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F Thorn, R Held, J Gwiazda; The Dynamics of Myopia Progression Onset and Offset Revealed by Exponential Growth Functions Fit to Individual Longitudinal Refractive Data . Invest. Ophthalmol. Vis. Sci. 2002;43(13):2866.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: A Gompertz double exponential growth function closely fits the time course of the refractive data of individuals developing myopia even though these data vary greatly among individuals (Thorn et al, ARVO, 2001). We now consider the implications of exponential function fits for an understanding of the dynamics of myopization, especially at the onset and offset of myopia progression. Methods: Longitudinal refractive data (noncycloplegic retinoscopy) from both eyes of 36 subjects were used. A Gompertz function was fit to the data for each eye (a mean of 14.64±3.84 data points at intervals of 1.00±0.22 years). A simple exponential function was fit to data that occurred at or after the onset of myopization (a mean of 8.86±2.60 data points at intervals of 0.97±0.22 years). To examine the abruptness of the onset of myopization, we compared the results of a Gompertz function (which models an accelerating onset) to a splined function that combines the pre-onset Gompertz function with the simple exponential function (which models an instantaneous onset). To examine the offset of myopization, 1. we tested for systematic errors in the simple exponential function and 2. we compared the Gompertz function fits for all the data to those for data prior to myopization deceleration. Results: The less abrupt Gompertz function fits the onset data better than the splined function showing onset inertia. At myopization offset, the simple exponential function systematically predicted a myopization offset that extended into middle age with excessive amounts of myopia. The Gompertz function fit to the data prior to deceleration also predicted an excessive amount of myopia and leveling off later than that shown by the fit to the complete data set. Conclusion: Exponential functions fit to the refractive data of individuals can reveal the dynamics of myopization. In most subjects, the onset of myopization is surprisingly abrupt but it is not instantaneous. The late stage of myopization slows faster than is predicted by a simple ballistic asymptote implying that a dampening factor is needed to explain the rapidity of the offset in most subjects.
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