Mechanical Models of the Dynamics of Vitreous Substitutes

We discuss some aspects of the fluid dynamics of vitreous substitutes in the vitreous chamber, focussing on the flow induced by rotations of the eye bulb. We use simple, yet not trivial, theoretical models to highlight mechanical concepts that are relevant to understand the dynamics of vitreous substitutes and also to identify ideal properties for vitreous replacement fluids. We first recall results by previous authors, showing that the maximum shear stress on the retina grows with increasing viscosity of the fluid up to a saturation value. We then investigate how the wall shear stress changes if a thin layer of aqueous humour is present in the vitreous chamber, separating the retina from the vitreous replacement fluid. The theoretical predictions show that the existence of a thin layer of aqueous is sufficient to substantially decrease the shear stress on the retina. We finally discuss a theoretical model that predicts the stability conditions of the interface between the aqueous and a vitreous substitute. We discuss the implications of this model to understand the mechanisms leading to the formation of emulsion in the vitreous chamber, showing that instability of the interface is possible in a range of parameters relevant for the human eye

A model for the linear stability of the interface between aqueous humor and vitreous substitutes after vitreoretinal surgery

We consider the motion of two immiscible viscous fluids induced by periodic oscilla- tions of a flat solid surface along its plane. The interface between the two fluids is parallel to the solid wall; one fluid occupies the region between the wall and the in- terface and the other extends from the interface to infinity. We study numerically the linear stability of the interface with respect to two-dimensional perturbations using the normal mode analysis and assuming quasi-steady flow conditions. The analysis is motivated by the need of understanding the behavior of vitreous substitutes inserted in the vitreous chamber of the eye after vitrectomy. This is a common surgical pro- cedure adopted to treat retinal detachments, whereby the vitreous humor is removed from the eye and replaced by fluids immiscible with water. Owing to their hydropho- bic nature vitreous substitutes coexist in the vitreous chamber with a certain amount of aqueous humor (the fluid produced in the anterior part of the eye) and, typically, a thin layer of aqueous separates the tamponade fluid from the retina. A common problem with this treatment is that, in some cases, the interface between the two fluids breaks down and this might eventually lead to the generation of an emulsion. It is believed that mechanics plays an important role in this process but the problem remains very poorly understood. We find that instability of the interface is possible in a range of parameters that is relevant for the problem that motivated the present analysis. This suggests that shear instability is likely a possible mechanism triggering the onset of vitreous substitutes\u2013aqueous interface instability

Equilibrium shape of the aqueous humor-vitreous substitute interface in vitrectomized eyes

Purpose: To predict the shape of the interface between aqueous humor and a gas or silicone oil (SO) tamponade in vitrectomized eyes. To quantify the tamponated retinal surface for various eye shapes, from emmetropic to highly myopic eyes. Methods: We use a mathematical model to determine the equilibrium shape of the interface between the two fluids. The model is based on the volume of fluids (VOF) method. The governing equations are solved numerically using the free so ware OpenFOAM. We apply the model to the case of idealized, yet realistic, geometries of emmetropic and myopic eyes, as well as to the real geometry of the vitreous chamber reconstructed from magnetic resonance imaging (MRI) images. Results: The numerical model allows us to compute the equilibrium shape of the interface between the aqueous humor and the tamponade fluid. From this we can compute the portion of the retinal surface that is effectively tamponated by the fluid. We compare the tamponating ability of gases and SOs. We also compare the tamponating effect in emmetropic and myopic eyes by computing both tamponated area and angular coverage. Conclusion: The numerical results show that gases have better tamponating properties than SOs. We also show that, in the case of SO, for a given filling ratio the percentage of tamponated retinal surface area is smaller in myopic eyes. The method is valuable for clinical purposes, especially in patients with pathological eye shapes, to predict the area of the retina that will be tamponated for a given amount of injected fluid