Mathematical framework for Traction Force Microscopy

Richard Michel (1) , Valentina Peschetola (1) , Guido Vitale (2) , Jocelyn Etienne (1) , Alain Duperray (3) , Davide Ambrosi (4) , Luigi Preziosi (5) , Claude Verdier (1)

1 DYFCOM - DYnamique des Fluides COmplexes et Morphogénèse [Grenoble]
2 LMS - Laboratoire de mécanique des solides
3 INSERM U823 - Institut d'oncologie/développement Albert Bonniot de Grenoble
4 MOX, Milano
5 Matematica, Politecnico di Torino

This paper deals with the Traction Force Microscopy (TFM) problem. It consists in obtaining stresses by solving an inverse problem in an elastic medium, from known experimentally measured displacements. In this article, the application is the determination of the stresses exerted by a living cell at the surface of an elastic gel. We propose an abstract framework which formulates this inverse problem as a constrained minimization problem. The mathematical constraints express the biomechanical conditions that the cell must satisfy. From this framework, two methods currently used can be derived, the adjoint method (AM) and the Fourier Transform Traction Cytometry (FTTC) method. An improvement of the FTTC method is also derived using this framework. The numerical results are compared and show the advantage of the AM, in particular it can capture details more accurately.

Mots clés: L -curve; Cell motility; Inverse problems; Tikhonov regularization; Adjoint Method (AM); Fourier Transform Traction Cytometry (FTTC); L -curve.

Domaines: Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]; Physique mathématique [math-ph]; Biophysique [physics.bio-ph]

Richard Michel, Valentina Peschetola, Guido Vitale, Jocelyn Etienne, Alain Duperray, et al.. Mathematical framework for Traction Force Microscopy. ESAIM: Proceedings, 2013, 42, pp.61-83. ⟨10.1051/proc/201342005⟩. ⟨hal-00772155v2⟩