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Ralf P. Tornow, Robert Laemmer, Friedrich E. Kruse, Folkert K. Horn, Christian Y. Mardin; The Bennett Formula Overestimates The Change In Ocular Magnification As A Function Of Axial Length. Invest. Ophthalmol. Vis. Sci. 2012;53(14):4069.
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Knowledge of the ocular magnification q is important to calculate the real size of retinal features from fundus images, for instance the diameter of the circle to measure peripapillary RNFL thickness using imaging devices. There are different formulas to calculate ocular magnification from parameters like e.g. axial length (AL), refractive error (RE_clinic), and corneal refractive power (CRP) or a combination of parameters. The purpose of this study was to test the validity of the widely-used formula q = 0.01306 (AL - 1.82) [Bennett et. al. 1994] to calculate the ocular magnification q.
In 132 eyes of 132 subjects axial length AL (IOL-master, Carl Zeiss Meditec, Jena, Germany), corneal refractive power CRP (IOL master or Zeiss bomb) and refractive error RE_clinic were measured. Linear regression was used to determine the slope of the clinical refraction RE_clinic as a function of AL. Additionally, the theoretical refractive error for each subject resulting from the assumption of the Bennett formular was calculated. This assumption is that the refractive power of the eye remains unchanged when AL changes. The slopes of the two function RE_clinic = f(AL) and RE_theo = f(AL) were compared.
The axial length (mean ± SD) was (23.8 ± 1.2) mm, range 21.3 to 27.4 mm, refraction (-0.82 ± 2.3) dpt, range -7.0 to 4,3 dpt and corneal refractive power (42.7 ± 1.7) dpt, range 37.25 to 46.50 dpt. There is a correlation of AL with RE_clinic (R = -0.692, p < 0.001) and CRP (R = -0.421, p < 0.001) but no correlation of RE_clinic with CRP (R = 0.083, p = 0.342). The two functions RE_clinic = f(AL) and RE_theo = f(AL) are shown in figure 1. The slope for RE_clinic is -1.33 dpt / mm, while for RE_theo it is more than twice this value (-2.75 dpt / mm). As for a given AL a decrease in refractive power of the eye results in decreased ocular magnification, these results show that the ocular magnification is less than expected by the Bennett formular.
The Bennett formula q = 0.01306 (AL - 1.82) overestimates the change of ocular magnification q as a function of axial length AL. This could be the reason why some studies where this formula was used to calculate q showed a statistical significant increase of retinal nerve fibre layer cross sectional area (RNFL csa) with increasing axial length.
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