz-passive, or heredity
(open-loop) model.  The prime concern was to keep the model as
simple as possible, consistent with the maximum number of facts
known about the natural eye's development.

            TESTING THE MODEL

    There are several standard methods used to test a
sophisticated biological system in order to establish it as a
neurological control systems, e.g., impulse, step, and ramp
functions.  These tests and corresponding responses are well known
to electrical and mechanical engineers.

    The major difficulty in checking a growth system is the
length of time taken for results to occur.  By computer simulation
of the normal eye's behavior, test conditions can be applied and
results obtained within minutes, rather than months.  This is the
major advantages of computer simulation of a physiological
process.

    The first model (open-loop) must be eliminated by experimental
testing.  This test has been accomplish an verifies in a
fundamental way that the eye is a closed-loop control system.

    By design and necessity, the normal eye is going to function
correctly from birth to maturity -- by adjusting its focal state
to the average visual environment.  We can confirm this basic
focal-setting process by changing the average visual environment
of the eye.

    This is shown by the tendency of men, working in the close
quarters of missile launch facilities, to develop a negative focal
state (myopia) related to their length of service.  (4) A step
input applied to the computer will produce this same effect.

    Developing more systematic and quantitative thinking beyond
the close work test, we can use a concave lens to artificially
create a confined visual environment.  In terms of refraction,
this lens will move all objects closer to the eye.  Applying a
negative lens (negative voltage) to our computer produces a change
of focal state of the normal eye after several months.

 THE EYE AS A CAMERA:    A STATIC CONCEPT VERSUS  A DYNAMIC CONCEPT

    The eye can be visualized as a static box camera.    In this
concept, the front-to-back distance is fixed.  If the distance
from the cornea to the retina is too great, as a fault of
heredity, the eye is nearsighted.  This concept simply ignores the
necessary dynamic qualities of the natural human eye.  The
converse of a static camera is a dynamic (cybernetic) model.

    From birth to maturity, the eye increases in size by about
thirty percent.  During this period, the eye's length and cornea
shape is continually controlled by the average value of
accommodation, thereby maintaining a high level of focal accuracy.
The accuracy is estimated to be better than one percent of the
total focal power of the normal eye.  Only a sophisticated (closed
loop) system could cope successfully with such a dynamic process.
A study of the literature will substantiate this long-term focal
control behavior, not only in animals but in man.  (5) (6)

            THEORY EVALUATION

    To evaluate two theories, we must consider their predictive
capabilities.  This requires that the two possible theories yield
full quantitative predictions that can be checked against reality
by actual test.

    A decision between the two competing theories can thereby be
made.  A Helmholtz-heredity theory that yields no qualitative or
quantitative predictions and is not consistent with the facts
already known about the eye's performance, is nothing more than a
sterile tautology.

    There are three major requirements of a theory in physical
science.  They are:  (7)

1.  A theory generally serves to correlate many separate facts in
   a logical and more easily grasped structure of thought.

2.  A theory or hypothesis, whether general or limited, is
   expected to suggest new relations.

3.  A theory must yield predictions of specific observable
   phenomena and provide for the solution of practical problems.

    The computer was constructed in compliance with the first two
requirements.  There is a whole range of predictions to be drawn
from the computer.  Among the more important are these:

1.  With proper supervision it is possible to prevent
   nearsightedness by the use of a convex (positive) lens.

2.  A concave (minus) lens will encourage an incipient case of
   nearsightedness to move more negative.

3.  Wearing a concave lens on a normal eye will cause a negative
   change in the eye's refractive status.  If a strong enough
   minus lens is worn long enough, the refractive status will
   move from positive to negative and the eye will be
   nearsighted.

    A prediction that can decide between the heredity model and
the feedback model is this:  It is possible to take any child and
intentionally change his focal state by the use of a concave
(negative) lens.  Clearly, if we can do this, the
Helmholtz-heredity open-loop theory is not valid as it concerns
the fundamental behavior characteristic of the natural eye.

    "In the last century, in Russia, minus (concave) glasses were
sometimes used to evade military conscription.    A few months
before the appearance for army examination, the conscript went to
an optical doctor and got a pair of strong minus glasses which he
wore steadily until prior to the examination.  He was then sure
that he would be rejected on account of his vision.  The minus
glasses has changed the focal status of his eyes and made his
distant vision very poor." (8)

    If anyone doubts this result, the experiment can be repeated.
In the model this result is expected.  If heredity controls the
long-term growth, the above result would not occur.  The
definitive test between the Helmholtz-passive theory and the
Helmholtz- dynamic theory would be to repeat, under controlled
conditions, the above uncontrolled test as it pertains to the
fundamental behavior characteristic of the natural eye.

    Obviously, as a practical matter, this verification must be
conducted on the young or adolescent primate (monkey) eye.

               REFERENCES

1.  Stark, L.  NEUROLOGICAL CONTROL SYSTEMS, Plenum Press, New
   York (1966)

2.  Milhorn, H.  T.  THE APPLICATION OF CONTROL THEORY TO
   PHYSIOLOGICAL SYSTEMS, Chapter 7, Philadelphia, Pa.  (1966)

3.  Wallman, J.  Turkel, J.  EXTREME MYOPIA PRODUCED BY MODEST
   CHANGE IN EARLY VISUAL EXPERIENCE, Science, Vol 201 Sept.
   (1978)

4.  Green, M.  A.  J.  Am Optometry.  Assoc.  41 1013 (1970)

5.  Young, F.  A.  "Young tested this close-work theory by keeping
   pig-tailed macaques seated in a monkey chair in an enclosed
   visual space for about a year; he reported a change of focal
   state (adolescent, 0.75 diopter change; young, 1.75 diopter
   change)..."  Am.  J.  Ophthalmology.  53 799
   (1961)

6.  Rose, L.  Yinon, U.  Belkin, M.  "Cats raised in cages are
   about 2 diopters negative (myopic) compared with feral (wild)
   cats." Vision Res.  14, 1029 (1974); Belkin, M.  Yinon, U.
   Rose, L.  Reisert, I.  DOC Ophthalmology.  42, 433 (1977)

7.  Holton, G.    Roller, D.  FOUNDATIONS OF MODERN PHYSICAL SCIENCE
   Chapter 8, Redding Massachusetts, Addison-Wesley Publishing
   Co.  (1958)

8.  Raphaelson, J.  OD Discussions with the author in Cincinnati,
   Ohio.  (1966)