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Myopia Progression Is Specified by a Double Exponential Growth Function

THORN, FRANK OD, PhD, FAAO; GWIAZDA, JANE PhD, FAAO; HELD, RICHARD PhD, FAAO

Optometry and Vision Science: April 2005 - Volume 82 - Issue 4 - p E286
doi: 10.1097/01.OPX.0000159370.66540.34
Original Article

Purpose. The purpose of this study was to demonstrate how well a modified Gompertz double exponential growth function delineates the diverse courses of myopia progression found in individual eyes. The function is: R = R e+ R c(0.07295)a(x−to) where the spherical equivalent refractive error at a given age R equals the initial refractive error (R e) plus the overall refractive change (R c) times a double exponential function with the base (0.07295) representing the proportion of R c that occurs when maximum acceleration is reached, a is a curvature coefficient, t o is the age of onset and x is age.

Methods. This function was fit to longitudinal refractive data (spherical equivalents) for both eyes of 36 myopic children. The fits were required to meet a stringent set of criteria, including fitting transitions in and out of myopia progression and having no systematic errors or arbitrary constants.

Results. Correlation between values on the refractive function and corresponding data of individual eyes is high (mean r = 0.973 ± 0.020), the sum of squares between the data and function is low, and all other criteria are met. The rates of refractive change and acceleration were derivable from this function. It has been shown that, if peak acceleration rate is used as a criterion for the onset of myopia progression, then myopization onset starts a year earlier (mean = 8.93 years) than when a -0.50-D onset criterion is used (mean = 9.93 years), and it usually starts before the spherical equivalent reaches zero (mean R = +0.09 D). Age of onset is highly correlated with the duration of myopia progression (r = 0.693), which in turn is correlated with the amount of myopia achieved (r = 0.443).

Conclusions. We demonstrate that the double exponential function delineates the dynamics of myopia progression onset, offset, and the derivatives that describe the mechanisms underlying the growth process that causes myopia and have explained the advantages of this function. The function can be used to more accurately portray the course of individual subject’s myopic progression.

Myopia Research Center, New England College of Optometry, Boston, Massachusetts

Received August 31, 2004; accepted January 18, 2005.

© 2005 American Academy of Optometry