Frog tongue segmentation data for a realistic vascular structure in modelling

In the last decade, numerical models have been an increasingly important
tool in biological and medical science both for the fundamental
understanding of physiology as well as the potential for novel diagnostics
and treatments tools in clinical application. 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 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
modelled as a two-compartment domain (artery and venous) using Darcy’s
law. The fluid exchange between the artery and venous capillary bed
compartments are 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 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.