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Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus layer coating the pulmonary airways is moved along and out of the lung by the activity of motile cilia, thus expelling the particles trapped in it. Here we compare ex vivo measurements of a Newtonian flow induced by cilia beating (using micro-beads as tracers) and a mathematical model of this fluid flow, presented in greater detail in a second companion article. Samples of nasal epithelial cells placed in water are recorded by high-speed video-microscopy and ciliary beat pattern is inferred. Automatic tracking of micro-beads, used as markers of the flow generated by cilia motion, enables us also to assess the velocity profile as a function of the distance above the cilia. This profile is shown to be essentially parabolic. The obtained experimental data are used to feed a 2D mathematical and numerical model of the coupling between cilia, fluid, and micro-bead motion. From the model and the experimental measurements, the shear stress exerted by the cilia is deduced. Finally, this shear stress, which can easily be measured in the clinical setting, is proposed as a new index for characterizing the efficiency of ciliary beating.

Mucociliary clearance is one of the major lines of defense of the human respiratory system. The mucus layer coating the airways is constantly moved along and out of the lung by the activity of motile cilia, expelling at the same time particles trapped in it. The efficiency of the cilia motion can experimentally be assessed by measuring the velocity of micro-beads traveling through the fluid surrounding the cilia. Here we present a mathematical model of the fluid flow and of the micro-beads motion. The coordinated movement of the ciliated edge is represented as a continuous envelope imposing a periodic moving velocity boundary condition on the surrounding fluid. Vanishing velocity and vanishing shear stress boundary conditions are applied to the fluid at a finite distance above the ciliated edge. The flow field is expanded in powers of the amplitude of the individual cilium movement. It is found that the continuous component of the horizontal velocity at the ciliated edge generates a 2D fluid velocity field with a parabolic profile in the vertical direction, in agreement with the experimental measurements. Conversely, we show than this model can be used to extract microscopic properties of the cilia motion by extrapolating the micro-bead velocity measurement at the ciliated edge. Finally, we derive from these measurements a scalar index providing a direct assessment of the cilia beating efficiency. This index can easily be measured in patients without any modification of the current clinical procedures.