Numerical Solution of Viscoelastic Fluid‐Structure‐Diffusion Systems with Applications in Ophthalmology

Abstract

AbstractThe research of fluid‐structure interaction problems is a continuously growing field, especially regarding applications in medicine and biology. We present the coupling of a potentially viscoelastic fluid with multiple hyperelastic structures incorporating chemical processes in the arbitrary Lagrangian Eulerian framework. This monolithic formulation allows a robust numerical solution with Newton's method. The discretization is based on the backward Euler scheme for temporal discretization and the Galerkin finite element method for spatial discretization. This fluid‐structure interaction problem is applied to ophthalmology in order to improve the medical treatment of retinal diseases. The physiological processes include the elastic response of various structures like the sclera, lens and iris coupled to the fluid‐like vitreous which is modeled by a viscoelastic Burgers type model for the healthy case and by the Newtonian Navier‐Stokes equations for the pathological case. Since most medical treatments are based on the injection of medicine we furthermore study the drug distribution, which is modeled by convection‐diffusion‐reaction equations, in the whole eye for healthy and non‐healthy pathologies.