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Multidimensional modelling for the carotid artery blood flow. (English) Zbl 1178.76395

Summary: A multidimensional 3D-1D FEM model of the whole arterial tree is implemented. It comprises a 3D compliant model of the carotid bifurcation coupled with a 1D model for the remaining part of the arterial tree. With this approach, difficulties arising from the treatment of boundary conditions for the 3D model are naturally handled. The Navier-Stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall. Also, the A.L.E. formulation is considered within the 3D blood regions taking into account the domain deformations produced by the moving artery wall. This 3D model is complemented with a 1D model of the entire arterial tree, in order to appropriately set inflow and outflow boundary conditions for the former. The reduced 1D model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network. Also, a volumetric flow rate is imposed at the inlet to model the systolic work of the heart. The peripheral arteriole beds are simulated with the well-known lumped Windkessel model. A standard geometry of the carotid bifurcation is discretized with P1 bubble-P1 tetrahedral elements. The obtained results properly reproduce the general flow patterns reported in the literature. Very good agreement between the outcomes of a pure 1D model and those of the combined multidimensional model was obtained. It is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases.

MSC:

76Z05 Physiological flows
76M10 Finite element methods applied to problems in fluid mechanics
92C10 Biomechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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