Suzanne Fielding

Modelling the rheology of biological tissue

The deformation and flow properties of biological tissue are important in processes such as embryo development, wound healing and tumour invasion. Indeed, processes such as these spontaneously generate stresses within a living tissue via active process at the single cell level. Tissues are also continually subject to external stresses and deformations from surrounding tissues and organs. The success of numerous physiological functions relies on the ability of cells to withstand stress under some conditions, yet to flow collectively under others. Biological tissue is furthermore inherently viscoelastic, with a slow time-dependent mechanics. Despite this rich phenomenology, the mechanisms that govern the transmission of stress within biological tissue, and its response to bulk deformation, remain poorly understood to date. Simplified vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape. In this talk, I shall review some recent progress in modelling the rheology of biological tissue. First, I shall discuss work predicting a strain-induced stiffening transition in a sheared tissue. Second, I shall discuss how the interplay of external deformations applied to a tissue as a whole with internal active stresses that arise locally at the cellular level, is predicted to lead to a host of fascinating rheological phenomena such as yielding, shear thinning, and continuous or discontinuous shear thickening. Third, I shall discuss the formulation of a continuum constitutive model that captures several of rich linear and nonlinear rheological phenomena noted above.