August 2012
Volume 53, Issue 9
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Cornea  |   August 2012
Modeling the Effect of Forward Scatter and Aberrations on Visual Acuity after Endothelial Keratoplasty
Author Notes
  • From the Department of Ophthalmology, Mayo Clinic, Rochester, Minnesota. 
  • Corresponding author: Jay W. McLaren, Department of Ophthalmology, Mayo Clinic, 200 First Street SW, Rochester, MN 55905; mclaren.jay@mayo.edu
Investigative Ophthalmology & Visual Science August 2012, Vol.53, 5545-5551. doi:10.1167/iovs.12-10011
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      Jay W. McLaren, Sanjay V. Patel; Modeling the Effect of Forward Scatter and Aberrations on Visual Acuity after Endothelial Keratoplasty. Invest. Ophthalmol. Vis. Sci. 2012;53(9):5545-5551. doi: 10.1167/iovs.12-10011.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To evaluate the effects on visual acuity of forward scatter and aberrations typical of those after Descemet stripping endothelial keratoplasty (DSEK).

Methods.: Twenty normal eyes of 20 subjects (ages 22–57 years) were examined with best spectacle correction. Under photopic conditions, high-contrast visual acuities (HCVAs) were measured by using ETDRS charts. Visual acuity was also measured by using aberrated charts that simulated the typical high-order aberrations at 12 months after DSEK. Forward scatter was induced by viewing the eye charts through a 1-mm-thick layer of scattering solution (Amco Clear, at a concentration of 4000 nephelometric turbidity units) and was measured with a straylight meter.

Results.: Forward scatter increased from 1.19 ± 0.11 log straylight parameter (log[s]; mean ± SD) without induced scatter to 1.57 ± 0.06 log(s) with induced scatter (P < 0.001). Induced scatter reduced HCVA on the nonaberrated chart by 2.7 Snellen letters, from 20/19 (Snellen equivalent) to 20/21 (P < 0.001) and by 2.1 letters on the aberrated chart, from 20/25 to 20/28 (P = 0.005). Addition of aberrations reduced HCVA by more than twice the number of Snellen letters than did induced scatter, by 6.4 letters with low scatter (P < 0.001), and by 5.8 letters with high scatter (P < 0.001).

Conclusions.: Under typical clinical testing conditions, increased forward scatter has minimal effect on visual acuity. High-order aberrations are a more likely cause of degraded visual acuity than is forward scatter in eyes with clear corneas after DSEK.

Introduction
Endothelial keratoplasty (EK) has surpassed penetrating keratoplasty (PK) as the treatment of choice for corneal endothelial diseases, 1 such as Fuchs endothelial dystrophy, primarily because of the advantageous visual outcome of better uncorrected visual acuity. 2 This improved visual outcome is the result of a predictable postoperative refractive error, often with a spherical equivalent close to zero, because of minimal disruption of the anterior corneal surface after EK compared with after PK. 35 Although average vision significantly improves after EK, most clinicians acknowledge that best-corrected high-contrast visual acuity during routine clinical examination does not return to 20/20 in many otherwise healthy eyes, 57 and many patients are still troubled with increased disability glare when compared with normal. 8,9 The quest for improving visual outcomes is one explanation for the rapid evolution of EK over the past decade. 10 Deep lamellar endothelial keratoplasty (DLEK) has been superseded by Descemet stripping endothelial keratoplasty (DSEK), which is currently the predominant EK procedure 11 with improved visual outcomes. 6,7 Descemet membrane endothelial keratoplasty (DMEK) is a newer EK technique with an interface between posterior host stroma and donor Descemet membrane, and results in a normal anatomical configuration, 12 possibly with improved vision compared with DSEK. 5,13  
Despite a clear cornea and lack of discernible interface abnormality, current dogma implicates corneal light scatter from the surgical lamellar interface as the cause of decreased visual acuity after EK. 6,14 In fact, more light is scattered from the anterior host cornea after DLEK and DSEK than from the interface, and similar increased anterior corneal scatter would be expected after DMEK because anterior host scatter is related to the underlying disease rather than the surgical procedure. 2,15,16 Irrespective of the exact source of forward scatter within the cornea after EK, the hypothesis that increased scatter causes decreased visual acuity after EK is reasonable because corneal haze (or backscatter) is higher than normal and forward scatter has been associated with decreased visual acuity. 2,14 Nevertheless, these associations do not establish a causal relationship between corneal light scatter and decreased visual acuity, and thus other factors that can degrade vision, such as aberrations, should not be excluded. 
Whole-eye high-order aberrations were recently found to be increased in pseudophakic eyes after DSEK, 8 and there is growing evidence that these aberrations originate from the anterior and posterior corneal surfaces after EK. 4,5,1720 Increased anterior corneal aberrations have also been associated with decreased visual acuity after DSEK, 4,18,19 and although a causal relationship has not been established, aberrations are more likely than scattered light to decrease visual acuity based on how these optical phenomena are known to degrade the retinal image point-spread function. 8,21,22 In normal eyes, the point-spread function has a central narrow, intense peak with a low-intensity peripheral flange. With optical degradation, the center of the point-spread function widens, its peak becomes less intense, and the peripheral flange can elevate. Visual acuity is determined by the shape of the center of the point-spread function, which is typically degraded by high-order aberrations. 21 Disability glare is determined by the periphery of the point-spread function, which is typically degraded by forward light scatter. 21 Thus, increased aberrations after DSEK could explain decreased visual acuity. 
The purpose of this study was to understand why best-corrected visual acuity after EK remains subnormal in otherwise healthy eyes, as is frequently found during routine clinical examination. We specifically examined the individual and combined effects of forward light scatter and high-order aberrations, similar to those experienced by eyes after DSEK, on the best-corrected visual acuity of normal healthy eyes. By modeling these effects in normal eyes, confounding causes of decreased visual acuity were eliminated, enabling us to investigate causal relationships between scatter and visual acuity and between aberrations and visual acuity. The effect of induced forward scatter on the center of the retinal image point-spread function was also measured to determine if changes of its shape were associated with changes in visual acuity. 
Methods
Subjects
Twenty healthy volunteers, between the ages of 20 and 57 years, were examined by slit-lamp biomicroscopy to ensure that they had normal eyes with clear ocular media and no ocular abnormalities that might affect visual acuity. The manifest refractive error of each participant was measured, and for inclusion, best-corrected visual acuity had to be 0.1 logarithm of the minimum angle of resolution (logMAR) or better (Snellen equivalent, 20/25 or better). Subjects viewed all study eye charts and other test fields through a trial frame that included their best-spectacle correction. One eye was examined per subject and an equal number of left and right eyes were selected at random for testing. This study was prospectively approved by the Institutional Review Board of Mayo Clinic, conformed to the Health Insurance Portability and Accountability Act (HIPAA), and followed the tenets of the Declaration of Helsinki. All subjects gave informed consent after discussion of the risks and possible consequences of the study. 
Induction of Forward Scatter
Forward scatter was induced by a layer of Amco Clear (GSF Chemicals, Columbus, OH) in a flat chamber 1-mm thick, placed in the trial frame with the corrective lenses. The chamber was constructed from two round glass plates, each approximately 1-mm thick, cemented to a C-shaped spacer (Fig. 1). Edges of the chamber were masked with black tape to create a central round aperture that was 20 mm in diameter. The central apertures of the trial frame lenses were 15 mm in diameter. One of two chambers was placed in the trial frame with the corrective lenses: one chamber was filled with Amco Clear stock solution at a concentration of 4000 nephelometric turbidity units (NTU) to induce forward scatter (high scatter), and the other was filled with water as a control (low scatter). Preliminary testing indicated that the forward scatter induced by this method was in excess of mean forward scatter in eyes at 24 months after DSEK. 15  
Figure 1. 
 
