Computational Modeling of Deformable Cell Sorting using Sequenced Micro-Pillars

D.B. Khismatullin
Tulane University,
United States

Keywords: cell separation, cell sorting, microchannel, pillar, computational fluid dynamics

Summary:

Embedded pillar microstructures have been shown to be an efficient approach for controlling and sculpting shear flow in a microchannel[1, 2], but it is not yet demonstrated to be effective for cell sorting and, in particular, for the separation of circulating cells with different size and deformability[3, 4]. Experiments with rigid particles passing through a sequence of longitudinally spaced pillars indicate that pillars can improve lateral (perpendicular to the flow) separation of cells[4]. In order to achieve efficient cell sorting, longitudinal spacing, lateral location, and the number of pillars need to be optimized via computational fluid dynamics that account for complex microchannel geometry and cell deformability. In this study, we used our custom computational algorithm for deformable cell migration (VECAM)[5, 6] to study these effects on the lateral separation of cells with different elasticity and size in a rectangular microchannel. The geometry of the VECAM computational domain is customizable, e.g., it can be reconstructed from a microchannel image (Fig. 1). Using VECAM, we modeled a pairwise migration of viscoelastic cells (Oldroyd-B fluid) in a microchannel that has a sequence of pillars with a circular cross-section (Fig. 1b,c). Pillars were characterized by radius Rp and longitudinal (X) and lateral (Y) locations. We investigated the separation of cells with different sizes (D = 14 to 20 ┬Ám) and shear elasticity (G = 50 to 2,500 Pa) that passed through the one-, two- or three-pillar configuration. The pillar diameter-to-channel width ratio 2Rp/W ranged from 0.3 to 0.75. According to our numerical analysis, changes in pillar size, pillar-to-pillar spacing, and their lateral position had a large impact on the cell-to-cell separation distance, leading to either focusing the cells in the lateral direction or their further separation. To characterize these effects, we plotted a difference in the lateral cell-to-cell separation distance before and after the cells passed through pillars (negative value of this parameter indicates cell focusing, while positive one tells about cell separation). In the single pillar case, cell focusing primarily occurred (Fig. 2). Cell separation was observed only when the pillar diameter was small and it was located far from the centerline (Fig. 2a). On the contrary, with two pillars, cell separation was observed in most of the runs, and the cell separation distance was much higher than the separation distance achievable with no pillar or with a single pillar, especially for asymmetric placement of pillars (when the pillar-to-centerline distances were different) (Fig. 3). A further increase in the cell separation distance was seen for asymmetric placement of three pillars. Our numerical simulation also confirmed a general rule of thumb that pillars separated longitudinally by the distance equal to four times the pillar radius (4Rp) provide good conditions for cell separation for different symmetric and asymmetric 2-pillar configurations (Fig. 3). The presented computational data point out that the optimal multi-pillar configuration exists for deformability- or size-based cell separation and sorting.