Corneal Asphericity and Its Implications for Photorefractive Keratectomy: a Mathematical Model

Effect of anterior corneal surface asphericity modification on fourth-order zernike spherical aberrations

PURPOSE

To evaluate the theoretical influence of the change in corneal asphericity (ΔQ) on the change in fourth-order Zernike spherical aberration coefficient (ΔC(4)0) with customized aspheric refractive correction of myopia and hyperopia.

METHODS

The initial anterior corneal surface profile was modeled as a conic section of apical radius of curvature R0 and asphericity Q₀. The postoperative corneal profile was modeled as a conic section of apical curvature R1 and asphericity Q1, where R1 was computed from defocus D, and Q₁ selected for controlling the postoperative asphericity. The corresponding change in fourth-order spherical aberration (ΔC(0)4) was computed within a 6-mm optical zone using inner products applied to the incurred optical path changes. These calculations were repeated for different values of D, R₀, Q₀, and various intended ΔC(4)0 values.

RESULTS

Increasing negative spherical aberration (ΔC(4)(0) < 0) requires a change toward more negative values of asphericity (increased prolateness; ΔQ < 0) for hyperopic and low myopic corrections, but more positive values (ΔQ < 0) for high myopic correction. The larger the intended change in corneal spherical aberration (ΔC(4)(0)), the more myopic the threshold value for which the required change in asphericity, ΔQ, becomes positive. The influence of the magnitude of paraxial defocus correction is less pronounced when larger changes in C(4)(0) are intended.

CONCLUSIONS

These results provide a basis for controlling the direction (sign) and the magnitude of spherical aberration changes when using customized aspheric profiles of ablation.

Asphericity of the anterior human cornea with different corneal diameters

PURPOSE

To measure the anterior corneal asphericity (Q) with different corneal diameters.

SETTING

Department of Physics (Optometry), University of Minho, Braga, Portugal.

METHODS

Thirty-six eyes of 36 patients were evaluated using a videokeratoscope, and the Q-values were recorded. Topographic data were also analyzed using Vol-CT 6.89 software (Sarver & Associates, Inc) to obtain the Q-values with different corneal diameters (3.0 mm, 4.0 mm, 5.0 mm, 6.0 mm, and 7.0 mm). Variable Q models of corneal sagittal height were compared against models assuming constant Q-values obtained with the Medmont E300 videokeratoscope (Medmont Pty. Ltd.) and a standard Q model of -0.26.

RESULTS

The peripheral rate of change in corneal Q with different corneal diameters increased as corneal astigmatism increased. As a result, differences in the sagittal height between the constant model and variable model were evident beyond the central 3.0 mm area. There were significant differences between low and high astigmatic corneas in Q-values measured by the Medmont along the flattest meridian (P = .004) and Q-values obtained with Vol-CT software with a 7.0 mm corneal diameter (P = .026).

CONCLUSIONS

There were differences in sagittal corneal height calculations considering constant or variable models of Q. Concern arises when surgical interventions depend on corneal Q-values to predict the outcomes. Surgeons should be aware which procedure is behind Q computing by different corneal topographers and that a constant Q-value cannot reflect the actual shape of the cornea as significant departures from the actual sagittal height can arise depending on which Q-value is assumed.

Spherical aberration after laser in situ keratomileusis and photorefractive keratectomy

PURPOSE

To assess changes in corneal asphericity after laser refractive surgery and mathematically model possible causes of the changes.

SETTING

Cornea and Laser Eye Institute, Hersh Vision Group, Teaneck, New Jersey, USA.

METHODS

The corneal topography (EyeSys 2000) of 20 eyes was measured before and after laser in situ keratomileusis, laser-assisted subepithelial keratectomy, and photorefractive keratectomy for myopia. All preoperative and postoperative maps were analyzed using the CTView 4.0, a computer software program for determining quantitative corneal spherical aberration. To define possible mechanisms of asphericity change, 2 mathematical models of corneal ablation were constructed and theoretical postoperative corneal asphericities were determined over a range of corrections from -12.0 to +6.0 diopters. Model 1 assumes homogeneous beam fluence over the ablation zone, and model 2 accounts for a theoretical ablation rate drop off peripherally as a result of the angle of incidence of the laser beam on the cornea. Postoperative clinical corneal spherical aberration was compared to the theoretically predicted asphericity values.

RESULTS

After excimer laser procedures, all corneas had positive asphericity within the ablation zone, generally changing from a prolate to an oblate optical contour. The mean asphericity (Q) was -0.17 +/- 0.14 (SD) preoperatively and +0.92 +/- 0.70 postoperatively. The mean change in spherical aberration was +1.09 +/- 0.67 of positive asphericity; the range of asphericity change was +0.40 to +2.73 in the direction of a more oblate corneal profile. A trend toward greater change in asphericity and more oblateness was observed among eyes receiving higher correction. A mathematical model taking into account theoretical beam fluence changes across the ablation zone was highly predictive of the actual postoperative asphericity measurements.