Chamber to hold scatter solution. The chamber was constructed from two glass disks and a spacer to create a gap of approximately 1 mm between the disks. The chamber was filled with Amco Clear, 4000 NTU stock solution to induce high scatter, or with water for a low-scatter control. The edges of the chamber were masked with black tape to create a central aperture, 20 mm diameter (not shown), and the assembly was placed in a trial frame for vision testing.
Figure 1. 
 
Chamber to hold scatter solution. The chamber was constructed from two glass disks and a spacer to create a gap of approximately 1 mm between the disks. The chamber was filled with Amco Clear, 4000 NTU stock solution to induce high scatter, or with water for a low-scatter control. The edges of the chamber were masked with black tape to create a central aperture, 20 mm diameter (not shown), and the assembly was placed in a trial frame for vision testing.
Simulation of High-Order Aberrations
Nonaberrated Early Treatment of Diabetic Retinopathy Study (ETDRS) charts were generated by using VOL-CT (Sarver and Associates, Carbondale, IL) at 100% contrast and 10% contrast. A second set of high- and low-contrast ETDRS charts was created by VOL-CT with aberrations that were typical of eyes after DSEK. 23 These whole-eye wavefront high-order aberrations were determined by Hartmann-Shack aberrometry from 21 eyes at 12 months after DSEK, in 19 patients who were participants in another study in our laboratory. 2325 Mean age was 65 years and mean best-corrected visual acuity was 0.18 logMAR (20/30). High-order aberrations were expressed as Zernike polynomials to the sixth order calculated over a 4-mm optical zone. As a reasonable representation of aberrations for the whole group, we calculated the mean of the absolute value of each Zernike coefficient (Table 1). Note that the use of whole-eye wavefront errors was intended to simulate the aberrations that affected the point-spread function after DSEK; we did not attempt to identify or simulate specific sources of these aberrations (anterior and posterior corneal surfaces). ETDRS charts with these aberrations were constructed by using VOL-CT to calculate the convolution of the chart with the point-spread function. 26,27 All convolutions were scaled to account for the angular size of the chart at 3 m. 
Table 1. 
 
Whole-Eye High-Order Wavefront Aberrations Used to Create Aberrated Eye Charts
Table 1. 
 
