Topographic determination of corneal asphericity and its lack of effect on the refractive outcome of radial keratotomy

Post-Ortho-K Corneal Epithelium Changes in Myopic Eyes

The study is aimed at evaluating corneal epithelial thickness changes associated with overnight orthokeratology (ortho-K). In this retrospective study, epithelial thickness was measured using optical coherence tomography (OCT) before and after 1 day, 1 week, 1 month, and 3 months ortho-K nightly lens wear. Compared with pre-orthokeratology measurements, central (2 mm) corneal epithelium thickness was significantly reduced at 1 day, 1 week, 1 month, and 3 months with ortho-K (P < 0.05). Paracentral (2 mm~5 mm annular ring) epithelial thickness was also significantly reduced at superior temporal, inferior temporal, temporal, and inferior locations after ortho-K (P < 0.05), while midperipheral (5 mm~6 mm annular ring) epithelial thickness was greater post- than pre-ortho-K at superior, superior temporal, inferior temporal, inferior, and inferior nasal locations (P < 0.05). In other zones, superior, superior nasal, nasal, and inferior nasal in paracentral annular ring and temporal and superior nasal in midperipheral ring, epithelial thickness underwent no significant change. Ortho-K lens wear caused the central corneal epitheliums to thin. The temporal half zones become thinner in paracentral zones and thicker in midperipheral zones.

Effect of Corneal Tilt on the Determination of Asphericity

Purpose: To quantify the effect of levelling the corneal surface around the optical axis on the calculated values of corneal asphericity when conic and biconic models are used to fit the anterior corneal surface. Methods: This cross-sectional study starts with a mathematical simulation proving the concept of the effect that the eye's tilt has on the corneal asphericity calculation. Spherical, conic and biconic models are considered and compared. Further, corneal asphericity is analysed in the eyes of 177 healthy participants aged 35.4 ± 15.2. The optical axis was determined using an optimization procedure via the Levenberg-Marquardt nonlinear least-squares algorithm, before fitting the corneal surface to spherical, conic and biconic models. The influence of pupil size (aperture radii of 1.5, 3.0, 4.0 and 5.0 mm) on corneal radius and asphericity was also analysed. Results: In computer simulations, eye tilt caused an increase in the apical radii of the surface with the increase of the tilt angle in both positive and negative directions and aperture radii in all models. Fitting the cornea to spherical models did not show a significant difference between the raw-measured corneal surfaces and the levelled surfaces for right and left eyes. When the conic models were fitted to the cornea, changes in the radii of the cornea among the raw-measured corneal surfaces' data and levelled data were not significant; however, significant differences were recorded in the asphericity of the anterior surfaces at radii of aperture 1.5 mm (p < 0.01). With the biconic model, the posterior surfaces recorded significant asphericity differences at aperture radii of 1.5 mm, 3 mm, 4 mm and 5 mm (p = 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively) in the nasal temporal direction of right eyes and left eyes (p < 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively). In the superior-inferior direction, significant changes were only noticed at aperture radii of 1.5 mm for both right and left eyes (p = 0.05, p < 0.01). Conclusions: Estimation of human corneal asphericity from topography or tomography data using conic and biconic models of corneas are affected by eyes' natural tilt. In contrast, the apical radii of the cornea are less affected. Using corneal asphericity in certain applications such as fitting contact lenses, corneal implant design, planning for refractive surgery and mathematical modelling when a geometrical centre of the eye is needed should be implemented with caution.

Age-Related Variations in Corneal Asphericity and Long-Term Changes

PURPOSE

Corneal front-surface asphericity is directly related with the optical quality of the eye and with contact lenses fitting. The purpose of this study was to evaluate the corneal asphericity as a function of age, sex, and refractive error measured with autokeratometry and corneal topography and its long-term changes (5- to 10-year period).

METHODS

The asphericity and corneal curvature were obtained with the autorefractometer/autokeratometer NIDEK ARK-700A and with the videokeratoscope MODI 2.0 and compared. Corneal asphericity was retrospectively analyzed with NIDEK ARK-700A. The longitudinal study of asphericity was conducted with the same device between 2 appointments within an interval of 5 to 10 years.

RESULTS

NIDEK ARK-700A showed agreement of asphericity values with those of MODI 2.0 (P=0.172) for a 7-mm diameter chord. The mean Q value of 1,484 right eyes (58.6% female), with a mean age of 40.2±18.4 years, was -0.24±0.12. No differences were found for Q value between sexes (P=0.424), age groups (P=0.268), and refractive error groups (P=0.107). The longitudinal analysis of corneal asphericity in 190 eyes (62.1% female) over a mean period of 5.9±1.4 years showed no significant differences in the Q value (0.00±0.08, P=0.813) over time. However, 14% showed asphericity changes of ±0.10 or higher while 86% of the subjects showed a change below ±0.10.

