Collision rates for rare cell capture in periodic obstacle arrays strongly depend on density of cell suspension.

Recently, computational modelling has been successfully used for determination of collision rates for rare cell capture in periodic obstacle arrays. The models were based on particle advection simulations where the cells were advected according to velocity field computed from two dimensional Navier-Stokes equations. This approach may be used under the assumption of very dilute cell suspensions where no mutual cell collisions occur. We use the object-in-fluid framework to demonstrate that even with low cell-to-fluid ratio, the optimal geometry of the obstacle array significantly changes. We show computational simulations for ratios of 3.5, 6.9 and 10.4% determining the optimal geometry of the periodic obstacle arrays. It was already previously demonstrated that cells in periodic obstacle arrays follow trajectories in two modes: the colliding mode and the zig-zag mode. The colliding mode maximizes the cell-obstacle collision frequency. Our simulations reveal that for dilute suspensions and for suspensions with cell-to-fluid ratio 3.5%, there is a range of column shifts for which the cells follow colliding trajectories. However we showed, that for 6.9 and 10.4%, the cells never follow colliding trajectories.