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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.

An improved solution to the mechanics-based mathematical model for retinal detachment developed by Bottega et al. (2013, Math. Med. Biol., 30, 287-310) is found by removing the simplifying assumption of negligible meridian displacement employed in that study. The model considers retinas with and without central tears and takes contraction of the vitreous and extension of its fibrils, along with a pressure difference across the retina, as the impetus for detachment propagation. Exact analytical solutions are established for the meridian and radial displacements of detaching retinas with and without tears, and numerical simulations are performed based on these solutions. Inclusion of the meridian displacements is seen to result in substantially larger radial displacements without affecting the 'dimpling' behaviour of the detaching retina observed previously. However, the critical stress for detachment propagation is substantially decreased by the inclusion of the meridian displacement. The effects of changes in material and geometric parameters, as well as the influence of the presence and size of the retinal tear on detachment propagation are also studied. The model predicts that retinal detachment propagates catastrophically, which is in agreement with the results found by Bottega et al. (2013, Math. Med. Biol., 30, 287-310) and also with clinical observations. Results show that the inclusion of the meridian displacements enhances the previously seen stabilizing effect a retinal tear can have with regard to detachment propagation. The meridian displacement is similarly seen to enhance the influence that the size of the tear has on this effect., (© The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.)