CONCLUSIONS

The mean Q value observed in this study agrees with the average values of a white population and contributes to slightly reduce the positive spherical aberration of the eye. For the large majority of this population, the asphericity did not show significant changes within a period of 5 to 10 years, but significant changes can be observed in some patients.

Group Analysis of Q Values Calculated with Tangential Radius of Curvature from Human Anterior Corneal Surface

Objective

To calculate the Q values from the human anterior corneal surface with the tangential radius of curvature and analyze its distribution characteristics in different age and refractive status groups.

Methods

Tangential power maps of the anterior cornea from Orbscan II were acquired for 201 subjects' right eyes. They were divided into groups of adults and children and then divided further into subgroups according to the refraction status. The Q values of each semimeridian were calculated by the tangential radius with a linear regression equation. The Q value distribution in both the nasal cornea and temporal cornea were analyzed.

Results

The mean temporal Q values of the emmetropia group of adults and all children's groups were significantly different from the mean nasal Q value. The mean nasal corneal Q values were more negative in children. The adult group showed differences only in the low myopia group. The mean Q value of the nasal cornea among different refractive groups of children was significantly different, and so was the temporal cornea between the adult myopia and emmetropia group.

Conclusion

The method using the tangential radius of curvature combined with linear regression to obtain anterior surface Q values for both adults and children was stable and reliable. When we analyzed the anterior corneal Q value, area division was necessary.

The analysis of corneal asphericity (Q value) and its related factors of 1,683 Chinese eyes older than 30 years

Purpose

To determine corneal Q value and its related factors in Chinese subjects older than 30 years.

Design

Cross sectional study.

Methods

1,683 participants (1,683 eyes) from the Handan Eye Study were involved, including 955 female and 728 male with average age of 53.64 years old (range from 30 to 107 years). The corneal Q values of anterior and posterior surfaces were measured at 3.0, 5.0 and 7.0mm aperture diameters using Bausch & Lomb Orbscan IIz (software version 3.12). Age, gender and refractive power were recorded.

Results

The average Q values of the anterior surface at 3.0, 5.0 and 7.0mm aperture diameters were -0.28±0.18, -0.28±0.18, and -0.29±0.18, respectively. The average Q value of the anterior surface at the 5.0mm aperture diameter was negatively correlated with age (B = -0.003, p<0.01) and the refractive power (B = -0.013, p = 0.016). The average Q values of the posterior surface at 3.0, 5.0, and 7.0mm were -0.26±0.216, -0.26±0.214, and -0.26±0.215, respectively. The average Q value of the posterior surface at the 5.0mm aperture diameter was positively correlated with age (B = 0.002, p = 0.036) and the refractive power (B = 0.016, p = 0.043).

Conclusion

The corneal Q value of the elderly Chinese subjects is different from that of previously reported European and American subjects, and the Q value appears to be correlated with age and refractive power.

Variations in corneal asphericity (Q value) between African-Americans and whites

PURPOSE

To search for differences in corneal asphericity on the basis of ethnicity between African-American and white populations.

METHODS

A prospective cohort design was used to analyze corneal asphericity (Q value) data obtained by Pentacam HR (Oculus, Wetzlar, Germany) on right eyes from African-American (n = 80) and white (n = 80). Subjects were stratified by ethnicity, age, and spherical equivalent (SE) refractive error. Q values were obtained from each quadrant (superior, nasal, inferior, and temporal) and two meridians (horizontal and vertical).

RESULTS

The mean Q values were African-Americans -0.26 ± 0.19 and whites -0.20 ± 0.12, indicating that the eyes of African-Americans were significantly more prolate (p = 0.003) than those of whites. There was a significant difference between mean Q values for ethnic groups only in the 30- to 39-year olds (p = 0.01) and there was a lack of correlation with age in both ethnic groups. Q value contrasts by gender were only significant between males (p = 0.01). There was a lack of correlation between Q value and SE for either ethnic group. Age group contrasts between ethnic groups found significant differences for those with SE greater than 0.00 D to -3.00 D (p = 0.05) and greater than 0.00 D to +3.00 D (p = 0.05). Comparison of mean Q values in opposing meridians within and across ethnic groups were significant, although neither group showed significant differences between horizontal and vertical meridians.

CONCLUSIONS

Corneal asphericity as represented by mean Q value varies significantly between African-Americans and whites. The greatest differences are evident in opposing quadrants and appear to be little influenced by age, gender, or SE.

