Goodness-of-prediction of Zernike polynomial fitting to corneal surfaces

Comparing the clinical applicability of wavefront phase imaging in keratoconus versus normal eyes

The aim of this work is to quantitatively assess the wavefront phase of keratoconic eyes measured by the ocular aberrometer t·eyede (based on WaveFront Phase Imaging Sensor), characterized by a lateral resolution of 8.6 µm without requiring any optical element to sample the wavefront information. We evaluated the parameters: root mean square error, Peak-to-Valley, and amplitude of the predominant frequency (Fourier Transform analysis) of a section of the High-Pass filter map in keratoconic and healthy cohorts. Furthermore, we have analyzed keratoconic eyes that presented dark-light bands in this map to assess their period and orientation with the Fourier Transform. There are significant statistical differences (p value < 0.001) between healthy and keratoconic eyes in the three parameters, demonstrating a tendency to increase with the severity of the disease. Otherwise, the quantification of the bands reveals that the width is independent of eye laterality and keratoconic stage as orientation, which tends to be oblique. In conclusion, the quantitative results obtained with t·eyede could help to diagnose and monitor the progression of keratoconus.

Technical variability of cornea parameters derived from anterior segment OCT fitted with Fringe Zernike polynomials

BACKGROUND

This study uses bootstrapping to evaluate the technical variability (in terms of model parameter variation) of Zernike corneal surface fit parameters based on Casia2 biometric data.

METHODS

Using a dataset containing N = 6953 Casia2 biometric measurements from a cataractous population, a Fringe Zernike polynomial surface of radial degree 10 (36 components) was fitted to the height data. The fit error (height - reconstruction) was bootstrapped 100 times after normalisation. After reversal of normalisation, the bootstrapped fit errors were added to the reconstructed height, and characteristic surface parameters (flat/steep axis, radii, and asphericities in both axes) extracted. The median parameters refer to a robust surface representation for later estimates of elevation, whereas the SD of the 100 bootstraps refers to the variability of the surface fit.

RESULTS

Bootstrapping gave median radius and asphericity values of 7.74/7.68 mm and -0.20/-0.24 for the corneal front surface in the flat/steep meridian and 6.52/6.37 mm and -0.22/-0.31 for the corneal back surface. The respective SD values for the 100 bootstraps were 0.0032/0.0028 mm and 0.0093/0.0082 for the front and 0.0126/0.0115 mm and 0.0366/0.0312 for the back surface. The uncertainties for the back surface are systematically larger as compared to the uncertainties of the front surface.

CONCLUSION

As measured with the Casia2 tomographer, the fit parameters for the corneal back surface exhibit a larger degree of variability compared with those for the front surface. Further studies are needed to show whether these uncertainties are representative for the situation where actual repeat measurements are possible.

Artificial neural network modeling of meteorological and geological influences on indoor radon concentration in selected tertiary institutions in Southwestern Nigeria

Exposure to indoor radon, with no safe level, has been reported to bear the possible radiological risk to humans. The indoor radon level of a total of one hundred and thirty-two offices and sixty classrooms of tertiary institutions within different lithology and at varied meteorological values in southwestern Nigeria was measured using Electret Passive Environmental Radon Monitor (E-PERM). The meteorological parameters were obtained from the National Aeronautics and Space Administration (NASA) database. MATLAB scripts of code were used to develop the Artificial Neural Network (ANN) model. The measured parameters were subjected to both descriptive and inferential statistics. The highest mean radon concentration was observed in offices built on granitic bedrock with a value of 64.3 ± 1.7 Bq.m^-3 while the lowest was observed in alluvium bedrock with a value of 52.5 ± 1.4 Bq.m^-3. To enhance prediction involving erratic parametric patterns, the measured data were subjected to an optimized Artificial Neural Network architecture training, validation, and testing, leading to a model determined to have a Nash-Sutcliffe efficiency coefficient value of 0.997, Average Absolute Relative Error of 0.0115, and Mean Squared Error of 0.07. The predicted result was compared favorably with the measured data with 0.054 Average Validation Error, 0.027 Mean Absolute Error 3.64 Mean Absolute Percentage Error, and 83.7% Goodness-of-Prediction values. About 21.4% of the values were found to be higher than the 100 Bq.m^-3 limits specified by the World Health Organization. Measured radon concentration and predicted ANN data as obtained in this work, being novel in this study area is useful for immediate assessment of the level of risk associated with radon exposure as well as for future predictions. The ANN developed is effective and efficient in predicting indoor radon concentration.

Performance of Zernike polynomials in reconstructing raw-elevation data captured by Pentacam HR, Medmont E300 and Eye Surface Profiler

PURPOSE

To investigate the capability of Zernike polynomials fitting to reconstruct corneal surfaces as measured by Pentacam HR tomographer, Medmont E300 Placido-disc and Eye Surface Profiler (ESP).

