KEY CONCEPTS
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Wavefront sensing has renewed interest in understanding and correcting ocular irregularities and improving human visual acuity. The different systems used to analyze wavefront aberrations of the eye are classically divided into ingoing and outgoing systems.
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Each imaging device reconstructs Zernike terms differently, using smoothing functions from the acquired data. From the wavefront aberration data, mathematical calculations enable simulation of the appearance of the retinal image.
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The integration of total and corneal wavefront data improves diagnostic accuracy of keratoconus.
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The application of wavefront analysis in cases of corneal ectasia is unquestionably valuable for diagnosis, staging, and treatment planning.
Introduction
Along with corneal imaging, major advances in image enhancement within the field of astronomy were adopted by ophthalmology for enhancing optical analysis of the eye. These concepts have been used to characterize refractive errors of the human eye using polynomial terms beyond sphere and cylinder, so that “irregular astigmatism” can be quantified and detailed. The difference between classical refraction, based on the sphere and cylinder, and wavefront aberrometry is analogous to the difference between keratometry and corneal topography. An understanding of the ocular wavefront has enabled a new era in customized refractive ablation techniques to improve optical results. , This chapter is focused on the clinical applications of ocular wavefront analysis for the evaluation of keratoconus (KC).
Understanding Wavefront Aberrations
In a “perfect” optical system, rays emanating from an object point are refracted to converge to the unique image point expected from Gaussian ray-tracing theory. If we consider divergent wavefront rays spreading out from the object to be changed by the optical system into convergent wavefront rays (such as the rays exiting the eye), in a “perfect” optical medium, the wavefronts will be perpendicular to the rays for any phase analyzed ( Fig. 17.1 A). However, if there are aberrations, the refracted rays no longer perfectly converge to the unique image point, and the wavefronts are no longer parallel to the rays (see Fig. 17.1 B). The wavefront aberration is the distance, usually measured in micrometers (μm) between an actual wavefront and an ideal “perfect” plano wavefront measured at the pupil. This distance is a difference in the optical path, which is referenced to the center of the exit pupil of the system, where the wavefront aberration should be zero.
Use of Zernike polynomial terms is recognized as the best method for the diagnostic characterization of wavefront aberrations ( Fig. 17.2 ). The terms were developed by Frits Zernike (1888–1966). , The Zernike polynomials are used in geometry to describe mathematically best-fit curves. These equations function as building blocks to better describe the details of the wavefront shape. Therefore, more terms included in the equation, the better the fit. In optical terms, this means that the more Zernike terms that are calculated, the more completely the aberrations will be characterized. The degree of aberration is calculated with the root mean square (RMS) of difference between the real and ideal wavefront for every term. These terms can be combined or presented as an isolated RMS term. It is critical to understand that the larger the pupil diameter, the greater the amount of aberrations, which will increase the RMS ( Fig. 17.3 ).
Other mathematical methods use wavefront data for planning custom ablations, which have a potential benefit because of the limitations of Zernike’s terms for describing very irregular shapes. However, Zernike’s polynomials excel in extracting clinically useful information for describing the wavefront aberrations of vision optics. The lower order aberrations (LOAs) include the components zero (piston), one (tilt), and two (defocus and astigmatism) of the Zernike polynomials pyramid (see Fig. 17.2 ). The second order terms are the ones that can be corrected by glasses. The higher order aberrations (HOAs) are considered from the third order onward and represent irregular astigmatism. The third (coma and trefoil) and fourth (spherical aberrations) orders are the most important high order coefficients and have higher impact on the quality of vision in patients with corneal irregularities, including KC and other types of ectasia.
From the wavefront aberration data, we can calculate the point-spread function, as well as the modulation transfer function for the contrast, as a function of the spatial frequency. Mathematical calculations for determining image formation allow for simulating the appearance of the retinal image, which can be used, for example, for a Snellen letter of any chosen size ( Fig. 17.4 ). ,
Types of Wavefront Systems
Currently, there are several commercially available systems that analyze wavefront aberrations of the eye. These are classically divided into ingoing and outgoing systems. Ingoing optical systems study the optical aberrations of a light beam projected onto the retina, such as the Tscherning aberrometer, which projects a grid, and the sequential retinal ray tracing of individual point scanning. The scanning of individual points allows measurement in corneas with more pronounced optical distortions and is very useful in cases of KC. In the analysis of outgoing optics, the wavefront is assessed exiting the eye. A light beam is projected and reflected from the retina, exiting the eye, and is analyzed by a sensor such as the Hartmann-Shack, which is the most popular system available in commercial instruments. One drawback of wavefront analysis for evaluating KC patients is that it is necessary to have a high dynamic range wavefront sensor to enable the optical analysis in more advanced cases. This measurement can be achieved by using a shorter focal length lenslet array in a Hartmann-Shack system. Dynamic skiascopy, which utilizes the scanning infrared slit refractometer, is another option. , Recently, pyramidal sensor wavefront analysis became available in the market (Osiris-T, Costruzione Strumenti Oftalmici, CSO, Florence, Italy). This system combines a corneal topographer with a total ocular aberrometer. This sensor design allows the aberrometer to measure aberrations with a resolution of 45,000 points (at the maximum pupil diameter), with a broad dynamic range.
