Muco-ciliary clearance: A review of modelling techniques

The airways of the human respiratory system are covered by a protective layer, which is known as airway surface liquid (ASL). This layer consists of two relatively distinct sub-layers; a mucus layer (ML), and a periciliary liquid layer (PCL). In addition, the airways are lined with a dense mat of hair-like structures, called cilia, which beat back and forth in a co-ordinated manner and mainly propel the mucus layer. Such interaction between the cilia and mucus is called 'muco-ciliary clearance' (MCC) which is essential to clear the respiratory airways from the inhaled toxic particles deposited on the mucus. The complex nature of lung clearance mechanisms limit the ability to conduct experiments to investigate micro-scale physiological phenomena. As such, modelling techniques are commonly implemented to investigate the effects of biological parameters on the lung muco-ciliary clearance. In the present work, modelling techniques of cilia-ASL interactions - including continuum cilia modelling and discrete cilia modelling - are reviewed and the numerical procedures and level of complexity related to each technique are explained. This is followed by a detailed analysis of the airway surface liquid modelling approaches. In addition, findings of numerical investigations related to the effects of various parameters such as ciliary beat frequency (CBF), mucus rheology, metachronal waves of cilia, surface tension at the PCL-mucus interface, ciliary length, ciliary density, and airway surface liquid depth on the bronchial and tracheal ASL transport are reviewed. This review also explains how these biological parameters can alter the internal power required to perform ciliary beating. Lastly, the main limitations of current numerical works are discussed and significant research directions are brought forward that may be considered in future models to better understand this complex human biological system and its vital clearance mechanism.