TY - JOUR TI - On the evolution of a detaching retina DO - https://doi.org/doi:10.7282/t3-m4j0-q947 PY - 2018 AB - Retinal detachment is an affliction of the eye in which the nine layers of the neurosensory retina detach from the outer layers of the eye along its interface with the retinal pigment epithelium. This dissertation represents a study of the application of mechanics based mathematical modeling to age-related and myopia-induced retinal detachments. A review of the theory of shells of arbitrary shape which provides clarification on the change in curvature of the shell is also presented. A corresponding multi-directional growth law for the propagation of detachments of arbitrary shape is established. A mechanics based mathematical model for retinal detachment in the emmetropic eye that takes contraction of the vitreous and extension of its fibrils, along with a pressure difference across the retina, as the impetus for detachment propagation is presented. A second mechanics based mathematical model for retinal detachment due to the geometric changes of the eye associated with the evolution of myopia is also developed. The model for myopic retinal detachment 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 models are formulated as propagating boundary value problems in the calculus of variations. This approach yields the self-consistent governing equilibrium equations, boundary conditions, and transversality conditions that establish the location of the propagating boundaries that correspond to equilibrium configurations of each the detaching ocular systems. Axisymmetric conditions are considered and exact analytical solutions to the corresponding boundary value problems are obtained for detaching retinas with and without a tear. 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 emmetropic model predicts that retinal detachment propagates catastrophically, which is in agreement with clinical observations. From application of the emmetropic model presented herein, 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 for the myopic model of the detaching retina 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. KW - Mechanical and Aerospace Engineering KW - Retinal detachment LA - eng ER -