Constitutive model for the rheology of biological tissue

Abstract: The rheology of biological tissue is key to processes such as embryo development, wound healing and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquid-like tissue. Alongside this jamming/unjamming behaviour, biological tissue also displays an inherent viscoelasticity, with a slow time and rate dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.