Beating in Fluid: Cilia and Biological Structures

Cilia, active hair-like appendages in biological cells serve many different functions. Cilia are present in lungs, intestines, and the inner ear where they serve specific functions by moving fluid. 

Hundreds of dynein molecular motors drive the beating of a single cilium, producing wavelike bending.

Mathematical models can be used to study coordination of the dynein motors, by using a simple dynamical law that governs the tension of each dynein motor, along with a geometrical constraint based on the microstructure of the cilium.

The Immersed Boundary method, first proposed by Charles Peskin, facilitates the study of a cilium’s fluid-mediated interaction by immersing the model cilia in fluid. 

The model demonstrates how the beat emerges spontaneously and shows how cilia interacts with fluid. Studies show remarkable tendency towards synchronization of nearby cilia regardless of initial conditions.

More about Beating in Fluid:

Beating in Fluid: Mathematical Anatomy of the Heart

Beating in Fluid: Hearts and Cilia by the Immersed Boundary Method