A multi-scale flow model for blood regulation in a realistic vascular system

Abstract In the last decade, numerical models have been an increasingly important tool in medical science both for the fundamental understanding of the physiology of the human body as well as for diagnostics and personalized medicine. In this paper, a multi-scale model is developed for blood flow and regulation in a full vascular structure of an organ. We couple a 1D vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille’s law, with pressure correction by elasticity and pressure drop estimation at vessels junctions. The porous capillary bed is modeled as a two compartments domain (arterial and venal) and Darcy’s law. The fluid exchange between the arterial and venal capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: 1) is closely dependent on the structure and parameters of both the vascular vessels and of the capillary bed, and 2) it provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to capture the underlying physiology reliably, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.