METHODS

The study utilised a collection of clinical data of 527 participants. Pentacam HR raw elevation data of 660 eyes (430 healthy and 230 keratoconic) were fitted to Zernike polynomials of order 2 to 20. Same analyses were carried out on 158 eyes scanned by Medmont E300 Placido-disc and 236 eyes were scanned by ESP for comparison purposes. The Zernike polynomial ​fitting was carried out using a random 80% of each individual eye surface's data up to a corneal radius of 5 mm and the root means squared fitting error (RMS) was calculated for the unused 20% portion of the surface data. The process was carried out for the anterior and posterior surfaces of the corneal measurements of the Pentacam HR and the anterior surfaces only with the ESP and the Medmont E300 measurements.

RESULTS

Statistical significances in reduction of RMS were noticed up to order 14 among healthy participants (p < 0.0001 for right eyes, p = 0.0051 for left eyes) and up to order 12 (p < 0.0001 for right eyes, p = 0.0002 for left eyes) in anterior surfaces measured by the Pentacam. Among keratoconic eyes, statical significance was noticed up to order 12 in both eyes (p < 0.0001 for right eyes, p = 0.0003 for left eyes). The Pentacam posterior corneal data, both right and left, healthy and keratotic eyes recorded significance (p < 0.0001) in reduction of RMS up to order 10 with same RMS values of 0.0003 mm with zero standard deviation. RMS of fitting Zernike polynomials to Medmont data up to order 20 showed a consistent reduction in RMS with the increase of the fitting order with no rise at high fitting orders. Minimum RMS = 0.0047 ± 0.0021 mm, 0.0046 ± 0.0019 mm for right and left eyes respectively were recorded at order 20 and were more than 15 times the minimum RMS of the Pentacam. RMS of fitting Zernike polynomials to ESP data also showed a consistent reduction in RMS with the increase of the fitting order with no sign of any rise at high fitting orders. Similar to the Medmont, minimum RMS of 0.0005 ± 0.0003 mm, 0.0006 ± 0.0003 mm was recorded at order 20 for right and left eyes respectively and was 2 times the minimum RMS of the Pentacam for right eyes and 1.7 times the minimum RMS of the Pentacam for left eyes.

CONCLUSIONS

Orders 12 and 10 Zernike polynomials almost perfectly matched the raw-elevation data collected from Pentacam for anterior and posterior surfaces, respectively for either healthy or keratoconic corneas. The Zernike fitting could not perfectly match the data collected from Medmont E300 and ESP.

Eye motion correction algorithm for OCT-based corneal topography

With its sequential image acquisition, OCT-based corneal topography is often susceptible to measurement errors due to eye motion. We have developed a novel algorithm to detect eye motion and minimize its impact on OCT topography maps. We applied the eye motion correction algorithm to corneal topographic scans acquired using a 70 kHz spectral-domain OCT device. OCT corneal topographic measurements were compared to those from a rotating Scheimpflug camera topographer. The motion correction algorithm provided a 2-4 fold improvement in the repeatability of OCT topography and its agreement with the standard Scheimpflug topographer. The repeatability of OCT Zernike-based corneal mean power, cardinal astigmatism, and oblique astigmatism after motion detection was 0.14 D, 0.28 D, and 0.24 D, respectively. The average differences between the two devices were 0.19 D for simulated keratometry-based corneal mean power, 0.23 D for cardinal astigmatism, and 0.25 D for oblique astigmatism. Our eye motion detection method can be applied to any OCT device, and it therefore represents a powerful tool for improving OCT topography.

Keratoconic eyes with stable corneal tomography could benefit more from custom intraocular lens design than normal eyes

We investigated whether eyes with keratoconic corneal tomography pattern could benefit more from aberration correction with custom intraocular lenses (IOLs) than normal cataractous eyes despite the effect of misalignment on the correction of aberrations. Custom IOLs (cIOLs) were calculated for twelve normal and twelve keratoconic eyes using personalized numerical ray tracing models. The Stiles-Crawford weighted root-mean-square spot-size (wRMS) at the virtual fovea was evaluated for cIOLs and aberration-neutral IOLs (nIOLs) in a simulated clinical study with 500 virtual IOL implantations per eye and per IOL. IOL misalignment (decentration, tilt, rotation) and pupillary ectopia (4.5 mm iris aperture) were varied upon each virtual implantation. The nIOLs achieved average wRMS of 16.4 ± 4.3 μm for normal, and 92.7 ± 34.4 μm for keratoconic eyes (mean ± standard deviation). The cIOLs reduced the average wRMS to 10.3 ± 5.8 μm for normal, and 28.5 ± 18.6 μm for keratoconic eyes. The cIOLs produced smaller wRMS than nIOLs in most virtual implantations (86.7% for normal and 99.4% for keratoconic eyes). IOL misalignment resulted in larger wRMS variations in the keratoconus group than in the normal group. Custom freeform IOL-optics-design may become a promising option for the correction of advanced aberrations in eyes with non-progressive keratoconic corneal tomography pattern.

