Mammalian spermatozoa motility is a subject of growing importance because of rising human infertility and the possibility of improving animal breeding. We highlight opportunities for fluid and continuum dynamics to provide novel insights concerning the mechanics of these specialized cells, especially during their remarkable journey to the egg. The biological structure of the motile sperm appendage, the flagellum, is described and placed in the context of the mechanics underlying the migration of mammalian sperm through the numerous environments of the female reproductive tract. This process demands certain specific changes to flagellar movement and motility for which further mechanical insight would be valuable, although this requires improved modeling capabilities, particularly to increase our understanding of sperm progression in vivo. We summarize current theoretical studies, highlighting the synergistic combination of imaging and theory in exploring sperm motility, and discuss the challenges for future observational and theoretical studies in understanding the underlying mechanics.

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum–fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape—no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.

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The flagellar beat is extracted from human sperm digital imaging microscopy and used to determine the flow around the cell and its trajectory, via boundary element simulation. Comparison of the predicted cell trajectory with observation demonstrates that simulation can predict fine-scale sperm dynamics at the qualitative level. The flow field is also observed to reduce to a time-dependent summation of regularized Stokes flow singularities, approximated at leading order by a blinking force triplet. Such regularized singularity decompositions may be used to upscale cell level detail into population models of human sperm motility.

The deformability of a cell is the direct result of a complex interplay between the different constituent elements at the subcellular level, coupling a wide range of mechanical responses at different length scales. Changes to the structure of these components can also alter cell phenotype, which points to the critical importance of cell mechanoresponse for diagnostic applications. The response to mechanical stress depends strongly on the forces experienced by the cell. Here, we use cell deformability in both shear-dominant and inertia-dominant microfluidic flow regimes to probe different aspects of the cell structure. In the inertial regime, we follow cellular response from (visco-)elastic through plastic deformation to cell structural failure and show a significant drop in cell viability for shear stresses >11.8 kN/m2. Comparatively, a shear-dominant regime requires lower applied stresses to achieve higher cell strains. From this regime, deformation traces as a function of time contain a rich source of information including maximal strain, elastic modulus, and cell relaxation times and thus provide a number of markers for distinguishing cell types and potential disease progression. These results emphasize the benefit of multiple parameter determination for improving detection and will ultimately lead to improved accuracy for diagnosis. We present results for leukemia cells (HL60) as a model circulatory cell as well as for a colorectal cancer cell line, SW480, derived from primary adenocarcinoma (Dukes stage B). SW480 were also treated with the actin-disrupting drug latrunculin A to test the sensitivity of flow regimes to the cytoskeleton. We show that the shear regime is more sensitive to cytoskeletal changes and that large strains in the inertial regime cannot resolve changes to the actin cytoskeleton.