Whole-Eye High-Order Wavefront Aberrations Used to Create Aberrated Eye Charts
Zernike Coefficient Aberration 1 y after DSEK Controls
Coefficient, μm Coefficient, μm
Z 3 − 3 Trefoil 0.0829 0.0376
Z 3 − 1 Coma 0.0734 0.0399
Z 3 1 Coma 0.0570 0.0438
Z 3 3 Trefoil 0.0976 0.0424
Z 4 − 4 Quadrafoil 0.0455 0.0114
Z 4 − 2 0.0344 0.0082
Z 4 0 Spherical 0.0963 0.0279
Z 4 2 0.0454 0.0135
Z 4 4 Quadrafoil 0.0493 0.0135
Z 5 − 5 0.0174 0.0040
Z 5 − 3 0.0126 0.0027
Z 5 − 1 0.0094 0.0036
Z 5 1 0.0129 0.0027
Z 5 3 0.0136 0.0022
Z 5 5 0.0124 0.0026
Z 6 − 6 0.0125 0.0024
Z 6 − 4 0.0086 0.0013
Z 6 − 2 0.0060 0.0008
Z 6 0 0.0125 0.0018
Z 6 2 0.0119 0.0009
Z 6 4 0.0095 0.0017
Z 6 6 0.0199 0.0018
Visual Acuity
Eight ETDRS charts were generated, four at 100% contrast and four at 10% contrast, each with a unique set of letters. Two of the 100% contrast charts were nonaberrated and two were aberrated, and two of the 10% contrast charts were nonaberrated and the other two were aberrated in the same way as the high-contrast charts (Fig. 2). Charts were exported as bitmap files, and imported into Microsoft Office PowerPoint (Microsoft Corporation, Redmond, WA) where they were scaled to the appropriate size to be viewed at 3 m. All charts were printed on a Hewlett Packard poster printer (HP Designjet 800 ps) on semigloss paper and mounted flat on white card stock. Charts were illuminated by vertical fluorescent lamps from the left and right sides to give uniform white background luminosity of 160 to 170 cd/m2. The largest letters on each chart represented 0.7 logMAR (or 20/100 Snellen equivalent), and the smallest letters represented −0.5 logMAR (20/5 Snellen equivalent). 
Figure 2. 
 
Example of five lines from test charts, with 100% and 10% contrast, and without and with aberrations. Test charts were generated by convolution of ETDRS charts with the point-spread function derived from aberrations representative of those measured in patients 12 months after Descemet stripping endothelial keratoplasty. Each chart had a unique set of letters (the same letters are shown on the aberrated and nonaberrated samples here for illustration). Aberrations were calculated by assuming that the charts would be read at 3 m, and each full chart included letters with sizes that ranged from 0.7 log MAR (20/100 Snellen equivalent) to −0.5 log MAR (20/5 Snellen equivalent).
Figure 2. 
 
Example of five lines from test charts, with 100% and 10% contrast, and without and with aberrations. Test charts were generated by convolution of ETDRS charts with the point-spread function derived from aberrations representative of those measured in patients 12 months after Descemet stripping endothelial keratoplasty. Each chart had a unique set of letters (the same letters are shown on the aberrated and nonaberrated samples here for illustration). Aberrations were calculated by assuming that the charts would be read at 3 m, and each full chart included letters with sizes that ranged from 0.7 log MAR (20/100 Snellen equivalent) to −0.5 log MAR (20/5 Snellen equivalent).
Each subject was asked to read each chart from 3 m through the trial frame with the subject's best-spectacle correction and the chamber with either the high- or low-scatter solution (Amco Clear or water). Charts were presented in the following order: 100% contrast nonaberrated, 10% contrast nonaberrated, 100% contrast aberrated, and 10% contrast aberrated. This sequence was repeated on the second set of charts with the other scatter solution in the chamber. The scatter solution used first was selected randomly for each subject with an equal number of subjects viewing the charts through the high- and low-scatter solutions first. 
Forward Scatter and Contrast Sensitivity
Forward light scatter was measured by using a straylight meter (C-Quant; Oculus, Lynwood, WA), which determined retinal straylight in the large-angle domain (mean, 7° from fixation) of the point-spread function by using a compensation comparison method. 28 Straylight was expressed as the logarithm of the straylight parameter, log(s), and was proportional to forward light scatter. We recorded the profile of the point-spread function in the infrared by using a double-pass method (OQAS; Visiometrics, S.L., Terrassa, Spain) and determined the width of the radial mean of the point-spread function at 50% of its height, a variable that can be affected by aberrations and is often used to express the sharpness of the point-spread function. This instrument also calculated an “Objective Scatter Index,” or OSI, which has been suggested to be a measure of forward scatter. 29  
Contrast sensitivity was determined as the sensitivity to decreasing contrast at spatial frequencies between 1.5 cyc/deg and 18 cyc/deg, in 5 steps (CST 1800 Digital Contrast Sensitivity; Vision Sciences Research Corporation, San Ramon, CA). Subjects were asked to indicate the orientation of bars (left, right, or vertical) at decreasing contrast and increasing spatial frequency, until they could no longer accurately detect the bars, as described previously. 2,30 Similar to measurement of visual acuity, forward scatter and contrast sensitivity were tested while the participants wore the trial frame that held the spherocylindrical correction and the high- or low-scatter chamber. 
Statistical Analysis
The primary outcome was the difference in best-corrected HCVA between high and low forward-scatter conditions. Assuming a test-retest standard deviation of 0.06 logMAR, a priori analysis indicated that a minimum difference of three letters of visual acuity (0.06 logMAR) on retesting could be detected with a sample of 18 eyes (α = 0.05, β = 0.10, paired analysis). All variables measured under high-scatter conditions were compared with the same variable under low scatter by using paired t-tests if data were normally distributed or signed rank tests if data were not normally distributed. Variances of log(s) (measured by the C-Quant) and the OSI (measured by the OQAS) were compared by using an F-test after normalizing data from each measurement to its respective mean. 
Results
Induced Forward Scatter
Forward light scatter, as measured by the straylight meter, increased from 1.19 ± 0.11 log(s) with low scatter to 1.57 ± 0.06 log(s) with high scatter (P < 0.001, mean ± SD). The high-scatter solution increased straylight in all participants (Fig. 3). 
Figure 3. 
 
