Calculation and application of the anterior surface area of a model human cornea

Abstract

The macroscopic anterior surface area was calculated for three models of the average human cornea. Two models, a general ellipsoid and a rotational ellipse (rotationally symmetric ellipsoid) gave a surface area of 132 mm2, while a spherical model gave 126 mm2. A general ellipsoidal model having the maximum radius horizontal (with-the-rule corneal astigmatism) has less surface area than a rotational ellipse with the same horizontal radius. For a corneal sagittal height of 2.59 mm, the surface area of an ellipsoidal cornea equals -19.2Q + 16.3R -0.476 which specifies a rotational ellipse (radius R, asphericity Q) of equal surface area. In a cornea with the maximum radius vertical (against-the-rule corneal astigmatism), the ellipsoid has slightly more surface area than a rotational ellipse with the same horizontal radius of curvature. For a given horizontal radius of curvature, the sphere has the lowest surface area. For a corneal sagittal height s of 2.59 mm, the sphere underestimates by 8% the surface area of a rotational ellipse with asphericity -0.5. The anterior corneal surface area of a rotational ellipse model, radius R, asphericity Q is given by 2 pi Rs- 19.2Q. In all three models, the surface area increases with horizontal radius of curvature. In the rotational ellipse model, the rate of increase (slope) is independent of asphericity, and the slope found in with-the-rule astigmatism is less than the slope found with against-the-rule astigmatism. The calculated surface area predicts a precorneal tear volume of 0.86 microliter for a 6.5 micron tear thickness. The apparent, or plane projected are of an epithelial lesion underestimates the curved surface area with a percentage error that increases rapidly with lesion diameter. For a 12 mm diameter lesion on a rotational ellipse model, the apparent area underestimates the surface area by 18%. The average posterior corneal surface in human is not spherical but imitates the anterior surface, and has an area of 137 mm2 or 3.8% greater than the anterior area.