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A reduced computational and geometrical framework for inverse problems in hemodynamics.

  • Lassila T 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.
  • Manzoni A
  • Quarteroni A
  • Rozza G
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  • 2013-06-27
Published in:
  • International journal for numerical methods in biomedical engineering. - 2013
fluid-structure interaction
hemodynamics
inverse problems
model reduction
parametrized Navier-Stokes equations
reduced-basis methods
shape optimization
Algorithms
Atherosclerosis
Bayes Theorem
Blood Pressure
Blood Vessel Prosthesis
Computer Simulation
Constriction, Pathologic
Elastic Modulus
Femoral Artery
Hemodynamics
Humans
Least-Squares Analysis
Models, Cardiovascular
Vascular Grafting
English 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.
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  • English
Open access status
green
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Persistent URL
https://sonar.ch/global/documents/120620
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