Stresses in growing soft tissues.

Biochemical processes of tissue growth lead to production of new proteins, cells, and other material particles at the microscopic level. At the macroscopic level, growth is marked by the change of the tissue shape and mass. In addition, the appearance of the new material particles is generally accompanied by deformation and, consequently, stresses in the surrounding material. Built upon a microscopic toy-tissue model mimicking the mechanical processes of mass supply, a simple phenomenological theory of tissue growth is used in the present work for explaining residual stresses in arteries and studying stresses around growing solid tumors/multicell spheroids. It is shown, in particular, that the uniform volumetric growth can lead to accumulation of residual stresses in arteries because of the material anisotropy. This can be a complementary source of residual stresses in arteries as compared to the stresses induced by non-uniform tissue growth. It is argued that the quantitative assessment of the residual stresses based on in vitro experiments may not be reliable because of the essential stress redistribution in the tissue samples under the cutting process. Concerning the problem of tumor growth, it is shown that the multicell spheroid or tumor evolution depends on elastic properties of surrounding tissues. In good qualitative agreement with the experimental in vitro observations on growing multicell spheroids, numerical simulations confirm that stiff hosting tissues can inhibit tumor growth.