A reduced computational and geometrical framework for inverse problems in hemodynamics

作者：Lassila Toni; Manzoni Andrea; Quarteroni Alfio; Rozza Gianluigi^*

来源：International Journal for Numerical Methods in Biomedical Engineering, 2013, 29(7): 741-776.

DOI：10.1002/cnm.2559

• inverse problems
• model reduction
• shape optimization
• fluid-structure interaction
• reduced-basis methods
• hemodynamics
• parametrized Navier-Stokes equations

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.

• 出版日期2013-7