Understanding the mechanics of growth: A large deformation theory for coupled swelling-growth and morphogenesis of soft biological systems

Abstract

Understanding the growth of soft biological systems is crucial in a wide range of applications with extensive societal consequences, such as plastic and reconstructive surgery, curbing the growth of tumors and bacterial colonies, tissue engineering of functional vascular grafts, etc. Solid tumors account for more than 85% of cancer mortality, and bacterial biofilms account for a significant part of all human microbial infections. Mechanics plays a crucial role in determining how these systems grow and acquire their shape (morphogenesis). The overarching theme of this thesis is in elucidating the mechanics of growth and morphogenesis in such soft systems, starting from universal underlying mechanisms. 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, with the swelling being an important driver of growth. However, most 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 3coupled 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 in this thesis, 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. We further show our theory is able to model and explain morphogenesis that arises in mechanically confined growth of a wide range of systems. Specifically, it reveals the key role played by the relative timescale of volumetric growth processes (such as cell division and extracellular matrix production) to that of remodelling processes (such as cellular rearrangement and microstructural evolution) in mechanics driven morphogenesis. The key insights from our analysis could build into future work that can elucidate more complicated biological growth and morphogenesis processes such as brain lobe development and embryogenesis. Additionally, compared to generalized mixture theories, our theory is amenable to relatively easy numerical implementation with a minimal physically motivated parameter space.