Numerical study on human cornea and modified multiparametric correction equation for Goldmann applanation tonometer

Glaucoma, a chronic eye disease, is quoted to be a second leading cause of blindness with 66.8 million people suspected to be victimised by the same in year 2000 (Morrison, 2003), and is caused due to an elevated intraocular pressure (IOP). Goldmann Applanation tonometer (GAT), a gold standard (Organization, 2001), suffers from inefficacies to measure intra-ocular pressure (IOP) independent of the biomechanical properties of an eye. Thus, the purpose of this paper is to study the importance of wide range of corneal parameters and to propose a multiparametric correction equation for GAT based on a numerically simulated comprehensive finite element model (Dohadwala et al., 1998; Morrison, 2003; Organization, 2001). Towards this end, with the help of numerical model, the parameters considered in correction equation proposed elsewhere (Elsheikh et al., 2011) were extended to include combined influence of central corneal thickness (CCT), central anterior curvature (R), peripheral corneal thickness (PCT), corneal asphericity (Pa), age, measured IOP itself and, was separately studied for role played by corneal support orientation (θ°) in this aspect. Findings indicate that for a wide range of parameters considered, while increased age is related with gain in corneal stiffness, the maximum (average) individual effects of variations in PCT, Pa, CCT, age and θ° on IOPG were estimated at 0.25mmHg/100µ of PCT, 0.073mmHg/0.1 of Pa, 1.9mmHg/100µ of CCT, 24.3%/decade relative of IOPT and 0.95mmHg/5° increase in θ°. The multiparametric correction equation has been modified accordingly. The GAT correction equation can consider the combined effect of PCT, Pa, CCT, and age on IOPG. Separately the non-linear effect of θ° on IOPG cannot be ignored for reasons of precision.

Multi-aspheric description of the myopic cornea after different refractive treatments and its correlation with corneal higher order aberrations

Background

To analyse the asphericity of the anterior corneal surface (ACS) for different diameters, and correlate those values with corneal higher order aberrations (cHOA) before and after myopic treatments with corneal refractive therapy (CRT) for orthokeratology and customized (CL) and standard laser (SL) assisted in situ keratomileusis (LASIK).

Setting

Clínica Oftalmológica NovoVisión, Madrid, Spain.

Methods

The right eyes of 81 patients (27 in each treatment group), with a mean age of 29.94 ± 7.5 years, were analysed. Corneal videokeratographic data were used to obtain corneal asphericity (Q) for different corneal diameters from 3 to 8 mm and cHOA root mean square (RMS) obtained from Zernike polynomials for a pupil diameter of 6 mm.

Results

There were statistically significant differences in asphericity values calculated at different corneal diameters for different refractive treatments and their changes. The difference between asphericity at 3 and 8 mm reference diameters showed statistically significant correlations with spherical-like cHOA that was also significantly increased after all procedures.

Conclusions

The shift in corneal asphericity and the differences among different treatment techniques are more evident for the smaller reference diameters. These differences can be much reduced or even masked for a peripheral reference point at 4 mm from centre, which is used by some corneal topographers.

Corneal elevation topography: best fit sphere, elevation distance, asphericity, toricity, and clinical implications

PURPOSE

To describe the effect of the corneal asphericity and toricity on the map patterns and best fit sphere (BFS) characteristics in elevation topography.

METHODS

The corneal surface was modeled as a biconic surface of principal radii and asphericity values of r1 and r2 and Q1 and Q2, respectively. The apex of the biconic surface corresponded to the origin of a polar coordinates system. Minimization of the squared residuals was used to calculate the values of the radii of the BFSs and apex distance (A-values: z distance between the corneal apex and the BFS) of the modeled corneal surface for various configurations relating to commonly clinically measured values of apical radius, asphericity, and toricity.

RESULTS

Increased apical radius of curvature and increased prolateness (negative asphericity) led to an increase in BFS radius but had opposite effects on the A-value. Increased prolateness resulted in increased BFS radius and A-value. Increasing toricity did not alter these findings. Color-plot elevation maps of the modeled corneal surface showed complete ridge patterns when toricity was increased and showed incomplete ridge and island patterns when prolateness was increased.

CONCLUSIONS

High A-values in patients with corneal astigmatism may result from steep apical curvature and/or high prolateness (negative asphericity). The BFS radius may help in distinguishing between these 2 causes of increased A-values. Increased prolateness and decreased apical radius of curvature (often seen in keratoconus) have opposite effects on the BFS radius but similar effects on the apex distance.

Relationship between anterior corneal asphericity and refractive variables

BACKGROUND

The anterior corneal surface is closely modelled by a conic section that is fully described by asphericity (Q) and the apical radius of curvature. Computerized corneal topographers have allowed for more accurate and complete descriptions of corneal shape. Our objective was to compare anterior corneal asphericity (Q) values determined for different corneal diameters in eyes of different refractive state.

METHODS

Q-values were determined in 118 eyes of 118 subjects using both a videokeratoscope (Atlas Mastervue, Humphrey Instruments-Zeiss) and Vol-CT 6.89 software (Sarver & Associates Inc.), which estimates Q-values for several corneal diameters (3.0 mm, 4.0 mm, 5.0 mm, 6.0 mm, 7.0 mm and 8.0 mm) using topographic data obtained with the instrument. For comparisons, Q-values were stratified three ways: by refractive error (myopic, emmetropic or hyperopic eyes), corneal power (low, intermediate and high) and corneal astigmatism (low, intermediate and high).

