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. © 2013 John Wiley & Sons, Ltd.
|Titolo:||A reduced computational and geometrical framework for inverse problems in hemodynamics|
|Autori:||Lassila, T; Manzoni, A; Quarteroni, A; Rozza, G|
|Rivista:||INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1002/cnm.2559|
|Appare nelle tipologie:||1.1 Journal article|