Hollow vesicular tissues of various sizes and shapes arise in
biological organs such as ears, guts, hearts, brains and even entire
organisms. Regulating their size and shape is crucial for their
function. Although chemical signaling has been thought to play a role
in the regulation of cellular processes that feed into larger scales, it is
increasingly recognized that mechanical forces are involved in the
modulation of size and shape at larger length scales. Motivated by a
variety of examples of tissue cyst formation and size control that show
simultaneous growth and size oscillations, we create a minimal
theoretical framework for the growth and dynamics of a soft, fluidpermeable, spherical shell. We show that these shells can relieve
internal pressure by bursting intermittently, shrinking and re-growing,
providing a simple mechanism by which hydraulically gated
oscillations can regulate size. To test our theory, we develop an in
vitro experimental set-up to monitor the growth and oscillations of a
hollow tissue spheroid growing freely or when confined. A simple
generalization of our theory to account for irreversible deformations
allows us to explain the time scales and the amplitudes of oscillations in
terms of the geometry and mechanical properties of the tissue shells.
Taken together, our theory and experimental observations show how
soft hydraulics can regulate the size of growing tissue shells.