On the mechanics of myopia and its influence on retinal detachment.

A mechanics-based mathematical model of retinal detachment due to the geometric changes of the eye associated with the evolution of myopia is developed. This includes deformation of the retina due to biological growth of the retina, as well as elastic deformation imposed on the retina by the myopic change in shape of the much stiffer choroid and sclera. The problem is formulated as a propagating boundary value problem in the calculus of variations, which yields self-consistent governing equations, boundary conditions, and transversality conditions that establish the location of the propagating boundaries that correspond to equilibrium configurations of the detaching ocular system. Axisymmetric conditions are considered, and exact, analytical solutions to the corresponding boundary value problem are obtained for detaching retinas with and without a tear. Based upon application of the model presented herein to the emmetropic retina, a value of the bond energy of the retina to retinal pigment epithelium interface is estimated using material properties found in the literature. Simulations based on the analytical solutions are performed for a detachment in the retina located at either the posterior or superior pole of the eye. The results support the clinical finding of an increased prevalence of retinal detachment in myopic eyes and provide insight into the potential causation for the increased prevalence.