Sperm motility in modulated microchannels

Sperm cells swim through the fluid by a periodic wave-like beating of
 their flagellum. At low Reynolds numbers and in confinement, the directed motion
 of sperm and other microswimmers is strongly influenced by steric and hydrodynamic
 wall interactions. We model sperm motility in mesoscale hydrodynamics simulations
 by imposing a planar traveling bending wave along the flagellum. Sperm are simulated
 swimming in curved, straight, shallow and zigzag-shaped microchannels. Changes in
 the sidewall modulations and the imposed beat pattern allow the identification of a
 strong dependence of the surface attraction on the beat-shape envelope of the sperm
 cell. For swimming in zigzag microchannels, the deflection-angle distribution at sharp
 corners is calculated and found to be in good agreement with recent microfluidic
 experiments. The simulations reveal a strong dependence of the deflection angle
 on the orientation of the beat plane with respect to the channel sidewall, and thus
 deepen the understanding of sperm navigation under strong confinement. Detachment
 of sperm, while swimming along curved walls, is dominated by the change of beat-
 plane orientation. Therefore, either the emergence of a nonplanar component of the
 flagellar beat with increasing wavelength or the strong confinement in shallow channels
 drastically increases wall attraction. Our simulation results reveal a consistent picture
 of passive sperm guidance that is dominated by the steric interactions of the beat
 pattern with the nearby surfaces