UC Santa Barbara

Understanding the mechanics and flow of biological tissues invites a rethinking of how to formulate faithful tissue scale continuum theories based on cell scale structure. A common approach in modeling biological material is to utilize or modify theories originally developed to describe passive solids or fluids. Many textbooks and theoretical studies, for instance, on the solid mechanics of tissues, such as muscle fibers, skin, or organs, are typically based on elastic models of rubber or fiber-reinforced composites. For flowing biological material, such as blood or metastasized cancer cells, a non-Newtonian fluid model is often utilized. While partly successful, these approaches do not consider that biological tissues are composed of flexible cells which may support self-tension and modify their own shape and are more akin to deformable droplets or foams than a conventional solid or fluid. Unlike a passive material with a preset structure, a biological tissue may adapt its mechanical properties at both the tissue and cell scale and presents a more challenging system to model. The research contained in this thesis addresses two questions. Firstly, how the solid-fluid transition of epithelial tissues can be understood as a consequence of geometric frustration where cells cannot achieve target shape to relax tension and thereby behave rigidly, and how cells may utilize this to fine tune tissue mechanical properties. And secondly, how to develop a hydrodynamic description which distinguishes between shape elongation, which signals the solid-fluid transition, and possible local nematic alignment.