title: Model reduction techniques for fast blood flow simulation in parametrized geometries.
abstract: In this paper, we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the computational domain and the reduced basis method to solve the associated parametrized flow equations. We propose a preliminary analysis carried on a set of arterial vessel geometries, described by means of a radial basis functions parametrization. In order to account for patient-specific arterial configurations, we reconstruct the latter by solving a suitable parameter identification problem. Real-time simulation of blood flows are thus performed on each reconstructed parametrized geometry, by means of the reduced basis method. We focus on a family of parametrized carotid artery bifurcations, by modelling blood flows using Navier-Stokes equations and measuring distributed outputs such as viscous energy dissipation or vorticity. The latter are indexes that might be correlated with the assessment of pathological risks. The approach advocated here can be applied to a broad variety of (different) flow problems related with geometry/shape variation, for instance related with shape sensitivity analysis, parametric exploration and shape design.
authors.affiliation: CMCS - Modelling and Scientific Computing, MATHICSE - Mathematics Institute of Computational Science and Engineering, EPFL - Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland. andrea.manzoni@epfl.ch.
authors.forename: Andrea
authors.initials: A
authors.lastname: Manzoni
authors.forename: Alfio
authors.initials: A
authors.lastname: Quarteroni
authors.forename: Gianluigi
authors.initials: G
authors.lastname: Rozza
mesh_terms: D000465:Algorithms; D002339:Carotid Arteries / Q000502:physiology*; D003198:Computer Simulation; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D008955:Models, Cardiovascular; D012039:Regional Blood Flow / Q000502:physiology*
keywords: Navier-Stokes equations; geometrical and computational reduction; haemodynamics; model reduction; radial basis functions; real-time simulation; reduced basis methods