Study of Morpho-Geometric Variables to Improve the Diagnosis in Keratoconus with Mild Visual Limitation

The validation of new methods for the diagnosis of incipient cases of Keratoconus (KC) with mild visual limitation is of great interest in the field of ophthalmology. During the asymmetric progression of the disease, the current diagnostic indexes do not record the geometric decompensation of the corneal curvature nor the variation of the spatial profile that occurs in singular points of the cornea. The purpose of this work is to determine the structural characterization of the asymmetry of the disease by using morpho-geometric parameters in KC eyes with mild visual limitation including using an analysis of a patient-specific virtual model with the aid of computer-aided design (CAD) tools. This comparative study included 80 eyes of patients classified as mild KC according to the degree of visual limitation and a control group of 122 eyes of normal patients. The metric with the highest area under the receiver operating characteristic (ROC) curve was the posterior apex deviation. The most prominent correlation was found between the anterior and posterior deviations of the thinnest point for the mild keratoconic cases. This new custom computational approach provides the clinician with a three-dimensional view of the corneal architecture when the visual loss starts to impair.

Characteristic of entire corneal topography and tomography for the detection of sub-clinical keratoconus with Zernike polynomials using Pentacam

The study aimed to characterize the entire corneal topography and tomography for the detection of sub-clinical keratoconus (KC) with a Zernike application method. Normal subjects (n = 147; 147 eyes), sub-clinical KC patients (n = 77; 77 eyes), and KC patients (n = 139; 139 eyes) were imaged with the Pentacam HR system. The entire corneal data of pachymetry and elevation of both the anterior and posterior surfaces were exported from the Pentacam HR software. Zernike polynomials fitting was used to quantify the 3D distribution of the corneal thickness and surface elevation. The root mean square (RMS) values for each order and the total high-order irregularity were calculated. Multimeric discriminant functions combined with individual indices were built using linear step discriminant analysis. Receiver operating characteristic curves determined the diagnostic accuracy (area under the curve, AUC). The 3rd-order RMS of the posterior surface (AUC: 0.928) obtained the highest discriminating capability in sub-clinical KC eyes. The multimeric function, which consisted of the Zernike fitting indices of corneal posterior elevation, showed the highest discriminant ability (AUC: 0.951). Indices generated from the elevation of posterior surface and thickness measurements over the entire cornea using the Zernike method based on the Pentacam HR system were able to identify very early KC.

Repeatability of Wavefront Aberration Measurements With a Placido-Based Topographer in Normal and Keratoconic Eyes

PURPOSE

To determine and compare the repeatability of anterior corneal higher order aberrations (HOAs) using a Placido-based topographer (Allegro Topolyzer; WaveLight Technologie AG, Alcon Laboratories, Erlangen, Germany) in a sample of normal and keratoconic eyes.

METHODS

Three repeated measurements of each cornea of normal and keratoconic eyes were taken with the Allegro Topolyzer. Repeatability of the HOAs (3rd- and 4th-order individual values and normalized polar Zernike coefficients, coma-like, root mean square (RMS) up to 8th-order values, HOA RMS, and total RMS for 6-mm pupil diameter) and central corneal power (3-mm pupil) were analyzed. Within-subject standard deviation (Sw), precision, repeatability, coefficient of variation (CV), and the intraclass correlation coefficient (ICC) were calculated.

RESULTS

Zernike coefficients were significantly different between the normal (36 eyes of 36 patients) and keratoconus (36 eyes of 36 patients) groups (P ≤ .03) except in Z(+1) 3, Z(+3) 3, Z(-4) 4, and Z(+4) 4. In the normal group, Sw was 0.031 µm or less, CV ranged from 6.49% (spherical aberration) to 37.18% (secondary astigmatism), and ICC values ranged from 0.227 to 0.982. In the keratoconus group, Sw was 0.059 µm or less, CV ranged from 2.06% (total RMS) to 25.82% (tetrafoil), and ICC values ranged from 0.839 to 0.996. In analyzing the keratoconus stages (Amsler-Krumeich classification), the repeatability of the Zernike coefficients tended to improve with increasing keratoconus stage.

CONCLUSIONS

The repeatability of corneal wavefront aberration provided by the Allegro Topolyzer was better in keratoconic eyes (good and moderate repeatability) than in normal eyes (moderate and poor repeatability). These results are important to eye care practitioners and refractive surgeons during refractive surgery planning or keratoconus detection, classification, and management. [J Refract Surg. 2016;32(5):338-344.].

