Modelling the fluid mechanics of propulsion through a complex microenvironment

Lead Research Organisation: University of Birmingham
Department Name: School of Mathematics


Microscopic swimming cells such as sperm and bacteria are fundamental to life on Earth. Despite this we are only beginning to understand how these cells function - in particular there is remarkably little knowledge of how and why the tens or hundreds of millions of sperm deposited at the cervix make their way through the female reproductive tract, survive for up to several days, and how one sperm may, very occasionally, fertilise the egg to produce a new life. There are a number of aspects of this process that are gradually being uncovered: chemical and biological signalling between sperm, womb/tubes and egg, and the physics of how sperm propel themselves through this fluid environment. The biological and physical aspects interact - for example chemical signals may cause the tail to move rapidly, which depending on the fluid properties could cause the cell to move faster in a straight line, or become trapped in a spinning motion known as 'hyperactivation'. We will focus on better understanding these physical aspects through mathematical modelling.

Being less than the width of a hair in length, microscopic swimmers encounter an environment very different from that we are used to in day-to-day life. A sperm in salt water in an IVF dish is subject to very different physical effects from a person swimming in the sea: there is no turbulence, and the fluid behaves like an extremely syrupy ('viscous') substance. This, along with the complex mechanism controlling the movement of the sperm tail means that it is difficult to build realistic laboratory models. However, mathematical models can be developed; this project is about developing these models.

The main challenge that we will be concerned with is the effect of complex 'maze-like' environments characteristic of fallopian tubes that sperm have to traverse, or microchip-based IVF devices that are currently in development. Because of the unexpected viscous effects occurring on very small scales, boundaries are very important, and change the way that cells swim in unexpected ways. These boundaries could be walls of a microchip maze, the closely-opposed internal folds of the female reproductive tract that sperm swim through or pores in a grain of soil inhabited by bacteria. The effects are remarkably difficult to understand; for instance scientists have spent around 50 years trying to understand a deceptively simple phenomenon: the attraction of sperm to the solid boundary of a microscope slide. A key development has been recent computational advances that allow the shape of the cell, its tail, and the boundaries themselves, to be taken into account accurately in a simulation. Recent findings show that enclosed channels have significant effects on guiding cells, and that curved channel walls can be used to separate cells based on the details of how their tails are beating. For example, it would be very beneficial if we could design a microchip maze to separate out an enriched population of 'good' sperm that are properly formed, have the right swimming characteristics to fertilise, and potentially have DNA which is not damaged (a common problem in subfertile couples) - this would assist fertility treatment. But to begin to exploit these effects, we need a much more systematic understanding of how the tail movement, sperm shape or 'morphology', and channel shape interact to alter cell trajectory. We shall do this by constructing a mathematical model that simulates swimming cells in complex environments.

Our model will take into account how fluid properties, such as viscosity, and the position and orientation of the cell relative to the wall, interact with the tail waveform, which in turn changes the swimming motion. We recently showed how unpredictable these effects can be. We will then use these findings to help to develop microchip devices that can be used to diagnose infertility and improve treatment, and help understand the mystery of how sperm reach and fertilise the egg.

Planned Impact

Subfertility is highly prevalent - around one in six UK couples fail to conceive after a year of trying; birth rates in developed countries are falling. Male factors are present in around 25% of couples undergoing IVF and 70% of couples undergoing ICSI (direct injection of a single sperm into an egg). Assisted reproduction has become a routine treatment in the UK, the number of IVF cycles performed annually increasing steadily over the last 20 years, reaching nearly 60000/year in 2010. Success rates have not however risen as rapidly, and on average are still below 25% per cycle. IVF has significant financial cost, limited availability, and takes a physical and emotional toll on the couple, particularly the woman. While ICSI has made treatment possible even with severe sperm motility deficiency, its expense and possible safety risks for the healthy female partner and resulting child continue to cause concern. Despite advances in computer-based motility assays and viscous penetration tests, real-life clinical diagnostics are generally restricted to visual assessments of sperm count, morphology and motility in low viscosity microscope slide environments.

