Abstract
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.