Correlation Between Corneal Radius Of Curvature And Corneal Eccentricity

receives its nutrients from the tear film, aqueous humor and the limbal vessels. (Pettersson,2011). The cornea has a diameter of 12 mm horizontally and 11.5 mm vertically and itaccounts for two thirds of the refractive power of the eye, 43 Dioptre (D). The centralthickness of the cornea is 0.5 mm and the thickness increases towards the periphery. Theshape of the cornea flattens towards the periphery, which creates an aspheric surface. Thisaspheric surface has different radii of curvature in the horizontal and vertical meridians,which are 7.8 and 7.7 mm respectively.The shape of the cornea is important for contact lens fitting, for studying the variation amongthe population and for making better schematic eyes. In addition, it is also important to knowthe effects of long-term contact lens wear on the shape and physiology of the cornea (Kiley,Smith & Carney, 1984). However, it is practically impossible to describe the shape of thecornea (Jayakumar, 2005).Since the cornea is a living tissue, it is quite complex, and hard to describe the shape by asingle unit (Swarbrick, 2004). With the advent of corneal topography and refractive surgeries,it became important to determine the corneal shape factor. Studies before the advent ofcorneal topography did not define the corneal shape and only mentioned them in relation toother ocular media. However, with the advent of modern technology accurate description ofcorneal shape became possible. Computer aided topographs have given us a more completeand accurate description of the corneal shape (Davis, Raasch, Mitchell, Mutti & Zadnik,2005). Corneal asphericity is one of the many indexes that describe the corneal shape and it isunit-less. It refers to the change in corneal curvature from the apex to the periphery.Normally, the cornea flattens from the apex towards the periphery and is related to the form ofa prolate ellipse. Just a small percentage of the population has corneas that are oblate ellipse,which is steepening of the cornea from the apex towards the periphery (Davis et al, 2005).The shape of the cornea may vary with the meridians, (e.g. 180 vs. 90) and even with hemimeridian (e.g. nasal vs. temporal). There may also be a small diurnal change; therefore, anycorneal descriptor only gives an average value of the shape (Swarbrick, 2004).Corneal shape factor can be described as following, P Q 1 and the eccentricity can belinked to the following formula Q -e2 (Mainstone, Carney, Anderson, Clem, Stephensen,Wilson, 1998). SF is the shape factor of the cornea and it is equal to e2. SF also equals to 1-Pand Q -e2 (See Table 1). So if given any one of the above-mentioned descriptors, all theothers can be calculated (Mainstone et al. 1998; Lindsay & Atchinson, 1998).4

When it comes to describing corneal shape, scientists assume corneal profile to be of a conicsection in any meridian. This is an easy way to describe the shape of the cornea; however, itdoes not give an adequate description of the cornea. Ellipsotoric models can be used todescribe the cornea more precisely but are more complex. So what is a conic section? A conicsection can be a hyperbola, a parabola, an ellipse, or a circle (See Table 2). To sum it up, aconic section can be fully described by using two parameters. The first parameter is the apicalradius and the second is the eccentricity (Lindsay & Atchison, 1998). The simplest way todescribe this aspheric conic section is by using Baker’s equation.wherep shape factorro apical radius of curvature (mm)x sagittal depth over a specified chord length (mm)y half chord length (mm)Many topographers use previously mentioned equation as a base for calculating the shapeindices. (Jayakumar, 2005)The relationship of the descriptors of the corneal shape can be linked to each other by thefollowing: See table 1:Table: 1 e2pSF ( e2)Q ( e2)e2 *1 pSF QP 1 e*1 SF1 Q1 p* Qp 1 SF*22SF eQ e2Table 1: Descriptors of the corneal shape and its relation towards the different types of conic sections is givenabove.5

Table: 2e2p (1 e2)SF (e2)Q ( e2)Hyperbola 1 0 1 1Parabola101 10 e 10 p 10 p 1 1 Q 0Circle0100Oblate ellipse 0 1 0 0Prolate ellipse2Table 2: Relationship of corneal descriptors to various ellipsoids is given above.Figure 1: Shows the different conic sections of the cornea.Figure 2: Shows the different conic sections, which can be used to describe the corneal shape.6

