Effects on visual function of approximations of the corneal-ablation profile during refractive surgery

Q-optimized Algorithms: Theoretical Analysis of Factors Influencing Visual Quality After Myopic Corneal Refractive Surgery

PURPOSE

To model the effect of pupil size, optical zone, and initial myopic level on the retinal image quality after Q-optimized myopic corneal refractive surgery.

METHODS

Different Q-optimized and paraxial Munnerlyn algorithms were tested using a schematic myopic eye model to analyze the optical quality of the final retinal image for initial myopic errors from -1.00 to -7.00 diopters (D). Different optical zones (5.5, 6, and 6.5 mm in diameter) and two pupil diameters (5 and 7 mm, mesopic-scotopic conditions) were included in the comparison. Modulation transfer function (MTF) and area under the MTF from 0 to 60 cycles per degree (MTFa) were calculated by ray tracing to evaluate this retinal image quality.

RESULTS

The Q-optimized algorithm with Q = -0.45 provided the highest MTF and MTFa results for myopic corrections less than -5.00 D. For refractive errors greater than -5.00 D, Q = -0.26 provided the highest MTF and MTFa results.

CONCLUSIONS

Q-optimized algorithms improve the visual outcomes with respect to the paraxial Munnerlyn algorithm for myopic corneal surgery. The results show that the Q value that optimizes the results of the Q-optimized algorithm depends on the degree of myopia to correct and the size of the pupil. [J Refract Surg. 2016;32(9):612-617.].

Hyperopic Q-optimized algorithms: a theoretical study on factors influencing optical quality

In this work, we analyze the way in which pupil size, optical zone, and initial hyperopic level influence optical quality for hyperopic Q-optimized corneal refractive surgery. Different Q-optimized algorithms and the Munnerlyn formula were tested to analyze the optical quality of the final retinal image for initial hyperopic errors from 1D to 5D. Three optical zones (5.5, 6, and 6.5 mm) and two pupil diameters (5 and 7 mm) were considered. To evaluate optical quality, we computed the modulation transfer function (MTF) and the area under MTF (MTFa). Q-optimized values at around Q = -0.18 were found to provide the best optical quality for most of the conditions tested. This optimum final asphericity for hyperopic ablation was not depending on the degree of hyperopia corrected, the optical zone or the pupil size being this information important for clinical practice.

Anterior corneal profile with variable asphericity

We present a corneal profile in which the eccentricity, e(Q=-e(2)), has a nonlinear continuous variation from the center outwards. This nonlinear variation is intended to fit and reproduce our current experimental data in which the anterior corneal surface of the human eye exhibits different values of e at different diameters. According to our clinical data, the variation is similar to an exponential decay. We propose a linear combination of two exponential functions to describe the variation of e. We then calculate the corneal sagittal height by substituting e in the first-order aspherical surface equation to obtain the corneal profile. This corneal profile will be used as a reference to analyze the resultant profiles of the customized corneal ablation in refractive surgery.

Long-term optical quality of the photoablated cornea

High-order coreal wavefront analysis was performed in a population of 60 myopic eyes that underwent photorefractive keratectomy. Corneal aberration data over 3, 5, and 7 mm pupils were collected for up to three years after surgery. The optical performance of the anterior cornea was characterized by estimation of the modulation transfer function (MTF) and the point-spread function. The high-order corneal wavefront aberrations were shown to stabilize one year after surgery. Over photopic pupils, after an early slight increase, corneal RMS-high-order aberrations (HOA) tended to decrease toward preoperative values. On the other hand, over mid- and large-pupil sizes, corneal HOA significantly increased compared with the preoperative state, while the optical performance of the cornea was diminished. The MTF ratio showed a distinct decline in the optical quality of postoperative corneas at low and middle spatial frequencies over larger pupils in the range between 6 and 19 c/deg, especially for deeper ablations.

Binocular Visual Performance After LASIK

PURPOSE

To analyze binocular visual function after LASIK.

METHODS

Eye aberrometry and corneal topography was obtained for both eyes in 68 patients (136 eyes). To evaluate visual performance, monocular and binocular contrast sensitivity function and disturbance index for quantifying halos were measured. Tests were performed under mesopic conditions.

RESULTS

Binocular summation and disturbance index diminished significantly (P<.0001) after LASIK with increasing interocular differences in corneal and eye aberrations. Binocular visual deterioration was greater than monocular deterioration for contrast sensitivity function and disturbance index.

CONCLUSIONS

Binocular function deteriorates more than monocular function after LASIK. This deterioration increases as the interocular differences in aberrations and corneal shape increase. Improvements in ablation algorithms should minimize these interocular differences.

Computer simulation of visual outcomes of wavefront-only corneal ablation

PURPOSE

To evaluate the effectiveness, predicted visual outcome, and limitations of a corneal ablation algorithm that uses wavefront aberration measurement alone without the need for corneal shape information.

