Analysis of refractive state ratios and the onset of myopia

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.

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: C1 = L/r1, C2 = L/L* and C3 = L/H, where r1 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.

The three ratios C1, C2 and C3 are increasing function of the myopia power, for example, C1 = 3.4, 3.1, 2.9 for D = -8, 0, +4 dioptres, respectively. The calculated C1* (for the emmetropic state) varies between 3.08 and 3.14, depending on corneal shape, and C3 = 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 dN), where dN = 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/r1. The A* is given by the crossing of L and L* curves, in which myopia onset occurs earlier for larger M dN.

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.