Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model

TL;DR

This study develops a numerical elastohydrodynamic model to analyze how sperm cells scatter when interacting with microchannel features, revealing the influence of viscosity and elastic forces on their trajectories.

Contribution

It introduces a new numerical method for modeling elastohydrodynamic interactions of active swimmers with microchannel features, specifically applied to sperm scattering.

Findings

Scattering depends on backstep height and force balance.

In high viscosity regimes, scattering angles are 5-10 degrees.

Viscosity modulates flagellar asymmetry and scattering direction.

Abstract

Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments, and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for the geometrically nonlinear elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a 'high viscosity' parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5-10 degrees. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasising the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.