1.4 Topography1.4.1 Different typesThere is a number of ways to analyze the shape of the cornea; the most used methodworldwide is to use a keratometer. However, one of the main disadvantages with akeratometer is that it only measures the central 3 mm2 of the cornea. For conditions such askeratoconus and in the field of refractive surgery, we might need to measure a wider area ofthe cornea in order to obtain a better data. Therefore, it is a good instrument to follow up theprogression of the changes throughout the surface of the cornea. (Benjamin, 2006)Technologies that are currently used for measuring the shape of the cornea are well developedand frequently used in clinical practices. Topographers available currently use reflectionbased or projection based techniques to evaluate the cornea (Klein, 2000). The most commonmethod is based on specular reflection from the air and tear-film. Due to the convex shape ofthe cornea, a virtual image is formed a few millimeters behind the corneal surface. Anilluminated pattern, normally Placido rings (a series of concentric bright and dark rings), isplaced in front of the eye, meanwhile a camera views and records the image formed by thecornea. By knowing the location of the cornea relative to the Placido discs and the recordingcamera, the shape of the cornea can be calculated from the image captured. A virtual image ofPlacido rings formed by the cornea is shown in Figure 2.Figure 2: Image of the Placido discs reflected from the cornea. We can alsosee the different corneal zones. The red ring shows the 8.0 mm corneal zoneand the red circle the 4.5 mm zone.7

The second corneal topographic method involves projecting a slit onto the cornea surfacefrom one angle, and examining the scattered light from another angle. Generally, the corneascatters of light poorly; therefore, fluorescein eye drops are often applied to create a morediffuse surface. Triangulation is the used to reconstruct the image of the corneal surface.Reflection based topographer’s uses the principle of analyzing the distortion of a knownpattern (the Placido rings) caused by reflection off the cornea.There are different instruments that can measure corneal topography using various principlessuch as videokeratoscopes, keratometer, and photokeratoscopes and most of them arereflection based topography systems. Reflection-based systems calculate the slope of thecorneal surface, and then calculate the curvature and power of the cornea. The slope obtainedcannot be directly converted into height without assumptions or additional measurements .Theradius of curvature can be calculated and afterwards be converted into dioptric change byusing standard keratometric index. All videokeratoscopes use the same mechanisms toprovide similar information. However, they vary in some of their features, such as the size ofthe cone of Placido rings. One other thing that might differ is if focusing is manual orautomatic (Corbett, 2000).The topographs can be of either small-cone or of big-cone placido disc, or slit-scanningdevice. Placido disc systems work by projecting series of concentric rings on the anteriorcorneal surface. It does not measure corneal elevation instead derive the anterior surfaceelevation by reconstructing the actual curvature measurements using algorithms. Small-conesystems projects more rings onto the cornea and have a shorter working distance than those ofbig-cone type, this gives greater amount of measurement points. However, they require amore steady hand to acquire an accurate image. Large-cone Placido disc systems uses a longerworking distance, which projects a fewer set of rings onto the cornea. This makes them moreforgiving when it comes to measuring patients with a deeper set of eyes. Slit scanning or otherelevation devices can directly measure both the anterior and posterior cornea by usingsomething called a light-base analysis or time domain. This data can then later on beconverted into diopters, or corneal thickness.1.4.2 Coloring scaleTopography maps are displayed by utilizing a coloring scale. Steeper curvatures are displayedin warm colors such as red or orange, whereas flatter curvatures are displayed in cool colors8

such as green or blue. The maps are displayed in either an absolute or a normalized scale. Theabsolute scale are a fixed range of curvature, is regardless of the map that is chosen. Thenormalized scale in the other hand shows the range of power, or curvature, calculated fromspecific maps that previously were chosen.Another good use for the topography is when applying rigid gas permeable lenses, or whenevaluating pupillary defects. According to Topcon CA-100F Corneal Analyzer manual is agood way to measure the corneal shape and it s also a good tool in the process of applyingsoft contact lenses. The topography displays the taken pictures in an absolute scale, whichdisplays the picture in the color range from different shades of blue to red. This makes itpossible for an experienced person to get a good overview in a just a short period of time.Good measuring can be done on both non-reflecting surfaces and/or surfaces that are notcompletely even.Mainstone et al. (1998) state that many ocular components are known to vary linearly withincreased refractive error and therefore it is likely that corneal asphericity may also vary withrefractive error. Carney et al (1996) found out that the cornea has a tendency to flatten lessrapidly towards the periphery with increased myopia. In recent years, there has been a rapidincrease in refractive surgeries worldwide. Knowledge of corneal shape will give a betterunderstanding of the post-operative outcome and its impact on visual acuity. It is alsoimportant to understand the difference between eyes as well as difference between individuals(Mainstone et al, 1998).9

2 AimThe primary aim of this study was to find if there is any correlation between the cornealradius of curvature and its eccentricity.10

