  A continuum description is built to characterize the stationary and transient
deformations of confluent tissues subject to heterogeneous activities. By
defining a coarse-grained texture matrix field to represent the shape and size
of cells, we derive the coarse-grained stress tensor for the vertex model.
Activity in the tissue takes the form of inhomogeneous apical contractions,
which can be modeled as reductions of the vertex model reference areas or
perimeters representing activity in the medial and perimeter regions of the
cells, respectively. For medial activity, the extra stress is just an isotropic
pressure, while for perimeter activity, it also has a deviatoric component,
which is aligned with the texture matrix. The predictions of the continuum
description are compared with the average spatiotemporal deformations obtained
in simulations of the vertex model subject to localized apical contractions,
showing an excellent agreement, even if the active patch is as small as one
cell. The fluctuations around the average are more prominent when the activity
is in the medial region due to the lack of negative active shape feedback,
which, coupled with the confluent property, increases cellular shape and size
variations.

Biological Physics