CONCLUSIONS

The cornea within the ablation zone becomes more oblate after laser refractive surgery. A mathematical model of the change in asphericity, which accounts for the angle of incidence of the laser beam across the ablation area, predicted this change in spherical aberration. If the model is correct, possible changes in laser algorithms, delivering more ablation to the peripheral optical zone, may better retain the native corneal prolate conformation. Moreover, wavefront-guided ablations may have to consider the effects of fluence variability across the optical zone to fully correct spherical as well as other aberrations.

Effect of preoperative keratometry on refractive outcomes after laser in situ keratomileusis

PURPOSE

To evaluate the effect of preoperative keratometry on the refractive outcome after laser in situ keratomileusis (LASIK) for myopia.

SETTING

University Eye Clinic, Prince of Wales Hospital, Hong Kong, China.

METHODS

In this retrospective study, the records of patients who had LASIK for myopia greater than -6.0 diopters (D) using the Chiron Automated Corneal Shaper and the Schwind Keratome-F excimer laser were reviewed.

RESULTS

Laser in situ keratomileusis was performed in 167 eyes of 103 patients (mean age 34.7 years +/- 7.5 [SD]). Preoperative myopic spherical equivalent (SE) refraction was -9.0 +/- 2.0 D (range -6.0 to -13.9 D). Three months after surgery, SE refraction was -0.04 +/- 1.1 D (range +2.3 to -3.3 D); uncorrected visual acuity > or = 20/40 was present in 91.8% of 110 eyes in which emmetropia was the postoperative goal. Mean preoperative keratometry was 43.9 +/- 1.5 D (range 40.3 to 48.1 D). When eyes were stratified by the degree of preoperative myopia in 1.0 D steps, a trend toward greater undercorrection was noted in eyes with preoperative keratometry < 43.5 D than in those with steeper keratometry (> 44.5 D) in all myopia groups except the -7.0 to -7.9 D group. This difference was statistically significant in eyes with a preoperative SE of -10.0 to -10.9 D and -11.0 to -11.9 D.

CONCLUSIONS

Preoperative keratometry appeared to influence the refractive outcome after myopic LASIK. Eyes with flatter corneas tended to have greater undercorrection than eyes with similar myopia and steeper corneas. Validation of these findings in larger data sets using the methodology described may improve the predictability of current LASIK nomograms, particularly in eyes with high myopia.

Characteristics influencing outcomes of excimer laser photorefractive keratectomy. Summit Photorefractive Keratectomy Phase III Study Group

PURPOSE

To identify preoperative and intraoperative characteristics associated with outcomes of photorefractive keratectomy (PRK).

METHODS

In the phase III multicenter clinical trials of the Summit Technology excimer laser for corrections of 1.5 to 6.0 diopters (D) of myopia, three principal outcomes of PRK on 612 patients were examined: (1) uncorrected visual acuity of 20/40 or better, (2) predictability of refractive outcome within 1.0 D of attempted correction, and (3) stability of refractive result between 12 and 24 months. Multiple logistic regression was used to test for independent associations of multiple preoperative and intraoperative characteristics with each of these outcomes.

RESULTS

Older age was independently associated with lesser likelihood of achieving 20/40 or better uncorrected visual acuity (odds ratio = 1.08 per incremental year of age, 95% confidence interval [CI] = 1.04-1.12) and with decreased predictability, specifically with overcorrection (odds ratio = 1.09, 95% CI = 1.06-1.12), but age was not associated with stability of refraction. Greater attempted correction was associated independently with a decreased likelihood of 20/40 or better uncorrected visual acuity (odds ratio = 2.78 for corrections of 3.5-5.5 D, 95% CI = 1.18-6.75; odds ratio = 4.19 for corrections of > or = 5.5 D, 95% CI = 1.66-10.58), with decreased predictability (odds ratio = 1.72 for corrections of 3.5-5.5 D, 95% CI = 1.05-2.85; odds ratio = 2.95 for corrections of > or = 5.5 D, 95% CI = 1.65-5.26), and with a reduced likelihood of stability of refraction (odds ratio = 3.46 for corrections of > or = 5.0 D, 95% CI = 1.32-9.11). No intraoperative characteristics were associated with any of the outcomes assessed.

CONCLUSIONS

Using this specific excimer laser system with an optical zone of 4.5 or 5.0 mm, patient age and attempted correction are important preoperative characteristics associated with postoperative uncorrected visual acuity and predictability of PRK. Stability of refraction is strongly associated with attempted correction. Such information may help guide patient selection, determine timing of fellow eye treatment, and suggest changes in the laser treatment algorithm for individual patients. Although these findings may be representative of PRK in general, similar analyses should be performed before modifying patient treatments using either a 6.0-mm treatment zone or other laser systems.