University College London
Mathematics

If we look closely enough, we find filaments everywhere. Whilst we might first think of our hair as the filament that has the biggest impact on our day-to-day lives, we only have to delve a little deeper to find a whole host of slender objects at constant work in our bodies. Cilia, thin hair-like protrusions from cells, are the backbone of the self-clearing mechanism of our airways and are thought to be responsible for the left-right asymmetry of our bodies. Cilia, as well as the flagella that propel sperm on the path to fertilisation, are in fact ubiquitous across eukaryotic organisms.

In many cases, this abundance can make them difficult to study. Indeed, you often won't find just a single cilium or flagellum, but many, potentially thousands, in close proximity, so it can be difficult to untangle the properties of one filament from the next. As isolating individuals can be impractical, filament motion has instead been simulated, making use of specialised mathematical techniques for both fluid mechanics and the elastic properties of these slender bodies. Unfortunately, these numerical studies have been limited in both scope and accuracy, with efficient accurate simulation limited to a single filament. Up until recently, researchers also needed large computing resources to perform these simulations. Despite these limitations, single-filament studies have been key in identifying many phenomena, both theoretical and biological. However, they are unable to shed light on the complex interactions of nearby filaments, for example the synchronised swimming of neighbouring sperm flagella.

The objective of this research is to develop the mathematical theory and tools needed to enable accurate and efficient study of the behaviours and properties of multiple slender filaments inhabiting the same environment. Seeking to mimic the surroundings of filaments in nature, I'll consider high, low and intermediate filament densities. These methods will then be used to investigate problems at the interface of mathematics, biology, medicine, and biophysics, for example, attempting to uncover the physical principle behind the remarkable wave-like beating of cilia. These explorations have the potential to further clinical diagnostics, from human ciliary disorders to the roots of infertility.