Three-dimensional numerical simulations of human pulmonary cilia in the periciliary liquid layer by the immersed boundary method

The airway surface liquid of human respiratory system consists of two layers which are the innermost watery periciliary liquid layer (PCL) and the uppermost non-Newtonian mucus layer. A three-dimensional numerical model is developed to simulate the human pulmonary cilia motion in the PCL. The governing equations are solved using the immersed boundary method combined with the projection method. The cilia beating pattern is imposed as an input for the simulations. The ciliary forces on the fluid are computed by the direct forcing method. The effects of the phase difference between cilia, the cilia beating frequency, the viscosity of PCL, the PCL height, and the ciliary length on the PCL motion are investigated. The numerical results show that the maximum PCL velocity in the stream-wise direction occurs if cilia have phase differences in both stream-wise and span-wise directions. Further numerical investigations demonstrate that the PCL velocity is proportionally dependent on the cilia beat frequency while the average PCL velocity increases at a decreasing rate if the PCL height increases. Moreover, shortened cilia significantly reduce PCL velocity while the PCL velocity depends rather insignificantly if the PCL viscosity varies within the order of the typical viscosity of PCL (0.01 P).

► We model motion of pulmonary cilia and periciliary liquid layer in three-dimension.
► If cilia have phase differences in both directions the PCL velocity is maximum.
► The PCL velocity is proportionally dependent on the cilia beat frequency.
► The PCL velocity does not significantly depend on PCL viscosity of O(0.01 P).
► The shortened cilia significantly reduce PCL velocity.