Modelling the fluid-structure interaction in flow sensing and cell adhesion

Abstract

The first part of this study concerns the modelling of the flow sensing of primary cilia via their passive deflection in an oscillating viscous flow. A two-way fluid-cilia interaction is considered in the modelling using an immersed boundary-lattice Boltzmann method (IB-LBM). Typically, the primary cilium is modelled as a slender filament with its basal end connecting to a nonlinear rotational spring to reproduce the experimentally observed basal rotation. The developed algorithm and code are first validated against some benchmark problems, and then applied to study the dynamics of a three-dimensional cilia array in an oscillating Newtonian flow. The simulation result indicates that the primary cilia do an in-plane flapping motion which is symmetrical in term of the cilium profiles. During the deflection, the flow-induced curvature at the lower part of the primary cilium synchronizes well with the applied pressure gradient signal, while an obvious phase lag in the curvature can be found for the rest parts of the cilium. Therefore, the lower part of primary cilia may be most responsible for detecting the variations of the flow information as it can provide real-time response. The simulation result also suggests that the location of the maximal tensile stress (MTS) may not always stay at the cilium's base region, instead is able to propagate from the cilium's base point to its tip for a certain distance. The presence of primary cilia is found to reduce the average wall shear stress (WSS) level and affect the oscillation characteristic of the WSS field by making the WSS in some regions less oscillatory. A follow-up parametric study which covers the peak Reynolds number (Repeak), the Womersley number (Wo), the cilium length, and the spacing interval, is also performed to investigate how these parameters affect the flow-cilia interaction. By examining the variations of curvature direction in the cilium profile, our simulations capture three typical stretch states. For primary cilia with short and medium length, an increase in the maximal tip deflection is accompanied with a greater propagation distance of the MTS location. While this may not be true for long primary cilia that extend into 1/3 of the lumen, as the possible emergence of the third stretch state could greatly suppress such propagation. Under the same flow condition, the decrease in the average WSS is found to be more significant when a cilium undergoes a larger span of deflection and/or when the spacing interval is reduced. Compared with the spacing interval, the span of deflection plays a marginal role in decreasing WSS. For the parameter ranges considered, an increase in the Repeak or cilium length is found to bring a larger cilium deflection and maximal curvature. An increase in the Wo, however, is found to decrease these two quantities. For a constant spacing interval, a larger span of deflection is found to correspond to a more uneven OSI distribution. The interacting between neighboring cilia becomes weaker as the spacing interval increases. A sparser cilia array therefore tends to have a larger deflection, maximal curvature, and propagation distance of the MTS location. For a medium Repeak and Wo, a spacing interval greater than twice the cilium length is found to effectively reduce the interference from the neighboring cilia thus improves the cilium's sensing accuracy. This could be the reason why there is only one primary cilium at most for each endothelial or epithelial cell whose diameter happens to be about 2-3 times the length of primary cilium. The power-law model is also integrated into our IB-LBM framework to study cilium dynamics in oscillating no-Newtonian fluids. The simulation result suggests that a sensory failure may occur when n=1.5, as the primary cilia could no longer capture the symmetry of the input pressure signal via their passive deflection. No significant difference in the flow structure is observable for different n values. However, as n increases, a larger affected area with smaller OSI value can be observed in the OSI distribution. Compared with the Newtonian fluid case, the decrease in the average WSS is more dramatic for a shear-thinning fluid while less obvious for shear-thickening fluid. Therefore, modelling a shear-thinning fluid as Newtonian underestimates the cilium's impact on the WSS while modelling a shear-thickening fluid as Newtonian tends to overestimate such impact. The second part of the thesis focus on the simulation of circulating tumor cell (CTC) adhesion in a three-dimensional curved microvessel. A comparative study is first performed to characterize the differences between the adhesion of CTC in straight and curved vessels. After that, a parametric study is performed to investigate the effect of the flow driven force density f (or Re) and membrane bending modulus Kb on CTC adhesion. Our simulation results suggest that the CTC is more likely to adhere to the curved vessel as more bonds will form around the curvature transition regions due to centrifugal effect which increases cell-wall contact. The parametric study indicates that an increase in the f or a decrease in the Kb (e.g., the cell becomes softer), increases the bond formation probability and cell-wall contact sites in the curved vessel. Increasing the f brings a larger centrifugal force while decreasing the Kb enables a more complete cell-wall contact by increasing the contact area, both of which promotes bond formation. In the curved-vessel case, the site where bonds are formed the most (hotspot) is found to vary with the applied f and the Kb. For the vessel geometry considered, the hotspot tends to be within the first bend of the vessel when the applied f is relatively low; however, the hotspot is found to shift to the second bend of the vessel as f increases or Kb decreases.