Estimates of intraocular forward scatter. Left: straylight, measured by the C-Quant, increased with induced scatter in all eyes (P < 0.001). Right: the OSI, measured by the OQAS, increased with induced scatter (P = 0.003). The variance of the OSI was greater than that of straylight (P < 0.001) and the OSI of four subjects decreased with induced scatter.
Figure 3. 
 
Estimates of intraocular forward scatter. Left: straylight, measured by the C-Quant, increased with induced scatter in all eyes (P < 0.001). Right: the OSI, measured by the OQAS, increased with induced scatter (P = 0.003). The variance of the OSI was greater than that of straylight (P < 0.001) and the OSI of four subjects decreased with induced scatter.
Visual Acuity and Contrast Sensitivity
The mean spherical equivalent refractive error in all participants was −1.23 ± 2.15 diopters. Mean best-corrected visual acuity with the nonaberrated 100%-contrast chart viewed through the chamber filled with water (low scatter) was −0.03 ± 0.03 logMAR (Snellen equivalent, 20/19). Visual acuity was not different between subjects who were selected for right-eye and those selected for left-eye testing (P > 0.14). Visual acuities, when tested with the various charts viewed through the low- and high-scatter chambers, are listed in Table 2. At 100% contrast, the addition of scatter reduced visual acuity by an average of 2.7 and 2.1 letters on nonaberrated (P < 0.001, signed rank test) and aberrated charts (P = 0.005) respectively (Table 2). At 10% contrast, high induced scatter reduced visual acuity by approximately 1 line (4.2 and 5.3 letters) for nonaberrated and aberrated charts respectively (P < 0.001, Table 2). 
Table 2. 
 
Loss of Visual Acuity by Addition of Forward Scatter, at High and Low Contrast, and on Charts with or without Aberrations Typical of Patients at 1 Year after DSEK
Table 2. 
 
Loss of Visual Acuity by Addition of Forward Scatter, at High and Low Contrast, and on Charts with or without Aberrations Typical of Patients at 1 Year after DSEK
Visual Acuity, LogMAR, Mean ± SD (Snellen Equivalent)
100% Contrast 10% Contrast
Non-Aberrated Aberrated Loss from Increased Aberrations (Letters) Non-Aberrated Aberrated Loss, from Increased Aberrations (Letters)
Low scatter −0.03 ± 0.03 (20/19) 0.10 ± 0.04 (20/25) 6.4¶ 0.11 ± 0.05 (20/26) 0.23 ± 0.06 (20/34) 6.2¶
High scatter 0.02 ± 0.07*† (20/21) 0.14 ± 0.06‡ (20/28) 5.8¶ 0.19 ± 0.06* (20/31) 0.34 ± 0.08* (20/44) 7.3¶#
Loss from increased scatter (letters) 2.7*† 2.1‡ 4.2*§ 5.3*||
The addition of aberrations to the charts with 100% contrast and 10% contrast decreased visual acuity by approximately six letters under low-scatter conditions (P < 0.001, Table 2). Under high-scatter conditions, the addition of aberrations to the charts with 100% and 10% contrast decreased visual acuity by 5.8 and 7.3 letters respectively (P < 0.001, Table 2). 
Contrast sensitivity decreased at all spatial frequencies under high-scatter conditions compared with low-scatter conditions (P ≤ 0.005, Fig. 4). 
Figure 4. 
 
Changes in contrast sensitivity with induced forward scatter. Contrast sensitivity decreased at all spatial frequencies with induced forward scatter (all comparisons, signed-rank test, except 12 cyc/deg, paired t-test). Markers show mean ± SD, and at the same spatial frequencies, markers are offset slightly for clarity.
Figure 4. 
 
Changes in contrast sensitivity with induced forward scatter. Contrast sensitivity decreased at all spatial frequencies with induced forward scatter (all comparisons, signed-rank test, except 12 cyc/deg, paired t-test). Markers show mean ± SD, and at the same spatial frequencies, markers are offset slightly for clarity.
Point-Spread Function
The width at 50% height of the point-spread function, which is an indicator of the sharpness of edges in the visual image, was unchanged with induced forward scatter (4.1 ± 1.1 arc min) compared to low scatter (4.1 ± 1.1 arc min, P = 0.89, Fig. 5). Induced scatter increased the mean OSI from 0.63 ± 0.42 to 0.95 ± 0.47 (P = 0.003, Fig. 3). Under high- and low-scatter conditions, the OSI was more variable than the straylight parameter relative to their respective means; the SD of the OSI, when normalized to its mean (0.66 and 0.49 at low and high induced scatter respectively), was greater than that of the straylight parameter normalized to its mean (0.09 and 0.04 at low and high induced scatter respectively; P < 0.001, F-tests). 
Figure 5. 
 
