Nonlinear mechanics of biological tissues and their tumors

The function and shape of biological tissues are tightly related. Indeed, one of the main indicators of disease, e.g., cancer is a disruption of normal tissue architecture. However, understanding the function-shape relation is extremely challenging due to the complexity of the material and thus requires combined efforts from biologists, experimental biophysicists, and theoretical biophysicists. The proposed project aims towards developing and studying advanced computational models of biological tissues to understand their viscoelastic properties, the formation of complex shapes, and mechanical triggers of disruptions from the normal tissue architecture, common for disease. In particular the project will address three related topics: (i) Nonlinear elasticity of epithelial wrinkling, (ii) Tumor growth, and (iii) Structure and rheology of three-dimensional cell aggregates. In part (I), we will be interested in the formation of wrinkled patterns in tissues at the surfaces of organs. In particular, we will use a combination of a discrete vertex model of epithelial cross section and an effective nonlinear elasticity theory to understand the conditions for wrinkling and the variety of possible shapes. We will particularly focus on understanding the nonlinear effects that establish the characteristic wavelength of these periodic patterns. Studying how these patterns depend on the mechanical properties of individual cells as well as on the mechanical properties of supporting structures, e.g., the basement membrane and the substrate, will be important for understanding in what way biological tissues differ from “usual” nonliving materials. In part (ii), we will address the mechanics of tumor growth both in epithelial monolayers as well as in multilayered epithelia. In particular, we will develop a discrete vertex model of epithelial tissues with a rapidly growing mass of mutated cells. We will focus on how the mechanical properties of the basement membrane and stroma, which support the cancerous epithelium, affect tumor growth and the subsequent tissues-scale deformations. Our results will improve the understanding of the role of mechanics in the formation and growth of tumors, which may be important for improving methods of prognosis and treatment. Finally, in part (iii), we will study the structure and rheology of three-dimensional cell aggregates. In particular, by combining a relatively simple statistical-mechanical approach, based on the Markov chain, and more detailed cell-based computational approaches, we will try to understand how rapid cell division in tumor spheroids determines the structure of the cell packing, under what conditions these cell masses behave like solids and under what conditions like fluids, and how different cell-scale active processes affect their rheological properties. Our results will also represent an important step forward in terms of methodology. Indeed, due to technical complexity of structure of these active materials, no computational tools exist that would comprehensively address the active mechanics of three-dimensional cell aggregates at the interface between the scale of individual cells and the whole-tissue scale. Our tools will certainly fill part of this void. Overall, the proposed project is expected to yield interesting results that will represent an important contribution to the field. More importantly, our novel approaches are going to open new avenues for the future research and offer improved computational methods for studying nonlinear mechanics of biological tissues and their tumors.