SETTING

Contact Lens and Visual Optical Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Australia.

METHODS

Corneal topography and wavefront error data from 22 eyes of 11 potential refractive surgery candidates were used. A computer simulation of the corneal ablation was performed, and the predicted postoperative visual outcome was assessed by calculating the resulting wavefront root-mean-square (RMS) values and visual Strehl ratios. Additionally, the effect of ablation alignment error was examined. Finally, the visual outcomes of the wavefront-only corneal ablations were compared to those in an age-matched group of 20 emmetropic patients.

RESULTS

Significant improvement in total and higher-order wavefront RMS was achieved postoperatively in both an ideal setting and in the case of ablation alignment errors. The predicted improvement in visual Strehl ratio in the potential refractive surgery candidates was significantly better than that in the untreated emmetropes. After additional simulated decentration of the pupil center by 150 microm, the result was slightly worse, but the change was found to not be significant when compared to the retinal image quality of emmetropes.

CONCLUSIONS

Wavefront-only corneal ablation algorithms could potentially lead to significantly better visual outcomes than those normally encountered in untreated emmetropes, provided that the alignment error is not large. The presented methodology may be used as a screening tool to predict patients' visual outcomes before the surgery.

Differences between real and predicted corneal shapes after aspherical corneal ablation

We study the differences between real and expected corneal shapes, using an aspherical ablation algorithm with a known equation and avoiding the limitation imposed by most studies of refractive surgery in which the ablation equations are not known. We have calculated the theoretical corneal shape predicted by this algorithm, comparing this shape with the real corneal topography. The results indicate that the deviations that appear in the corneal shape are significant for visual performance and for the correction of eye aberrations. If we include in this analysis the effect of reflection losses and nonnormal incidence on the cornea, we can reduce corneal differences, but they will remain significant. These results confirm that it is essential to minimize corneal differences to achieve effective correction in refractive surgery.

Wavefront-optimized ablation profiles

PURPOSE

To describe a method for calculating wavefront-optimized ablation profiles to precompensate for the spherical aberration and higher-order astigmatism induced by myopic, hyperopic, and astigmatic corneal laser corrections.

SETTING

IROC-Institut für Refraktive und Ophthalmo-Chirurgie, and Institute for Biomedical Engineering, Swiss Federal Institute of Technology, Zürich, Switzerland.

METHODS

The basic ablation profile for myopic, hyperopic, and astigmatic correction is derived from the 2nd-order Zernike representation of wavefront aberrations. Including 4th-order spherical aberration and higher-order astigmatism in the theoretical calculation of the ablation profile allows precompensation for the expected amount of higher-order aberrations (HOAs). The shapes of wavefront-optimized ablation profiles are compared with the shapes of "classic" ablation profiles for myopic and astigmatic corrections.

RESULTS

The introduction of precompensating spherical aberration and higher-order astigmatism leads to a more aspheric ablation profile with a significant increase in ablation depth (up to 35%) in the midperiphery of the optical zone. The central ablation depth remains unchanged in the myopic correction but increases by 3% in cylinder correction.

CONCLUSIONS

Wavefront-optimized ablation profiles provide a simple method to precompensate for the expected 4th-order spherical aberration and higher-order astigmatism in the average eye. Further clinical studies must be performed to prove the theoretical results; demonstrate the reduction in HOAs; and predict safety, predictability, and stability of wavefront-optimized ablation profiles.

Corneal asphericity after refractive surgery when the Munnerlyn formula is applied

We deduce a mathematical equation for corneal asphericity after refractive surgery when the Munnerlyn formula is used. For this, an analytical least-squares procedure is used. The equation explains the discrepancies found by different authors when the Munnerlyn formula or its paraxial approximation is used. Equations for corneal asphericity deduced here may be of clinical relevance, for example, in studying quantitatively the role of different factors (decentration, type of laser, optical role of the flap, wound healing, biomechanical effects, technical procedures) during corneal ablation.

Changes in corneal asphericity after laser in situ keratomileusis

PURPOSE

To analyze the origin of the changes in corneal asphericity (p-factor) after laser in situ keratomileusis (LASIK) and the effect of postsurgery asphericity on contrast-sensitivity function (CSF) under photopic conditions.

SETTING

Department of Optics, University of Granada, Granada, Spain.

METHODS

The p-factor and CSF (best corrected before surgery and 1, 3, and 6 months after surgery) were measured in 24 eyes.

RESULTS

An increase in the p-factor after LASIK was noted; there was an 87.2% change in the asphericity using the paraxial formula of Munnerlyn and coauthors. Other factors such as decentration, type of laser, optical role of the flap, wound healing, biomechanical effects, technical procedures, and reflection losses of the laser on the cornea could account for the greater than expected increase (12.8%) in the p-factor. The CSF measurements deteriorated after LASIK; the change was significant (P<.05) in patients with myopia worse than -4.0 diopters at frequencies of 9.2, 12, 15, and 20 cycles per degree.

