Research
The focus of my research is on mathematical and computational models of multiscale biological systems including fluid-structure interaction. My work is motivated by the need for new tools to interpret clinical data. I am excited by the potential of using mathematical models that describe the physical phenomena governing biological systems in synergy with experimental data to elucidate the mechanisms behind a biological process, ultimately aiding the future development of medicine.
Current Research Topics and Selected Publications/Presentations
Contact Lenses
About one in ten Americans wears contact lenses. To understand what makes contact lenses comfortable or not, we study the interaction between the contact lens and the eye. Additionally, recent studies have shown the potential for delivering ocular medications via extended wear contact lenses. My group is working on developing mathematical and computational models of the interaction between the contact lens and the eye that accounts for the deformability of the eye. This project is in collaboration with Prof. Kara Maki and Prof. David Ross at RIT.
Ocular Hemodynamics
Ocular hemodynamics play a crucial role in many ocular diseases, such as galucoma and age related macular deneration. My group is working in developing multiscale mathematical models that describe the deformation of ocular structures and ocular blood flow using reduced-order fluid-structure interaction models. These models are used, in synergy with experimental data, to investigate the driving mechanisms of oculary dyanmics.
Ocular Pharmacokinetics
Current treatments for ocular diseases such glaucoma and age-related macular degeneration have several disadvantages, since less than 5% of an eye drop reaches the target tissue, and interocular injections create a high financial burden and distress in the patient. My group is working on developing a mathematical and computational framework to model and analyze the potential of alternative ocular drug treatments and the resultant ocular pharmacokinetics. This framework involves compartmental pharmacokinetics and reduced-order fluid-structure interaction models.
Biological Mico-swimmers
Example of biological micro-swimmers interacting with the surrounding fluid include spermatozoa (sperm) in search of an egg, cilia beating within airways, and microtubules in the cytoplasm during cell division and cell migration. My group is working on developing mathematical and computational models to study three-dimensional micro-swimmer motility accounting for biochemical signaling, interaction with confined environment and between two or more micro-swimmers.
Operator Splitting Algorithms
Operator splitting algorithms allows for the resolution of different block of the coupled problem in different steps, that are solved sequentially without the need of sub-iterations (i.e. saving computational time). My group is working on developing energy-based operator splitting algorithms for multiscale coupling, like 3D-0D, of fluid and elastic structures problems.
Jasmonic Acid Biosynthesis
Jasmonic acid (JA) is a hormone in plants that serves as defense to wounding or insects. The precise mechanisms regulating the JA biochemical reactions in vivo remain to be characterized. My group is working together with Prof. Eli Borrego (RIT) group to develop an interdisciplinary mathematical and biological framework to study JA production during the maize wound response. The mathematical models are developed together with "wet lab" experiments to isolate and quantify the relative contribution of factors that are difficult to separate in vivo and to test hypothesis.