We aim to impact subfertility in the long term in two ways:

(1) Improving differential diagnosis, so that less invasive and expensive treatments can be used where appropriate. A related goal is better identification of men with more severe motility deficiencies before expensive and emotionally-draining failed IVF cycles. These aims require better, but inexpensive, diagnostic tools. If just one quarter of the couples undergoing IVF could be transferred to much cheaper intra-uterine insemination, this would save the UK approximately 25000 IVF cycles/year, each costing several thousand pounds - potentially saving the UK tens of millions of pounds/year. Novel microchannel-based diagnostics have the potential to assist with this; an important requirement is to understand how cells may be sorted based on diagnostically-relevant characteristics.

(2) Improving IVF. It would be of benefit if IVF instead of ICSI or donor insemination could be used for patients with a small number of motile cells. This goal requires the development of techniques that can achieve fertilisation with smaller numbers of motile cells, for example by integrating the sorting and concentrating of motile cells on a microfluidic device, and ideally also fertilisation and embryo culture on the same device.

Both of these technological advances are realistic in the medium-term, and build on recent successes, for example the home fertility test Fertell (invented and FDA-trialled by Dr Jackson Kirkman-Brown in Birmingham), and advances in microfluidic sperm sorting and IVF internationally. While phenomenological modelling of sperm behaviour in such devices has been done, a requirement for further development is a physically-based understanding of how cells may be differentiated on the basis of morphological quality through their interaction with a viscous microenvironment. Basic fluid mechanics research can be translated into very significant benefits with worldwide impact, as proved by Beltsville Sperm Sexing. The discovery in 1998 of an improved flow cytometer nozzle design, based on fluid dynamic considerations, resulted in a doubling of the yield of cells correctly sorted by gender.

Finally, improved understanding of the behaviour of flagellated swimmers in microenvironments has relevance to many other problems, including pathogens (trypanosomatics, bacteria for example) and algae in energy-producing bioreactors - the potential societal and economic impacts are therefore very broad.


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Description 1) We developed a computational model of how sperm cells interact with their fluid environment and surrounding walls. Sperm are tiny swimming cells that have to migrate to the egg in order to fertilise. Problems with swimming (motility) are a major cause of infertility and there is significant international interest in microfluidic devices which can be used to sort sperm for quality. We were able to show that the way sperm 'scatter' when they encounter abrupt changes in the walls is related to the mechanical properties of the sperm tail and the viscosity ('gloopiness') of the surrounding fluid, and associated changes to the shape of the tail beat. The methods developed may be useful in the future design of microfluidic devices to sort sperm based on their mechanical characteristics.

2) We developed a computational model of Kupffer's vesicle, a tiny structure in zebrafish embryos which is the earliest left/right symmetry-breaking event. Your heart is on the left side of your chest and your liver on the right - but did you ever wonder how the embryo 'knows' which side is which? Zebrafish provide an animal model to explore this important biological phenomenon. Fluid flow in Kupffer's vesicle is created by whirling cilia, but the nature of how this flow is 'felt' by the cells (shear stress) is very difficult to determine from experiments, also the effect of the huge variability seen in nature is hard to quantify. Our model enabled the first computational predictions of shear stress distributions, and the first quantification of how the number of cilia affects the chance of something going wrong in development. These findings, along with those of our experimental collaborators, helped to show that the mechanisms underlying the heart and liver positioning are distinct.
Exploitation Route 1) Developers of microfluidic devices for sorting sperm (human fertility and animal breeding).

2) Biological groups studying left/right symmetry-breaking in vertebrates.
Sectors Healthcare,Pharmaceuticals and Medical Biotechnology
Description EPSRC Healthcare Technologies Challenge Awards
Amount £958,023 (GBP)
Funding ID EP/N021096/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom of Great Britain & Northern Ireland (UK)
Start 04/2016 
End 03/2021