Rotational microrheology of multilayered finite elastic media

International audience; This paper presents derivations of the torque-rotation angle relationship for a rigid spherical bead embedded in a composite medium made of n isotropic and linear elastic layers. Analytical solutions are provided for both compressible and incompressible solids, assuming no-slip conditions between the rigid spherical inclusion and its adjacent medium as well as between elastic layers. Thanks to these general formulas, we investigated the effect of finite size media on the torque-bead rotation response and derived the exact relationship linking apparent and intrinsic elastic moduli of the medium. Thus, this result can be applied to characterize precisely the mechanical heterogeneity and architecture of soft biomaterials, including cells, from real magnetocytometry experiments. This point is exemplified in the case of a bilayer medium which, interestingly, allows distinguishing cellular cortex from deep cytoskeleton. We found that rotational microrheology experiments are well suited to characterize locally the elastic properties of the layer in contact with the probe as soon as the layer thickness is larger than two-bead diameters.