CONTROL THEORY APPLIED TO THE HUMAN EYE
A proposed myopia prevention study;
“Mathematical Model of College Myopia
By Dr. Antonio Medina, M. I. T., and
Dr. Peter Greene, Harvard
Supporting Analysis of Applying Control Theory to all Normal Eyes:
Written by Antonio Medina OD, Ph.D.
Dr. Medina, used this concept of, “prevention” on his own two children – which is true science. Here is the abstract of his theory – as applied to his own children. Recent publication:
That is real success. You must keep “after” your own children to wear the plus for all close work, while they still read and pass the 20/20 line.
The Engineer-Optometrist analysis of the normal eye: Please read this:
The progression Medina (Otis) of Myopia.
Analysis of Induced Myopia: Translated from the Spanish
Figures 1, 2, and 3
Original Drawings in this paper:
Feedback loop that controls the long term refraction of the eye.
Figure 4: BLOCK DIAGRAM
The feedback servo diagram is represented in Fig. 4
The information that the feedback system has on the refractive state of the eye may be deduced from the states of accommodation from the ciliary muscle.
This is possible as shown in Figure 4, which represents the possible states of accommodation in a subject of any refraction. In this figure (this very simplified) it can be seen that the brain would be capable of detecting ametropia in the interval +/- 5 diopters. This is done in the block “H” of the feedback loop in Fig. 4.
The block marked as “-” calculates the difference between this input signal from block H, which is between -5 and +5 D, and the control signal. If the difference is zero the eye is emmetropic or has the genetically advised refraction, so the servo takes no further action.
If the difference is non-zero, the error detector delivers a signal that, once processed and amplified by block “A” is an indicator that the eye should start a plus or minus trend.
The eye begins to change its parameters which determine refraction. Those that are more easily changed are the curvature of the lens and length of the anteroposterior axis.
By varying any of these parameters and therefore the refraction as ordered by the control signal, the block “H” in the feedback loop begins to deliver an error signal to the error detector closer to the input value. Once achieved equality, the error signal is zero and the eye stops changing its parameters.
Figure 5: GRAPH DIAGRAM
Fig. 5 – Diagram showing the accommodation used (vertical axis) by an uncorrected adult of any degree of ametropia (horizontal axis). Values are approximate averages and depend on the subject and age. It shows that a myope of -5 D or more will essentially not use accommodation. A hyperope of +5 D or more will use accommodation continuously and an emmetrope will accommodate between 0 and 4 D. The 4 D accommodation interval is variable with age and it was arbitrarily chosen for illustration.
MATHEMATICAL MODELS OF COLLEGE MYOPIA
By Dr. Antonio Median, M.I.T, and Dr. Peter Greene, Harvard
This is an idealized pure prevention study – proposed for military or engineering students – to take a leadership position for their own study.
Science – requires bold new concept and ideas. This type of science, would require direct involvement of each engineer in the study – to understand the concept, and make his own confirming refractive measurements – himself.
These paragraphs have tried to explain very simply the behavior of the servo controlled eye. To work with it quantitatively, to predict a patient’s ametropia after a number of years, for example, we need the servo in detail, which is not described in these lines, and all the parameters of the differential equation of the servo, which must be measured from the patient.
As an example let’s see the cause of school myopia with the light of the above lines. An individual with no genetic predisposition for myopia has little chance of acquiring myopia. However, a combination of factors, such as small genetic predisposition and continued use of accommodation, especially with artificial light (remember that the interval of accommodation decreases with the level of illumination) causes a progression of myopia to about 3-5 D.
This is because the block “H” in the feedback loop of Fig. 4, which deduces the eye’s refraction as a function of accommodation, takes it by hypermetropic because of its frequent accommodation and there is an error signal that directs myopizing. The prescription of glasses in these cases not only does not benefit from a standpoint of reduction of myopia, but aggravates it by the increment in the error signal.
THE COMPLETE PAPERS BY DR. MEDINA:
Dr. Medina has completed and excellent analysis of the eye’s behavior, including analysis of progression, due to the minus lens:
Here is the English translation, Dr. Medina’s complete paper: “The Origin of Ametropia”
The highly insightful concept that recognizes that the natural eye is a two-stage control system.
Open-loop accommodation analysis by Dr. Strang
Remarks about methods to measure visual acuity.
Critical to fundamental, or pure-science is the repeatable experiment that always produces the same result. (See above, Earl Smith III)
It is essential to prove that a normal eye will change its refraction – in both directions, with change in average value of accommodation. This paper proves that issue.
SOURCE OF THE CONCEPT OF “OFFSET” FOR ALL NORMAL EYES.
I never wanted a, “medical fight” about all natural eyes as “control systems”.
To me, it always seemed perfectly logical that the should, and must be control system. I just can not think of all natural eyes – in any other way than that.
In this “pure math model”, the refractive STATE of all natural eyes – controls its refractive STATE – to the average of the accommodation system.
Thus, you look to “change” the average value of accommodation, and look for the refractive STATE, to change as you would expect it to – and must.
But allow me to clarify the concept of, “OFFSET”, and why it must exist for all natural eyes (and why it is so difficult to, “prove it”.)
Let me start with a simple concept – to clarify the idea.
1) All light rays – hitting the eye are either parallel, (0 diopters), or diverging (Negative diopters). I think we both agree with that basic physics.
2) There fore, a simple control system, that had an accommodation system at about -1/2 diopters, (average between 0.0 D, and -2 diopters, for close looking, would have an estimated average of -1/2 diopters. (Stay with me in this analysis.)
3) Therefor, in a SIMPLE system, my refractive STATE would have to eventually become, -1/2 diopters – as a control system.
4) But I respect this “design” to be smarter than that. Our physiological system, must, “off set” the average value of accommodation, by a certain amount – so that our our STATE remains positive, when living in the wild.
5) This is where Dr. Young’s “wild” data is important.
6) The normal refractive STATES have values between -1/2 to +2 diopters (approximately).
7) To achieve these values, our “system” must offset, the average value of accommodation — by about +1.5 diopters.
8) No, this proves nothing about myopia, hyperopia, ametropia, emmetropia, “emmetropization” – at all.
9) But if you are looking for all natural eyes to be dynamic – in the first place — then you search to establish this issue for all normal eyes – that work as control systems.
10) This is simply “black box” testing, where you apply a “step input” to the system, and look for the refractive STATE to change, as you would expect to do so.
As always – I do not see how any OD or MD, could ever change anything.
The only exception – was yourself – and your support for your own two children.
You are the only success that I know of, for your own children!