Hostname: page-component-6dbcb7884d-wnk8j Total loading time: 0 Render date: 2025-02-14T06:58:15.553Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic propulsion of human sperm

Published online by Cambridge University Press:  14 April 2009

ERIC A. GILLIES ,
RICHARD M. CANNON ,
RICHARD B. GREEN  and
ALLAN A. PACEY
ERIC A. GILLIES
Affiliation:
Department of Aerospace Engineering, University of Glasgow, Glasgow G12 8QQ, UK
RICHARD M. CANNON
Affiliation:
Department of Aerospace Engineering, University of Glasgow, Glasgow G12 8QQ, UK
RICHARD B. GREEN
Affiliation:
Department of Aerospace Engineering, University of Glasgow, Glasgow G12 8QQ, UK
ALLAN A. PACEY*
Affiliation:
Academic Unit of Reproductive and Developmental Medicine, School of Medicine and Biomedical Sciences, University of Sheffield, Sheffield S10 2SF, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The detailed fluid mechanics of sperm propulsion are fundamental to our understanding of reproduction. In this paper, we aim to model a human sperm swimming in a microscope slide chamber. We model the sperm itself by a distribution of regularized stokeslets over an ellipsoidal sperm head and along an infinitesimally thin flagellum. The slide chamber walls are modelled as parallel plates, also discretized by a distribution of regularized stokeslets. The sperm flagellar motion, used in our model, is obtained by digital microscopy of human sperm swimming in slide chambers. We compare the results of our simulation with previous numerical studies of flagellar propulsion, and compare our computations of sperm kinematics with those of the actual sperm measured by digital microscopy. We find that there is an excellent quantitative match of transverse and angular velocities between our simulations and experimental measurements of sperm. We also find a good qualitative match of longitudinal velocities and computed tracks with those measured in our experiment. Our computations of average sperm power consumption fall within the range obtained by other authors. We use the hydrodynamic model, and a prototype flagellar motion derived from experiment, as a predictive tool, and investigate how sperm kinematics are affected by changes to head morphology, as human sperm have large variability in head size and shape. Results are shown which indicate the increase in predicted straight-line velocity of the sperm as the head width is reduced and the increase in lateral movement as the head length is reduced. Predicted power consumption, however, shows a minimum close to the normal head aspect ratio.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 445 - 474
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ainley, J., Durkin, S., Embid, R., Boindala, P. & Cortez, R. 2008 The method of images for regularized stokeslets. J. Comput. Phys. 227, 4600–4616.CrossRefGoogle Scholar
Aitken, R. J., Sutton, M., Warner, P. & Richardson, D. W. 1985 Relationship between the movement characteristics of human spermatozoa and their ability to penetrate cervical mucus and zona free hamster oocytes. J. Reprod. Fertil. 73, 441–449.CrossRefGoogle ScholarPubMed
Birkhead, T. 2000 Promiscuity: An Evolutionary History of Sperm Competition and Sexual Conflict. Faber & Faber.Google Scholar
Blake, J. R. 1971 Infinite models for ciliary propulsion. J. Fluid Mech. 49, 209–222.CrossRefGoogle Scholar
Blake, J. R. & Chwang, A. T. 1974 Fundamental singularities of viscous flow. Part 1. The image system in the vicinity of a stationary no-slip boundary. J. Engng Math. 8, 23–29.CrossRefGoogle Scholar
Brennen, C. & Winet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.CrossRefGoogle Scholar
Brenner, H. 1962 The effects of finite boundaries on the stokes resistance of an arbitrary particle. J. Fluid Mech. 12, 35–48.CrossRefGoogle Scholar
Brokaw, C. J. 1970 Bending moments in free-swimming flagella. J. Exp. Biol. 43, 155–169.CrossRefGoogle Scholar
Cisneros, L. H., Cortez, R., Dombrowski, C., Goldstein, R. E. & Kessler, J. O. 2007 Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations. Exper. Fluids 43, 737–753.CrossRefGoogle Scholar
