Journal of Refractive Surgery

Correlation Between Attempted Correction and Keratometric Refractive Index of the Cornea After Myopic Excimer Laser Surgery

Giacomo Savini, MD; Piero Barboni, MD; Maurizio Zanini, MD

Abstract

ABSTRACT

PURPOSE: Given that the standard keratometric refractive index of 1.3375 is no longer valid after excimer laser surgery, we aimed to investigate how this value changes postoperatively and if any correlation to the attempted correction exists.

METHODS: The pre- and postoperative data of 98 patients who underwent either myopic photorefractive keratectomy (PRK) or LASIK were reviewed. Using post-operative videokeratography, the corneal radius (r) was obtained; the corrected corneal power (P^sup c^) was measured by separately calculating the dioptric power of the anterior and posterior corneal surfaces. The postoperative index of refraction (n^sup post^) was derived from these values using the formula: n^sup post^ = (rP^sup c^)+1.

RESULTS: As the amount of refractive change increases, n^sup post^ progressively decreases (P<.0001, r=0.9581). Linear regression provided the subsequent formula to calculate the postoperative index of refraction: n^sup post^ = 1.338 + 0.0009856 × attempted correction.

CONCLUSIONS: Myopic PRK and LASIK induce a decrease in the keratometric refractive index. This reduction correlates to the amount of attempted correction. When the latter is known, calculating n^sup post^ may enable the measurement of corneal power and thus provide an additional method for calculating intraocular lens power in eyes that have undergone myopic PRK or LASIK. [J Refract Surg. 2007;23:461-466.]

Abstract

ABSTRACT

PURPOSE: Given that the standard keratometric refractive index of 1.3375 is no longer valid after excimer laser surgery, we aimed to investigate how this value changes postoperatively and if any correlation to the attempted correction exists.

METHODS: The pre- and postoperative data of 98 patients who underwent either myopic photorefractive keratectomy (PRK) or LASIK were reviewed. Using post-operative videokeratography, the corneal radius (r) was obtained; the corrected corneal power (P^sup c^) was measured by separately calculating the dioptric power of the anterior and posterior corneal surfaces. The postoperative index of refraction (n^sup post^) was derived from these values using the formula: n^sup post^ = (rP^sup c^)+1.

RESULTS: As the amount of refractive change increases, n^sup post^ progressively decreases (P<.0001, r=0.9581). Linear regression provided the subsequent formula to calculate the postoperative index of refraction: n^sup post^ = 1.338 + 0.0009856 × attempted correction.

CONCLUSIONS: Myopic PRK and LASIK induce a decrease in the keratometric refractive index. This reduction correlates to the amount of attempted correction. When the latter is known, calculating n^sup post^ may enable the measurement of corneal power and thus provide an additional method for calculating intraocular lens power in eyes that have undergone myopic PRK or LASIK. [J Refract Surg. 2007;23:461-466.]

Inaccurate calculation of intraocular lens (IOL) power after refractive surgery has been the subject of considerable attention in the past decade. It is widely recognized that using videokeratography underestimates corneal flattening after myopic excimer laser surgery. As a consequence, standard keratometric values lead to IOL power underestimation (with subsequent hyperopia) in eyes that have previously undergone myopic photorefractive keratectomy (PRK) or LASIK.1'2

Errors in IOL calculation after PRK/LASIK depend on two factors. The first is the incorrect effective lens position calculated by third-generation theoretical formulas, which use the keratometry (K) value after refractive surgery. To overcome this problem, Aramberri introduced the double-K method.3 The second is the difficulty of correctly determining the keratometric diopters to be entered into IOL power calculation formulas as a measure of the central corneal power. The reason for such difficulty lies in the fact that current videokeratoscopes use a standardized keratometric index of refraction (in most cases 1.3375) to convert the measured radius into corneal diopters. Based on Gullstrand's eye model, this index refers to a theoretical single refractive lens representing both the anterior and posterior surface of the cornea. Taking into account the optical pathway throughout the cornea, it assumes a stable ratio of anterior corneal curvature to posterior corneal curvature. Myopic refractive surgery by excimer laser flattens the anterior corneal surface, thus disrupting this ratio and invalidating the use of the standardized keratometric corneal index.

