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Analysis of refractive state ratios and the onset of myopia
Author(s) -
Lin J. T.
Publication year - 2006
Publication title -
ophthalmic and physiological optics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.147
H-Index - 66
eISSN - 1475-1313
pISSN - 0275-5408
DOI - 10.1111/j.1475-1313.2005.00354.x
Subject(s) - emmetropia , refractive error , radius , optics , cornea , dimension (graph theory) , materials science , mathematics , physics , visual acuity , combinatorics , computer security , computer science
Purpose: To develop formulae for the refractive state ratios, axial length growth and the age of onset ( A *) of myopia. Calculated results are compared with measurements. Methods: Using an image equation, the axial length in the ametropic state ( L ) is related to the length in the emmetropic state ( L *) and refractive error ( D ) by a rate of change M (D mm −1 ). Three refractive state ratios are defined: C 1 = L / r 1, C 2 = L / L * and C 3 = L / H , where r 1 and H are the anterior surface radius of the cornea and the transverse dimension of the eye, respectively. The age of onset A * is calculated by the rate of change of refractive error ( M ) and the axial growth rates N and N * in the ametropic and emmetropic states, respectively. Results: The three ratios C 1, C 2 and C 3 are increasing function of the myopia power, for example, C 1 = 3.4, 3.1, 2.9 for D = −8, 0, +4 dioptres, respectively. The calculated C 1* (for the emmetropic state) varies between 3.08 and 3.14, depending on corneal shape, and C 3 = 0.985, 1.0, 1.04 for D = +3, 0, −3 dioptres: these values are consistent with measured data. For a typical system with effective focal length F = 22.25 mm, L * = 24.2 mm and L = 23.4, 24.9, 25.9 mm for D = +2, −2, −5 dioptres, respectively. The calculated rates of change of refractive error M = 2.3–2.9 D mm −1 for F = 22–23 mm are also consistent with measured values 2.4–2.7 D mm −1 . The age of onset A * is calculated to be proportional to 1/( M d N ), where d N = N − N * is the axial growth rate difference between the ametropic and emmetropic states and may be used as a better predictor for myopia onset than the conventional ratio L / r 1. The A * is given by the crossing of L and L * curves, in which myopia onset occurs earlier for larger M d N . Conclusion: The theory provides formulae to calculate various refractive state ratios, which are consistent with measurements. By defining two rate functions, M and N , the onset of myopia can be predicted.