PREDICTING AXIAL LENGTH USING AGE, KERATOMETRY AND CYCLOREFRACTION LIONEL KOWAL & PRASHANT SAHARE Center for Eye Research Australia & Ocular Motility Clinic, Royal Victorian Eye and Ear Hospital, Melbourne, Australia

ABSTRACT We measured axial length in 51 consecutive patients having strabismus surgery. We found significant correlation between axial length and the three factors of age, keratometry and cyclorefraction. We derived a formula which predicts axial length with an accuracy of ≤±1.0 mm in 88% of patients Axial length = age – keratometry [DS] – cyclorefraction.

INTRODUCTION Strabismus surgeons derive surgical doses from tables describing millimetre doses of surgery. A given mm repositioning of a muscle can be expected to have a larger angular effect on a small globe and a smaller effect on a large globe, yet surgical dose tables do not take globe size into account. Several attempts to modify surgical doses by considering globe size have had inconclusive outcomes. One difficulty of research in the area is obtaining reliable axial length measurements in the relevant age group. In our study we asked: Can we predict axial length using age, keratometry and cyclorefraction?

MATERIALS AND METHODS Charts were reviewed of all strabismus patients on whom axial length measurements were made in the previous 6 months, either in- office with the Zeiss IOL Master® or by ultrasound under anaesthesia. Fifty one consecutive charts with complete data were included in this study. Keratometry was measured with the Nidek KM-500® autokeratometer; averaged keratometry was used for analysis. Refractive error was measured using streak retinoscopy after cycloplegia with cyclopentolate; spherical equivalent readings were used for analysis. The data was analysed by linear regression analysis. Diagnostic plots including the normal quantile - quantile plot and residual vs. predicted value plot were analysed.

RESULTS Fifty one eyes were measured. Age range: 6 months to 55 years (mean 9.9 y). Axial lengths: mm (mean 22.26) Keratometry: D (mean 43.04D). Cyclorefraction: –7.25 to +9 DS (mean +1.8DS). The estimated coefficients for age, keratometry and cyclorefraction were all statistically significant (p <0.001).

RESULTS Correlation between Axial Length, Age, and Refractive Error Patient group factors correlated correlation coefficient p value All patients axial length and age All patients axial length and refractive error Age<2 years age and axial length Age>2 years age and axial length Age<10 years age and axial length Age >10 years age and axial length All myopes axial length and refractive error All hyperopes axial length and refractive error

Fig 1 In a linear regression analysis, the data fitted the model well and explained 87% of variation (r 2 =0.87).The equation for predicting axial length for a given age, keratometry and cyclorefraction is Axial length = age – K – C

Quantile- quantile plot Fig 2 The distribution of axial length is normally distributed as shown in probability and quantile- quantile plot. The diagnostic plots, including the normal quantile-quantile plot below and the residual vs. predicted value plot (Fig 3) did not show any apparent departure from the assumptions of the linear model.

Fig 3 Residual vs. predicted value In 53% of patients [27/51] the axial length predictions were within  0.5mm of the measurement, in 35% [18/51] within 0.5 – 1.0 mm of the measurement and in 12% [6/51] within mm.

DISCUSSION In correcting an angular misalignment with strabismus surgery, we change muscle position / length linearly. Various authors have suggested that we consider globe size when we choose a surgical dose. Such measurements are difficult in younger children and may require general anaesthesia. In our series, regression analysis derived a formula [based on age, keratometry, and cyclorefraction] suitable for estimating axial length. In a remarkably similar series of patients, Kushner had previously shown that examining age and refractive error and assuming an average keratometry of 43.5D for all patients produced greater variation in axial length predictions than we found. He found 41% of predicted lengths to be within  0.5mm of measured lengths [we found 53%] and 79% within 1mm [we found 88%]. The multiple regression analyses in his series resulted in r 2 values ranging from 0.38 to 0.49 c.f in ours. It seems that accurate measurement of keratometry is the necessary extra factor for reliably predicting axial length.

CONCLUSION For those who wish to modify strabismus surgical dose measurements in larger and smaller globes, axial length can be predicted with considerable accuracy using a formula involving age, keratometry and cyclorefraction

REFERENCES Gillies and McIndoe The use of ultrasonography in determining the amount of extra ocular muscle surgery in strabismus Australian Jnl of Ophthalmology 1982;10: Kushner, Luchese and Morton Variation in Axial Length and Anatomical landmarks in Strabismic Patients Ophthalmology 1991: 98: Kushner, Luchese and Morton The influence of axial length on the response to strabismus surgery Arch Ophthalmol 1989;107: Kushner, Qui, Lucchese and Fisher Axial length estimation in strabismic patients JPOS 1996;33: