Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model.

T D Montenegro-Johnson,D J Smith,H Gadêlha

doi:10.1098/rsos.140475

T D Montenegro-Johnson, D J Smith + Show 1 more

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https://doi.org/10.1098/rsos.140475

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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 large-amplitude 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°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing 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.

Highlights

Human sperm propel themselves by propagating a travelling wave along a single, active flagellum; this motility is essential2015 The Authors
We will develop a mathematical model of a cell interacting with its environment, and its computational implementation, and study the dynamics of a realistic model sperm swimming over a backstep feature to study the effect of elastic, viscous and geometric parameters
The semi-axes of the ellipsoidal head, modelled with the boundary element method, are ax = 0.05L, ay = 0.03L, az = 0.04L, which correspond to a 5 × 3 × 4 μm head for a flagellum of length L = 50 μm

Summary

Introduction

Human sperm propel themselves by propagating a travelling wave along a single, active flagellum; this motility is essential2015 The Authors. Cell scattering at simple geometric features, such as the outside of a corner, appear to be dependent on viscosity and temperature; developing mechanical models to understand, interpret and optimize these effects for their exploitation is of considerable interest. We will develop a mathematical model of a cell interacting with its environment, and its computational implementation, and study the dynamics of a realistic model sperm swimming over a backstep feature to study the effect of elastic, viscous and geometric parameters. The model will combine geometric nonlinearity of the elastic flagellum with nonlocal hydrodynamic interactions, and will be solved numerically via an implicit finite difference method for the elastohydrodynamic equations, combined with a hybrid slender body theory/boundary integral method for the low Reynolds number fluid dynamics

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