Modelling muco-ciliary transport in the lung
This thesis is concerned with modelling the liquid lining of the airways, which is transported towards the pharynx by beating cilia. It is not understood whether the ciliated epithelium normally absorbs water. Surface area decreases moving up the bronchial tree but the depth of the periciliary liquid (PCL) remains constant, hence if there is significant flux of PCL up the bronchi, there must be absorption by the epithelium. Theoretical analyses of cilia have previously concluded that flux of PCL is small, however experiments appear to show significant transport of PCL. In chapter 1 we review the biology of the muco-ciliary system, previous modelling and the conflict between theory and experiment. In chapter 2 we present a ‘traction layer’ model of the fluid flow, assuming no absorption by the epithelium, which provides insight into the mechanisms by which efficient mucus transport does or does not occur. Pressure gradients caused by surface and interface tension are crucial to maintaining efficient transport. From justified parameter values we predict mucus transport rates of 40 microns/second, close to that observed in cultures, and very small mean PCL transport. In chapter 3 we discuss the problem of modelling the cilia as discrete objects. We consider the PCL as a fluid bounded by two parallel plates, the epithelium and the mucus interface. We extend models of cilia in a confined domain using a Stokeslet and dipole distribution in the near-field and an averaged Stokeslet distribution in the far-field, so that a numerical solution can be found efficiently. We calculate solutions that are accurate in both the near and far-fields. There is significant positive transport of PCL during the recovery stroke, indicating how the traction layer model may be improved. In chapter 4 we model tracer dispersion experiments with a two dimensional advection-diffusion model which is solved numerically. Steady and oscillatory profiles from chapter 2, together with other suggested profiles are used for the advective flux. It is found that a plane Couette flow in the PCL is sufficient to reproduce experimental results, and that the profiles of chapter 2 produce results remarkably close to experiment, however further work is needed to clarify the problem fully.