Modelling sperm dispersion within and guidance by microarchitecture

In natural fertility, a population of tens to hundreds of millions of self-motile sperm cells is faced with the task of migrating through the complex microenvironment of the female reproductive tract. Usually only tens or hundreds of cells reach the site of fertilisation, and usually at most one sperm will fertilise the egg. A quantitative and physically-based understanding of this process is lacking, despite decades of research; in particular it is not known how the initial concentration and motility of cells affects the likelihood of conception, the extent to which the microarchitecture (folds, high viscosity fluid, cilia- and peristaltic- currents) influence dispersion, or how this could be modulated as part of fertility treatment or contraception. This project is motivated by the opportunity provided by microfluidic experiments, which enable features of the female tract, for example walls and grooves, and the rheology of the fluid, to be assessed experimentally in a controlled way. Preliminary data are already available from Centre for Human Reproductive Science, Birmingham Women's Hospital, evidencing that both walls and slightly raised viscosity can substantially increase sperm transport. The mathematical and computational methods involved in the project will include partial differential equations (building on for example the Goldstein-Kac telegraph equation), individual-based models, and Bayesian parameter estimation. The ultimate aim will be to uncover the mechanistic relationships through which sperm motility and concentration, fluid properties, flow and microarchitecture influence the likelihood of conception, providing vital information in diagnostics for male infertility, and enabling female patients to avoid more invasive treatments such as in vitro fertilisation.