The Impact of Keratoconus Apex’s Slope on Visual Acuity and Contrast Sensitivity

Background: The image optical quality is affected by changes in corneal shape of patients with keratoconus. The goal of this study was to explore which corneal parameters determine the visual quality in keratoconus subjects, which corneal slope parameter has the strongest correlation with visual quality and contrast sensitivity. Methods: The study covered eyes of 77 subjects, graded from the first to third keratoconus stages. To characterize the shape of cornea, we obtained measurements in two ways: (a) projected two perpendicular axes onto a cornea – the main axis passed through the central point of the cornea (visual axis projection) and keratoconus apex, while the second axis was perpendicular to the main axis – and read elevation values at points on theses axis; (b) projected circles with different diameters around the central part of the cornea (1, 2 and 3 mm) and read elevation values at points equally displaced on these circles. The measurements were used to calculate various elevation change (slope) parameters. Results: According to the acquired data, the visual acuity of a corrected eye does not have a strong correlation with the measured keratoconus apex slope. Contrast sensitivity displayed a strong correlation with keratoconus slope in the central part of the cornea (with a radius of 1 mm). Correlations in different spatial frequencies ranging from 0.47 to 0.6. Conclusion: Contrast sensitivity is more important parameter which describes the visual quality of keratoconus subjects than visual acuity. The most important region which determines the visual quality in keratoconus subjects is the region with a 1 mm radius of the corneal centre in the opposite direction of keratoconus apex.


Background
The optics of the eye consists of three main components: a cornea, a pupil and an optical lens of the eye. The cornea, especially its anterior optical surface, including a tear film, is the first and most determining structure of optical power (around 70 %), and as such it is primarily responsible for aberrations of the eye [1]. For a perfect eye lens, according to the basic laws of geometrical optics, light rays from any point of an object are focused in an image point at a specific distance, and wavefronts are spherical. In case of eye aberrations, such as spherical aberration, coma and oblique astigmatism, light rays do not focus in one point, and wavefronts are no longer spherical, although light rays and wavefronts are still orthogonal [2]. A deviation of light ray (optical aberration) creates an unclear image and reduces visual quality [1]. Inaccuracies of the optics of the eye are measured and expressed as wavefront aberration errors. Aberrations characterise how a light ray is changed by going through the optical system, and this is usually described in mathematics as Zernike polynomials [1,3]. Subjects without pathology tend to demonstrate the largest spherical aberration [4][5][6] which significantly affects the retinal image quality. Corneas with a larger slope of corneal anterior surface have larger spherical aberration [4].
Changes in spherical nature of the cornea may be caused by spontaneous, induced or irregular astigmatism and keratoconus [7]. Subjects with keratoconus have significantly larger ocular and higher-order aberrations than the subjects whose corneal surface has a regular form. It is deemed that the higher-order aberrations are in fact responsible for deterioration of visual quality [8]. It is possible with the help of corneal topography to obtain the display of individual points of corneal anterior surface; however, it should be noted that the retinal image is formed by the light passing through all points of the cornea which are located in the area of the pupil. Therefore, it is impossible to forecast the retinal image quality only from the image of corneal anterior surface topography [9]. Subjects with pathological topography show significantly reduced contrast sensitivity, while the bestcorrected visual acuity does not change under high-contrast conditions in comparison with the subjects with normal topography [10]. In case of keratoconus the corneal anterior surface is the most important source of optical errors; moreover, aberrations are 3 to 4 times larger for the corneal anterior surface than for the corneal posterior surface [11][12][13]. According to the Zadnik, complaints from keratoconus subjects do not correlate with a value of high-contrast visual acuity. For keratoconus subjects low-contrast visual acuity is more informative than their vision [14].
Historically keratoconus has been an absolute contraindication for the use of an excimer laser due to potential deterioration of corneal destabilisation and ectasia. However, it is possible to use a laser for subjects with keratoconus in order to correct the corneal anterior surface on the basis of topographical data of subjects [15].
It is the cornea, especially its anterior surface, which is the most significant structure of the eye determining visual quality in keratoconus subjects. The corneal anterior surface may be changed by employing the topoguided cross-linking method which includes reduction of curvature of the corneal anterior surface resulting in improved visual quality. The purpose of our study has been to perform an analysis of corneal parameters in order to establish importance of corneal parameters and model the potential effect of intervention that optimally changes these parameters to improve visual quality in keratoconus subjects.

