Why antiplectic metachronal cilia waves are optimal to transport bronchial mucus

The coordinated beating of epithelial cilia in human lungs is a fascinating problem from the hydrodynamics perspective. The phase lag between neighboring cilia is able to generate collective cilia motions, known as metachronal waves. Different kinds of waves can occur, antiplectic or symplectic, depending on the direction of the wave with respect to the flow direction. It is shown here, using a coupled lattice Boltzmann-immersed boundary solver, that the key mechanism responsible for their transport efficiency is a blowing-suction effect that displaces the interface between the periciliary liquid and the mucus phase. The contribution of this mechanism on the average flow generated by the cilia is compared to the contribution of the lubrication effect. The results reveal that the interface displacement is the main mechanism responsible for the better efficiency of antiplectic metachronal waves over symplectic ones to transport bronchial mucus. The conclusions drawn here can be extended to any two-layer fluid configuration having different viscosities, and put into motion by cilia-shaped or comb-plate structures, having a back-and-forth motion with phase lags.

Figure 1

Discrete velocities arrangement on a lattice cell: (a) D2Q9 lattice; (b) D3Q19 lattice.

Figure 2

Schematic view of the domain. The PCL phase is in blue and the mucus phase is in yellow. One can see the displacement of the PCL-mucus interface as a consequence of the hydrodynamic coupling between the fluid and solid motions.

Figure 3

Results obtained for $r_{\nu }=10, b/L=0.18$, and $h/L=0.91$ for (a) a synchronous wave ($\mathrm{\Delta }\mathrm{\Phi }=0$); (b) an antiplectic MCW with $\mathrm{\Delta }\mathrm{\Phi }=\pi /4$; and (c) a symplectic MCW with $\mathrm{\Delta }\mathrm{\Phi }=-\pi /4$. Vectors indicate the flow propagation, and the same scale is used in each case. In these figures, for clarity purpose, only one-third of the computational domain is shown.

Figure 4

Normalized average velocity $U^{*}=U^{\text{av}}/U_{\text{max}}^{\text{av}}$ as a function of the cilia spacing $b/L$ in the $y$-direction for different phase lags $\mathrm{\Delta }\mathrm{\Phi }$. The value of $r_{\nu }$ is set to 10, and the PCL depth to $h/L=0.91$.

Figure 5

Normalized average velocity $U^{*}=U^{\text{av}}/U_{\text{max}}^{\text{av}}$ as a function of PCL depths $h/L$ for different phase lags $\mathrm{\Delta }\mathrm{\Phi }$. The value of $r_{\nu }$ is set to 10, and $b/L$ to 0.45.

Figure 6

Normalized average velocity $U^{*}=U^{\text{av}}/U_{\text{max}}^{\text{av}}$ as a function of the ratio of viscosity $r_{\nu }$ for different phase lags $\mathrm{\Delta }\mathrm{\Phi }$. The value of $b/L$ is set to 0.45, and the PCL depth to $h/L=0.91$.

Figure 7

Normalized average velocity ${\tilde{U}}^{\text{meta}}$ as a function of the cilia spacing $b/L$ in the $y$-direction for three values of the viscosity ratio $r_{\nu }$, for antiplectic metachronal waves with $\mathrm{\Delta }\mathrm{\Phi }=\pi /4$ and $\mathrm{\Delta }\mathrm{\Phi }=\pi /12$. The solid black line represents the value of ${\tilde{U}}^{\text{lub}}$. The value of the PCL depth is set to $h/L=0.91$.