Geodesic
Parameter identification for a one-dimensional blood flow model
Vincent Martin1 ; Francois Clément2 ; Astrid Decoene3 ; Jean-Frédéric Gerbeau4
1 MOX, Dpto di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy ;
2 Estime, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ;
3 Bang, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ;
4 Reo, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ;
ESAIM. Proceedings, Tome 14 (2005), pp. 174-200.

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The purpose of this work is to use a variational method to identify some of the parameters of one-dimensional models for blood flow in arteries. These parameters can be fit to approach as much as possible some data coming from experimental measurements or from numerical simulations performed using more complex models. A nonlinear least squares approach to parameter estimation was taken, based on the optimization of a cost function. The resolution of such an optimization problem generally requires the efficient and accurate computation of the gradient of the cost function with respect to the parameters. This gradient is computed analytically when the one-dimensional hyperbolic model is discretized with a second order Taylor-Galerkin scheme. An adjoint approach was used.
Some preliminary numerical tests are shown. In these simulations, we mainly focused on determining a parameter that is linked to the mechanical properties of the arterial walls, the compliance. The synthetic data we used to estimate the parameter were obtained from a numerical computation performed with a more accurate model: a three-dimensional fluid-structure interaction model. The first results seem to be promising. In particular, it is worth noticing that the estimated compliance which gives the best fit is quite different from the values that are commonly used in practice.
DOI : 10.1051/proc:2005014

Vincent Martin 1 ; Francois Clément 2 ; Astrid Decoene 3 ; Jean-Frédéric Gerbeau 4

1 MOX, Dpto di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy ;
2 Estime, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ;
3 Bang, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ;
4 Reo, Inria Rocquencourt, BP 105, 78153 Le Chesnay, France ; 
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     author = {Vincent Martin and Francois Cl\'ement and Astrid Decoene and Jean-Fr\'ed\'eric Gerbeau},
     title = {Parameter identification for a one-dimensional blood flow model},
     journal = {ESAIM. Proceedings},
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Vincent Martin; Francois Clément; Astrid Decoene; Jean-Frédéric Gerbeau. Parameter identification for a one-dimensional blood flow model. ESAIM. Proceedings, Tome 14 (2005), pp. 174-200. doi : 10.1051/proc:2005014. http://geodesic.mathdoc.fr/articles/10.1051/proc:2005014/

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