Methods
The study was performed at the Dr. Lukins' Eye Clinic. The study was approved by University of Latvia Scientific research ethics commission and conformed to the ethical principles for medical research according to the Helsinki Declaration. In total 77 keratoconic eyes from 44 subjects with keratoconus of first, second and third stages with central and peripheral apex localisation were analysed. If the keratoconus apex was in a 1.5 mm large radius around the centre of the pupil, then we assumed that the keratoconus apex was at the centre. If the apex was outside the circle, then we assumed that the apex was located at the periphery of the cornea (see Table 1). There were no eyes with opacity (determined by eye biomicroscopy), subject's age ranged from 18 to 40, and they had a cross-linking treatment for at least six months.
The following measurements were done for subjects: • the best corrected visual acuity; • corneal topography; • the measurement of pupil size in mesopic conditions; • contrast sensitivity for eight spatial frequencies with and without the visual correction.
The visual acuity and contrast sensitivity were measured at a 3-metre distance with spectacle correction using the FrACT software 3.9.3. (Bach, 2007). The sine-wave grating contrast sensitivity was measured at the following frequencies: 3, 5, 7, 9, 11, 13 and 15 cpd. The contrast sensitivity was measured 10 times in four directions by employing the psychometric method on the computer display. The visual acuity was measured using the C optotype. Measurement of visual acuity started with the recognition of C optotype and, depending on the subjects' response, the optotypes size was increased or decreased. Measurements have been taken only once for each subject. Measurements were done in 10 lux illuminances. The illuminance was measured with a Konica Minolta T-10M luxmeter. The average luminance from the computer display was 99 cd/m 2 , and luminance from surrounding walls was 0.83 cd/m 2 . The luminance was measured with a Konica Minolta Chroma meter CS-100A.
In the study various parameters characterizing geometric shape of the cornea -designed to measure the slope between different parts of cornea -were introduced and analysed. The shape of cornea is described using measurements from the elevation map of the corneal anterior surface (with respect to ideal shape of cornea) in keratoconus subjects obtained from ALLEGRO Oculyzer. A real corneal surface elevation from the ideal corneal sphere has been expressed in micrometres (µm) (see Fig. 1).
Corneal measurements were read at the following locations (see Fig. 2): (1) the corneal centre -(C); (2) the points evenly distributed on the circles of 1, 2, 3 mm radius around the corneal centre (greycolored points); (3) the points located at distances of 1, 2, 3 mm from the corneal centre on an axis which goes through the corneal centre and keratoconus apex (ax), and on an axis perpendicular to it (P ax).
The study introduces parameters characterising the corneal surface in order to determine their correlation with the parameters characterising visual quality, such as visual acuity and contrast sensitivity. On the basis of the measurements at points (2) described above, the highest and the lowest corneal points were identified, i.e. the points with the greatest and the smallest elevation, respectively, taking an imaginary ideal corneal sphere as a reference, as well as a difference between these points. On the basis of the measurements at points (3) In each direction the change in elevation was determined at 1, 2, 3 mm distances from the apex. It should be noted that the positioning of these axis was chosen for better comparison of corresponding measurements between different eyes.
The research work envisaged determination of correlation coefficients between visual acuity and contrast sensitivity and various parameters describing slope of the cornea. The correlation coefficients were analysed both for all keratoconus subjects together and individually with the central and peripheral apex.
Statistical methods. An association between variables were evaluated using Spearman's rank correlation coefficient which is reported together with the corresponding p value. Statements about statistical significance are based on significance level alpha of 0.05. Contrast sensitivity was transformed to logarithmic scale before analysis and referred to as log-contrast sensitivity.

