 
Summary: Journal of Mathematical Biology manuscript No.
(will be inserted by the editor)
Traction patterns of tumor cells
D. Ambrosi · A. Duperray · V. Peschetola ·
C. Verdier
Received: date / Revised: date
Abstract The traction exerted by a cell on a planar deformable substrate can be in
directly obtained on the basis of the displacement field of the underlying layer. The
usual methodology used to address this inverse problem is based on the exploitation of
the Green tensor of the linear elasticity problem in a half space (Boussinesq problem),
coupled with a minimization algorithm under force penalization. A possible alternative
strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimiza
tion requirement. The resulting system of coupled elliptic partial differential equations
is applied here to determine the force field per unit surface generated by T24 tumor
cells on a polyacrylamide substrate. The shear stress obtained by numerical integration
provides quantitative insight of the traction field and is a promising tool to investigate
the spatial pattern of force per unit surface generated in cell motion, particularly in
the case of such cancer cells.
Introduction
Cell locomotion occurs through complex interactions that involve, among others, actin