Golden angle based scanning for robust corneal topography with OCT

Corneal topography allows the assessment of the cornea's refractive power which is crucial for diagnostics and surgical planning. The use of optical coherence tomography (OCT) for corneal topography is still limited. One limitation is the susceptibility to disturbances like blinking of the eye. This can result in partially corrupted scans that cannot be evaluated using common methods. We present a new scanning method for reliable corneal topography from partial scans. Based on the golden angle, the method features a balanced scan point distribution which refines over measurement time and remains balanced when part of the scan is removed. The performance of the method is assessed numerically and by measurements of test surfaces. The results confirm that the method enables numerically well-conditioned and reliable corneal topography from partially corrupted scans and reduces the need for repeated measurements in case of abrupt disturbances.

Optical coherence tomography-based topography determination of corneal grafts in eye bank cultivation

Vision loss due to corneal injuries or diseases can be treated by transplantation of human corneal grafts (keratoplasty). However, quality assurance in retrieving and cultivating the tissue transplants is confined to visual and microbiological testing. To identify previous refractive surgery or morphological alterations, an automatic, noncontact, sterile screening procedure is required. Twenty-three corneal grafts have been measured in organ culture with a clinical spectral-domain optical coherence tomographer. Employing a biconic surface fit with 10 degrees of freedom, the radii of curvature and conic constants could be estimated for the anterior and posterior corneal surfaces. Thereupon, central corneal thickness, refractive values, and astigmatism have been calculated. Clinical investigations are required to elaborate specific donor–host matching in the future.

A novel zernike application to differentiate between three-dimensional corneal thickness of normal corneas and corneas with keratoconus

PURPOSE

To evaluate a novel Zernike algorithm to differentiate 3-dimensional (3-D) corneal thickness distribution of corneas with keratoconus (KC) from normal corneas.

DESIGN

A retrospective development and evaluation of a diagnostic approach.

METHODS

Corneal tomography with Scheimpflug imaging was performed in normal (43 eyes) and KC (85 eyes) corneas. Axial and tangential cone location magnitude index (axial CLMI and tangential CLMI, respectively) of the anterior and posterior surface were calculated. The aberrations of the anterior corneal surface were analyzed with Zernike polynomials. Pachymetric Zernike analyses (PZA) were used to map the 3-D thickness distribution of the cornea. Logistic regression was performed to develop a diagnostic procedure for KC using CLMI, PZA, and aberrations. A receiver operating characteristic curve was constructed for each regression model. Corneal volume was also compared between normal and KC corneas. Only the central 5 mm zone was used for all analyses.

RESULTS

Among the PZA coefficients, second- and third-order root mean squares of PZA coefficients were the best predictors of KC corneas (P < .0001). Among the CLMI variables, axial CLMI of anterior and tangential CLMI of posterior surface were the best predictors of KC (P < .0001). Among the Zernike corneal aberration coefficients, second- and third-order root mean squares of coefficients were the best predictors of KC (P < .0001). Sensitivity and specificity of Zernike corneal aberrations, CLMI, and PZA logistic regression model were similar (P > .05).

CONCLUSIONS

The entire 3-D corneal thickness was mapped with Zernike. The PZA method was comparable to CLMI and anterior corneal wavefront aberrations in detecting KC.

Wavefront aberration changes caused by a gradient of increasing accommodation stimuli

PURPOSE

The aim of this study was to investigate the wavefront aberration changes in human eyes caused by a gradient of increasing accommodation stimuli.

DESIGN

This is a prospective, single-site study.

METHODS

Healthy volunteers (n=22) aged 18-28 years whose refraction states were emmetropia or mild myopia, with astigmatism <1 diopter (D), were included in this study. After dilating the right pupil with 0.5% phenylephrine drops, the wavefront aberration of the right eye was measured continuously either without or with 1, 2, 3, 4, 5, or 6D accommodation stimuli (WFA1000B psychophysical aberrometer). The root mean square (RMS) values of the total wavefront aberrations, higher-order aberrations, and 35 individual Zernike aberrations under different accommodation stimuli were calculated and compared.

RESULTS

The average induced accommodations using 1, 2, 3, 4, 5, or 6D accommodation stimuli were 0.848, 1.626, 2.375, 3.249, 4.181, or 5.085 D, respectively. The RMS of total wavefront aberrations, as well as higher-order aberrations, showed no significant effects with 1-3 D accommodation stimuli, but increased significantly under 4, 5, and 6 D accommodation stimuli compared with relaxed accommodation. Zernike coefficients of significantly decreased with increasing levels of accommodation.

CONCLUSION

Higher-order wavefront aberrations in human eyes changed with increased accommodation. These results are consistent with Schachar's accommodation theory.

Describing the corneal shape after wavefront-optimized photorefractive keratectomy

PURPOSE

To develop a procedure for describing wavefront-optimized photorefractive keratectomy (PRK) corneas and to characterize PRK-induced changes in shape.

