A Viscoelastic Traction Layer Model of Muco-Ciliary Transport |
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Authors: | D J Lubkin E A Gaffney J R Blake |
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Institution: | (1) School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK |
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Abstract: | A new mathematical model of the transport of mucus and periciliary liquid (PCL) in the airways by cilia is presented. Mucus
is represented by a linearly viscoelastic fluid, the mat of cilia is modelled as an ‘active porous medium.’ The propulsive
effect of the cilia is modelled by a time-dependent force acting in a shear-thinned ‘traction layer’ between the mucus and
the PCL. The effects of surface and interface tension are modelled by constraining the mucus free surface and mucus–PCL interface
to be flat. It is assumed that the epithelium is impermeable to fluid. Using Fourier series, the system is converted into
ODEs and solved numerically. We calculate values for mean mucus speed close to those observed by Matsui et~al. {J. Clin.
Invest.}, 102(6):1125–1131, 1998], (∽40 μms-1). We obtain more detail regarding the dynamics of the flow and the nonlinear relationships between physical parameters in
healthy and diseased states than in previously published models. Pressure gradients in the PCL caused by interface and surface
tension are vital to ensuring efficient transport of mucus, and the role of the mucus–PCL interface appears to be to support
such pressure gradients, ensuring efficient transport. Mean transport of PCL is found to be very small, consistent with previous
analyses, providing insight into theories regarding the normal tonicity of PCL.
An erratum to this article can be found at |
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Keywords: | Mucus Cilia Muco-ciliary clearance Salt– fluid controversy Periciliary transport |
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