Mean normalized point-spread function with low (light line) and high (dark line) scatter, as measured by double-pass method. The graph on the right is an expansion of the graph on the left, rescaled to 0.2 maximum, to illustrate differences at distances greater than 10 arc min from the center. The normalized point-spread function at 50% of its height (0.5 on ordinate) was not different with induced high scatter than with low scatter, indicating that induced forward scatter did not affect the center of the point-spread function, the region of the point-spread function that determines visual acuity. With induced scatter, the point-spread function was elevated at distances greater than 7 arc min from the center. It is not known if this elevation represents a true elevation at these high angular distances from the center or if it represents the consequence of normalization of the profile to a lower mean peak, which would also increase the point-spread function at higher angles.
Figure 5. 
 
Mean normalized point-spread function with low (light line) and high (dark line) scatter, as measured by double-pass method. The graph on the right is an expansion of the graph on the left, rescaled to 0.2 maximum, to illustrate differences at distances greater than 10 arc min from the center. The normalized point-spread function at 50% of its height (0.5 on ordinate) was not different with induced high scatter than with low scatter, indicating that induced forward scatter did not affect the center of the point-spread function, the region of the point-spread function that determines visual acuity. With induced scatter, the point-spread function was elevated at distances greater than 7 arc min from the center. It is not known if this elevation represents a true elevation at these high angular distances from the center or if it represents the consequence of normalization of the profile to a lower mean peak, which would also increase the point-spread function at higher angles.
Discussion
Induced forward scatter higher than that typically experienced after DSEK 25 caused a minimal decrease in best-corrected visual acuity, whereas high-order aberrations typical of those after DSEK decreased visual acuity much more. These findings challenge the dogma that decreased best-corrected visual acuity, as measured during routine clinical conditions, in otherwise healthy eyes after EK, is caused by corneal light scatter, or haze, whether the scatter originates from the lamellar interface or from the anterior host cornea. 15  
Clinicians have often associated back-scattered light, visible in the slit lamp, as corneal haze after lamellar keratoplasty, with decreased best-corrected visual acuity. 14 Back-scattered light itself cannot affect vision because it does not degrade the retinal image, but it is associated with changes in the cornea that also induce forward-scattered light, 2,15,16 which spreads across the retina and decreases the contrast of the image on the retina. Because the anterior corneal surface is minimally disrupted after EK and therefore much less aberrated than it is after PK, 3 forward light scatter associated with corneal haze from the surgical lamellar interface has often been suggested as the cause of decreased best-corrected visual acuity after EK. Indeed, corneal haze is present at the interface, and also in the subepithelial region, after DSEK, and although this haze improves slightly during the first 2 years after DSEK, it does not return to normal. 15 Similarly, forward scatter after DSEK remains higher than normal at least to 1 year after DSEK and is correlated with decreased visual acuity. 24 Nevertheless, in this study we determined the causal relationship between forward light scatter and visual acuity, and even though the induced forward scatter experienced by subjects in this study (1.57 log[s]) was 1.7 times higher than that experienced after DSEK for Fuchs dystrophy (approximately 1.35 log[s]), 9,24 visual acuity decreased by fewer than three letters. This suggests that the mean loss of visual acuity that can be attributed to elevated forward scatter in eyes after DSEK is likely to be less than that measured in this study. 
If forward scatter only minimally reduces visual acuity, why do some patients with otherwise healthy eyes after DSEK for Fuchs dystrophy suffer from decreased best-corrected visual acuity? Another cause of decreased acuity after EK could be high-order aberrations, which might coexist with elevated scatter. Although EK is associated with much lower aberrations from the anterior corneal surface than those after PK, 3,14,17,19 eyes after EK are more aberrated than normal. 8,23 Increased aberrations after EK originate at the anterior and posterior corneal surfaces, 4,5,1720 and are higher than those encountered after excimer laser refractive surgery. 31 In this study, we simulated the typical whole-eye high-order aberrations encountered by eyes at 12 months after DSEK and found that these aberrations degraded high-contrast visual acuity in normal eyes by 6.4 letters to 0.10 logMAR (Snellen equivalent, 20/25), much more than the degradation caused by forward scatter, and similar to the best-corrected visual acuity of 0.16 logMAR (Snellen equivalent, 20/29) at 12 months after DSEK. 24 In addition, reduction of high-order aberrations by using adaptive optics has been associated with improved visual acuity after DSEK, 32 providing further support for our findings. 
The present study was designed to differentiate the effects of forward scatter and whole-eye aberrations on visual acuity, and not to determine the source of aberrations after DSEK. Whole-eye aberrations are usually dominated by aberrations on the anterior corneal surface rather than the posterior surface, because of the larger step in refractive index from air to cornea than from cornea to aqueous humor. Nevertheless, Yamaguchi et al. 20 recently showed that although posterior corneal aberrations directly opposed and reduced the effect of anterior corneal aberrations in normal corneas and penetrating grafts, the same was not true after DSEK. Thus, although the magnitude of posterior corneal aberrations is small compared with those of the anterior surface, after DSEK, posterior corneal aberrations might increase rather than decrease whole-eye aberrations, and therefore cannot be ignored. 
We generated the aberrated eye charts as the convolution of an ETDRS chart with a typical point-spread function after DSEK, similar to other investigations of the effect of aberrations. 26,27 The point-spread function was derived from the means of absolute values of Zernike coefficients of eyes at 12 months after DSEK in a previous study. 8 By using the absolute values of Zernicke coefficients, we preserved the magnitude of specific aberrations, whereas if we had used the mean values of the coefficients, which can be either positive or negative, we would have derived aberrations with a much lower magnitude than was typical in DSEK patients. In fact, in our earlier study, 8 DSEK patients experienced a broad range of visual degradation from wavefront aberrations, and even those eyes with total high-order aberrations that were numerically similar to the median showed differences in the quality of the retinal image (Fig. 6). Thus, although the aberrations used to create our eye charts were similar to typical aberrations after DSEK, they did not represent the extremes. In addition, varying contributions of different high-order aberrations can have different effects on visual acuity. 26,27  
Figure 6. 
 
