Sequential parameter estimation for fluid-structure problems: Application to hemodynamics

• Published in: International journal for numerical methods in biomedical engineering 2012-04, Vol.28 (4), p.434-455
• Main Authors: Bertoglio, Cristóbal, Moireau, Philippe, Gerbeau, Jean-Frederic
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis of PDEs; Aortic Aneurysm, Abdominal - physiopathology; arterial stiffness estimation; fluid-structure interaction; Hemodynamics - physiology; Humans; inverse problem; Mathematics; Models, Cardiovascular; reduced-order unscented Kalman filter; Vascular Stiffness - physiology
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.1476

SUMMARY We present a robust and computationally efficient parameter estimation strategy for fluid–structure interaction problems. The method is based on a filtering algorithm restricted to the parameter space, known as the reduced‐order unscented Kalman filter. It does not require any adjoint or tangent problems. In addition, it can easily be run in parallel, which is of great interest in fluid–structure problems where the computational cost of the forward simulation is already a challenge in itself. We illustrate our methodology with the estimation of the artery wall stiffness from the wall displacement measurements – as they could be extracted from medical imaging – in a three‐dimensional idealized abdominal aortic aneurysm. We also show preliminary results about the estimation of the proximal Windkessel resistance, which is an important parameter for setting appropriate fluid boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd. Reduced‐order unscented Kalman filtering for fluid‐structure systems. It does not require any adjoint or tangent problems and can be easily run in parallel. Three‐dimensional examples for the estimation of artery wall stiffness and Windkessel proximal resistance from the wall displacement measurements are illustrated.