Hybrid computational approaches for flagellar waveform development in complex fluids with application to human sperm propulsion

Neal, Cara Victoria ORCID: 0000-0002-5940-4101 (2022). Hybrid computational approaches for flagellar waveform development in complex fluids with application to human sperm propulsion. University of Birmingham. Ph.D.

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The journey of the human spermatozoa to the ovum is a complex and essential process, fraught with challenges that successful fertilisers must overcome. Sperm cells must traverse the intricate geometry of the female reproductive tract, generating active bending to progress through cervical mucus – a polymer suspension exhibiting complex, non-Newtonian properties. In general, only a dozen cells will reach the egg, with the situation even worse for the one in six couples worldwide with fertility issues. Thus, it is becoming increasingly important to study how human sperm swim and what can influence this process.

We examine how mathematical modelling can provide insight into how two aspects of this complex fluid-structure problem can impact the propulsion of human sperm. Firstly, we explore the effect of the sperm flagellar end piece – a region of depleted axoneme structure occupying the most-distal few microns of the human sperm flagellum. Lacking the organised “9+2” axoneme structure predominant in the rest of the flagellum, the end piece is unlikely to have the ability to generate active bending. Through elastohydrodynamic modelling, we demonstrate that the end piece gives rise to increased swimming speed and efficiency compared to cells with a fully active flagellum. The beneficial effect of the end piece on these statistics can be as large as 430%, with the optimal inactive length being between 2–18% of the total length, and depending on both wavenumber and viscous-elastic ratio.

Out of the non-Newtonian properties exhibited by cervical mucus, shear-thinning rheology, in which fluid viscosity decreases with increased shear rates, has been comparatively under-explored. Thus, we develop a hybrid computational approach for solving the non-linear equations associated with modelling human sperm in three-dimensional shear-thinning fluids. This approach utilises known Newtonian solution techniques to approximate the rapidly varying flow surrounding a swimmer, with a non-Newtonian correction term obtained through solving using the finite element method over a coarse mesh. Combined with a model of swimmer elasticity, we present a first study on the effects of shear-thinning rheology on the propulsion of human sperm with flexible elastic flagella. We uncover that shear-thinning rheology tends to hinder cell progress, although propulsion can also be enhanced, depending on a balance of fluid and swimmer properties. We suggest that the mechanism by which propulsion of sperm cells is hindered in a shear-thinning fluid is via shape changes due to fluid-flagellum interactions, resulting in the development of sub-optimal waveforms for progression.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Smith, DavidUNSPECIFIEDorcid.org/0000-0002-3427-0936
Gallagher, MeurigUNSPECIFIEDorcid.org/0000-0002-6512-4472
Licence: All rights reserved
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/12606


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