METHODS

We analyzed preoperative and postoperative corneal elevation data of 41 eyes of 41 patients (mean [±SD] age, 38 [±11] years) who underwent a myopia-correcting (preoperative spherical equivalent refraction -3.9 [±1.5] diopters) wavefront-optimized PRK, assessed with Scheimpflug imaging. Zernike polynomials were fitted to the elevation data. The diameter of the greatest corneal zone that could be analyzed and the number of Zernike orders needed to make a reliable fit were determined, based on the fitting error. The PRK-induced changes in corneal shape were studied.

RESULTS

All subjects could be included for analysis of zones up to 6 mm in diameter. This was 90, 83, and 44% for 7, 8, and 9 mm, respectively. The number of Zernike orders (terms) needed for an accurate fit ranged from four (15) for a 4-mm analyzed zone diameter to eight (45) for 8 mm. For the anterior surface, the spherical aberration term decreased significantly (p < 0.01) after PRK for the 4-mm analyzed zone diameter (-0.09 μm), remained unchanged for 5 mm (+0.01 μm; p = 0.56), and increased significantly for 6 mm (+0.40 μm) and above (p < 0.01). There was no significant change in any other higher-order Zernike term, but the square root of the sum of the squares of all higher-order terms increased significantly for all analyzed zone diameters. Photorefractive keratectomy did not influence the posterior corneal shape.

CONCLUSIONS

The cornea after wavefront-optimized PRK can be described as accurately as a healthy cornea and with a similar number of Zernike polynomials. The anterior corneal shape changes significantly after treatment, whereas the posterior corneal shape remains unchanged. The observed effect of wavefront-optimized ablation on the spherical aberration term depends on the diameter of the analyzed zone.

Patterned corneal collagen crosslinking for astigmatism: computational modeling study

PURPOSE

To test the hypothesis that spatially selective corneal stromal stiffening can alter corneal astigmatism and assess the effects of treatment orientation, pattern, and material model complexity in computational models using patient-specific geometries.

SETTING

Cornea and Refractive Surgery Service, Academic Eye Institute, Cleveland, Ohio, USA.

DESIGN

Computational modeling study.

METHODS

Three-dimensional corneal geometries from 10 patients with corneal astigmatism were exported from a clinical tomography system (Pentacam). Corneoscleral finite element models of each eye were generated. Four candidate treatment patterns were simulated, and the effects of treatment orientation and magnitude of stiffening on anterior curvature and aberrations were studied. The effect of material model complexity on simulated outcomes was also assessed.

RESULTS

Pretreatment anterior corneal astigmatism ranged from 1.22 to 3.92 diopters (D) in a series that included regular and irregular astigmatic patterns. All simulated treatment patterns oriented on the flat axis resulted in mean reductions in corneal astigmatism and depended on the pattern geometry. The linear bow-tie pattern produced a greater mean reduction in astigmatism (1.08 D ± 0.13 [SD]; range 0.74 to 1.23 D) than other patterns tested under an assumed 2-times increase in corneal stiffness, and it had a nonlinear relationship to the degree of stiffening. The mean astigmatic effect did not change significantly with a fiber- or depth-dependent model, but it did affect the coupling ratio.

CONCLUSIONS

In silico simulations based on patient-specific geometries suggest that clinically significant reductions in astigmatism are possible with patterned collagen crosslinking. Effect magnitude was dependent on patient-specific geometry, effective stiffening pattern, and treatment orientation.

FINANCIAL DISCLOSURES

Proprietary or commercial disclosures are listed after the references.

Four discriminant models for detecting keratoconus pattern using Zernike coefficients of corneal aberrations

PURPOSE

We compared the ability of four discriminant models to detect keratoconus (KC) using Zernike coefficients of corneal aberrations.

METHODS

We studied 51 eyes with KC, 46 with KC suspect, 50 after laser in situ keratomileusis, and 65 normal eyes. Four statistical discriminant analyses-linear discriminant analysis, k-nearest neighbor algorithm, Mahalanobis distance method, and neural network method-were performed using Zernike coefficients of corneal aberrations obtained by a Placido-based topographer. The detection scheme was constructed using a training set of data from one half of the randomly selected study participants, and performance was evaluated by a validation set in the other half.

RESULTS

Performance of the four models was different when <12 explanatory variables were included. Performance using the 2nd- to 4th-order Zernike terms did not differ significantly among models; average accuracy was 79 %.

CONCLUSIONS

Determining explanatory variables of Zernike expansion coefficients of the corneal topography in discriminant models may contribute to improving accuracy of KC detection over the discriminant model, as appropriate selection of explanatory variables gave similar results despite different discriminant models.