Several studies have attempted to calculate the actual corneal power after excimer laser surgery, but only rarely have these studies focused on the real problem, ie, the change in the keratometric refractive index.24"10 The aim of this study was to investigate how the keratometric refractive index is modified by excimer laser surgery.

PATIENTS AND METHODS

The analysis was carried out on the same group of patients recently described in a theoretical study.11 Briefly, the pre- and postoperative data of 98 patients were reviewed. All patients had undergone either PRK (54 cases) or LASIK (44 cases) in a private ambulatory surgical center (Centro Salus, Bologna, Italy) to correct a myopic defect between ?1.13 and ?11.38 diopters (D) (mean: -5.18?2.21 D) and had a postoperative manifest refraction within 0.25 D of emmetropia. Surgery was performed using the NIDEK EC-5000 (NIDEK Co Ltd, Gamagori, Japan) excimer laser; in LASIK surgery, a Bausch & Lomb Hansatome microkeratome (Claremont, Calif) was used to create the flap. Pre- and postoperative videokeratography was performed with the TMS- 2 Topography System (Tomey, Erlangen, Germany), which calculated the simulated keratometry ( SimK) .

Linear regression was used to assess the correlation between n^sup post^ (taken as the dependent variable) and the amount of refractive change at the spectacle plane (taken as the independent variable). A P value <.05 was considered statistically significant. Statistical tests were performed using GraphPad InStat version 3a for Macintosh (GraphPad Software, San Diego, Calif). In patients who had bilateral surgery, only the first operated eye was considered for statistical analysis.

RESULTS

The mean postoperative corneal power, as measured by videokeratography, and corneal radius, as calculated by Eq.(l), were 39.21±2.10 D (range: 32.50 to 45.02 D) and 8.63?0.48 mm (range: 7.5 to 10.38 mm), respectively.

The mean corrected corneal power, calculated using the method of separately considering the anterior and posterior corneal surface, was 38.69±2.25 D (range: 31.43 to 44.92 D). The mean n^sup post^, as calculated by Eq.(6), was 1.332960?0.002 (range: 1.326237 to 1.336798).

Linear regression disclosed a statistically significant relation between n^sup post^ and attempted correction (P<.0001, r=0.9581, rp 2=0.9170) (Fig).

Figure. Scattergram of postoperative keratometric index of refraction (n^sup post^) versus attempted correction (P<.0001, r = 0.9581, rp 2 = 0.9170),

Figure. Scattergram of postoperative keratometric index of refraction (n^sup post^) versus attempted correction (P<.0001, r = 0.9581, rp 2 = 0.9170),

To assess the predictability of Eq.(7), P^sup post^ was calculated in all 98 eyes and compared to P^sup c^ values. As expected, the difference between P^sup post^ and P^sup c^ was minimal (mean arithmetic error: 0.03?0.06D; range: ?0.22 to 0.20 D; mean absolute error 0.05?0.05 D).

Equation 8 was also adopted to calculate the IOL power in four consecutive patients who underwent cataract surgery and IOL implantation after myopic excimer laser surgery. All patients (whose preoperative LASIK/PRK data were available) had satisfactory results, with postoperative refraction between sphere -0.50 and ?0.75 D. The Table shows the results for these patients and includes the corneal and IOL power calculated by means of nine other methods.1"9 As was recently done by Walter et al,14 the "true" IOL power was retrospectively determined by taking the resultant manifest refraction after cataract surgery and the implanted IOL power and calculating the IOL that would have resulted in emmetropia. This was accomplished with the knowledge that every diopter of IOL power is equal to approximately 0.70 D in refraction at the spectacle plane.915

Although a statistical analysis was not possible due to the small sample size, it can be observed that the mean IOL provided by Eq. (8) is the closest to that calculated by the double-K clinical history method, which is usually considered the most accurate method to obtain IOL power after corneal refractive surgery311; when compared to the mean "true" IOL power, Eq.(8) seems to result in a slight IOL power overestimation ( + 0.48D).

