Traction force microscopy : an inverse problem with pointwise observations
Lundi 9 septembre 2013 14:00
- Duree : 1 heure
Lieu : Laboratoire Interdisciplinaire de Physique (ex LSP), Conference Room - 140 Avenue de la Physique Domaine Universitaire - Saint-Martin-d’Hères
Orateur : Guido VITALE (Laboratoire de Mécanique des Solides - Ecole Polytechnique, Palaiseau, France)
Traction Force Microscopy is an inversion method that allows to obtain
the stress field applied by a living cell on the environment on the
basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms
of Green functions, can be alternatively tackled using a variational
framework and then a finite elements discretization. In such a case, a
variation of the error functional under suitable regularization is
operated in view of its minimization. This setting naturally suggests
the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this talk we illustrate the rigorous theory of
the two— and three— dimensional problem, involving in the former case
a distributed control and in the latter case a surface control. The
pointwise observations require to exploit the theory of elasticity
extended to forcing terms that are Borel measures. Moreover, we also
illustrate a numerical strategy of the inversion method that discretizes
the partial differential equations associated to the optimal control
problem by finite elements. A detailed discussion of the numerical
approximation of a test problem (with known solution) that contains most of the mathematical difficulties of the real one, allows a precise
evaluation of the degree of confidence that one can achieve by in the
numerical results.
Contact : sigolene.lecuyer@ujf-grenoble.fr
Discipline évènement : (Physique)
Entité organisatrice : (LIPhy)
Nature évènement : (Séminaire)
Evènement répétitif : (Séminaire Mat. Molle/grise)
Site de l'évènement : Domaine Universitaire de St Martin d’Hères
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