CONCLUSION

The increase in corneal asphericity after surgery, greater with a higher degree of myopia, and the deterioration in CSF with high myopia justify new ablation algorithms and further study of the variables that could modify the ablation unpredictably.

The asphericity, curvature and tilt of the human cornea measured using a videokeratoscope

The EyeSys videokeratoscope (VK) measurements of the principal corneal meridians of 98 subjects already analysed by Douthwaite et al. [Ophthal. Physiol. Opt. (1999)19:467-474] were re-analysed in order to revise the assessment of asphericity, to derive information on corneal tilt and to assess the degree to which the corneal section approximates to that of a conic section. The range of normality for the revised p-value (asphericity) was from 0.57 to 0.97 for the near horizontal and from 0.56 to 1.08 in the near vertical principal meridians. The approximate corneal tilt angles ranged from -3.95 to +8.13 degrees in the horizontal and from -8.99 to +9.33 degrees in the vertical meridian. A tilted conicoidal surface will display a linear relationship (r = 1) when a scatterplot is drawn of the perpendicular distance squared vs radius squared, after first averaging the two semimeridian results for each VK ring. Analysing the results from the human cornea in the same way allows an assessment of the degree to which the corneal section approximates to that of the conic section.

Impact of interocular differences in corneal asphericity on binocular summation

PURPOSE

To evaluate the impact that interocular differences in corneal asphericity (Q) exert on binocular summation measured as the contrast-sensitivity function.

DESIGN

Interventional case series.

METHODS

A total of 92 emmetropic subjects took part in the experiment, classified according to the interocular differences in corneal asphericity (deltaQ) measured with an EyeSys-2000 corneal topographer. Fifty-four subjects had deltaQ < 0.1; 21 subjects had 0.1 < or = deltaQ < or = 0.2; and 17 had deltaQ > 0.2. The contrast-sensitivity function (CSF) was measured monocularly (for each eye) and binocularly with a B VAT II device. The spatial frequencies used were as follows: 2.4, 3.7, 6.0, 9.2, 12, 15, 20, and 24 cycles per degree.

RESULTS

Although the binocular CSF for the three groups studied was greater than the monocular in all the spatial frequencies studied, there were significant differences in binocular summation. The average binocular summation (for all the spatial frequencies) for the group with deltaQ < 0.1 was 1.46, significantly higher than the group with 0.1 < or = deltaQ < or = 0.2, in which the average binocular summation was 1.39 (P = .035), which was also significantly higher than the group deltaQ > 0.2, for which the average binocular summation was 1.26 (P < .0001). In this last group, the summation decreased to the level of the probability summation.

CONCLUSIONS

Differences in corneal asphericity may affect the binocular visual function by diminishing the binocular contrast-sensitivity function. This result may have important implications in refractive surgery given that, although the subject becomes emmetropic, if interocular differences are induced in corneal asphericity, it could reduce binocular visual performance.

Equation for Corneal Asphericity After Corneal Refractive Surgery

PURPOSE

To determine the exact theoretical asphericity after refractive surgery when the parabolic approximation of the Munnerlyn formula is utilized.

METHOD

From a least-square analysis and considering the conicoid model for anterior cornea, we calculated the final asphericity (p'-factor) from the preoperative asphericity and the radii before and after surgery.

RESULTS

The final p'-factor is given by p'=p(R'3/R3); R' is the final radius of curvature; R is the preoperative radius; and p is the preoperative p'-factor.

CONCLUSIONS

This equation for postoperative asphericity may be useful in studying the influence on asphericity of different surgical variables. It allows comparisons of real asphericity with the asphericity that should theoretically result. It also explains the increased spherical aberration after refractive surgery and the deterioration of retinal image quality that some authors have found experimentally.

Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration

PURPOSE

To calculate ablation profiles for wavefront-guided correction of ametropia and primary spherical aberration.

SETTING

Bascom Palmer Eye Institute, University of Miami, Miami, Florida, USA.

METHODS

The primary spherical aberrations of the ocular surfaces of an aspheric eye model were calculated before and after simulated ablations for correction of myopia ranging from 0 to 10 diopters. The corneal asphericity to correct primary spherical aberration and the corresponding ablation profiles were also calculated.

RESULTS

The corneal asphericity factor that produces zero primary spherical aberration ranges from -0.45 to -0.47. The calculated ablation profiles are parabolic in first approximation, and the ablation depth varies linearly with the amount of correction. To control residual primary spherical aberration with a tolerance of one-quarter wavelength, the precision of the ablation must range from 0.2 to 0.3 microm.

CONCLUSIONS

Ocular aberrometry and corneal topography can be used to calculate ablations for the correction of ametropia and primary spherical aberration. Precise control of postoperative spherical aberration appears to be feasible in theory.