Abstract
In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional 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 modelled as a two-compartment domain (artery and venous) using Darcy’s Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, 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.
Highlights
Nowadays, computational approaches have become one of the complementary tools in studying structure, function and blood regulation of the vascular systems [1,2,3,4,5,6,7,8,9,10]
The inaccuracy of vessel radii caused by a combination of the three above-mentioned reasons may result in a lower pressure drop across the vessel compared to the anatomically realistic pressure drop
We have introduced a nonlinear multi-scale modelling framework incorporating important features of blood flow in a full organ vasculature
Summary
Computational approaches have become one of the complementary tools in studying structure, function and blood regulation of the vascular systems [1,2,3,4,5,6,7,8,9,10]. The challenging modelling issues for these systems is the fact that vascular systems are made of vessels at 2 different scales [8], ranging from large arteries with close to turbulent blood flow, to smaller arteries and arterioles with mostly laminar flow, and to capillaries, with perfusion of cellular particles between artery and vein capillaries. This complexity makes it difficult to fully understand the connection between scales and the effect of localized changes on the whole organ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
