I am fascinated by the mysteries of nature, especially how cells interact and how those interactions manifest at the level of tissues. Cells are like tiny particles that can move and interact in a variety of ways. They can be pushed around in by external flows, they can diffuse depending on the local concentration or be influenced by their neighbours. There are three distinct ways to look at this behaviour, depending on how closely are we looking. If we look very closely where we can see each cell then that’s called the micro level. And if we look form very far away we can only see the boundary of the collection of cells then it becomes an evolving boundary problem.
I look at this behaviour from a distance midway between these two, where a collection of cells start to behave like a fluid and these dynamics are called macro dynamics. I use Partial Differential Equations to describe the dynamics of this fluid like group of cells over time. These PDEs are special in the sense that they are parabolic, have non negative solutions and obey laws of Physics like conservation of mass and decay of order over time(Gradient Flow Structure).
My current research interest include but are not limited to,
- modelling inter-cellular interactions involving multiple species,
- studying the relationships between different tissue growth models,
- understanding tissue growth on surfaces,
- and last but not the least, fitting PDE models with biological data.