RESULTS

Mean corneal asphericity was -0.35 +/- 0.03, differing significantly from reported data (Student's t-test). Asphericities determined using both methods did not vary significantly with regard to refractive error or corneal power, but did differ among the corneal astigmatism groups (p < 0.01). A trend was observed towards more negative Q-values with increasing corneal diameter, but differences in corneal asphericity according to corneal diameter were only significant in the astigmatism group (p < 0.01).

CONCLUSION

Q-values varied according to the refractive properties examined. However, the relationship between refractive state and corneal asphericity was found to be determined more by the geometric properties of the eye (corneal power and axial length) than by manifest refraction.

Cornea Measurement Comparison with Orbscan II and EyeSys Videokeratoscope

PURPOSE

To compare the performance of the Orbscan II topographer with a videokeratoscope for a set of tilted test buttons with known aspheric surface profile characteristics, and for a series of measurements made on normal human corneas.

METHODS

Measurements of apical radius and p-value were obtained from 12 aspheric test surfaces using the Orbscan II, the EyeSys videokeratoscope, and Form Talysurf analysis. Measurements from the corneas of 18 human subjects were assessed by comparison with data from the EyeSys videokeratoscope. Repeatability of Orbscan measurement was also assessed for both the test surfaces and the human corneas.

RESULTS

Measurement of the aspheric surfaces produced small but significant differences between the three instruments. For human corneas, the Orbscan apical radius measure under-read from 0.020 to 0.070 mm, and the p-value measure under-read from 0.011 to 0.085 compared with the EyeSys results.

CONCLUSIONS

The Orbscan appears to under-read slightly for both apical radius and p-value when compared to both the Talysurf and the EyeSys on both the aspheric surfaces and the corneas. The differences are small but statistically significant. The corneal shape factor provided by the Orbscan instrument display is of limited value.

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.

Correlations Between Central and Peripheral Changes in Anterior Corneal Topography After Myopic LASIK and Their Implications in Postsurgical Contact Lens Fitting

PURPOSE

To investigate the changes in central and peripheral anterior corneal curvatures after myopic laser in situ keratomileusis (LASIK) and to correlate them with the manifest refractive change to discuss how such results could affect post-LASIK corneal topography profiles and midterm stability and their implications in postsurgical contact lens fitting.

METHODS

Topographic and refractive data from 18 eyes of 11 patients that had undergone myopic LASIK were collected for 6 months after surgery. Short-term and midterm topographic responses were investigated and correlated with spherical equivalent manifest refractive changes.

RESULTS

There was a strong correlation between eccentricity changes and manifest refractive change 15 days after surgery (r = 0.753, P < 0.001), with no significant changes thereafter for the following 6 months (r = 0.148, P = 0.114). A strong linear relationship was found between baseline manifest refraction and changes in corneal curvature at the center (r = 0.810, P < 0.001), 4-mm chord (r = 0.895, P < 0.001), and 6-mm chord (r = 0.696, P < 0.001). Statistically significant changes were also found after the first 15 days (P < 0.005) and showed a regression effect that affects the three zones. In this case, a weaker relationship was found between curvature regression and the final refractive change for the central location (r = 0.412, P = 0.004), 4-mm chord area (r = 0.430, P = 0.003), and 6-mm chord area (r = 0.283, P = 0.023). CONCLUSIONS.: After myopic LASIK, the anterior corneal dioptric power is expected to change, on average, approximately 77% of the attempted spherical equivalent correction at the center; 60% at the 4-mm chord region, where the stronger correlation between topographic and refractive change is found; and 30% at the 6-mm chord area. The paracentral area 4 mm from the center seems to be more likely to predict baseline corneal curvature from manifest refractive change. Some degree of regression in the midterm period is expected to occur after myopic LASIK, which shows a significant correlation with the manifest refractive change. Again, this effect is more evident and more accurately predicted at the 4-mm chord area. The results of the current study are of interest for those fitting contact lenses after myopic LASIK.

The shape of the anterior and posterior surface of the aging human cornea

PURPOSE

To determine the shape and astigmatism of the posterior corneal surface in a healthy population with age, using Scheimpflug photography corrected for distortion due to the geometry of the Scheimpflug imaging system and the refraction of the anterior corneal surface.

METHODS

Scheimpflug imaging was used to measure in six meridians the cornea of the right eye of 114 subjects, ranging in age from 18 to 65 years.

RESULTS

The average radius of the anterior corneal surface was 7.79+/-0.27 (SD) mm and the average radius of the posterior corneal surface was 6.53+/-0.25 (SD) mm. Both surfaces were found to be flatter horizontally than vertically. The cylindrical component of the posterior surface of 0.33 mm is twice that of the anterior surface (0.16 mm). The asphericity of both the anterior and the posterior surface was independent of the radius of curvature at the vertex, refractive error and gender. In contrast with that of the anterior corneal surface, the asphericity of the posterior corneal surface varied significantly between meridians. With age, the asphericity of both the anterior and the posterior corneal surface changes significantly, which results in a slight peripheral thinning of the cornea.

