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Correlation between corneal and refractiveastigmatism with power vectors

Carlo Corradi,*Domenico Musolino, *Marina Serio, Marco Rossotto

Department of Optics and Optometry, University of Turin, Italy*

Scandinavian Journal of Optometry and Visual Science (SJOVS)

Abstract: This work aimed to investigate the correlation between cornealand refractive astigmatism. Along with the WTR and the ATRtypes of astigmatism, the oblique astigmatism was considered,unlike previous literature (Javal, 1890).A sample of 62 eyes was analysed, estimating the cornealastigmatism by the Allergan Humphrey auto keratometermodel 420 (autoker), and the refractive astigmatism by an op-tometric exam.The subjects’ ametropia ranged from -11.00 D to+8.00 D with astigmatism ranging from 0.75 D to 5.00 D.Subjects affected by corneal ectasia and those with an astig-matism less or equal than 0.50 D were excluded from our sam-ple. The corneal astigmatism and refractive astigmatism datawere converted into a vector key (see Figure 1) and the analy-sis was carried out to derive a possible relationship between thetwo (Liu et al., 2011;Remón et al., 2009).After converting all data from clinical notation to vector nota-tion and estimating the average value of internal astigmatism (-0.60 ±0.01 D axis 90.47°), four linear regressions were performedto study a relationship between:

1) refractive astigmatism RJ0 and corneal astigmatism CJ0

2) refractive astigmatism RJ45 and corneal astigmatism CJ45

3) internal astigmatism LJ0 and internal astigmatism LJ45

4) and refractive astigmatism and corneal astigmatism

Since refractive and corneal astigmatism are linearly correlated, it is possible to estimate refractive astigmatism using corneal astigmatism:
Refractive astigmatism = corneal astigmatism ×(0.94 ± 0.06) – (0.60 ± 0.01 D) axis 90°.
This formula is very similar to the approach of the Javal’s rule, with the added possibility of making oblique astigmatism predictions by making them more exact and plenary.

Power vectors have been found to facilitate the description of refraction more accurately and comprehensively. In this case it allows us to conduct the analysis and calculations related to the various elements in a mathematical way (Harris, 2007), something that could not happen with clinical notation alone.
Comparisons with previous studies showed that some of the detected parameters of the linear relationship between refractive and corneal values were compatible with those determined in this study.

Harris, W. F. (2007). Power vectors versus power matrices, and the mathematical
nature of dioptric power. Optometry and vision Science, 84(11), 1060–1063.
Javal, É. (1890). Memoires d’opthalmometrie. G. Masson, Editeur.
Liu, Y.-C., Chou, P., Wojciechowski, R., Lin, P.-Y., Liu, C. J.-L., Chen, S.-J., Liu,
J.-H., Hsu, W.-M., & Cheng, C.-Y. (2011). Power vector analysis of refractive,
corneal, and internal astigmatism in an elderly chinese population: The shihpai
eye study. Investigative Ophthalmology & Visual Science, 52(13), 9651–9657.
Remón, L., Benlloch, J., & Furlan, W. D. (2009). Corneal and refractive astigmatism in adults: A power vectors analysis. Optometry and Vision Science, 86(10),