Variability of whole-eye high-order aberrations in DSEK patients 12 months after surgery. Each chart represents an image on the retina as determined by convolution of the eye chart with the point-spread function determined by wavefront errors for a specific eye. The wavefront errors were from the median total high-order aberrations (HOA, RMS wavefront error) of a group of patients with otherwise normal pseudophakic eyes and wavefront aberrations from pseudophakic eyes after DSEK in a previous study. 23 The image from the normal pseudophake (upper left) was similar to the image from the DSEK eye with the lowest HOA (middle left). The image from the DSEK eye with the highest HOA indicates that HOAs could be responsible for decreased best-corrected visual acuity. Aberrations from the DSEK patient with the median HOA (center right) and the two patients with HOAs closest to the median (upper and lower right) illustrate the variable appearance of the letters with a small change in RMS high-order aberrations and the variable effect of different combinations of aberrations on the retinal image.
Figure 6. 
 
Variability of whole-eye high-order aberrations in DSEK patients 12 months after surgery. Each chart represents an image on the retina as determined by convolution of the eye chart with the point-spread function determined by wavefront errors for a specific eye. The wavefront errors were from the median total high-order aberrations (HOA, RMS wavefront error) of a group of patients with otherwise normal pseudophakic eyes and wavefront aberrations from pseudophakic eyes after DSEK in a previous study. 23 The image from the normal pseudophake (upper left) was similar to the image from the DSEK eye with the lowest HOA (middle left). The image from the DSEK eye with the highest HOA indicates that HOAs could be responsible for decreased best-corrected visual acuity. Aberrations from the DSEK patient with the median HOA (center right) and the two patients with HOAs closest to the median (upper and lower right) illustrate the variable appearance of the letters with a small change in RMS high-order aberrations and the variable effect of different combinations of aberrations on the retinal image.
The minimal reduction of visual acuity with induced forward scatter in this study does not mean that forward scatter after EK is not important for everyday vision. Although the goal of this study was to assess the effect of forward scatter on visual acuity as measured under routine clinical conditions, adverse environmental conditions, such as glare sources, could induce extreme forward scatter that would have a greater effect on visual acuity. Increased forward scatter could also further degrade contrast and perception of marginally clear objects in the visual field. Indeed, we found that visual acuity decreased by more than three lines (18 letters) with high induced forward scatter when tested on the aberrated 10%-contrast chart as compared with low scatter tested on the high-contrast nonaberrated charts. Sources of forward scatter should be reduced as much as possible to improve the total visual experience; however, as we have shown, reducing forward scatter will only marginally improve visual acuity as it is tested in the clinic. 
Recently, there has been a trend toward using very thin DSEK grafts or DMEK because early results have suggested better postoperative visual acuity than with the typically thicker grafts used in DSEK. 13,3336 The results of our study suggest that best-corrected visual acuity could be improved after EK by using procedures that promote a more regular posterior corneal (graft) surface and reduce aberrations than that after standard DSEK. Indeed, the posterior corneal surface is more regular after DMEK and high-order aberrations from this surface are significantly less, 5 because the graft consists of only Descemet membrane and endothelium that appose directly to host posterior stroma. After DSEK, the regularity of the posterior corneal surface is dependent on the match in curvature between the anterior graft and posterior host surfaces as well as the regularity of the donor stromal thickness. 
The forward scatter induced by the Amco Clear solution was approximately the same as that experienced by patients with Fuchs dystrophy before DSEK, and higher than that experienced by patients after DSEK for Fuchs dystrophy. 8,9 However, in our model we assumed that the scattering solution generated forward scatter with similar characteristics to scatter from the cornea after EK. In fact, the scatter from the solution may be more homogeneous than that from the cornea because corneal haze originates from a mixture of high- and low-scatter regions in an irregular distribution. In addition, in the eye, forward scatter as expressed by the straylight parameter increases slightly at angles greater than 7 degrees from the center of the point-spread function, 37 the average angle used to measure straylight by the C-Quant. However, the straylight parameter measured through Amco Clear increases rapidly at angles higher than 7 degrees (van den Berg T, written personal communication, July 18, 2011). When testing visual acuity through Amco Clear, the greater scatter outside this angle could decrease direct transmission and reduce brightness at the center of the point-spread function. The effect of this difference on visual acuity is unknown, but it suggests that forward scatter from the cornea would affect visual acuity less than would the scatter from the Amco Clear solution. 
The width of the point-spread function's central peak did not change when measured through the low- and high-scatter solutions. This indicates that there is minimal degradation of edge sharpness on the retinal image, and is consistent with the minimal effect of induced scatter on visual acuity, because visual acuity is determined by the shape of the center of the point-spread function. 8,21 Of interest, the mean OSI metric (output by the OQAS double-pass instrument) increased with induced forward scatter, although the effect of induced forward scatter on the OSI was much more variable than that of the straylight parameter (measured by the C-Quant). The OSI has been used to discriminate between grades of cataract, 29 which typically scatter more light than the cornea does after DSEK. 38 However, the OSI metric might not be as robust a measure of low intensities of forward scatter as straylight is, and studies of the cornea that report this metric should be interpreted with caution. 39  
In summary, this study suggests that under standard testing conditions, forward scatter in excess of that typically experienced after DSEK degrades visual acuity less than do typical high-order aberrations after DSEK. Subjects lost only three letters of vision and the center of their point-spread function was not widened by induced forward scatter. High-order aberrations in post-EK patients are a more likely cause of decreased best-corrected visual acuity than is forward scatter. 
Acknowledgments
The authors thank Thomas van den Berg, at the Netherlands Institute for Neuroscience from the Dutch Royal Academy, Amsterdam, The Netherlands, for providing helpful discussions of straylight and careful laboratory measurements of the scatter characteristics of Amco Clear. 
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Footnotes
 Presented in part as a poster at the annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, May 1–5, 2011.
Footnotes
 Supported by Research to Prevent Blindness, New York, New York (unrestricted departmental grant and Olga Keith Wiess Scholar [SVP]); Mayo Foundation, Rochester, Minnesota.
Footnotes
 Disclosure: J.W. McLaren, None; S.V. Patel, None
Figure 1. 
 