CONCLUSION

On average, the astigmatism of the posterior corneal surface (-0.305 D) compensates the astigmatism of the anterior corneal surface (0.99 D) with 31%. The results show that the effective refractive index is 1.329, which is lower than values commonly used. There is no correlation between the asphericity of the anterior and the posterior corneal surface. As a result, the shape of the anterior corneal surface provides no definitive basis for knowing the asphericity of the posterior surface.

Optical models for human myopic eyes

Data from the author's investigations and other studies are used to construct refractive dependent models. These models include a gradient index lens and aspheric corneal, lens and retinal surfaces. Elements that alter with refraction are anterior corneal radius, vitreous length and retinal shape (vertex radius of curvature and asphericity) and decentration. Two versions of the models are produced, one with centred and symmetrical optical elements, and one with tilts of the lens and decentrations and tilts of the retina. The centred model predicts increase in spherical aberration in myopia. It predicts the relative change in mean sphere in the periphery between the horizontal and vertical meridians that has been observed in a recent experimental study. It overestimates peripheral astigmatism by about 50%. The decentred version has limited success in predicting changes in peripheral refraction of average eyes.

Differences in nasal and temporal responses of the cornea after photorefractive keratectomy

PURPOSE

To examine the differences in the biomechanical response of the peripheral regions of the cornea after photorefractive keratectomy (PRK).

SETTING

Department of Ophthalmology, Catholic University of Rome, Rome, Italy.

METHODS

Preoperative and 1-, 3-, 6-, and 12-month postoperative corneal topographies of 70 eyes that had PRK with the Technolas 217C excimer laser (Bausch & Lomb) were obtained. The eyes were divided into 4 groups according to the preoperative spherical equivalent refraction. Preoperative and follow-up topographic data were imported into custom software that computed the average composite corneal map and difference maps in each group to scientifically evaluate the corneal response to the surgery. The software was also used to analyze regional corneal changes after the laser ablation. Corneal peripheries up to 9.0 mm were evaluated.

RESULTS

The preoperative corneas had a flatter nasal periphery than temporal periphery. The corneal surfaces in the right eyes and left eyes showed a mirror symmetry. Significant differences in the regional response of the cornea were observed (P<.05), with a greater increase in the curvature of the nasal periphery than in the temporal periphery.

CONCLUSIONS

To refine modeling of the cornea, the different regional anatomic features and biomechanical responses must be considered. Modifying existing ablation algorithms to compensate for the differences between nasal and temporal corneal flattening of the preoperative corneal surface and between the nasal and temporal responses may improve the postoperative corneal shape and quality of peripheral optics.

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.

Corneal asphericity after hyperopic laser in situ keratomileusis

PURPOSE

To analyze corneal asphericity after hyperopic laser in situ keratomileusis (LASIK) and its relationship to the clinical outcomes.

SETTING

Corneal and Refractive Surgery Service, Massachusetts Eye and Ear Infirmary, Boston, Massachusetts, USA.

METHODS

In a retrospective case series, 23 patients (33 eyes) with hyperopia or hyperopic astigmatism who had LASIK were evaluated. A computer program (Holladay Diagnostic Summary, EyeSys Laboratories) was used to analyze corneal asphericity (Q) before and after LASIK. Corneal asphericity was evaluated to determine the association with the postoperative refractive error, best spectacle-corrected visual acuity (BSCVA), uncorrected visual acuity (UCVA), achieved refractive correction, mean corneal power (K), refractive yield (achieved/attempted correction), and keratometric yield (change in keratometry/attempted correction).

RESULTS

After hyperopic LASIK, all corneas exhibited increased negative central Q. The postoperative corneal radius of curvature, BSCVA, and refractive and keratometric yields were not significantly correlated with the preoperative Q values. The asphericity change, Delta Q, was highly correlated with the achieved correction (r = 0.747, P <.0001). The postoperative Q value correlated well with the preoperative value (r = 0.534, P <.05) and the achieved correction (r = 0.601, P <.05) but not with the Delta Q. Neither the postoperative Q nor the Delta Q was correlated with the spherical equivalent, K, BSCVA, or UCVA.

CONCLUSIONS

Asphericity may be a useful quantitative descriptor of the corneal optical contour after hyperopic LASIK. Negative central Q increased after hyperopic LASIK, especially when greater degrees of refractive correction were attempted.

Conoidal Fitting of Corneal Topography Height Data After Excimer Laser Penetrating Keratoplasty

PURPOSE

To demonstrate a mathematical method for approximation of discrete corneal topography height data with a biconic model surface for better appreciation of the optical performance of the graft after penetrating keratoplasty.