Visual acuity
All keratoconus subjects together demonstrated a medium correlation in absolute value 1  6

Contrast sensitivity
Parameters characterising the corneal surface had higher correlations with the log-contrast sensitivity than visual acuity. In all keratoconus subjects together, the correlation between log-contrast sensitivity and change in elevation (slope) of the corneal surface varied across spatial frequencies of the log-contrast sensitivity. The correlation (in absolute values) between the highest corneal elevation and log-contrast sensitivity in different spatial frequencies ranged from r=0.25 (p=0.03) at 3 cpd to r=0.47 (p<0.01) at 9 cpd. In subjects with central keratoconus apex, correlations between log-contrast sensitivity and elevation of the highest corneal point ranged from r=0.10 (p=0.61) at 3 cpd to r=0.38 (p=0.05) at 9 cpd. As to the subjects with peripheral keratoconus apex, the correlation between the log-contrast sensitivity and elevation of the highest corneal point ranged from r=0.33 (p=0.02) at 3 cpd to r=0.53 (p<0.01) at 9 cpd.
In all keratoconus subjects together, the absolute value of correlation between the lowest corneal point and logcontrast sensitivity ranged from r=0.33 (p=0.09) at 5 cpd to r=0.40 (p<0.01) at 11 cpd. In subjects with central keratoconus apex the absolute value of correlation between the lowest corneal point and log-contrast sensitivity ranged from r=0.32 (p=0.09) at 7 cpd to r=0.49 (p<0.01) at 15 cpd. As to the subjects with peripheral keratoconus apex, correlation ranged from r=0.32 (p=0.03) at 3 cpd to r=0.47 (p<0.01) at 9 cpd.
As described above, for subjects with central keratoconus apex log-contrast sensitivity's correlation with maximum elevation was lower than with minimum elevation, while for subjects with peripheral keratoconus apex the correlation coefficients were similar with maximum and minimum elevation.

Visual acuity
The study focused on two directions characterising changes in the surface (slope)the direction through the corneal centre and keratoconus apex (ax), and the direction perpendicular to it (P ax). Visual acuity had higher correlations with the changes in elevation along the (ax) direction (see Table 2).
Analysing change in elevation along the axis that goes through the corneal centre and the keratoconus apex (ax), separately in the direction from the corneal centre to the opposite direction of the keratoconus apex (CB) and to the keratoconus apex (CA), visual acuity had higher correlations with the (CB) direction (see Table 2).
The highest correlation of visual acuity in all keratoconus subjects together was that with the changes in elevation along the axis which goes through the corneal centre and keratoconus apex in a 1 mm radius (ax direction CB) (see Table 2). A situation was similar in the subjects with peripheral apex, namely the highest correlation of visual acuity was that with an elevation change in a 1 mm radius along the axis passing through the keratoconus apex (ax) direction, while the subjects' eyes with central keratoconus apex do not demonstrate statistically significant correlations between shape of cornea parameters and visual acuity at any distance from the corneal centre.

Contrast sensitivity
Higher correlation between change in elevation (slope) and log-contrast sensitivity for all keratoconus subjects together were associated with the direction which goes through the keratoconus apex and the corneal centre (ax) rather than the direction perpendicular to it (P ax) (see Table 3). The highest correlation between log-contrast sensitivity and changes in the elevation can be observed in the central area of the cornea in a 1 mm radius around the corneal centre for the direction (CB), both for all keratoconus subjects together and individually with the central and peripheral apex.
Not all spatial frequencies of the log-contrast sensitivity are equally relevant to the quality of life of the keratoconus subjects. Since changes in the corneal elevation in keratoconus subjects most significantly affect changes at 6 cpd [27], then the individual data of keratoconus subjects regarding log-contrast sensitivity's correlation with the corneal elevation in the direction (CB) for an area of 1 mm were presented at 7 cpd (see Fig.   4), as well as in the direction (CA) (see Fig. 5).
The log-contrast sensitivity showed higher correlation with the corneal elevation than the visual acuity. The direction characterising log-contrast sensitivity most efficiently is that one from the central part of the cornea to the opposite direction of the apex in a 1 mm radius (CB). It is clear that the median value of the change in elevation in this direction significantly depends on the location of the apex in a keratoconus subjecteither central or peripheral (see Fig. 6). Thus, knowledge of the elevation in a 1 mm radius from the corneal centre to the opposite direction of the apex (CB) might be a good indicator to determine whether the keratoconus apex could be central or peripheral.

