  Cilia are elastic hairlike protuberances of the cell membrane found in
various unicellular organisms and in several tissues of most living organisms.
In some tissues such as the airway tissues of the lung, the coordinated beating
of cilia induce a fluid flow of crucial importance as it allows the continuous
cleaning of our bronchia, known as mucociliary clearance. While most of the
models addressing the question of collective dynamics and metachronal wave
consider homogeneous carpets of cilia, experimental observations rather show
that cilia clusters are heterogeneously distributed over the tissue surface.
The purpose of this paper is to investigate the role of spatial heterogeneity
on the coherent beating of cilia using a very simple one dimensional model for
cilia known as the rower model. We systematically study systems consisting of a
few rowers to hundreds of rowers and we investigate the conditions for the
emergence of collective beating. When considering a small number of rowers, a
phase drift occurs, hence a bifurcation in beating frequency is observed as the
distance between rowers clusters is changed. In the case of many rowers, a
distribution of frequencies is observed. We found in particular the pattern of
the patchy structure that shows the best robustness in collective beating
behavior, as the density of cilia is varied over a wide range.
