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[A study on the mathematical model of normal adult cornea]
Ming-guang Shi1, Bo Wang, Ting-ting Shao
1The Second Hospital Affiliated to Wenzhou Medical College, Wenzhou 325027, China. pshimg@wzhealth.com
Objective:
To explore the method on the conic equation to establish the mathematical model of the adult cornea and its preliminary result.
Methods:
The curvature of anterior cornea and of posterior cornea, the corneal thickness of the points in the distance of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 mm away from the apex in the meridians of 0 degrees , 30 degrees , 60 degrees , 90 degrees , 120 degrees , 150 degrees , 180 degrees , 210 degrees , 240 degrees , 270 degrees , 300 degrees , 330 degrees meridians were collected from the Orbscan II topography. Cartesian coordinate was established with the origin at the apex of cornea and its horizontal, vertical and optical axes were defined as axis of X, Y and Z respectively. Then every point was located. The coordinate was circumrotated to establish a new coordinates to relocate the data of the points at the oblique meridians. The mathematical formulas of the meridians sections of the anterior and posterior surface were analyzed as: anterior surface: x2 = a1z2 + a2z, posterior surface: x2 = a1 (z-d0)2 + a2 (z-d0) (d0 is the corneal thickness). And the asphericity Q could be deduced. The mathematical formulas of the anterior and the posterior cornea surface as: anterior surface: x2 a2 + y2 b2 + (z-c)2 c2 = 1, posterior surface: x2 a2 + y2 b2 + (z-c-d0)2 c2 = 1.
Results:
The mathematical models of the meridian section of the anterior and posterior surface of the cornea show conic formula as ellipse. The mathematical formulas of the anterior and the posterior cornea surface show conic surfaces.
Conclusions:
The paper reported a new method in conic formula to establish the mathematical model of the normal cornea. The shape of the meridians sections of the anterior and posterior surface of cornea are ellipse. The shape of the anterior and the posterior corneal surface are both ellipsoid.