METHODS

In this retrospective study we included 50 eyes of 50 patients (30 keratoconus; 20 Fuchs' dystrophy) undergoing nonmechanical excimer laser penetrating keratoplasty. Conventional keratometry, corneal topography (TMS-1), subjective refraction, and best spectacle-corrected visual acuity (BSCVA) were assessed preoperatively, 3 and 6 months postoperatively, and before/after suture removal. A biconic model surface was fitted to the topographic raw data (8.0-mm region of interest) minimizing the root mean square error and a set of parameters (meridional power, axis, conic constant, and approximation error) was determined. The refractive cylinder was correlated with keratometric power readings, the Simulated Keratometry (SimK) of the topography system, and the respective parameters of the model surface.

RESULTS

Keratometric/SimK astigmatism increased from preoperatively (3.40/4.30 D) to 3 months (4.30/4.80 D) and decreased to 3.40/3.90 D after suture removal. Refractive cylinder/cylinder of the biconic increased slightly from 2.10/2.60 D preoperatively to 3.20/3.30 D after suture removal. The topographic cylinder SimK yielded the highest and the refractive cylinder the lowest values at each follow-up examination. Central keratometric power readings were stable before suture removal and decreased (about 1 D) due to suture removal. The conic constants in both meridional cross-sections changed from a prolate to a spherical shape in the early time course after penetrating keratoplasty and reconverted to a prolate shape after suture removal. Regarding cylinder axis, there was a significant correlation of the model surface with the refractive cylinder at all examination (P < .05) but only a mild correlation of the keratometric and SimK cylinder axis to the refractive cylinder axis at some examination stages.

CONCLUSION

Approximation of corneal topography height data with a biconic model surface renders reconstruction of clinically relevant corneal topography parameters including corneal asphericity with marked data compression. The correlation of amount/axis of refractive cylinder was best represented with the model surface parameters.

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

We offer an analysis that shows that the approximations made for the ablation depth during practical refractive surgery, in which the square-root terms are replaced by the first two terms of the series expansion, can limit the visual function of the observer by reducing the modulation transfer function (MTF). To simulate the refractive-surgical operation, we considered two groups of myopic patients with different ametropia who were emmetropized with different ablation profiles. We made the MTF calculations by taking the spherical aberration into account. In addition, a fuller analysis showed that these approximations limit the possibility of considering surfaces that are aspherical for reshaping the anterior cornea to optimize the observer's visual function.

Posterior corneal curvature changes after myopic laser in situ keratomileusis

OBJECTIVE

To assess the posterior corneal power and asphericity changes after myopic laser in situ keratomileusis (LASIK) and to correlate these changes with the amount of correction and the residual stromal bed thickness.

DESIGN

Prospective nonrandomized (self-controlled) comparative study.

PARTICIPANTS

Fifty-seven eyes of 14 women and 15 men, mean age at the time of surgery 33 +/- 9 (range, 19-53) years with a spherical equivalent (SEQ) of -1.00 to -15.50 (mean, -5.07 +/- 2.81) diopters (DI).

INTERVENTION

All procedures were performed with the Keratom II Coherent-Schwind excimer laser and and the Moria Model One microkeratome (150-microm head). Subjective refractometry, Orbscan slit scanning corneal topography analysis and pachymetry were performed before and 3 months after LASIK for myopia (n=35, -1.00 to -15.50 D, mean -4.75 +/- -3.07 D) or myopic astigmatism (n=22, sphere 0.00 to -9.75 D, mean -4.75 +/- 2.36 D; cylinder -0.75 to -3.50 D, mean -1.68 +/- 0.86 D). Intended ablation depth ranged from 12 to 108 (mean, 48 +/- 22) microm. Topographic raw data were decomposed into a set of Zernike polynomials as published in detail previously, and parameters potentially indicative for detection of a "mild keratectasia" were derived.

MAIN OUTCOME MEASURES

Posterior central corneal power and asphericity before and after LASIK were compared, and changes of these variables were correlated with the SEQ change (deltaSEQ)and the residual corneal bed thickness RBT).

RESULTS

The mean RBT after LASIK was 280 +/- 42 microm. Overall, change of posterior power (-6.28 +/- 0.22 D/ -6.39 +/- 0.23 D, P=0.02) was statistically significant and change of asphericity (0.98 +/-0.07/1.14 +/- -.20, P<0.0001) was highly significant. In eyes with RBT < or =250 microm, the average change of posterior central power (-0.20 +/- 0.10 D vs. -0.08 +/- 0.18 D) was significantly greater than in eyes with RBT >250 microm (P=0.003). The change of posterior corneal power correlated significantly with deltaSEQ (P=0.004) and the RBT (P=0.002).

CONCLUSIONS

Increased negative keratometric diopters and oblate asphericity of the posterior corneal curvature suggest that mild "keratectesia" of the cornea may be common early after LASIK. Further stuudies with longer follow-up are required to clarify whether this biomechanical deformation is progressive and whether a residual bed thickness of >250 microm can completely prevent it.

Longitudinal changes in corneal asphericity in myopia

PURPOSE

To report the change in shape of the peripheral cornea (asphericity, Q) as it relates to myopia progression in adolescence.

