Transition from Directional Fluid Pumping to Disordered Flows in Heterogeneous Ciliary Carpets

Cilia are essential for transporting fluids across epithelial surfaces, serving a critical function in human respiratory, reproductive, and cerebrospinal health. Variations in ciliary length, beat frequency, and density can significantly affect fluid transport and synchronization. However, it remains unclear which of these variations maintain healthy function and which indicate diseased conditions. In this study, we develop a mathematical model of ciliated tissues represented as a 2D lattice of force monopoles in a 3D viscous fluid. Using the Blake-Oseen solution, we construct the flow field induced by this lattice and examine its effects on the coordination of the force monopoles. Particularly, we study how heterogeneities in ciliary properties that mimic those observed in biological tissues affect coordination and fluid transport. Our simulations reveal that non-uniform ciliary distributions could lead to significant changes in fluid transport and synchronization patterns and disruption of the coordinated wave-like motion of cilia. These findings provide systematic and quantitative maps from structure to function in ciliated tissues.