Lyapunov stability of competitive cells dynamics in tumor mechanobiology

Poromechanics plays a key role in modelling hard and soft tissue behaviours, by providing a thermodynamic framework in which chemo-mechanical mutual interactions among fluid and solid constituents can be consistently rooted, at different scale levels. In this context, how different biological species (including cells, extra-cellular components and chemical metabolites) interplay within complex environments is studied for characterizing the mechanobiology of tumor growth, governed by intratumoral residual stresses that initiate mechanotransductive processes deregulating normal tissue homeostasis and leading to tissue remodelling. Despite the coupling between tumor poroelasticity and interspecific competitive dynamics has recently highlighted how microscopic cells and environment interactions influence growth-associated stresses and tumor pathophysiology, the nonlinear interlacing among biochemical factors and mechanics somehow hindered the possibility of gaining qualitative insights into cells dynamics. Motivated by this, in the present work we recover the linear poroelasticity in order to benefit of a reduced complexity, so first deriving the well-known Lyapunov stability criterion from the thermodynamic dissipation principle and then analysing the stability of the mechanical competition among cells fighting for common space and resources during cancer growth and invasion. At the end, the linear poroelastic model enriched by interspecific dynamics is also exploited to show how growth anisotropy can alter the stress field in spherical tumor masses, by thus indirectly affecting cell mechano-sensing. GraphicAbstract