DISCUSSION

Our study shows a significant correlation between the postoperative value for keratometric refractive index and the attempted correction by excimer laser, in that the former progressively decreases with increasing values of the latter. Hamed et al16 previously reported a similar result. In our analysis, linear regression showed an even closer relationship between the keratometric refractive index and the degree of surgically induced correction (rp 2=0.9170 in our study, rp 2=0.3091 in the study by Hamed et al). Such a difference is probably due to the different methods used to calculate corneal radius and power. Nevertheless, we concur with them that it is not possible to obtain a single keratometric refractive index for all eyes that have undergone LASIK or PRK.

Table

TABLEPerioperative Data of Four Consecutive Patients Who Underwent Phacoemulsification and Intraocular Lens Implantation After Myopic Excimer Laser Surgery

TABLE

Perioperative Data of Four Consecutive Patients Who Underwent Phacoemulsification and Intraocular Lens Implantation After Myopic Excimer Laser Surgery

The decreased values of the keratometric refractive index are probably due to the changed ratio between the anterior and posterior corneal curvatures. Other causes may also play a role. Patel et al,17 for example, postulate that the reduction in the refractive index of the corneal stroma after excimer laser surgery is likely to account for the discrepancy between the actual change in refraction and the change in central corneal surface power. According to these authors, the reduction in the corneal refractive index may be related to the variation in hydration along the depth of the stroma, as the anterior corneal stroma is less hydrated than the posterior stroma.17 Both PRK and, to a lesser extent, LASIK remove the anterior corneal stroma, thus leaving the more hydrated posterior region of the stroma. We agree that such a relative increase of corneal hydration may account, at least in part, for the lower postoperative keratometric refractive index. However, as previous studies have shown that the mean difference between the refractive index of the anterior and posterior corneal surfaces is 0.007,18 a value that may be considered low compared to the progressive reduction calculated in our own sample, it is likely that other factors, such as changes in the profile (from prolate to oblate) or transparency of the cornea, play a role.

Other investigators have aimed to assess the changes in the keratometric refractive index following excimer laser surgery. Camellin and Calossi10 found the keratometric refractive index to be a function of the surgically induced correction, a result consistent with our own findings. Ferrara et al8 described a theoretical variable index depending on axial length (rather than on the correction); they subsequently used this value to calculate the IOL power after refractive surgery. The main limitation of their method lies in the fact that axial length and refractive correction are not always mutually correlated; it is not uncommon, for example, that low amounts of myopia are corrected in patients with long eyes if the cornea is naturally flat. As a consequence, the predictive power of their method may be lessened in some eyes.11 The formula developed by Ferrara, however, has a considerable advantage in that it is completely independent from preoperative data, whereas preoperative refraction values are needed to assess the keratometric refractive index in our method.

Mandell13 and, a few years later, Gobbi et al19 proposed that the index of 1.376 (corresponding to the refractive index of the anterior corneal surface) should be used to convert radius into corneal power after excimer laser surgery; as an alternative the standard reading can be multiplied by the factor 1.114. Hugger et al20 reported that a refractive index of 1.4083 would further reduce the difference between the change in keratometry and refraction.

Conversely, the findings of the present study, as well as those of Ferrara et al,8 Camellin and Calossi,10 and Hamed et al,16 suggest that the postoperative index of refraction is lower than 1.3375 and is likely to change according to the amount of myopic correction.

