Sperm dynamics

We have been collaborating with Dr Jackson Kirkman-Brown (The Assisted Conception Unit, Birmingham Women's Hospital), Professor John R. Blake (Department of Mathematics, University of Birmingham) and Dr David J. Smith (Departments of Mathematics and Medicine, University of Birmingham, and Honorary Research Fellow, The Assisted Conception Unit, Birmingham Women's Hospital) on a problem concerning sperm dynamics.

Falling male sperm counts and subfertility have been regularly reported and has become of national and international concern. However, traditional semen analysis provides only limited information for a couple seeking fertility treatment, motivating the investigation of further tests for sperm fitness and function. Mathematical modelling has a clear potential to play a vital role in providing the necessary understanding for the design of novel tests in this area.

Traditionally, the modelling of sperm dynamics has assumed spherical heads and helical tail beats which are oversimplifications. For example, under the microscope, sperm are observed to swim along boundaries with their heads undergoing oscillatory rotations in synchrony with the period of the flagellum beat. Drag is orientation dependent for a non-spherical particle translating and rotating close to a boundary in Stokes flow. In addition, oblate spheroid rigid bodies are predicted to exhibit complex dynamics in external flows once they are close to a boundary. Consequently, the oblateness of the sperm head geometry is likely to have significant influence on the forces and torques experienced by sperm, and therefore on their overall motility.

In this recently established collaboration, we are developing techniques to analyse sperm movies and to subsequently predict the forces on sperm as they swim, without resort to simplified geometries.The helical flagellum beat model has already been shown to be inappropriate for human sperm and motility signatures have been developed which can differentiate between different types of sperm beating.

Possible future applications are numerous; in the short term we will investigate how the forces on and motility of a sperm flagellum alter on perturbation of the surrounding viscosity and rheology, which would offer insight into the mechanism of action of the progesterone-only pill. In the long term, our clinical aim will be to scale up these techniques to correlate different flagellum beat patterns, motility characteristics and force profiles between normal versus infertile sperm for improving the screening of sperm samples for male fertility treatments.

Please contact Dr Eamonn Gaffney for more details. 

A non-rolling cell in high viscosity liquid, shown at nominal frames 1, 40 and 100
(frame rate 332 Hz, total time interval betweenimages a and c is 0.298s).
Image taken from Smith et al. (2009).

Key references in this area 

  • E. A. Gaffney, H. Gadhelha, D. J. Smith, J. R. Blake and J. C. Kirkman-Brown (2011). Mammlian sperm motility: observation and theory. Ann. Rev. Fluid Mech. 43:501-528. (eprints)
  • H. Gadelha, E. A. Gaffney,  D. J. Smith and J. C. Kirkman-Brown (2010). Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration? J. Roy. Soc. Interface 7:1689-1697. (eprints)
  • D. J. Smith, E. A. Gaffney, H. Gadelha, N. Kapur and J. C. Kirkman-Brown (2009). Bend propagation in the flagella of migrating human sperm, and its modulation by viscosity. Cell. Motil. Cytoskel. 66:220-336. (eprints)