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CELLULAR TRACTION AS AN INVERSE PROBLEM Abstract. The evaluation of the traction exerted by a cell on a planar substrate is here con-

Abstract. The evaluation of the traction exerted by a cell on a planar substrate is here con-
sidered as an inverse problem: shear stress is calculated on the basis of the measurement of the
deformation of the underlying gel layer. The adjoint problem of the direct two-dimensional plain
stress operator is derived by a suitable minimization requirement. The resulting coupled systems
of elliptic partial differential equations (the direct and the adjoint problem) are solved by a finite
element method and tested vs. experimental measures of displacement induced by a fibroblast cell
Introduction. The study of the basic mechanisms of cell migration has received
a tremendous increment in the last few years. Cell locomotion occurs through a
very complex interaction that involves, among others, actin polymerization, matrix
degradation, chemical signaling, adhesion and pulling on substrate and fibers [12].
All these ingredients concur not only in single cell migration but also in collective
morphogenetic behaviors [15].
When focusing on mechanical aspects only, a major issue is the determination of the
dynamical action of the cells on the environment during migration: the cells adhere,
pull the surrounding matrix and move. As a cell can have more than one hundred of
focal adhesion sites, each one with thousand of integrins, it is quite difficult to obtain
a pointwise description of the forces exerted by moving cells on a direct basis. Never-


Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino


Collections: Mathematics