# American Institute of Mathematical Sciences

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2015, 12(5): 1107-1126. doi: 10.3934/mbe.2015.12.1107

## Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study

 1 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, United States 2 Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, United States

Received  January 2015 Revised  March 2015 Published  June 2015

Mucociliary clearance is the first line of defense in our airway. The purpose of this study is to identify and study key factors in the cilia motion that influence the transport ability of the mucociliary system. Using a rod-propel-fluid model, we examine the effects of cilia density, beating frequency, metachronal wavelength, and the extending height of the beating cilia. We first verify that asymmetry in the cilia motion is key to developing transport in the mucus flow. Next, two types of asymmetries between the effective and recovery strokes of the cilia motion are considered, the cilium beating velocity difference and the cilium height difference. We show that the cilium height difference is more efficient in driving the transport, and the more bend the cilium during the recovery stroke is, the more effective the transport would be. It is found that the transport capacity of the mucociliary system increases with cilia density and cilia beating frequency, but saturates above by a threshold value in both density and frequency. The metachronal wave that results from the phase lag among cilia does not contribute much to the mucus transport, which is consistent with the experimental observation of Sleigh (1989). We also test the effect of mucus viscosity, whose value is found to be inversely proportional to the transport ability. While multiple parts have to interplay and coordinate to allow for most effective mucociliary clearance, our findings from a simple model move us closer to understanding the effects of the cilia motion on the efficiency of this clearance system.
Citation: Ling Xu, Yi Jiang. Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1107-1126. doi: 10.3934/mbe.2015.12.1107
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