Shape analysis of a parametric human lens model based on geometrical constraints

Abstract

Several simple models, such as conicoid models, are usually adopted to describe the surfaces of the human crystalline lens; unfortunately they do not provide a continuous junction between the anterior and the posterior surface of the lens and then they cannot qualify for biomechanical simulation. Vice versa, more complex mathematical models give a continuous junction between the anterior and the posterior surface, but do not provide a geometrical or optical interpretation of the coefficients of the model. In this work we propose a continuous curvature lens model in which the coefficients are derived by geometrical constraints. In this way, both the continuity in the junction zone and a geometrical-physical interpretation of the coefficient involved in the model are obtained. Shape, volume and curvature of the proposed model were compared with four models presented in the literature: two independent conic equations, two interdependent figuring conicoid equations, conic patches model and modulated hyperbolic cosine.

Keywords:

• human crystalline lens
• shape
• curvature
• volume
• geometrical constraint