A continuum model of the viscoelastic response of the vitreous gel

The vitreous gel is a transparent, hydrated extracellular matrix filling the posterior cavity of the eye behind the lens and is surrounded by and attached to the retina. More specifically it is a composite material primarily made of a dilute network of stiff collagen fibrils and flexible polysaccharide (Hyaluronic Acid) chains within an aqueous solution. It has complex viscoelastic properties but becomes progressively fluid-like with age, leading to a number of pathologies. Here we develop a continuum mathematical model of the vitreous gel by drawing from two-fluid models of semi dilute polymer solutions. We solve a system of coupled partial differential equations for the soft and flexible networks, and the fluid via a combination of spectral and Runge-Kutta methods, and obtain the frequency dependent viscoelastic properties of the system as a function of polymer stiffness and density, and fluid viscosity. Our results will help to better understand rheological experiments on the vitreous, and provide new insights into the origin of vitreous liquefaction.