Chamber to hold scatter solution. The chamber was constructed from two glass disks and a spacer to create a gap of approximately 1 mm between the disks. The chamber was filled with Amco Clear, 4000 NTU stock solution to induce high scatter, or with water for a low-scatter control. The edges of the chamber were masked with black tape to create a central aperture, 20 mm diameter (not shown), and the assembly was placed in a trial frame for vision testing.
Figure 1. 
 
Chamber to hold scatter solution. The chamber was constructed from two glass disks and a spacer to create a gap of approximately 1 mm between the disks. The chamber was filled with Amco Clear, 4000 NTU stock solution to induce high scatter, or with water for a low-scatter control. The edges of the chamber were masked with black tape to create a central aperture, 20 mm diameter (not shown), and the assembly was placed in a trial frame for vision testing.
Figure 2. 
 
Example of five lines from test charts, with 100% and 10% contrast, and without and with aberrations. Test charts were generated by convolution of ETDRS charts with the point-spread function derived from aberrations representative of those measured in patients 12 months after Descemet stripping endothelial keratoplasty. Each chart had a unique set of letters (the same letters are shown on the aberrated and nonaberrated samples here for illustration). Aberrations were calculated by assuming that the charts would be read at 3 m, and each full chart included letters with sizes that ranged from 0.7 log MAR (20/100 Snellen equivalent) to −0.5 log MAR (20/5 Snellen equivalent).
Figure 2. 
 
Example of five lines from test charts, with 100% and 10% contrast, and without and with aberrations. Test charts were generated by convolution of ETDRS charts with the point-spread function derived from aberrations representative of those measured in patients 12 months after Descemet stripping endothelial keratoplasty. Each chart had a unique set of letters (the same letters are shown on the aberrated and nonaberrated samples here for illustration). Aberrations were calculated by assuming that the charts would be read at 3 m, and each full chart included letters with sizes that ranged from 0.7 log MAR (20/100 Snellen equivalent) to −0.5 log MAR (20/5 Snellen equivalent).
Figure 3. 
 
Estimates of intraocular forward scatter. Left: straylight, measured by the C-Quant, increased with induced scatter in all eyes (P < 0.001). Right: the OSI, measured by the OQAS, increased with induced scatter (P = 0.003). The variance of the OSI was greater than that of straylight (P < 0.001) and the OSI of four subjects decreased with induced scatter.
Figure 3. 
 
Estimates of intraocular forward scatter. Left: straylight, measured by the C-Quant, increased with induced scatter in all eyes (P < 0.001). Right: the OSI, measured by the OQAS, increased with induced scatter (P = 0.003). The variance of the OSI was greater than that of straylight (P < 0.001) and the OSI of four subjects decreased with induced scatter.
Figure 4. 
 
Changes in contrast sensitivity with induced forward scatter. Contrast sensitivity decreased at all spatial frequencies with induced forward scatter (all comparisons, signed-rank test, except 12 cyc/deg, paired t-test). Markers show mean ± SD, and at the same spatial frequencies, markers are offset slightly for clarity.
Figure 4. 
 
Changes in contrast sensitivity with induced forward scatter. Contrast sensitivity decreased at all spatial frequencies with induced forward scatter (all comparisons, signed-rank test, except 12 cyc/deg, paired t-test). Markers show mean ± SD, and at the same spatial frequencies, markers are offset slightly for clarity.
Figure 5. 
 
Mean normalized point-spread function with low (light line) and high (dark line) scatter, as measured by double-pass method. The graph on the right is an expansion of the graph on the left, rescaled to 0.2 maximum, to illustrate differences at distances greater than 10 arc min from the center. The normalized point-spread function at 50% of its height (0.5 on ordinate) was not different with induced high scatter than with low scatter, indicating that induced forward scatter did not affect the center of the point-spread function, the region of the point-spread function that determines visual acuity. With induced scatter, the point-spread function was elevated at distances greater than 7 arc min from the center. It is not known if this elevation represents a true elevation at these high angular distances from the center or if it represents the consequence of normalization of the profile to a lower mean peak, which would also increase the point-spread function at higher angles.
Figure 5. 
 