From a practical point of view, it should be highlighted that the value obtained from the formula nP0St = 1.338 + 0.0009856 × attempted correction can be used to calculate the postoperative corneal power. This increases the number of available methods for calculating IOL power after myopic excimer laser surgery where the refractive change is known and reliable. Three other methods requiring only this value have been developed by Latkany et al,4 Shammas et al,6 and Feiz et al.9 In these cases, the authors did not modify the keratometric refractive index, but rather used linear regression either to directly adjust the IOL power according to the myopic correction (Latkany and Feiz) or to calculate the postoperative keratometry (Shammas). Although the results achieved by means of our method (Table) are promising, further investigations are required to assess which of these formulas may provide the most accurate postoperative keratometry. In addition, it should be noted that our method may achieve accurate results only if the double-K formulas by Aramberri are used: this means that not only the attempted correction but also the preoperative LASIK/PRK keratometry must be known; alternatively, the calculated IOL power should be adjusted according to the nomogram published by Koch and Wang.21

In the design of our study we made two important assumptions, which warrant review as a possible source of error or limitation. The former concerns Eq.(6), which we used to calculate the postoperative keratometric refractive index: we chose the corneal power calculated by considering the anterior and posterior corneal surfaces separately, as described by Seitz and Langenbucher1 and Speicher.2 Although this method is appealing from a theoretical point of view, it has never been tested in clinical practice. For this reason, we performed the same calculation using the keratometric values from the clinical history method. We still obtained a mean refractive index (1.335265?0.0044) that was lower for higher corrections (P<.0001), although the correlation (r=0.4594, rp 2=0.211) was not as close as when the former method was used. The lack of an explanation for such a discrepancy highlights the need for further studies evaluating the accuracy of the clinical history method. The latter regards our sample, which was limited to patients whose postoperative spherical equivalent was within 0.25 D of emmetropia, so that the surgically induced refractive change and the attempted correction were equivalent ? different results might have been obtained in eyes with a different postoperative refractive outcome.

Our data show that after myopic excimer laser surgery the conventional keratometric refractive index of 1.3375 should be adjusted downward by an amount that is directly proportional to the amount of refractive change. In eyes that have previously undergone LASIK or PRK, the application of nP0St may help in calculating the corneal power to be entered into the formula used to calculate the appropriate IOL power in cataract surgery. Further studies are needed to define the reduction in the keratometric refractive index more precisely and assess its effectiveness from a clinical point of view.

REFERENCES

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10. Camellin M, Calossi A. A new formula for intraocular lens power calculation after refractive corneal surgery. J Refract Surg. 2006;22:187-189.

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14. Walter KA, Gagnon MR, Ho op es PC, Dickinson PJ. Accurate intraocular lens power calculation after myopic laser in situ keratomileusis, bypassing corneal power. J Cataract Refract Surg. 2006;32:425-429.

15. American Academy of Ophthalmology. Basic and clinical science course: optics, refraction and contact lenses. 1996-7;3:176.

16. Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology. 2002;109:651-658.

17. Patel S, Alio JL, Perez-Santonja JJ. A model to explain the difference between changes in refraction and central ocular surface power after laser in situ keratomileusis. J Refract Surg. 2000;16:330-335.

18. Patel S, Marshall J, Fitzke FW III. Refractive index of the human corneal epithelium and stroma. J Refract Surg. 1995;11:100-105.

19. Gobbi PG, Carones F, Brancate R. Keratometric index, vide o - keratography, and refractive surgery. J Cataract Refract Surg. 1998;24:202-211.

20. Hugger P, Kohnen T, La Rosa FA, Holladay JT, Koch DD. Comparison of changes in manifest refraction and corneal power after photorefractive keratectomy. Am J Ophthalmol. 2000;129:68-75.

21. Koch DD, Wang L. Calculating IOL power in eyes that have had refractive surgery. J Cataract Refract Surg. 2003;29:2039-2042.

TABLE

Perioperative Data of Four Consecutive Patients Who Underwent Phacoemulsification and Intraocular Lens Implantation After Myopic Excimer Laser Surgery

10.3928/1081-597X-20070501-07

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