A simple mathematical model of retinal reattachment after scleral buckling

Rhegmatogenous retinal detachment (RRD) is a dangerous pathological condition that can lead to blindness and requires surgical treatment. Scleral buckling is a surgical technique that has been in use for many years to repair RRD. It consists in the application of a piece of silicone on the outer surface of the sclera, that pushes the eye wall inwards and modifies its curvature in correspondence of the retinal tear. It is observed that this facilitates retinal reattachment. Various authors speculated that basic principles of fluid mechanics can be invoked to explain the reattachment process, though a convincing explanation of the mechanics underlying the process is still elusive. In this study, we propose an idealized two-dimensional model of a detached retina, surrounded by liquefied vitreous and study its dynamics secondary to eye movements. This is done using an immersed boundary numerical code. The retinal flaps are modeled as slender one-dimensional elastic bodies, one extremity of which is clamped to the retinal wall. For simplicity we model the retina as a rigid, flat wall. We account for the presence of scleral buckling by inserting a wall bump underneath the detached filaments. We show that the dynamics of the detached filaments is very complicated and that the presence of a buckle significantly contributes to reduce the time averaged distance between the detached filaments and the wall, thus facilitating reattachment. The mechanisms involved are inherently associated with the dynamics of the filament.