Viscoelastic model of tissue mechanics in 3D with active surfaces

Epithelia are biological tissues made up of a large number of cells arranged as a connected monolayer. They are one of the most critical and often-studied structures in animal bodies; yet their mechanics are still not well-understood. In particular, until recently, epithelia had frequently been modeled as a two-dimensional, planar system. However, recent microscopic technologies have begun to reveal dynamics in the third dimension of the tissue. With these dynamics in mind, we have developed a self-sculpting, three-dimensional model of epithelia whose dynamics are driven by active forces on its surface. The model describes mechanical properties such as viscoelasticity, as well as active forcing, biologically relevant tissue geometry, and fluid surroundings. We represent epithelia in a continuum framework as a Stokes fluid with extra viscoelastic stress. We present analytical and numerical solutions of the system, including its response to various forms of driving. Employing this model, we can make quantitative predictions about cell shapes and cell dynamics in a three-dimensional setting, allowing for physics-based studies of animal morphogenesis and development of body plans.