Three-Dimensional Simulations of Ciliary Flow

Abstract

In many physiological scenarios such as the respiratory epithelium, fluid propulsion is achieved through the coordinated beating of an array of organelles called cilia. However, how these cilia couple to one another hydrodynamically to achieve coordinated beating is still unclear. In this chapter, we describe a three-dimensional numerical method to show how these cilia-fluid interactions may lead to the spontaneous generation of metachronal waves, a type of traveling wave produced by the sequential movement of the cilia. Our numerical method is based on the Immersed boundary method, which we have implemented and solved by massively parallel computing methods. By exploiting such massive parallelism, we are able to systematically investigate how changes in cilia stiffness and number density affect the properties of metachronal wave propagation. We also illustrate the use of our numerical method to simulate realistic experiments, such as how the localized reversal of the cilia stroke induced by the photorelease of caged calcium ions destabilizes the metachronal wave and how it can be reestablished. We also study fluid transport along the substrate and conclude that there exists an optimum cilia number density that gives a maximum slip velocity at the plane of the cilia tips. Finally we show that passive tracers in the vicinity of the cilia can display both diffusive and advective trajectories, depending on their distance from the cilia tips.