Mathematical and Numerical Modeling of Solute Dynamics in Blood Flow and Arterial Walls

The numerical modeling of solutes absorption processes by the arterial wall is of paramount interest for the understanding of the relationships between the local features of blood flow, the nourishing of the inner arterial wall by the blood solutes, and the pathologies that can appear when this process is for some reason perturbed. In the present work, two models for the solutes dynamics are investigated. In the first model, which is essentially based on the one introduced by Rappitsch and Perktold [J. Biomech. Engrg., 118 (1996), pp. 511-519] and Rappitsch, Perktold, and Pernkopf [Internat. J. Numer. Methods Fluids, 25 (1997), pp. 847-857], the Navier-Stokes equations for an incompressible fluid, describing the blood velocity and pressure fields, are coupled with an advection-diffusion equation for the solute concentration. The wellposedness of this model is discussed. The second model considers also the solutes dynamics "inside" the arterial wall, described by a pure diffusion equation. Actually, this is a heterogeneous model, coupling different equations in different parts of the domain at hand. Its wellposedness is proven. Moreover, in view of the numerical study, an iterative finite element method by subdomains is proposed and its convergence properties are analyzed. Finally, several numerical results comparing the different models in situations of physiologic interest are illustrated.