A reduced computational and geometrical framework for inverse problems in hemodynamics

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  • Toni Lassila
    Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique Fédérale de Lausanne (EPFL) Station 8, CH‐1015 Lausanne Switzerland
  • Andrea Manzoni
    Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique Fédérale de Lausanne (EPFL) Station 8, CH‐1015 Lausanne Switzerland
  • Alfio Quarteroni
    Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique Fédérale de Lausanne (EPFL) Station 8, CH‐1015 Lausanne Switzerland
  • Gianluigi Rozza
    Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique Fédérale de Lausanne (EPFL) Station 8, CH‐1015 Lausanne Switzerland

説明

<jats:title>SUMMARY</jats:title><jats:p>The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier–Stokes equations by a computationally less‐expensive reduced‐basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems both in the deterministic sense, by solving a least‐squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in hemodynamics modeling are considered: (i) a simplified fluid–structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall on the basis of pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements. Copyright © 2013 John Wiley & Sons, Ltd.</jats:p>

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