  Ciliated tissues such as in the mammalian lungs, brains, and reproductive
tracts, are specialized to pump fluid. They generate flows by the collective
activity of hundreds of thousands of individual cilia that beat in a striking
metachronal wave pattern. Despite progress in analyzing cilia coordination, a
general theory that links coordination and fluid pumping in the limit of large
arrays of cilia remains lacking. Here, we conduct in-silico experiments with
thousands of hydrodynamically-interacting cilia, and we develop a continuum
theory in the limit of infinitely-many independently beating cilia by combining
tools from active matter and classical Stokes flow. We find, in both
simulations and theory, that isotropic and synchronized ciliary states are
unstable. Traveling waves emerge regardless of initial conditions, but the
characteristics of the wave and net flows depend on cilia and tissue
properties. That is, metachronal phase coordination is a stable global
attractor in large ciliary carpets, even under finite perturbations to cilia
and tissue properties. These results support the notion that functional
specificity of ciliated tissues is interlaced with the tissue architecture and
cilia beat kinematics and open up the prospect of establishing
structure-to-function maps from cilium-level beat to tissue-level coordination
and fluid pumping.