Individual IOL surface topography analysis by the WaveMaster Reflex UV

Purpose. In order to establish inspection routines for individual intraocular lenses (IOLs), their surfaces have to be measured separately. Currently available measurement devices lack this functionality. The purpose of this study is to evaluate a new topography measurement device based on wavefront analysis for measuring individual regular and freeform IOL surfaces, the “WaveMaster Reflex UV” (Trioptics, Wedel, Germany). Methods. Measurements were performed on IOLs with increasingly complex surface geometries: spherical surfaces, surfaces modelled by higher-order Zernike terms, and freeform surfaces from biometrical patient data. Two independent parameters were measured: the sample's radius of curvature (ROC) and its residual (difference of sample topography and its best-fit sphere). We used a quantitative analysis method by calculating the residuals' root-mean-square (RMS) and peak-to-Valley (P2V) values. Results. The sample's best-fit ROC differences increased with the sample's complexity. The sample's differences of RMS values were 80 nm for spherical surfaces, 97 nm for higher-order samples, and 21 nm for freeform surfaces. Graphical representations of both measurement and design topographies were recorded and compared. Conclusion. The measurements of spherical surfaces expectedly resulted in better values than those of freeform surfaces. Overall, the wavefront analysing method proves to be an effective method for evaluating individual IOL surfaces.

Characterization of corneal structure in keratoconus

The increasing volume of patients interested in refractive surgery and the new treatment options available for keratoconus have generated a higher interest in achieving a better characterization of this pathology. The ophthalmic devices for corneal analysis and diagnosis have experienced a rapid development during the past decade with the implementation of technologies such as the Placido-disk corneal topography and the introduction of others such as scanning-slit topography, Scheimpflug photography, and optical coherence tomography, which are able to accurately describe not only the geometry of the anterior corneal surface but also that of the posterior surface, as well as pachymetry and corneal volume. Specifically, anterior and posterior corneal elevation, corneal power, pachymetry maps, and corneal coma-like aberrometry data provide sufficient information for an accurate characterization of the cornea to avoid misleading diagnoses of patients and provide appropriate counseling of refractive surgery candidates.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

Method for expressing clinical and statistical significance of ocular and corneal wave front error aberrations

PURPOSE

The significance of ocular or corneal aberrations may be subject to misinterpretation whenever eyes with different pupil sizes or the application of different Zernike expansion orders are compared. A method is shown that uses simple mathematical interpolation techniques based on normal data to rapidly determine the clinical significance of aberrations, without concern for pupil and expansion order.

METHODS

Corneal topography maps (TOMEY, Inc, Nagoya, Japan) from 30 normal corneas were collected, and the corneal wave front error was analyzed by Zernike polynomial decomposition into specific aberration types for pupil diameters of 3, 5, 7, and 10 mm and Zernike expansion orders of 6, 8, 10, and 12. Using this 4 × 4 matrix of pupil sizes and fitting orders, the best-fitting 3-dimensional functions were determined for the mean and standard deviation of the root-mean-square error for specific aberrations. The functions were encoded into a software application to determine the significance of data acquired from nonnormal cases.

RESULTS

The best-fitting functions for 6 types of aberrations were determined: defocus, astigmatism, prism, coma, spherical aberration, and all higher-order aberrations. A clinical screening method of color coding the significance of aberrations in normal, postoperative laser in situ keratomileusis, and keratoconus cases having different pupil sizes and different expansion orders is demonstrated.

CONCLUSIONS

A method to calibrate wave front aberrometry devices using a standard sample of normal cases was devised. This method could be potentially useful in clinical studies involving patients with uncontrolled pupil sizes or in studies that compare data from aberrometers that use different Zernike fitting-order algorithms.

Higher-order aberrations after wavefront-optimized photorefractive keratectomy and laser in situ keratomileusis

PURPOSE

To analyze the changes in higher-order aberrations (HOAs) that occur after wavefront-optimized photorefractive keratectomy (PRK) and laser in situ keratomileusis (LASIK).

SETTING

Emory Eye Center and Emory Vision, Atlanta, Georgia, USA.

METHODS

This retrospective analysis comprised eyes that had PRK or LASIK from June 2004 through October 2005. Postoperative outcome measures included 3-month uncorrected visual acuity (UCVA), best spectacle-corrected visual acuity (BSCVA), manifest refraction spherical equivalent (MRSE), changes in the root mean square (RMS) and grouped coefficient HOAs (microns) measured with a corneal analyzer, and subjective assessment of visual aberrations.

RESULTS

One hundred consecutive eyes of 54 patients had PRK, and 100 contemporaneous consecutive eyes of 71 patients had LASIK. The PRK and LASIK populations were similar in general demographics, preoperative HOAs, and postoperative UCVA and BSCVA. The mean MRSE was slightly hyperopic after PRK (mean +0.11 diopters [D]) and slightly myopic after LASIK (mean -0.19 D) (P< .0001). There were no statistically significant changes in RMS or grouped coefficient HOA values after PRK or LASIK, nor were there significant differences in postoperative RMS or grouped coefficient HOA values between PRK and LASIK. One percent of PRK and LASIK patients reported a subjective increase in postoperative visual aberrations; 5% reported a subjective improvement postoperatively.

