Relations between network topology, hemodynamic and oxygen supply investigates by a 1D numerical model of microcirculation

Pathologies like diabetes or arterial hypertension affect vessels of the microcirculation and lead to the emergence of vascular anomalies as occlusions. Non-oxygen perfused areas (ischemic) then appear, altering surrounding tissues and organ function. In the retina, this leads to local or global vision disorders. In-vivo imaging of the retina allows establishing correlations between ischemic area, troubles of blood circulation, and morphology. We wonder to what extent the topological characteristics of the network, unique to each person, are involved in the development of vascular anomalies. We want then to investigate the relations between network topology, hemodynamics, and oxygen supply. The oxygen distribution in a microvascular network is heterogeneous and complex because of the variety of physical phenomena that exists at this scale close to that of a red blood cell (RBC). We develop a 1D numerical model of circulation with the specificities of the micro-scale blood rheology (Fahraeus-Lindqvist, Zweifach-Fung effects). We simulate blood flow and transport of RBCs and oxygen through networks with several spatial symmetries. These simulations allow an exhaustive study on global quantities as energy, blood resistance, or amount of delivered oxygen.