Using Lagrangian methods to analyze flow structures in biological fluid dynamics

Methods from dynamical systems theory are applied to examine flow structures resulting from the interaction of actuated elastic structures with a surrounding fluid. In particular, finite-time Lyapunov exponent (FTLE) fields are employed in order to gain geometric insight to flow structures of biological relevance. Ridges of the FTLE fields correspond to Lagrangian coherent structures (LCS), which are fluid-fluid boundaries separating fluid domains into regions of qualitatively different flow. We begin by studying the flow in the periciliary region of the upper respiratory tract of the lungs generated by a motile, internally-actuated cilium. An integrative model that couples the force-generating mechanics of a cilium with the external fluid mechanics is examined. The computed LCS uncovers a fluid boundary that separates the fluid that gets advected downstream from the fluid that recirculates near the cilium, which arises from the asymmetric beat form and gives rise to complex mixing.In many biological settings, fluid that is pumped peristaltically has non- Newtonian responses. We compare well-known geometric flow structures due to peristaltic pumping of a Newtonian fluid to those in a viscoelastic fluid, both in the case of a periodic channel and in a cavity with closed ends. The presence of sidewalls introduces a return flow that must result due to volume conservation. Cellular flow patterns are observed for Newtonian and Oldroyd-B fluids.Finally, we analyze a time-periodic model of pulmonary airway reopening, modelled as a pulsatile finger of air in a fluid-occluded tube. The computed LCS uncovers flow structures which separate fluid that gets pushed downstream from fluid that flows into the upstream thin-film region. In certain flow regimes, a third region which moves along the bubble interface both upstream and downstream is observed.