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A reduced computational and geometrical framework for inverse problems in hemodynamics
Author(s) -
Lassila Toni,
Manzoni Andrea,
Quarteroni Alfio,
Rozza Gianluigi
Publication year - 2013
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2559
Subject(s) - inverse problem , uncertainty quantification , mathematics , mathematical optimization , residual , finite element method , inverse , basis (linear algebra) , compressibility , computer science , algorithm , mathematical analysis , geometry , engineering , statistics , structural engineering , aerospace engineering
SUMMARY 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.