Modeling of human vitreous as viscoelastic fluid considering the orientation of collagen fibers

For the most common treatment of retinal diseases worldwide by drug distribution in the human vitreous we developed the mathematical model of the vitreous. Compare to previous works we focus on the vitreous as a viscoelastic fluid including its heterogeneous property due to the orientation of collagen fibers. By using the incompressible viscoelastic Burgers-type model based on experimental data as the specific constitutive equation in the setting of continuum mechanics we considered its non-Newtonian nature. This viscoelastic response is derived from the interaction between hyaluronan, aqueous humor and elastic collagen fibers. The stability analysis of the spatially inhomogeneous non-equilibrium steady state for the incompressible heat conducting viscoelastic Burgers-type fluid was proven. The steady state is asymptotically stable irrespective of the initial conditions and of the shape of the domain. To investigate the influence of the rheology of the vitreous we analyzed its mechanical behavior in a deforming eye ball leading to a fluid-structure-interaction problem. We found that the healthy vitreous predicted by the Burgers-type model showed twice as high stress as the liquefied one predicted by the Navier–Stokes model. The coupling of the viscoelastic Burgers-type model with the drug distribution through the stress driven diffusion provides a fully coupled system of partial differential equations in contrast to the proposed models in the literature. The diffusion in the vitreous depends on the viscoelastic properties of the vitreous which act as a barrier to the drug distribution. The extension to an anisotropic stress driven diffusion reflects the tendency to follow the preferential direction along the collagen fibers depending on the molecule size. As an innovative approach we derived a thermodynamically consistent model for the vitreous as a viscoelastic fluid whose elastic reaction is anisotropic and took into account the heterogeneous property of the vitreous and its orientated collagen fibers. Our developed models about the mechanical behavior of the human vitreous and its influence on the drug distribution give a better understanding of the physiological and pathological processes in the eye.