Numerical study on the dynamics of primary cilium in pulsatile flows by the immersed boundary-lattice Boltzmann method

Abstract

An explicit immersed boundary-lattice Boltzmann method is applied to numerically investigate the dynamics of primary cilium in pulsatile blood flows with two-way fluid–structure interaction considered. To well characterize the effect of cilium basal body on cilium dynamics, the cilium base is modeled as a nonlinear rotational spring attached to the cilium’s basal end as proposed by Resnick (Biophys J 109:18–25, 2015. https://doi.org/10.1016/j.bpj.2015.05.031). After several careful validations, the fluid–cilium interaction system is investigated in detail at various pulsatile flow conditions that are characterized by peak Reynolds numbers ($Re_{{\rm peak}}$) and Womersley numbers ($Wo$). The periodic flapping of primary cilium observed in our simulations is very similar to the in vivo ciliary oscillation captured by O’Connor et al. (Cilia 2:8, 2013. https://doi.org/10.1186/2046-2530-2-8). The cilium’s dynamics is found to be closely related to the $Re_{{\rm peak}}$ and $Wo$. Increase the $Re_{{\rm peak}}$ or decrease the $Wo$ bring to an increase in the cilium’s flapping amplitude, tip angular speed, basal rotation, and maximum tensile stress. It is also demonstrated that by reducing the $Re_{{\rm peak}}$ or enhancing the $Wo$ to a certain level, one can shift the flapping pattern of cilium from its original two-side one to a one-side one, making the stretch only happen on one particular side. During the flapping process, the location of the maximum tensile stress is not always found at the basal region; instead, it is able to propagate from time to time within a certain distance to the base. Due to the obstruction of the primary cilium, the distribution of wall shear stress no longer remains uniform as in the absence of cilia. It oscillates in space with the minimum magnitude which is always found near where the cilium is located. The presence of cilium also reduces the overall level of wall shear stress, especially at the region near the cilium’s anchor point.