Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow.

In this work we introduce and discuss several mathematical models, based on partial differential equations, devised to study the coupled transport of macromolecules as low-density lipoproteins in the blood stream and in the arterial walls. These models are accurate provided that a suitable set of physical parameters characterizing the physical properties of the molecules and of the wall layers are available. Here we turn our attention on this aspect, and propose a new methodology to compute the physical parameters needed for the model set up, starting from available in vivo measurements. Then, we focus on the study of the accumulation of low-density lipoproteins in vascular districts featuring a highly disturbed flow. Our results demonstrate that mathematical models whose set up procedure benefits from an experimental feedback provide reliable information not only qualitatively, but also quantitatively. Their application to geometrically perturbed vascular districts (as for example a severe stenosis) shows that geometrical parameters such as curvature and variations of the lumenal section strongly influence the accumulation of low-density lipoproteins within the wall. For instance, in a stenotic segment with 75% area constriction, the LDL concentration at the lumenal side of the wall is about 10% higher than for the undisturbed segment.