Motivated by the need for numerical modeling of solute absorption processes by the arterial wall, the authors study relationships between the local features of blood flow. The nourishing of the inner arterial wall by blood solutes and other pathologies can appear when the absorption process is for some reason perturbed. Two models for the solute dynamics are investigated. In the first model, the Navier-Stokes equations for incompressible fluid, describing the blood velocity and pressure fields, are coupled with an advection-diffusion equation for solute concentration. The well-posedness of the model has been discussed. The second model considers also the solute dynamics inside the arterial wall described by a pure diffusion equation. The well-posedness of this heterogeneous model, coupling different equations in different parts of the domain, also has been shown. An iterative finite element method for subdomains has been proposed, and its convergence has been analysed.