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Purpose This study seeks to demonstrate the existence of a feedback loop controlling myopia by comparing the prediction of a feedback model to the actual progression of corrected myopia. In addition to theoretical results, confirming clinical data are presented. Methods The refraction of 13 continuously corrected myopic eyes was collected over a period of time ranging from 4 to 9 years from the time of their first correction. Refractive data was collected in an optometry office from myopic young subjects from the general population in Boston. Subjects were myopes, ages 2 to 22 at the time of first correction selected randomly from a larger population. All individuals were fully corrected with lenses; new lenses were prescribed every time that their myopia increased by 0.25 diopters or more. Subjects wore their spectacle lenses during the followed period. Results Subjects exhibit a linear time course of myopia progression when corrected with lenses. The observed rate of myopia increase is 0.2 to 1.0 diopters/year, with a mean correlation coefficient r =−0.971, p<0.005. Conclusions This report establishes that feedback control theory applies to the clinical phenomenon of progressive myopia. Continuous correction of myopia results in a linear progression that increases myopia. The Laplace transformation of temporal refractive data to the s-domain simplifies the study of myopia and emmetropia. The feedback transfer function predicts that continuous correction of myopia results in a linear progression because continuous correction opens the feedback loop. This prediction is confirmed with all subjects.

The Letter to the Editor BRefractive correction and myopia progression^[1] (Bthe Letter^) makes some good points about the article BThe progression of corrected myopia^ [2] that the article had already addressed in part.Medina's feedback model for emmetropization predicts that correction of myopes aggravates their condition, and that delaying correction will result in less progression rate and probably a reduced myopic final level. The model also predicts that under-correcting myopia would have a small effect in reducing the progression rate.The Letter advises that there is controversy on the issue of whether under-correction of myopia will have any beneficial effect, citing four published reports [3][4][5][6] involving distance under-correction. Medina [2] cites those reports, and others, noting the conflict and suggesting experimental problems. The Letter overlooks several reports that show that undercorrection for near vision with bifocals reduces myopia progression, e.g. [7] and those cited in [2].In response to the Letter, the effect of distance undercorrection would be difficult to detect experimentally due to the small effect and the difficult experiment. Reports [3][4][5][6]8] discussed in the paragraphs below confirm the small and conflicting effect and exemplify the difficulty.Chung and Mohidin [3] showed a small (0.23 D) but significant greater rate of progression in a group of 47 children under-corrected by about 0.75 D as compared to another group of 47 children fully corrected for a period of 2 years. They paired the data in an attempt to avoid the problem of intersubject variation. However, the myopia progression rate is very variable, even for paired subjects of the same age and initial refractive error. Adler and Millodot [4] show no significant myopia progression difference between two groups of 23 fully corrected myopes and 25 myopes under-corrected by 0.50 D for a period of 18 months.Vasudevan et al.[5] found a significant positive correlation between the degree of under-correction of refractive error and the rate of myopic progression. This result is contradicted by a later study [8]. The difference in myopia progression between the groups with full correction and under-corrected by 0.5 D is less than 0.25D. See its Figure 1 (as amended [9]).Ong et al.[6] in a longitudinal study concluded that, over a period of at least 3 years, refractive shifts were not significantly different among a group of full-time wearers (n = 8) of spectacle correction and a group of non-wearers (n = 5), when the data were corrected for age effects. The non-wearers, however, developed less myopia than the fulltime lens wearers, and the difference was borderline significant when there was no Bcorrection^for age effects. The age Bcorrection^may be questionable given the large variation in progression rate and the reduced number of subjects. The natural variation in myopia progression is much larger than the effect of undercorrection.A recent study of two groups of under-corrected and fully corrected children [8] fail...

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The response of a second-order feedback system is used to describe the controlling process that regulates the refraction of the human eye to achieve optimal visual acuity over the years (emmetropization). From data collected in past refractions, the equation of the feedback system has been derived for individual eyes and used to predict changes in their refraction with age with an accuracy of 0.50 diopters for 89.1% of the eyes tested. If the model is applied to other populations, the root mean square error of prediction will be between 0.20 and 0.36 diopters with a 95% degree of confidence. The model indicates that corrective lenses applied to the eyes, especially in the early years of life, will cheat the servo system and defeat the emmetropization process.

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Numerical experiments are performed on a first order exponential response function subjected to a diurnal square wave visual environment with variable duty cycle. The model is directly applicable to exponential drift of focal status. A two-state square wave is employed as the forcing function with high B for time H and low A for time L. Duty cycles of (1/3), (1/2) and (2/3) are calculated in detail. Results show the following standard linear system response: (1) Unless the system runs into the stops, the ready state equilibrium settling level is always between A and B. The level is linearly proportional to a time-weighted average of the high and low states. (2) The effective time constant t(eff) varies hyperbolically with duty cycle. For DC = (1/3) and t1 = 100 days, the effective time constant is lengthened to 300 days. An asymptote is encountered under certain circumstances where t(eff) approaches infinity. (3) Effective time constants and steady state equilibria are independent of square wave frequency f, animal time constant t1, magnitude and sign of A & B, and diurnal sequencing of the highs and lows. By presenting results on dimensionless coordinates, we can predict the drift rates of some animal experiments. Agreement between theory and experiments has a correlation coefficient r = 0.97 for 12 Macaca nemestrina eyes.