Methods for Assessing Corneal Bilateral Symmetry

1. World Cornea Congress VI - 2010 Supported by research funds from Research to Prevent Blindness, Inc.; Lions Eye Foundation, Inc.; and the National Eye Institute (EY002377). Methods for Assessing Corneal Bilateral Symmetry The authors have no financial interest in the subject matter of this poster. Michael K. Smolek & Panagiotis Kompotiatis Department of Ophthalmology LSU Eye Center of Excellence, New Orleans

2. Introduction • Bilateral symmetry analysis of the cornea is well-known,1 but remains an under-utilized diagnostic test. • It can be highly effective in screening for suspected corneal ectatic disease or disorders such as dry eye. • There are multiple ways to describe and evaluate corneal bilateral symmetry, which are described in this presentation. • Each method has potential pitfalls for users to avoid. 1. Wilson SE, Klyce SD. Screening for corneal topographic abnormalities before refractive surgery. Ophthalmology 1994; 101: 147-152.

3. Background • Corneal bilateral symmetry can be described using any of 3 primary methods: • Qualitative VISUAL ASSESSMENT of the contour pattern differences in dioptric curvature maps. • Quantitative differences between specific CORRESPONDING POINTS on curvature maps. • Quantitative differences between morphological measures of CORRESPONDING SHAPE COMPONENTS, such as Zernike polynomial terms.

4. Visual Assessment Method • This method has varying degrees of success, depending in part on the ability of the screener. • The method also depends on the dioptric display scale.2 • A small dioptric contour scale (< 1.0 D) makes the curvature maps appear overly complex and difficult to compare. • Normalized scales are also difficult to compare. • The optimum absolute display scale appears to be 1.5 D. • A drawback of Visual Assessment is that it lacks a NUMERICAL INDEX to define clinical significance. 2. Smolek MK, Klyce SD, Hovis JK. The Universal Standard Scale: Proposed improvements to the ANSI Standard Scale for corneal topography. Ophthalmology 2002; 109:361-369.

5. OD OS Fellow corneas with suspicious asymmetry would benefit from numerical scoring. OD OS

6. Corresponding Point Method • This method requires the ability to derive dioptric curvature values at specific points on fellow eye maps. • Typically this requires an interpolation algorithm. • Once a grid of specific points is defined for fellow corneas, it is a simple matter of measuring differences between corresponding points of each cornea. • Additional complexity comes from: • 1) Deciding the corresponding point sampling density. • 2) Determining how to collapse many hundreds or thousands of corresponding point differences into a single Bilateral Symmetry Index (BSI).

7. Examples of Raw Corresponding Point Analysis We can derive single indices in several different ways. For example, we can look at the frequency distribution (above) from which we can then calculate statistics such as skewness, kurtosis, SD, peak value, and Pearson R. The slope of the raw data (red line on left-hand graphs) is a poor method.

8. Corresponding Points:Frequency Distribution & Slope We can also derive the Gaussian Cumulative Frequency distribution and compute the slope of corresponding point differences. This slope is a sensitive measure for distinguishing normal pairs of corneas from ectatic or ectatic suspect corneas.3 3. Kompotiatis P, Smolek MK. A quantitative method for analysis of bilateral corneal asymmetry in different corneal categories. J Optom 2009; 2:173-181.

9. Corresponding Shape Components:Zernike Polynomial Method • Corresponding shapes in fellow corneas can be extracted by methods such as Zernike decomposition of corneal wavefronts or corneal surface elevation and then compared. • It is CRITICAL that computing the bilateral symmetry of Zernike terms is understood. The sign of the RMS error values must be adjusted correctly when comparing right and left eyes.4 Note that all rotationally symmetric terms can be ignored. • There is no standardized way to define a Bilateral Symmetry Index based on shape components. However, computing the sum of the RMS error or variance for all differences in shape terms is a valid approach. • 4. Smolek MK, Klyce SD, Sarver EJ. Inattention to nonsuperimposable midline symmetry causes wavefront analysis error. Arch Ophthalmol 2002; 120:439-447.

10. Tabular Data Results Table 1. Examples of anterior corneal surface difference measures in single cases. Pearson R Mean Diff. Std Dev Peak Frequency Kurtosis Skewness Normal - Normal 0.915 -0.063 0.077 1521.5414.5601.750 Dry Eye - Dry Eye 0.776 -0.240 0.186 650.23 1.218 -0.520 KCS - KCS 0.436 -0.0600.214 561.10 0.677 -0.198 KCS - KC1 0.775 0.1570.378 324.21 -0.711 0.524 Table 2. Bilateral symmetry expressed by Zernike polynomial fitting* Sum RMS Error Sum Variance Sum RMS Error Sum Variance (λ µm) (λ µm) (elev. mm) (elev. mm) Normal - Normal 0.900 0.795 0.923 0.850 Dry Eye - Dry Eye 0.705 0.497 0.572 0.348 KCS - KCS 0.770 0.597 0.543 0.294 KCS - KC1 0.390 0.150 0.370 0.139 *Using 1st, 2nd, and 3rd order terms only and excluding defocus, which is rotationally symmetric.

11. Graphical Comparison On the left we see Zernike shape-based bilateral symmetry collapsed into 4 different error values. The sum of the RMS error is probably not as effective as the variance summed across all terms. Elevation variance looks to be superior as a BSI method. On the right we see some of the corresponding point method values, which appear to be very sensitive to bilateral symmetry, except for the Pearson Product Moment statistic. Pearson R is NOT APPROPRIATE for comparing fellow corneas because it only reflects the noisiness and linearity of a correlation and not the corresponding point symmetry!

12. Conclusions • We have identified multiple ways to measure a Bilateral Symmetry Index (BSI) of the cornea, but more work is needed to further identify the optimum clinical method. • Working with corresponding points may be more acceptable because it involves less manipulation of the data than the corresponding shape approach. • Clinicians should already be using visual comparisons of fellow eyes to screen for disease. • Future work will include assessment of bilateral symmetry between the posterior surfaces and between pachymetry maps of fellow eyes.