One dimensional models for blood flow in arteries
Monday 15th July 2002
Formaggia, Luca; Lamponi, Daniele; Quarteroni, Alfio
We investigate a family of one dimensional nonlinear systems which model the blood pulse propagation in compliant arteries. They are obtained by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the semplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a well known algebraic relation between intramural pressure and vessel section area, we analyse in turn the effects of terms accounting for inertia, longitudinal pre-stress and viscoelasticity. We also consider the problem of how to account for branching and possible discontinuous wall properties, the latter aspect is relevant in the presence of prosthesis and stents. To this purpose we employ a domain decomposition approach and we provide conditions which ensure the stability of the coupling. We propose a numerical method based on a finite element Taylor-Galerkin scheme combined with operator splitting techniques, and carry out several test cases for the assessment of the proposed models.