|Abstract:|| 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, involving the resolution of an adjoint problem, was used.
Some preliminary numerical tests are shown. In these simulation, we mainly focused on detrmining a parameter that is linked to the mechanical properties of the arterial walls, the compliance. The synthetic data we used to estimated the parameter were obtained from a numerical computation performed with a more precise model: a three-dimensional fluid structure interaction model. The first results seem to be promising. In particular, it is woth noticing that the estimated compliance which gives the best fit is qiute different from the values one would have expected a priori.|