Abstract
Organs that pump fluids by the coordinated beat of motile cilia through the lumen are integral to animal physiology. Such organs include the human airways, brain ventricles, and reproductive tracts. Although cilia organization and duct morphology vary drastically in the animal kingdom, ducts are typically classified as either carpet or flame designs. The reason behind this dichotomy and how duct design relates to fluid pumping remain unclear. Here, we demonstrate that two structural parameters -- lumen diameter and cilia-to-lumen ratio -- organize the observed duct diversity into a continuous spectrum that connects carpets to flames across all animal phyla. Using a unified fluid model, we show that carpet and flame designs maximize flow rate and pressure generation, respectively. We propose that convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance, along with universal design rules for ciliary pumps.