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

Abstract

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.

Regional Differences in Mucociliary Clearance in the Upper and Lower Airways

“…There are numerous reports in the literature documenting that the murine trachea is very sparsely ciliated [30–37% ( Pack et al, 1980 ; Klein et al, 2009 ; Kiyota et al, 2014 )] and that ciliated cells in the trachea are found in scattered patches ( Pack et al, 1980 ). In fact, Pack et al (1980) commented that in the murine trachea the ciliated cells “were so far apart that is difficult to envisage how such a mucous sheet would be propelled.” As it has been previously shown that there is a positive correlation between cilial density and the rate of MCC ( Smith et al, 2008 ; Xu and Jiang, 2015 ; Chatelin and Poncet, 2016 ; Leung et al, 2019 ), it is likely that the difference in the rate of MCC between the PNP and trachea is in large part a result of significantly more abundant ciliated cells in the PNP. Additionally, this likely explains the circuitous route (non-linear) that beads/mucus follows during MCC in the trachea, compared to the linear paths observed in the PNP.…”

“…Although mucociliary clearance (MCC) plays a critical role in maintaining health throughout the respiratory system, one might expect a more robust MCC in the nasal cavity compared to that of the lower airways. An enhanced MCC could be accomplished in several ways: (1) an increase in density of ciliated cells, (2) an elevated rate of ciliary beat frequency, both of which have been shown to increase the rate of MCC ( Smith et al, 2008 ; Sears et al, 2015 ; Xu and Jiang, 2015 ; Chatelin and Poncet, 2016 ; Leung et al, 2019 ), and (3) an “optimized” mucus layer (e.g., more favorable composition or concentration of mucins) that is more efficient at trapping deleterious inhaled substances and/or is more effectively cleared by the cilia.…”

Mathematical Modeling of Mucociliary Clearance: A Mini-Review

“…As a frame of reference, the typical Re value for a swimming bacterium (e.g., E. coli in water) is in the order of 10−4, the smallest fish is about 1, a human swimmer is 104, and a blue whale is 4×108. The value of Re in the mammalian respiratory tract is around 0.01 [34], suggesting a dominating viscous force in the mucociliary system. Mathematically, the Navier–Stokes equations [74] make up the standard model that governs the fluid flow dynamics.…”

“…Xu and Jiang [34] aimed to identify key factors in the cilia motion that influence the ability of fluid transport in mucociliary clearance. In their simulations, the rod-propel-fluid model (Figure 6c) treated cilia as stiff rods that followed prescribed motions.…”

“…( a ) The cilium modeled as a finite element beam and the nearby body-fitted grid, from Mitran [85] with permission; ( b ) the cilium modeled as an elastic spring network, from Yang, Dillon and Fauci [87] with permission; ( c ) streamlines in the fluid flow induced by five cilia (rods) at a sequence of times, from Xu and Jiang [34] with permission; ( d ) snapshot of an large array of beating cilia, from Elgeti and Gompper [88] with permission.…”