Hydrodynamic Clustering of Human Sperm in Viscoelastic Fluids

Abstract

We have numerically investigated sperm clustering behaviours, modelling cells as superpositions of regularised flow singularities, coarse-grained from experimentally obtained digital microscopy of human sperm, both in watery medium and a highly viscous–weakly elastic, methylcellulose medium. We find that the cell yaw and cell pulling dynamics inhibit clustering in low viscosity media. In contrast clustering is readily visible in simulations modelling sperm within a methylcellulose medium, in line with previous observations that bovine sperm clustering is much more prominent in a rheological polyacrylamide medium. Furthermore, the fine-scale details of sperm flagellar movement substantially impact large-scale collective behaviours, further motivating the need for the digital microscopy and characterization of sperm to understand their dynamics.

Pairwise hydrodynamic interactions of synchronized spermatozoa

“…Having simulated the behaviors of nearby swimmers using a high-accuracy boundary element method, we explored the qualitative accuracy of a simplified, coarse-grained approach for multi-swimmer simulation, as implemented by Ishimoto and Gaffney [41]. We seen that this simplified approach is sufficient to capture qualitative features of sideby-side swimming, supporting its use in such circumstances.…”

“…We will aim to evaluate the accuracy of a recent regularized singularity representation [40,53,54], as used by Ishimoto and Gaffney [41] to simulate population-level behaviors of spermatozoa confined to a plane, in particular considering its natural extension to motion in three spatial dimensions. Here we briefly recapitulate the key principles of the methodology, and direct the reader to the original publications [40,41,53,54] for further details.…”

“…7. Simulating pairwise swimmer motion as in Ishimoto and Gaffney [41], we proceed to evaluate the accuracy of using such singularity representations for the simulation of swimmer interaction by repeating the analysis of Sections III A, III B and III D using this approximate framework.…”

“…The pairwise interactions between such simple model swimmers results in hydrodynamic attraction irrespective of the configuration of the swimmers, owing to the symmetry of the flow field representation, though this may not be realistic due to the noted dependence of swimming on cell morphology [39]. Recently a theoretical coarse-grained approach for the simulation of swimmer populations was suggested by Ishimoto et al [40], and later implemented by Ishimoto and Gaffney [41], seeking to refine the most-basic singularity representation of a spermatozoon. This methodology aims to approximate the flow field induced by a lone swimmer by a small number of regularized singularities [42] with time-varying coefficients for use in large-scale simulations, seeking to improve upon simple far-field singularity representations.…”

Computer-assisted beat-pattern analysis and the flagellar waveforms of bovine spermatozoa

“…Finally, a further objective will be to utilise the captured waveform data in the generation of evidence-based synthetic flagellar waveforms by a simple sampling method. In doing so we will provide a methodology for the construction of arbitrary numbers of evidence-based synthetic flagellar waveforms for use in biophysical population modelling, with current modelling frameworks accommodating hundreds [24] and even up to one thousand [25] virtual spermatozoa. In turn, this will enable future studies to assess the physical consequences of evidence-based population variability in explorations of flagellated swimmer active matter.…”