METHODS

Forty-eight subjects with initial ages between 11 and 13 years of age were observed for 5 years. Each subject had participated in a variety of soft contact lens studies and all had worn daily wear soft contact lenses successfully for the 2 years before collection of the second data set.

RESULTS

Myopia increased by an average of 1.46 D and was strongly correlated with a 0.56-mm increase in axial length. There was no contribution to the change in myopia from the change in central radius of the cornea. A significant (p < 0.01, one tail) correlation was found between Q and the progression of myopia. Principal axis analysis yielded a slope of -0.04 in Q per diopter of increase in myopia.

CONCLUSION

These data show a shift to a more positive Q (in the oblate direction) with increased myopia.

The EyeSys videokeratoscopic assessment of apical radius and p-value in the normal human cornea

The EyeSys videokeratoscope was used to assess the corneal topography in 98 subjects. Scatterplots of distance squared versus radius squared were plotted for the near horizontal and near vertical principal meridians of the two eyes. The regression lines allowed calculation of the surface apical radius and the p-value. The group average apical radius was 7.93 mm (horizontal) and 7.78 mm (vertical). The group average p-value was 0.76 (horizontal) and 0.82 (vertical). Both apical radius and p-value were similar when comparing the two eyes for both the horizontal and the vertical meridians. The two meridians in a single eye, however, had different values for both apical radius and p-value. Male apical radii were longer than those of females but the p-values were the same. There is no apparent association between age and either apical radius or p-value for the subjects used in this study. The asphericity of the cornea does not show any apparent association with corneal curvature in this group of subjects.

Image quality in polypseudophakia for extremely short eyes

AIM

To evaluate the image quality produced by polypseudophakia used for strongly hypermetropic and nanophthalmic eyes.

METHODS

Primary aberration theory and ray tracing analysis were used to calculate the optimum lens shapes and power distribution between the two intraocular lenses for two example eyes: one a strongly hypermetropic eye, the other a nanophthalmic eye. Spherical aberration and oblique astigmatism were considered. Modulation transfer function (MTF) curves were computed using commercial optical design software (Sigma 2100, Kidger Optics Ltd) to assess axial image quality, and the sagittal and tangential image surfaces were computed to study image quality across the field.

RESULTS

A significant improvement in the axial MTF was found for the eyes with double implants. However, results indicate that this may be realised as a better contrast sensitivity in the low to mid spatial frequency range rather than as a better Snellen acuity. The optimum lens shapes for minimum spherical aberration (best axial image quality) were approximately convex-plano for both lenses with the convex surface facing the cornea. Conversely, the optimum lens shapes for zero oblique astigmatism were strongly meniscus with the anterior surface concave. Correction of oblique astigmatism was only achieved with a loss in axial performance.

CONCLUSIONS

Optimum estimated visual acuity exceeds 6/5 in both the hypermetropic and the nanophthalmic eyes studied (pupil size of 4 mm) with polypseudophakic correction. These results can be attained using convex-plano or biconvex lenses with the most convex surface facing the cornea. If the posterior surface of the posterior intraocular lens is convex, as is commonly used to help prevent migration of lens epithelial cells causing posterior capsular opacification (PCO), then it is still possible to achieve 6/4.5 in the hypermetropic eye and 6/5.3 in the nanophthalmic eye provided the anterior intraocular lens has an approximately convex-plano shape with the convex surface anterior. It was therefore concluded that consideration of optical image quality does not demand that additional intraocular lens shapes need to be manufactured for polypseudophakic correction of extremely short eyes and that implanting the posterior intraocular lens in the conventional orientation to help prevent PCO does not necessarily limit estimated visual acuity.

Evaluation of relationships among refractive and topographic parameters

PURPOSE

To examine the relationships among several refractive and topographic parameters.

SETTING

Cullen Eye Institute Department of Ophthalmology, Baylor College of Medicine, Houston, Texas, USA.

METHODS

Using computerized videokeratography (EyeSys Corneal Analysis System), 287 corneas of 150 patients were retrospectively analyzed. The Holladay Diagnostic Summary (HDS) refractive maps were used to evaluate relationships among variables of the HDS and refractive error.

RESULTS

Myopic spherical equivalent refraction (P = .0003) and more negative asphericity (Q-values) (P = .0119) were correlated with steeper corneas. The Q-values were less negative in eyes with moderate myopia (2.0 to 6.0 diopters [D]) than in those with hyperopia (1.0 D or greater). The Q-values below -0.3 were correlated with less favorable values for predicted corneal acuity and corneal uniformity index values. Mean corneal curvature measurements obtained by computerized videokeratography and standard keratometry showed a strong degree of correlation (P = .0001).

CONCLUSION

As the degree of myopia and negative asphericity increased, the corneal radius of curvature decreased. Corneal Q-values less than -0.3 were associated with reduced optical performance of the cornea.

