1. Qualitative and Quantitative Analysis of Aspheric Symmetry and Asymmetry on Corneal Surfaces
Carlos G. Arce, MD
Associate Researcher and Ophthalmologist
Ocular Bioengineering & Refractive Surgery Sectors,
Institute of Vision, Department of Ophthalmology,
Paulista School of Medicine, Federal University of São Paulo, Brazil
Medical Director - R & D Consultant, Ziemer Group AG, Port, Switzerland
Speaker, Bausch & Lomb do Brasil
Territory Manager for Latin America, Vista Optics Limited, Widnes, UK
Author does not have financial interest in the commercialization of equipments mentioned

2. Purpose:
To describe a method how aspheric symmetry or asymmetry of corneal surfaces may be assessed and the patterns found in normal corneas and with keratoconus
Qualitative: Galilei best fit toric aspheric (BFTA) elevation maps with a custom ANSI style 5 μm color scale were used to evaluate the aspheric symmetry or asymmetry of both corneal surfaces
Quantitatively 1: Kraneman-Arce index was defined
Quantitatively 2: The coma found with the Galilei corneal wave front report was correlated with the patterns found using the BFTA elevation maps
Methods:

3. Concept of Asphericity:
All corneas have symmetric or asymmetric toric aspheric surfaces.
Symmetric aspheric meridians have uniform change of curvature from the center to the periphery in both hemimeridians
Symmetric aspheric meridians fits well the BFTA referential surface and therefore will have elevation values close to zero with points within the green range (± 5 µm)
Asymmetric aspheric meridians have different change of curvature from the center to the periphery in each hemimeridian
When curvature has a slower progression rate the elevation values are negative and therefore points are within the blue range (≤ -10 µm)
When curvature has a faster progression rate the elevation values are positive and therefore points are within the yellow range (≥ +10 µm)

4. Concept of Asphericity:
Kranemann-Arce index: Designed to quantify the asymmetry of asphericity of a corneal surface
K-A Index is the total difference between the maximum negative BFTA elevation and maximum positive BFTA elevation (without considering mathematic sign) within central 6-mm-diameter data zone
Example (Anterior Surface):
Max negative elevation (in the blue range) = -10 µm
Max positive elevation (in the yellow range) = + 15 µm
Kranemann-Arce index = = 25 µm
Example (PosteriorSurface):
Max negative elevation = -28 µm
Max positive elevation = + 30 µm
Kranemann-Arce index = = 58 µm
Symmetric aspheric meridian: Both hemimeridians within the green range in the 120° to 300° meridian (blue line)
Asymmetric asphericity: Hemimeridians with blue or yellow in the 20° to 200° meridian (red line)
In this case both surfaces had congruent symmetry and asymmetry of asphericity

5. Case A: Congruent symmetric asphericity of both surfaces in normal astigmatic cornea
Case B: Incongruent symmetric asphericity of anterior surface and asymmetric asphericity of posterior surface in a cornea with crossed astigmatic
Case C: Congruent asymmetric asphericity of both surfaces in normal astigmatic cornea with asymmetry more related with the flatter axis of astigmatism
Case D: Congruent asymmetric asphericity of both surfaces in a cornea with keratoconus with asymmetry more related with the steeper axis of astigmatism
BFS (at left) and BFTA
(at right) elevation
maps of anterior (top)
and posterior (bottom)
corneal surfaces
Red line:
- Steeper axis of astigmatism
Asymmetric aspheric meridian
Blue line:
- Flatter axs of astigmatism
- Symmetric aspheric meridian C

6. Custom Selection of IOL Spherical Aberration = 0.29 μm = -0.22 D
Coma = °
Standard (SA = μm)
AcrySof IQ (SA = μm)
Tecnis (SA = μm)
SofPort (SA = 0 μm)
Rayner (SA = 0 μm)
Spherical Aberration = 0.29 μm = D
central rays
focus beyond
outer rays
central rays
focus in front of
outer rays
Galilei measures the total corneal wave front from
both surfaces
Spherical aberration is linked to contrast sensitivity
Coma is linked to aspheric asymmetry and
keratoconus progression
Hypothesis: Symmetry or asymmetry of aspheric corneal
surfaces may be related with satisfaction or visual symptoms
and complains after implantation of IOLs with symmetric
aspheric surfaces
All rays are
focused at
same point

7. Conclusions:
Normal corneas and with keratoconus have a variety of patterns of BFTA elevation maps.
Aspheric asymmetry of corneal surfaces is easy recognized by using the BFTA elevation maps.
Aspheric symmetry was represented by a more green map and asymmetry was recognized by blue and yellow zones usually in the same meridian but opposite side.
Aspheric asymmetry of anterior surface seems to correlate with the amount of corneal coma especially when asymmetric (irregular) astigmatism was present.
Normal corneas had aspheric symmetry of both corneal surfaces, asymmetry of only one of them, or asymmetry on both.
The axis of the aspheric asymmetry may fit the flatter axis of astigmatism, the steeper axis of astigmatism or none of them.
The aspheric asymmetry of both surfaces may be oriented in the same or in different axis.
Corneas with keratoconus use to have congruent asymmetry of both surfaces at the same axis.
The relation of these corneal surface shapes and visual symptoms after multiphocal IOL implantatio is under study