CONCLUSIONS

Wavefront-optimized excimer laser surgery did not induce significant HOAs after PRK or LASIK. The 2 techniques were equally efficacious and had equivalent postoperative HOA profiles.

Multizone model for postsurgical corneas: analysis of standard and custom LASIK outcomes

A multizone model for postsurgical corneal topography is presented and applied to a comparative analysis of the outcome of standard and customized myopic LASIK. The different zones are segmented automatically by a clustering algorithm. The algorithm uses a set of three local descriptors, which correspond to normalized physical magnitudes computed for each point of the corneal topography map: Gauss curvature, root-mean-square (RMS) fit error to an ellipsoid surface model, and distance to the center of the topographic map. Both presurgical and post-LASIK corneal topographies of 31 eyes were analyzed using monozone and multizone models. The patients were classified into three groups according to the different LASIK treatments applied: Allegretto, Zyoptix, and PlanoScan. For post-LASIK corneas, the multizone model provided a lower fit error, an average of 1.2+/-0.4 microm versus 2.4+/-0.7 microm (monozone). The comparative analysis of the three different LASIK treatments showed no improvement of custom over standard treatments. The outcomes of Zyoptix and PlanoScan were basically equivalent and consistent with previous findings: The higher-order aberration (HOA) increased by a factor of two. The increase in HOA was higher, by a factor of three, after the Allegretto treatment. The multizone model shows a higher-fidelity representation and permits a deeper understanding of the postsurgical cornea.

Pseudo forward ray-tracing: a new method for surface validation in cornea topography

PURPOSE

A pseudo forward ray-tracing (PFRT) algorithm is developed to evaluate surface reconstruction in corneal topography. The method can be applied to topographers where one-to-one correspondence between mire and image points can be established.

METHODS

The PFRT algorithm was applied on a corneal topographer designed and constructed at the VU University Medical Center, Amsterdam, The Netherlands. Performance of the algorithm was evaluated using artificial test surfaces and two sample eyes. The residual output of the PFRT algorithm is displayed as pixel displacements of actual feature points on the corneal image. Displacement of 1 pixel indicates submicrometer corneal height accuracy.

RESULTS

PFRT residual increases with complexity of the measured surface. Using Zernike radial order 6, the mean residual for the artificial surfaces is subpixel. The mean residual for the regular cornea and the irregular cornea is 1.16 and 2.94 respectively. To some extent, increasing the Zernike radial order improves the accuracy. The improvement from order 6 to 20 is factor 2.3 for the irregular cornea. Using the residuals to further improve the accuracy brought local changes as high as 0.28 D in some areas of the reconstructed corneal power map.

CONCLUSION

PFRT can be used to evaluate how close a reconstructed corneal surface is to the actual one. The residue information obtained from this algorithm can be displayed simultaneously with the corneal image. This provides accurate information about the corneal shape that is useful for application in laser refractive surgery.

Fitting behaviors of Fourier transform and Zernike polynomials

PURPOSE

To evaluate the residual fit errors for wavefront measurements and corneal surfaces in virgin and post-surgery eyes using the Fourier transform and Zernike 6th- and 10th-order expansions.

METHODS

Using MatLab (The MathWorks, Inc.) and VOLCT program (Sarver and Associates, Inc.), wavefront gradient fields derived from the Hartmann-Shack lenslet array of the CustomVue System (Visx, Inc.) and the corneal surface obtained from the Humphrey Atlas topographer (Carl Zeiss, Inc.) were fitted with the Fourier transform and Zernike 6th- and 10th-order expansions. The wavefront gradient fields and corneal surfaces reconstructed by the 3 methods were compared with original ones, and the residual fit errors were analyzed (6.0 mm pupil). Ten eyes in each of the 4 groups (virgin eyes, post-laser in situ keratomileusis (LASIK) for myopia, post-LASIK for hyperopia, and post-radial keratotomy) were included.

RESULTS

Wavefront gradient fields reconstructed with Fourier transform produced significantly smaller residual fit errors than Zernike 6th-order in all groups and Zernike 10th-order in all eyes except post-myopic-LASIK eyes. In all groups, wavefront gradient fields reconstructed with Zernike 10th order yielded significantly smaller residual errors than Zernike 6th order (all P<.05). Higher residual errors were produced by these 3 methods in more highly aberrated eyes. When corneal surfaces for all groups were reconstructed, the Fourier transform produced significantly lower residual fit errors than Zernike 6th order and 10th order and the Zernike 10th order yielded significantly lower residual errors than Zernike 6th order (all P<.05). As corneal higher-order aberrations increased, higher residual surface fit errors were produced by Zernike 6th-order and 10th-order expansions but not by Fourier transform.

CONCLUSIONS

Fourier transform reconstructed ocular wavefront and corneal topographic maps more accurately than Zernike polynomials up to the 10th order. Clinical implications require further study.