Axial, instantaneous, and refractive formulas in computerized videokeratography of normal corneas

PURPOSE

To compare the values for corneal power determined by the axial, instantaneous and refractive formulas when imaging normal human corneas using computerized videokeratography.

SETTING

Cullen Eye Institute, Baylor College of Medicine, Houston, Texas, USA.

METHODS

This prospective clinical trial involved 60 corneas of 30 normal volunteers. Computerized videokeratography was performed to determine corneal power at the center and the 1, 3, 5, and 7 mm zones using the 3 formulas.

RESULTS

Mean central corneal power was 42.86 diopters (D) with each of the formulas. The mean corneal powers for the axial, instantaneous, and refractive formulas were 43.09, 43.21, and 42.98 D at the 1 mm zone; 43.10, 42.92, and 43.46 D at the 3 mm zone; 42.75, 41.63, and 44.02 at the 5 mm zone; 42.21, 40.30, and 44.79 D at the 7 mm zone, respectively. The differences among powers for the 3 formulas at the 3, 5, and 7 mm zones were statistically significant (P < .01).

CONCLUSION

In normal corneas, clinically significant differences exist in the corneal power values calculated by the axial, instantaneous, and refractive formulas.

Corneal shape in hyperopia

Background: A trend towards decreased peripheral corneal flattening with increasing myopia has recently been demonstrated. The present study was conducted to determine whether corneal asphericity also varies significantly with hyperopic refractive error. Methods: Thirty-five eyes with spherical equivalent refractive error ranging from -0.37 D to +6.00 D were examined. A conicoid equation was fitted to videokeratoscopic (Topographic Modeling System) data and corneal asphericity and apical radius of curvature values were calculated for each subject. Axial length measurements were made using a hand-held biometric ruler. Keratometry was also performed on each eye. Results: The relationship between corneal asphericity (Q) and spherical equivalent refractive error was not statistically significant (p = 0.7419). In addition, no association could be demonstrated between Q and corneal radius of curvature or between Q and axial length. Corneal radius of curvature was positively correlated with axial length (r = 0.367, p = 0.0298). Axial length was found to decrease as hyperopic refractive error increased (r = 0.753, p = 0.0001). Conclusions: For hyperopic eyes, corneal asphericity does not appear to be significantly correlated with refractive error, a finding that is at variance with previous data for myopic eyes showing an association between these two variables. The results suggest that there may be differences between hyperopic and myopic eyes with regard to the anterior segment changes that occur during refractive error development.

The prediction of surgically induced refractive change from corneal topography

PURPOSE

To develop a method to predict the refractive power of the cornea from corneal topography.

METHODS

We reviewed preoperative and postoperative cycloplegic refraction, keratometry, and corneal topography in 40 eyes of 40 patients who had undergone photorefractive keratectomy, radial keratotomy, myopic keratomileusis in situ, or hyperopic lamellar keratoplasty. For each axial dioptric power map, we calculated the aspheric ellipsoid that best fit that map. Central corneal points were weighted more heavily than peripheral points, based on the Stiles-Crawford effect. The equation of the best-fit ellipsoid yielded the spherical and astigmatic power and axis for each cornea preoperatively and postoperatively.

RESULTS

The preoperative corneal spherical and astigmatic powers measured by the best-fit method were consistent with the spherical and astigmatic powers measured by keratometry and simulated keratometry. The change in corneal spherical power predicted by the best-fit method was significantly (P < .05) more accurate at predicting the change in spherical equivalent refraction than change either in spherical equivalent keratometry or in spherical equivalent simulated keratometry. The prediction of the astigmatic change was less precise than that of the spherical, but the best-fit method was the most accurate.

CONCLUSIONS

The best-fit method is more accurate than simulated keratometry and standard keratometry are in evaluating corneal refractive power after refractive surgery. An improved method of calculating corneal refractive power may facilitate subjective refraction after refractive surgery, improve the accuracy of intraocular lens power calculation for eyes that have had previous refractive surgery, and improve ablation profiles for excimer laser refractive surgery.

Corneal topography bow-tie pattern: artifact of videokeratoscopy?

PURPOSE

To test the hypothesis that the bow-tie corneal topography pattern results from corneal asphericity in the presence of astigmatism.

METHODS

Astigmatic color-coded power maps using different shape factors were computer generated. Each simulation was based on the calculation of dioptric power at 20 points along each of 180 hemimeridia, for a total of 3600 points. The calculations were made independent of the capture or measurement of video-keratographs. These simulations were compared to power maps taken from clinical records.

RESULTS

A shape factor of 1.00 resulted in a spherocylinder color-coded map with straight-edged sectors of power. The familiar bow-tie pattern was generated using an elliptical model with a shape factor of less than 1.00. This pattern was reversed by modeling the cornea as an oblate ellipsoid using a shape factor greater than 1.00.

CONCLUSIONS

By simple alteration of the amount of corneal asphericity through manipulation of the shape factor, computer simulation showed that this surface characteristic is responsible for the bow-tie pattern observed in corneal topography power maps.