Corneal Wavefront Measurements
Polynomial mathematical calculations may also be used to describe front and back corneal elevation data from tomography systems, as well as front surface data from topography systems. The integration of wavefront data from the whole eye and from the cornea enables the characterization of the impact of distinct ocular elements in the overall optical property of the eye. Using corneal aberrations to describe the optical quality of the cornea is highly relevant. The detection of KC based on Zernike coefficients from the corneal front surface was pioneered by Schwiegerling. However, there are some discrepancies in the performance of such parameters to discriminate KC from normal corneas. For example, Gobbe showed that the best detector to differentiate between suspected KC and normal corneas was vertical coma with a specificity of 71.9% and sensitivity of 89.3%. Buhren and coworkers have successfully utilized first surface HOAs for diagnosing subclinical KC, with an area under the receiver operating characteristic curve (AUC) of 0.98. However, it is important to note that each instrument will reconstruct Zernike terms differently, using smoothing functions from the acquired data.
Total Wavefront for Diagnosing Keratoconus
Maeda and coworkers reported corneal and ocular wavefront aberrations of normal and keratoconic eyes. Thirty-five keratoconic eyes and 38 normal controls had HOAs in total refraction measured with the KR-9000 Analyzer (Topcon Corporation, Tokyo, Japan), which is a Hartmann-Shack sensor combined with a Placido disk–based topography. Significantly more total ocular HOAs were found in the KC eyes, such as coma, which was found to be 2.32 times more frequent than spherical-like aberrations in keratoconic eyes. In this study, wavefront sensing enabled not only evaluation of the quality of vision but also differentiation of KC eyes from normal eyes by analysis of the characteristics of the HOAs. In another prospective case-control study involving 55 eyes of 30 patients with KC and 100 eyes of 50 refractive surgery candidates, Miháltz and coworkers evaluated total wavefront aberrations with a Hartmann-Shack sensor. The results revealed a statistically higher level of aberration in KC eyes compared with normal controls. The authors also described the changes in the axis of line of sight (LoS) among keratoconic patients. A significant displacement of the LoS was observed in these eyes, which relates to the position of the cone on topography and the vertical coma measured by aberrometry. Saad and Gatinel also investigated the application of anterior corneal and ocular aberrations in detecting mildly ectatic corneas. The authors used the NIDEK Corneal Navigator System automated corneal classification software (NIDEK, Gamagori, Japan) to classify the patients. Corneal and ocular tilt, vertical coma, and trefoil were significantly different in the forme fruste keratoconus (FFKC) group when compared with the normal control group. The discriminating functions between the FFKC and the normal group, and between the KC and the normal group, reached an AUC of 0.98 and 0.96, respectively.
Ray-Tracing Aberrometry for Ectasia Diagnosis
We also performed a study to describe and compare the ocular and anterior corneal wavefront data derived from normal, KC, and FFKC eyes. The iTrace (Tracey Technologies, Houston, TX) was used for the wavefront analysis. The aberrometer uses the ray-tracing principle, which sequentially projects 256 near-infrared laser beams into the eye in a specific scanning pattern. , Topographies were captured using the Placido-based corneal topographer (EyeSys Vision LLC, Houston, TX) mounted on the same device. Demographic data for each group are presented in Table 17.1 . The data from the Pentacam HR (OCULUS Optikgeräte GmbH, Wetzlar, Germany) were also used to classify these patients. The normal (N) group comprised 84 eyes randomly selected from 84 vision correction candidates. These patients presented unremarkable Scheimpflug tomography in both eyes (Ambrósio Relational Thickness Maximum [ART Max] greater than 400 microns; BAD [Belin Ambrósio Display] D value less than 1.60), based on previous reports. The Amsler-Krumeich KC (TKC) grading score, which is derived from the front corneal surface indices, was also null in these eyes. Fig. 17.5 illustrates a cornea with unremarkable topographic and tomographic findings on the Pentacam examination. The KC group included 70 eyes randomly selected from 70 patients who had bilateral KC. All eyes of this group presented a positive score on the TKC grading system. The FFKC group enrolled 31 topographically normal eyes of patients with clinical KC in the fellow eye ( Figs. 17.6 and 17.7 ).
| N | KC | FFKC | |||
|---|---|---|---|---|---|
| Eyes ( n ) | 84 | 70 | 31 | ||
| Age (mean ± SD) | 28.869 ± 6.655 [10; 40] | 28.329 ± 6.814 [17; 41] | 31.806 ± 7.968 [17; 45] | ||
| Sphere (D) [range] | −3.138 ± 3.683 [−11; 8.25] | −1.898 ± 3.482 [−13.25; 2.62] | −1.064 ± 2.632 [−10.12; 2.5] | ||
| Cylinder (D) [range] | −1.560 ± 1.399 [−5.75; 0] | −3.969 ± 2.181 [−9.12; −0.12] | −1.417 ± 1.288 [−4.12; −0.25] |
The wavefront data were decomposed for only one pupil size (5.0 mm). Only the individual Zernike terms were selected for analysis, using the available data automatically extracted from each scan into an Excel spreadsheet (Microsoft Corporation, Redmond, Washington DC) by the software. Tables 17.2 and 17.3 display the cutoff values, the AUC, and the standard error 95% confidence intervals of the individual corneal and ocular Zernike coefficients that were statistically different between the N versus KC groups and N versus FFKC groups, respectively. The overall performance of using individual Zernike terms to identify KC and FFKC eyes was comparable to previous studies. Nevertheless, the differences in the AUC and cutoff values of the Zernike terms are justified by the methodology implemented in the studies, such as distinct scanning technology and patient selection criteria. Similar to previous reports, individual Zernike coefficients derived from the corneal topography demonstrated better performance than those derived from the total wavefront. ,