Cortez, R. 2001 The method of regularized stokeslets. SIAM J. Sci. Comput. 23 (4), 1204–1225.CrossRefGoogle Scholar
Cortez, R., Fauci, L. & Medovikov, A. 2005 The method of regularized stokeslets in three dimensions: analysis, validation, and application to helical swimming. Phys. Fluids 17.CrossRefGoogle Scholar
Dresdner, R. D. & Katz, D. F. 1981 Relationships of mammalian sperm motility and morphology to hydrodynamic aspects of cell function. Biol. Reprod. 25, 920–930.CrossRefGoogle ScholarPubMed
Dresdner, R. D., Katz, D. F. & Berger, S. A. 1980 The propulsion by large amplitude waves of uniflagellar micro-organisms of finite length. J. Fluid Mech. 97, 591–621.CrossRefGoogle Scholar
Fauci, L. J. & Dillon, R. 2006 Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech. 38, 371–394.CrossRefGoogle Scholar
Fulford, G. R. & Blake, J. R. 1983 On the motion of a slender body near an interface between two immiscible fluids at low Reynolds numbers. J. Fluid Mech. 127, 203–217.CrossRefGoogle Scholar
Gomendio, M., Malo, A. F., Garde, J. & Roldan, E. R. S. 2007 Sperm traits and male fertility in natural populations. Reproduction 134, 19–29.CrossRefGoogle ScholarPubMed
Gray, J. & Hancock, G. J. 1955 The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32, 82–814.Google Scholar
Gueron, S. & Liron, N. 1992 Ciliary motion modelling, and dynamic multicilia interactions. Biophysical J. 63, 1045–1058.CrossRefGoogle ScholarPubMed
Hancock, G. J. 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. Lond. A 217, 96–121.Google Scholar
Happel, J. & Brenner, H. 1981 Low Reynolds Number Hydrodynamics, 2nd ed. Springer.Google Scholar
Higdon, J. J. L. 1979 A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685–711.CrossRefGoogle Scholar
Ishikawa, T., Sekiya, G., Imai, Y. & Yamaguchi, T. 2007 Hydrodynamic interactions between two swimming bacteria. Biophys. J. 93, 2217–2225.CrossRefGoogle ScholarPubMed
Johnson, R. E. & Brokaw, C. J. 1979 Flagellar hydrodynamics: a comparison between resistive-force theory and slender-body theory. Biophys. J. 25, 113–127.CrossRefGoogle ScholarPubMed
Katz, D. F. 1974 On the propulsion of micro-organisms near solid boundaries. J. Fluid Mech. 64, 33–49.CrossRefGoogle Scholar
Kim, S. & Karilla, J. S. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth Heinemann.Google Scholar
Larsen, L., Scheike, T., Jensen, T. K., Bonde, J. P., Ernst, E., Hjollund, N. H., Zhou, Y., Skakkebaek, N. E. & Giwercman, A. 2000 Computer-assisted semen analysis parameters as predictors for fertility of men from the general population. Hum. Reprod. 15, 1562–1567.CrossRefGoogle ScholarPubMed
Lighthill, J. 1976 Flagellar hydrodynamics: the John von Neumann lecture. SIAM Review 18, 161–229.CrossRefGoogle Scholar
Mortimer, D. 1994 Practical laboratory andrology, chapter 7. In Computer-Aided Sperm Analysis. Oxford University Press.Google Scholar
Owen, D. H. & Katz, D. F. 2005 A review of the physical and chemical properties of human semen and the formulation of a semen simulant. J. Androl. 26 (4), 459–469.CrossRefGoogle ScholarPubMed
Phan-Thien, N., Tran-Cong, T. & Ramia, M 1987 A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 184, 533–549.CrossRefGoogle Scholar
Ramia, M., Tullock, D. L. & Phan-Thien, N. 1993 The role of hydrodynamic interaction in the locomotion of microorganisms. Biophys. J. 65, 755–778.CrossRefGoogle ScholarPubMed
Reynolds, A. J. 1965 The swimming of minute organisms. J. Fluid Mech. 23, 241–260.CrossRefGoogle Scholar
Rothschild, Lord 1963 Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature 198, 1221.CrossRefGoogle Scholar
Suarez, S. S. & Pacey, A. A. 2006 Sperm transport in the female reproductive tract. Hum. Reprod. Update 20, 23–37.CrossRefGoogle Scholar
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar
WHO 1999 WHO Laboratory Manual for the Examination of Human Semen and Sperm–Cervical Mucus Interaction, 4th ed. Cambridge University Press.Google Scholar
Yundt, A. P., Shack, W. J. & Lardner, T. J. 1975 Applicability of hydrodynamic analyses of spermatozoan motion. J. Exp. Biol. 62, 27–41.CrossRefGoogle ScholarPubMed