Modelling sperm dispersion within and guidance by microarchitecture

在自然生育中，数千万到数亿个自我活动的精子细胞面临着通过女性生殖道复杂的微环境进行迁移的任务。通常只有数十或数百个细胞到达受精部位，通常最多只有一个精子使卵子受精。尽管进行了几十年的研究，但对这一过程缺乏定量和基于物理的了解；特别是不知道细胞的初始浓度和运动性如何影响受孕的可能性，微结构(折叠、高粘度液体、纤毛电流和蠕动电流)对扩散的影响程度，或者作为生育治疗或避孕的一部分如何调节这一点。该项目是由微流体实验提供的机会所推动的，该实验能够以受控的方式通过实验评估女性管道的特征，例如管壁和沟槽，以及流体的流变性。伯明翰女子医院人类生殖科学中心已经提供了初步数据，证明两壁和略微升高的粘度都可以显著增加精子的运输。该项目涉及的数学和计算方法将包括偏微分方程式(建立在例如Goldstein-Kac电报方程的基础上)、基于个体的模型和贝叶斯参数估计。最终目的将是揭示精子运动和浓度、流体特性、流动和微结构影响受孕可能性的机制关系，为男性不育的诊断提供重要信息，并使女性患者能够避免更具侵入性的治疗，如体外受精。

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.