Zernike versus Fourier treatment tables for myopic patients having CustomVue wavefront laser in situ keratomileusis with the S4 excimer laser

PURPOSE

To compare the efficacy, predictability, and safety of Zernike-based versus Fourier-based treatment tables in myopic eyes 1 year after CustomVue wavefront laser in situ keratomileusis (LASIK) using the S4 excimer laser (Visx).

SETTING

Department of Ophthalmology, Stanford University School of Medicine, Stanford, California, USA.

METHODS

A prospective analysis of 32 eyes of 16 patients with myopia who had CustomVue LASIK with the S4 excimer laser was conducted using Zernike or Fourier treatment tables. Mean spherical equivalent (SE), uncorrected visual acuity (UCVA), best spectacle-corrected visual acuity (BSCVA), and higher wavefront analyses were determined.

RESULTS

The mean postoperative SE was -0.27 diopter (D) +/- 0.41 (SD) in Zernike-treated eyes and -0.20 +/- 0.29 D in Fourier-treated eyes. Twenty-eight of 32 eyes were available for analysis. Ninety-two percent of eyes in the Zernike group and all eyes in the Fourier group had 20/20 or better acuity (P = .85). Seventy-nine percent and 92%, respectively, were within +/-0.50 D of emmetropia (P = .68). All eyes in the Zernike group and 93% of eyes in the Fourier group had no change or gained at least 1 Snellen line of BSCVA (P = .85). Mean higher-order aberration values (mum) in the Zernike group and Fourier group were as follows: total root mean square, 0.91 and 0.99, (P = 0.95); defocus, 0.71 and 0.74, (P = 0.98); astigmatism, 0.15 and 0.31, (P = 0.81); coma, 0.21 and 0.20, (P = 0.99); trefoil, 0.11 and 0.11, (P = 1); and spherical aberration, 0.17 and 0.30, (P = 0.85), respectively.

CONCLUSIONS

Myopic eyes that had CustomVue LASIK had better visual outcomes in the Fourier group than in the Zernike group. Higher-order wavefront aberration results were similar between the 2 groups.

Defining subclinical keratoconus using corneal first-surface higher-order aberrations

PURPOSE

To describe corneal higher-order wavefront aberrations of clinically inconspicuous fellow eyes in patients with early keratoconus (KC).

DESIGN

Prospective comparative case series, conducted at a university eye hospital outpatient clinic.

METHODS

Twenty-three eyes (group 1) were newly diagnosed with KC; 10 eyes (group 2) were asymptomatic fellow eyes that showed neither major topographic anomaly nor clinical signs of KC; 127 healthy eyes of 74 patients served as negative controls (group 3). A seventh-order Zernike decomposition of first-surface aberrations was performed. Single Zernike coefficients, higher-order aberration root mean square (HOA RMS) values, the Z3 index and the output values of discriminant analysis D(13) (with input from groups 1 and 3) and D(23) (groups 2 and 3) were assessed for their usefulness to discriminate between clinically normal fellow eyes, KC eyes and controls by plotting receiver-operating characteristic (ROC) curves.

RESULTS

There were significant differences between group 1 and group 3 for 11 Zernike coefficients, Z3, total HOA RMS, coma RMS and third-order RMS. Group 2 and 3 showed significant differences only for the coefficients Z(3)(-1) and Z(5)(-1). Z(3)(-1), D(13), and D(23) discriminated between groups 1 and 3 with maximum sensitivity and specificity. For discrimination between groups 2 and 3, D(23) turned out to be the best parameter (A(z) ROC = 0.98), followed by Z(3)(-1) (A(z) ROC = 0.96).

CONCLUSIONS

Clinically normal fellow eyes of eyes with early KC showed significant differences of first-surface aberrations compared to normal eyes and could therefore be considered as eyes with subclinical KC.

Optimizing higher-order aberrations with intraocular lens technology

PURPOSE OF REVIEW

Aspheric intraocular lens technology has been implemented during the past 5 years, and more and more intraocular lenses with different amounts of asphericity are becoming available. Despite the efficacy in the correction of spherical aberration and the good results on implanted eyes, the theoretical advantages of aspheric intraocular lenses are still controversial.

RECENT FINDINGS

All investigations showed the ability of the aspheric intraocular lenses to correct the positive spherical aberration of the cornea, with variable impact on the total eye wavefront but with constant advantages in the optical quality of the eyes as measured by the Modulation Transfer Function, the Point Spread Function, and the contrast sensitivity of implanted patients. Theoretical studies on model eyes underlined some possible limitations of aspheric intraocular lenses, especially sensitivity to decentration. In addition, the actual optical quality in implanted eyes is also affected by light scattering, a parameter missed by simple aberration analysis.

SUMMARY

Aspheric intraocular lenses effectively reduce spherical aberration in implanted eyes, with improvement in optical quality over the parent spherical intraocular lens. The advantages for implanted eyes could be limited by decentration, by small pupil diameter, and by reduced media transparency.