A New Concept Of Bilateral Symmetry Characterization Based On A Shape-Related Power Law

To obtain bilateral symmetry in healthy corneas from their respective topographies basing on a shape-related power law.

Study performed in the National Network of Cooperative Research in Ophthalmology (RETICS), Universidad Politécnica de Cartagena, Spain.

Raw data obtained from tomographies of the corneal surface of 165 patients with the SIRIUS tomographer (CSO, Italy) were registered. Mean values of maximum and minimum elevations were obtained as a function of the radius for each corneal surface and its fellow cornea (OD and OS). Maximum and minimum points were adjusted to the shape-related power law: Z₀ (r)=φ₀∙r^q+φ₁ . Interocular symmetry was evaluated basing on a pattern of corneal shape (q the exponent of the power, φ₀ a constant of proportionality).

The general model of shape-related power law provided a perfect goodness of fit (R² = 1). Regarding the minimum elevation values, values coincide for every scalar of the model in each corneal surface. Regarding the maximum values, coefficients of fitting of the model for the corneal surface between fellow corneas were anterior_OD (q=2.090; φ₀=0.061); anterior_OS (q=2.089; φ₀=0.062); posterior_OD (q=2.047; φ₀=0.080); posterior_OS (q=2.044; φ₀=0.081).

Shape-related power law showed a strong direct symmetry in relation to mean elevation values of the corneal surface. This new pattern of patient-specific bilateral asymmetry could help in the detection of pathologic anomalies, validation of measures and in surgical planification.