The Mathematical Institute, University of Oxford, Eprints Archive

A viscoelastic traction layer model of mucociliary flow

Smith, D J and Gaffney, E. A. and Blake, J R and Lubkin, D J (2007) A viscoelastic traction layer model of mucociliary flow. Bulletin of Mathematical Biology, 69 (1). pp. 289-327. ISSN 0092-8240

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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.

Item Type:Article
Uncontrolled Keywords:Mucus - Cilia - Muco-ciliary clearance - Salt–fluid controversy - Periciliary transport
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:881
Deposited By:Eamonn Gaffney
Deposited On:14 Jan 2010 07:54
Last Modified:13 Mar 2011 22:07

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