A novel multiscale modelling for the hemodynamics in retinal microcirculation with an analytic solution for the capillary-tissue coupled system

Abstract

Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the multiscale nature of the retinal vasculature and its coupling to surrounding tissue. To address this, we develop a multiscale model that couples retinal vasculature across scales with interstitial tissue. Our model combines the one-dimensional (1D) model for arterioles and venules with the coupled Darcy equations for capillaries and tissue. The model uses an analytic solution for capillary-tissue coupled system that provides a simple interpretation of the results along with much faster computation. The analytic solution implies a dynamic coupling condition that links the capillary bed with upstream arteriolar and downstream venular flows. The model is mathematically robust, demonstrated through analysis of the solution's truncation error and convergence. Its predictive accuracy is validated against experimental data and other models, making it useful in interpreting experimental results. Finally, the role of various parameters in controlling retinal hemodynamics is explored.