research

My main interests lie in the applications of mathematical analysis in biomedicine. This includes developing new models in pathophysiology, analysing their structure and developing numerical methods to explore them. Here are some of the projects that I’ve been involved with so far!

microscale hemodynamics and gas exchange

Porous media fluid mechanics, nonlinear elasticity, transport phenomena, finite element methods, nonlinear analysis.

Alveoli are the little structures in your lungs where oxygen enters the bloodstream and carbon dioxide leaves it. You breathe to make this happen, but nonetheless this process can fail locally for many reasons: if blood isn’t flowing, if your red blood cell count is low, if air isn’t going to the alveolus, or if the contents of said air are not quite right. These little alveoli are arranged in a fascinatingly intricate fashion, allowing for greater effectiveness and robustness of this crucial process. With Prof. Daniel E. Hurtado, we developed a fully three-dimensional system of partial differential equations that models this, and a numerical method to approximately solve it.

ciliated tissue biomechanics

Low Reynolds number fluid mechanics, fluid-structure interaction, high performance computing.

The tissue that comprises your body is made of cells which, more often than not, are lined with tiny appendages called cilia. In some cases, such as your brain and airways, these cilia work actively, like little mechanical arms that move surrounding fluid. Every time you inhale, for example, there’s a chance that dangerous pathogens flow into your respiratory system. That’s why your airways are lined with a complex fluid called mucus, that traps most of these pathogens. The cilia in your lung cells then move the mucus to expel it and keep you safe. I’m currently working with Dr. Eric Keaveny to model the properties and dynamics of these types of tissues.