MATHEMATICAL MODELLING OF CILIA

Abstract

Cilia are small slender tails that attach to the external surface of cells of both unicellular and multicellular organisms. To understand their behavior, we need a numerical model of the coupled solid-fluid system accounting for both the internal structure of cilia and their interaction with the surrounding fluid. The purpose of this thesis is to develop such a model. After a comprehensive literature review of previous numerical models of cilia, and experimental works on dynein proteins, we propose an efficient numerical model of cilia that uses Stokeslet and rotlet singularities. We then present a novel conceptual model based on experimental findings, mechanical principles, and physiological considerations about dynein proteins. The fluid-solid interaction (FSI) model considers the main features of dynein proteins and properly applies the traction and no-slip boundary conditions. It successfully compares with published results for one cilium, and simulates metachronal waves in a patch of 50 cilia.