Methods for assimilating blood velocity measures in hemodynamics simulations: Preliminary results

Abstract New measurement devices and techniques in biomedical images provide medical doctors with a huge amount of data on blood flow and vascular morphologies. These data are crucial for performing (and validating) individualbased simulations of hemodynamics (see e.g. [1]). Availability of velocity measures inside a region of interest poses problems that are new to the community of computational hemodynamics and however well known in other engineering fields. In particular, integration of data (measures) and numerical simulations has been an issue of utmost relevance in the prediction of fluid geophysics phenomena and, in particular, weather forecast. In computational hemodynamics a mathematically sound assimilation of data and numerical simulations is needed, on one hand for improving reliability of numerical results, on the other one for filtering noise and measurements errors. In this paper we consider and compare some possible methods for integrating numerical simulations and velocity measures in some internal points of the computational domain. Preliminary numerical results for a 2D Stokes problem are presented both for noise free and noisy data, investigating convergence rate and noise sensitivity.

[1]  Philippe Courtier,et al.  Unified Notation for Data Assimilation : Operational, Sequential and Variational , 1997 .

[2]  David A. Steinman,et al.  A Framework for Geometric Analysis of Vascular Structures: Application to Cerebral Aneurysms , 2009, IEEE Transactions on Medical Imaging.

[3]  V. Kozlov,et al.  Iterative methods for data assimilation for Burgers' equation , 2006 .

[4]  A. Quarteroni.  Cardiovascular mathematics , 2000 .

[5]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[6]  Charles Taylor,et al.  EXPERIMENTAL AND COMPUTATIONAL METHODS IN CARDIOVASCULAR FLUID MECHANICS , 2004 .

[7]  David A. Steinman,et al.  Image-Based Computational Fluid Dynamics Modeling in Realistic Arterial Geometries , 2002, Annals of Biomedical Engineering.

[8]  Dominique Chapelle,et al.  Cardiac function estimation from MRI using a heart model and data assimilation: Advances and difficulties , 2006, Medical Image Anal..

[9]  Max Gunzburger,et al.  Perspectives in flow control and optimization , 1987 .

[10]  Maxime Sermesant,et al.  Cardiac Function Estimation from MRI Using a Heart Model and Data Assimilation: Advances and Difficulties , 2005, FIMH.

[11]  Christian Vergara,et al.  An approximate method for solving incompressible Navier–Stokes problems with flow rate conditions , 2007 .

[12]  E. Haber,et al.  On optimization techniques for solving nonlinear inverse problems , 2000 .

[13]  Enrique Zuazua,et al.  Controllability and Observability of Partial Differential Equations: Some Results and Open Problems , 2007 .

[14]  J L Lions,et al.  On the controllability of distributed systems. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Alfio Quarteroni,et al.  Complex Systems in Biomedicine , 2006 .