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Corneal Asphericity after Hyperopic Laser Ablation
Author Response: Corneal Asphericity after Hyperopic Laser Ablation
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Jose R Jimenez, Professor Departamento de Optica. Facultad de Ciencias. Universidad de Granada. Granada. Spain, Rosario G. Anera and Luis Jiménez del Barco
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jrjimene{at}ugr.es Jose R Jimenez, et al.
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The article by Gatinel et al.,1 which makes an important contribution to the study of post-surgical corneal asphericity for hyperopia, can be complemented with the works published previously by Jiménez et al.2,3,4 on the same subject. In their work, Gatinel et al.1 provide information (using a numerical method based on minimization of squared residuals) on the way in which corneal asphericity is altered after hyperopic ablation. Also, they give an approximate equation for the resulting asphericity. The works of Jiménez et al.2,3,4 present two analytical formulas on post-surgical corneal asphericity for initial hyperopia and myopia when the Munnerlyn formula and its paraxial approximation are used. When the Munnerlyn formula is used, we get: p' = p*((R'/R)^3), where p' and p are, respectively, the p-factor of the anterior cornea post- and pre-surgery, while R' and R are, respectively, the post- and pre-surgical corneal radius. The p-factor is related to corneal asphericity, Q, in the following way: p = Q + 1. In the case of the paraxial approximation, the resulting equation is: Q' = Q*((R'/R)^3). Experimental data on hyperopia5 are partially explained by the equations3 shown here. The advantage of the equations shown here and of the procedure used to deduce them2,3,4 is that they enable us to establish in an exhaustive way the relationship between the geometric variables involved in the ablation and make it possible to predict the behavior of these variables after refractive surgery. A simple numerical confirmation shows that the data provided by Gatinel et al.1 on corneal asphericity for hyperopia computed by the Munnerlyn formula are predicted with high accuracy using the equations shown here. Our equations are also of clinical relevance to study quantitatively the influence of different factors (decentration, type of laser, optical role of the flap, wound healing, reflection losses,6 biomechanical effects, technical procedures) during corneal ablation. These equations can also help in studying the deviations between real and expected corneal data, a very important question in refractive surgery, as Gatinel et al.1 also point out. Jose Ramon Jiménez Department of Optics, University of Granada, Granada, Spain References 1. Gatinel D, Malet J, Hoang-Xuan T, Azar DT. Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding Zernike expansions. Invest Ophthalmol Vis Sci. 2004;45:1349-1359. |
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Dimitri T. Azar
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dazar{at}meei.harvard.edu Dimitri T. Azar
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We would like to thank Dr. Jiménez et al. for their correspondence. We agree that the alteration of the corneal asphericity after spherically based (Munnerlyn) conventional hyperopic treatment can be predicted using our numeric and their analytical methods of minimization of squared residuals.1 Jiménez et al. have clearly demonstrated that their prior paraxial approximation could be misleading and their analytical method confirms our numeric results.2,3,4 This could also be approximated by the equation which we published in the same article1:
Jiménez et al. have provided a different equation to approximate the postoperative corneal asphericity after conventional spherically based treatment:
Since 3/(n-1) » 8, our equation (equation 1) can be rewritten as follows: dQ = -3 [D/(n-1)] Q1R1 Using equation 2, the ratio D/(n-1) can be replaced by (1/R2 -1/R1). Integration of both sides of the obtained equality leads to the equation proposed by Jiménez et al. (equation 3). Thus equation 1 can similarly be used to establish the relationship between the geometric variables involved in the ablation and make it possible to predict the behavior of these variables after refractive surgery.5 In our article, we have also addressed additional questions of interest that could not be predicted by equations 1 or 3: we determined the corneal profile changes using Zernike polynomial expansions and studied variations of the coefficients C20 and C40 for various clinically relevant magnitudes of treatment, asphericity, and radius of curvature. We also used Taylor series expansion to approximate the effect of customized aspheric treatments on postoperative corneal asphericity and corresponding Zernike polynomial expansions.1 Damien Gatinel Massachusetts Eye & Ear Infirmary, Boston, Massachusetts References 1. Gatinel D, Malet J, Hoang-Xuan T, Azar DT. Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding Zernike expansions. Invest Ophthalmol Vis Sci. 2004;45:1349-1359. |
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