Mean normalized point-spread function with low (light line) and high (dark line) scatter, as measured by double-pass method. The graph on the right is an expansion of the graph on the left, rescaled to 0.2 maximum, to illustrate differences at distances greater than 10 arc min from the center. The normalized point-spread function at 50% of its height (0.5 on ordinate) was not different with induced high scatter than with low scatter, indicating that induced forward scatter did not affect the center of the point-spread function, the region of the point-spread function that determines visual acuity. With induced scatter, the point-spread function was elevated at distances greater than 7 arc min from the center. It is not known if this elevation represents a true elevation at these high angular distances from the center or if it represents the consequence of normalization of the profile to a lower mean peak, which would also increase the point-spread function at higher angles.
Figure 6. 
 
Variability of whole-eye high-order aberrations in DSEK patients 12 months after surgery. Each chart represents an image on the retina as determined by convolution of the eye chart with the point-spread function determined by wavefront errors for a specific eye. The wavefront errors were from the median total high-order aberrations (HOA, RMS wavefront error) of a group of patients with otherwise normal pseudophakic eyes and wavefront aberrations from pseudophakic eyes after DSEK in a previous study. 23 The image from the normal pseudophake (upper left) was similar to the image from the DSEK eye with the lowest HOA (middle left). The image from the DSEK eye with the highest HOA indicates that HOAs could be responsible for decreased best-corrected visual acuity. Aberrations from the DSEK patient with the median HOA (center right) and the two patients with HOAs closest to the median (upper and lower right) illustrate the variable appearance of the letters with a small change in RMS high-order aberrations and the variable effect of different combinations of aberrations on the retinal image.
Figure 6. 
 
Variability of whole-eye high-order aberrations in DSEK patients 12 months after surgery. Each chart represents an image on the retina as determined by convolution of the eye chart with the point-spread function determined by wavefront errors for a specific eye. The wavefront errors were from the median total high-order aberrations (HOA, RMS wavefront error) of a group of patients with otherwise normal pseudophakic eyes and wavefront aberrations from pseudophakic eyes after DSEK in a previous study. 23 The image from the normal pseudophake (upper left) was similar to the image from the DSEK eye with the lowest HOA (middle left). The image from the DSEK eye with the highest HOA indicates that HOAs could be responsible for decreased best-corrected visual acuity. Aberrations from the DSEK patient with the median HOA (center right) and the two patients with HOAs closest to the median (upper and lower right) illustrate the variable appearance of the letters with a small change in RMS high-order aberrations and the variable effect of different combinations of aberrations on the retinal image.
Table 1. 
 
Whole-Eye High-Order Wavefront Aberrations Used to Create Aberrated Eye Charts
Table 1. 
 
Whole-Eye High-Order Wavefront Aberrations Used to Create Aberrated Eye Charts
Zernike Coefficient Aberration 1 y after DSEK Controls
Coefficient, μm Coefficient, μm
Z 3 − 3 Trefoil 0.0829 0.0376
Z 3 − 1 Coma 0.0734 0.0399
Z 3 1 Coma 0.0570 0.0438
Z 3 3 Trefoil 0.0976 0.0424
Z 4 − 4 Quadrafoil 0.0455 0.0114
Z 4 − 2 0.0344 0.0082
Z 4 0 Spherical 0.0963 0.0279
Z 4 2 0.0454 0.0135
Z 4 4 Quadrafoil 0.0493 0.0135
Z 5 − 5 0.0174 0.0040
Z 5 − 3 0.0126 0.0027
Z 5 − 1 0.0094 0.0036
Z 5 1 0.0129 0.0027
Z 5 3 0.0136 0.0022
Z 5 5 0.0124 0.0026
Z 6 − 6 0.0125 0.0024
Z 6 − 4 0.0086 0.0013
Z 6 − 2 0.0060 0.0008
Z 6 0 0.0125 0.0018
Z 6 2 0.0119 0.0009
Z 6 4 0.0095 0.0017
Z 6 6 0.0199 0.0018
Table 2. 
 
Loss of Visual Acuity by Addition of Forward Scatter, at High and Low Contrast, and on Charts with or without Aberrations Typical of Patients at 1 Year after DSEK
Table 2. 
 
Loss of Visual Acuity by Addition of Forward Scatter, at High and Low Contrast, and on Charts with or without Aberrations Typical of Patients at 1 Year after DSEK
Visual Acuity, LogMAR, Mean ± SD (Snellen Equivalent)
100% Contrast 10% Contrast
Non-Aberrated Aberrated Loss from Increased Aberrations (Letters) Non-Aberrated Aberrated Loss, from Increased Aberrations (Letters)
Low scatter −0.03 ± 0.03 (20/19) 0.10 ± 0.04 (20/25) 6.4¶ 0.11 ± 0.05 (20/26) 0.23 ± 0.06 (20/34) 6.2¶
High scatter 0.02 ± 0.07*† (20/21) 0.14 ± 0.06‡ (20/28) 5.8¶ 0.19 ± 0.06* (20/31) 0.34 ± 0.08* (20/44) 7.3¶#
Loss from increased scatter (letters) 2.7*† 2.1‡ 4.2*§ 5.3*||
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