Juvenile Myopia. Predicting the Progression Rate
Peter R. Greene1*, Antonio Medina2
1B.G.K.T. Consulting Ltd. Bioengineering Huntington, New York.
2Massachusetts Institute of Technology, Research Laboratory of Electronics, Cambridge, Mass, 02139.
Corresponding Author: Peter R Greene, B.G.K.T. Consulting Ltd. Bioengineering Huntington, New York, 11743, Tel: +1 631 935 56 66; E-Mail:prgreeneBGKT@gmail.com
- Received Date: 24 Dec 2016 Accepted Date: 09 Jan 2017 Published Date: 13 Jan 2017
- Copyright © 2017 Greene PR
Citation: Greene PR and Medina A. (2017). Juvenile Myopia. Predicting the Progression Rate. M J Opht. 2(1): 012.
Regression plots are generated showing the strong correlation of myopia onset age with its progression rate, r = -0.77,
p< 0.0025, and strong correlation of accumulated myopia 5 years after onset, r = -0.78, p < 0.001. Theory is confirmed, with
all subjects showing excellent correlation coefficients,
Emmetropia; Emmetropization; Myopia; Susceptibility; Feedback Model; Under Correction.
TMyopia has an estimated prevalence of 41% among adults in
the United States, and the myopia prevalence is increasing
Vitale et al. . Among Asian populations, the prevalence is
even higher with rates as high as 60% among adolescents age
11 to 17 yrs in China [2-4].
The course of myopia typically follows a pattern that begins with an initial emmetropic phase, followed by a myopic onset that usually occurs in the early school years, which is followed by a myopic depression that tends to stabilize in the mid to late teenage years . These are general trends, early or late onset myopia is also possible and a more modest progression may occur during early adulthood before fully stabilizing.
Figure 1a: The transfer function that describes emmetropization is F(s) = 1/ (ks+1), where k is the time constant of each individual and s is the complex variable. G(s) = 1/ks is the forward function of the transfer function.
Several facts are established that allow an understanding of refraction development of the eye as a system. Emmetropization
and refractive development is a feedback process in humans
[6-11]. There is now considerable evidence showing
that there is feedback control of emmetropization.
Emmetropic or uncorrected eyes follow an exponential development
of refractive error in humans, as shown in Figure 1a.
An exponential development is the response of a first-order
feedback system to a constant-level step input signal [9, 10].
Such a 1st order model will quantitatively model not only the
mechanism of emmetropization, but also the effect of lenses
The refractive state of the eye is alterable with external stimuli, including lid suture. (Meyer et al. ; Raviola & Wiesel ; Greene & Guyton ; Hoyt at al. ; Wallman & Winawer ). Medina & Fariza  showed that corrective lenses applied to the eye are step input stimuli to the emmetropization system and that the response of a first order system (Feedback Theory) to an input determined by the power of the corrective lenses fits refraction data from ametropic subjects that wore those lenses .
Medina [9, 10] showed that a myope that is fully corrected continuously places the emmetropization feedback system in an open loop condition, as shown in Figure 1b. Continuous correction alters the feedback loop rendering it inoperative. He also found that refractive data from the eyes of 13 myopic subjects followed straight lines as predicted by Feedback Theory, Figure 2. Fledelius presents distribution diagrams of onset age for myopia from age 6 to 27 (N=184 subjects), which can be compared to Figure 2 here .
Figure 1b: Open loop transfer function of the feedback system of transfer function 1/ (ks+1). Broken lines denote the loop is open. This open loop function describes continuous correction or visual form deprivation (constant error). The variables are t, time and s, complex variable.
Figure 2 shows the refractive errors of right eyes of 13 myopic
human subjects versus age (symbols) and linear prediction
of open loop system (solid lines). Myopia rates range from
-0.2 to -1.0 D/yr. Correlation coefficients range from -0.907
to -0.998, with a mean of
Figure 2: Refractive errors of right eyes of 13 myopic human subjects versus age (symbols) and linear prediction of open loop system (R/k, solid lines), from Medina [9, 10].
The clinical techniques and data reduction procedures employed
to generate Figure 2 are described in Medina et al.
[9, 10]. These straight-line trajectories are typical of juvenile
progressive myopes. The slope of these lines allows us to correlate
average myopia progression rate
Figure 3a: Myopia progression rate vs. age of onset, r = - 0.77, p < 0.0025, < R’> = - 0.55 D/yr +/- 0.27 D/yr.
Figure 3b: Myopia level 5 years after onset vs. onset age, r = - 0.78,
Figures 3a and 3b show that myopia rate and total acquired
myopia 5 years after onset are strongly correlated with onset
age, r = -0.77, p< 0.0025, and r = -0.78, p< 0.001 respectively.
Average myopia onset age is
These results indicate that the juvenile myope is twice as susceptible to myopia progression at age 5 as at age 15 (-0.8 D/yr. versus -0.4 D/yr.) and twice as susceptible at age 10 as at age 18 (-0.6 D/yr. vs. -0.3 D/yr.). Likewise, at onset, the initial refraction at age 5 is expected to be 50% greater than at age 18, (-1.3 D. vs. -0.9 D. respectively). Confirming these results it was recently found that the risk of high myopia can be predicted based on age of onset of myopia . Feedback Theory predicts the results as it provides that the slope of the progression line is proportional to the myopia at onset.
Feedback Theory and the observations described here have some practical implications concerning the correction or under correction of myopes [24-28].