  There is significant interest in modelling the mechanics and physics of
growth of soft biological systems such as tumors and bacterial biofilms. Solid
tumors account for more than 85% of cancer mortality and bacterial biofilms
account for a significant part of all human microbial infections.These growing
biological systems are a mixture of fluid and solid components and increase
their mass by intake of diffusing species such as fluids and nutrients
(swelling) and subsequent conversion of some of the diffusing species into
solid material (growth). Experiments indicate that these systems swell by large
amounts and that the swelling and growth are intrinsically coupled. However,
many existing theories for swelling coupled growth employ linear
poroelasticity, which is limited to small swelling deformations, and employ
phenomenological prescriptions for the dependence of growth rate on
concentration of diffusing species and the stress-state in the system. In
particular, the termination of growth is enforced through the prescription of a
critical concentration of diffusing species and a homeostatic stress. In
contrast, by developing a fully coupled swelling-growth theory that accounts
for large swelling through nonlinear poroelasticity, we show that the emergent
driving stress for growth automatically captures all the above phenomena.
Further, we show that for the soft growing systems considered here, the effects
of the homeostatic stress and critical concentration can be encapsulated under
a single notion of a critical swelling ratio. The applicability of the theory
is shown by its ability to capture experimental observations of growing tumors
and biofilms under various mechanical and diffusion-consumption constraints.
Additionally, compared to generalized mixture theories, our theory is amenable
to relatively easy numerical implementation with a minimal physically motivated
parameter space.