Discussion
A number of studies have suggested that the most informative daily functional vision evaluation in keratoconus subjects is exactly the evaluation of contrast sensitivity instead of the visual acuity under high-contrast 8 conditions [14,22,[28][29][30][31]. Our study showed that contrast sensitivity had higher correlation with shape parameters of keratoconus anterior corneal surface comparing to visual acuity, considering such corneal surface parameters as maximum, minimum point, the difference between them, and keratoconus apex elevation (slope) data. Visual quality has larger correlation with parameters characterizing the extremes of corneal surface (max, min, difference) than parameters of change in elevation (slope). As the result we assume that visual quality of the eye is better understand by keratoconus apex elevation (slope) data. In other words, the height of the corneal apex doesn't define visual quality in keratoconus subject neither in central, neither in peripheral apex position.
The visual quality is more predictable from keratoconus apex height created slope in the corneas central area with 1 mm radius. Correlation between parameters characterising the corneal surface and visual acuity as well as contrast sensitivity was higher for subjects with peripheral apex localization then central apex localization.
Correlation between the corneal elevation and contrast sensitivity demonstrate that the contrast sensitivity may be better associated with the axis which goes through the central part of the cornea and keratoconus apex (ax) rather than the direction perpendicular to it (P ax). Moreover, the highest correlations between contrast sensitivity and parameters of the corneal anterior surface may be observed in the central part of the cornea with a 1 mm radius for the direction from the central cornea to the opposite direction of apex (CB).
A slope caused by the keratoconus apex in the central part of the cornea affects contrast sensitivity of the keratoconus subjects. The highest corneal point of elevation in the keratoconus subjects with central apex is located closer to the central part of the cornea (visual ax), therefore the slope in the centre is higher in the subjects with central keratoconus apex then peripheral keratoconus apex. It is because the maximum corneal point is further away from the central part of the cornea in keratoconus subjects with peripheral apex, and thus the slope in the central part of the cornea is lower.
Shape characteristics of the cornea (at 1 mm radius) had higher correlations with the contrast sensitivity rather than the visual acuity in high-contrast conditions. Although the correlations with contrast sensitivity were higher than those with the visual acuity, they are different on various spatial frequencies of contrast sensitivity; moreover, the spatial frequencies of contrast sensitivity are not equally important in daily life. The medium frequencies of contrast sensitivity were the most relevant to the daily functional vision, but the higher spatial frequencies are important for the resolution of fine details. The quality of life of keratoconus subjects is mostly affected by the changes at a spatial frequency of 6 cpd [27].
Similarly, as in the case of the correlation between the visual acuity and corneal parameters, the correlation between the contrast sensitivity and the corneal parameters were higher in the subjects with peripheral keratoconus apex than the subjects with central apex. Again, higher correlations between contrast sensitivity and the central corneal area (1 mm radius) in the opposite direction of apex may be observed.

Conclusions
This study explored correlation between keratoconus corneal apex and visual acuity and contrast sensitivity. The study had found that it is not possible to evaluate visual quality in keratoconus subjects only from their visual acuity measurements. Contrast sensitivity is the single critical parameter which shows whether the visual quality of keratoconus subjects is going to be improved after treatment or not. The study had found that the most important region which determines the visual quality is the region above the corneal centre with a 1 mm radius in the opposite direction of keratoconus apex (direction (ax) CB). It should further be identified how the changes in this region would affect the visual quality in order to predict to what extent the topo-guided cross-linking treatment could improve the visual quality in keratoconus subjects.

Declarations
Ethics approval and consent to participate: The study was approved by University of Latvia Scientific research ethics commission and conformed to the ethical principles for medical research according to the Helsinki Declaration. The informed consent obtained from study participants was written.

Consent for publication: Not applicable
Availability of data and materials: The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Competing interests: The authors declare that they have no competing interests.
Funding: Not applicable Authors' contributions: SL performed the examination of the keratoconus subject and was a major contributor in writing the manuscript. AL statistical analysed and interpreted the subject data. GK supervised and corrected manuscript. All authors read and approved the final manuscript.