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Cilia are elastic hairlike protuberances of the cell membrane found invarious unicellular organisms and in several tissues of most living organisms.In some tissues such as the airway tissues of the lung, the coordinated beatingof cilia induce a fluid flow of crucial importance as it allows the continuouscleaning of our bronchia, known as mucociliary clearance. While most of themodels addressing the question of collective dynamics and metachronal waveconsider homogeneous carpets of cilia, experimental observations rather showthat cilia clusters are heterogeneously distributed over the tissue surface.The purpose of this paper is to investigate the role of spatial heterogeneityon the coherent beating of cilia using a very simple one dimensional model forcilia known as the rower model. We systematically study systems consisting of afew rowers to hundreds of rowers and we investigate the conditions for theemergence of collective beating. When considering a small number of rowers, aphase drift occurs, hence a bifurcation in beating frequency is observed as thedistance between rowers clusters is changed. In the case of many rowers, adistribution of frequencies is observed. We found in particular the pattern ofthe patchy structure that shows the best robustness in collective beatingbehavior, as the density of cilia is varied over a wide range.

Role of spatial heterogeneity on the collective dynamics of cilia beating in a minimal 1D model