  Growing tissues are highly dynamic, flowing on sufficiently long time-scales
due to cell proliferation, migration and tissue remodeling. As a consequence,
living tissues can be approximated as liquids. This means the shape of
microtissues is governed by a surface stress state as in fluid droplets. Recent
work showed that cells in the near-surface region of fibroblastic or
osteoblastic microtissues contract with highly oriented actin filaments, thus
making the surface stress state anisotropic, in contrast to what is expected
for an isotropic fluid. Here, we extend the Young-Laplace law to include
mechanical anisotropy of the surface. We then take this into account to
determine equilibrium shapes of rotationally symmetric bodies subjected to
anisotropic surface stress states and derive a family of surfaces of revolution
in analogy to the Delaunay surfaces. A comparison with recently published
shapes of microtissues shows that this theory accurately predicts both the
surface shape and the direction of the actin filaments in the surface. The
anisotropic version of the Young-Laplace law might help describing the growth
of microtissues and also predicts the shape of fluid bodies with highly
anisotropic surface properties.