3 Material and Method3.1 InclusionsThe study was performed at Linnaeus University, Kalmar, Sweden. 45 subjects participated inthis study, 16 men and 29 women. The subjects were both students and people recruited out ofthe general population. Included in the study were 24 emmetropes, 18 myopes and 3hyperopes. The age ranged from 18 to 61 with the mean value of 25 7. The study includedsubjects within the range of normal refractive error. Therefore subjects with an astigmaticrefraction bigger than -1.00 DC where excluded. None of the subjects was diagnosed with anysystemic or ocular diseases.3.2 MaterialDuring the study, the following instruments and tools were used:Topcon CA-100F Corneal AnalyzerTrial frameSlit lamp- Keeler SL-40 (Keeler Ltd Berkshire UK)3.3 MethodBefore the procedure started all the subjects were informed both in writing and verbally aboutthe procedures. All subjects signed an informed consent. All subjects were treated inaccordance with the tenets of the Declaration of Helsinki. Thereafter, a screening for ocularanatomy abnormalities using the slit-lamp biomicroscopy was conducted. The main reasonwas to exclude subjects who had media opacities. All the subjects had normal ocular health,were free of any ocular diseases or systemic disease. None of the subjects had any history ofocular surgery or trauma.Non-cycloplegic binocular subjective sphero-cylinder refraction was performed by using aJackson cross-cylinder in a phoropter. This was done to ensure all the subjects had goodvisual acuity of 1.0 or better in the right eye. Corneal topography and palpebral fissuremeasures have a tendency to exhibit a high degree of symmetry between the left and right eye.Therefore, only the right eye of the subjects was used for all measurements in the study. Noneof the subjects was full time contact lens wearers. Only part time users were allowed, butinstructed not to use lenses the day before the measurement was performed.11

Videokeratographic digital images were taken of anterior corneas of all 45 adult participants.All the subjects were instructed to sit comfortably with the chin and forehead well restedagainst the topograph. The subjects were asked to fixate and try to look as steady as possibleat the green light, while a picture was maintained on the screen. The apparatus were adjustedback and forth with a joystick, which made it possible to maintain a clear and steady picture.All the pictures were stored on the hard drive. Three pictures were taken on the subject’s righteye and averaged. All three pictures had to be of good quality for this, if not, new picture weretaken. The pictures that were taken were displayed in an absolute scale.12

4 ResultsThe main aim for this study was to find if there is any correlation between the eccentricity andthe radius of curvature on the anterior surface of the cornea. We measured by topography andobserved values for two zones, 4.5 mm, and 8.0 mm. Within these two zones, we measuredeccentricity and the corneal radius of curvature at two different meridians. Mean values of themeridians and eccentricity were obtained from the instrument.Each of the meridians and the average of the two different meridians were compared with thecorneal radius of curvature with a Pearson correlation coefficient test. Thereafter a trend linewas added to display the angle of the correlation. The radius of curvature and the eccentricitychanged between the meridians as well as between the analyzed zones (4.5 mm vs. 8.0 mm).When looking at the meridians separately, and comparing them with the eccentricity nostatistically significance could be found (see figure 3 and 4). However, for the average of theboth meridians combined we found a weak but significant correlation (see figure 5).Displayed below are the figures for the 4.5 mm zone.Figure 3: The correlation between meridian 1 and the radius of curvature for the 4.5 mm zone. (R2 0.076r 0.276 and a p-value of 0.072)13

Figure 4: The correlation between corneal radius of curvature for meridian 2 and the eccentricity for the 4.5 mmzone (R2 0.059, r 0.242, p 0.104).Figure 5: shows the correlation between the average value of corneal radius of curvature and eccentricityobtained from both meridians for the 4.5 mm zone (R2 0.153, r 0.391 and a p-value of 0.007).14

The same statistically analysis were performed for the 8.0 mm zone. We used a Pearsoncorrelation coefficient test to see how strong of a correlation there is between the radius ofcurvature and the eccentricity. No significant correlation could be validated when looking atmeridians separately (see figure 6 and 7), nor could it be found for the averaged value of theboth meridians combined (see figure 8). Displayed below are the figures for the 8.0 mm zone.Figure 6: shows the correlation between meridian 1 and the radius of curvature for the 8.0 mm zone. R 2 0.058,r 0,240 and p 0.110.Figure 7: The correlation between corneal radius of curvature for meridian 2 and the eccentricity for the 8.0 mmzone (R2 0.078, r 0.279 and p 0.062)15

Figure 8: The correlation between the average value of corneal radius of curvature and eccentricity obtainedfrom both meridians for the 8.0 mm zone, R2 0.077, r 0278 and p 0.068.Since we did not find any strong correlation between radius of curvature and cornealeccentricity, we correlated refractive error (spherical equivalent) with radius of curvatureobtained for the 4.5 mm zone. Figure 9 shows poor correlation between the two components.Figure 9: The spherical equivalent plotted against the radius of curvature. (R2 0.0008 r 0.028 p 0.85)16

Figure 10 shows the mean of eccentricity for each measured zone, with standard deviations aserror bars. The mean SD for the 4.5 mm and 8.0 mm zone was 0.23 0.21, and 0.46 0.08respectively. The values of the

Correlation between Corneal Radius of Curvature and Corneal Eccentricity Patrik Fredin Degree Project Work in Optometry, 15 hp . there may be other factors that could influence the overall corneal shape like eye shape, . aspheric surface has different radii of curvature in the horizontal and vertical meridians,