Research

I am thankful to work under the supervision of Prof. Michael Sacks, the director of the Willerson Center for Cardiovascular Modeling. developing computational biomechanical models for understanding heart valve and heart disease progression for developing clinical interventions. My research reflects the Oden Institute ethos where we integrate mathematics, computational science, and engineering. With this in mind, I work on clinically relevant problems, creating high-speed computational tools to solve them while maintaining a rigorous mathematical foundation.

Current Research Areas:

Foundations: 1. Finite Elements: The mathematical theory that describes how numerical solutions can be computed for many PDEs. 2. Operator Learning: Operators are the fundamental objects describing PDEs. Operator learning is how we try to approximate these objects through machine learning.

Methods: 1. Neural Network Finite Element: This method showcases a marriage of traditional finite elements with modern machine learning for solving a family of parameterized PDEs simultaneously.

Applications: 1. Solid Mechanics: Solid mechanics describes the deformation of a solid given various boundary conditions on the system. I specifically focus on soft biological tissues which are highly nonlinear, hyperelastic materials. 2. Ion modeling: Ion models describe the subcellular process of action potentials, and importantly for cardiac modeling, calcium concentrations that trigger muscle activation. 3. Electrophysiology: Electrophysiology describes the way electrical signals propagate across the tissue of the heart. 4. Electromechanics: Electromechanics couples the above into one system where the electrophysiology triggers action potentials of the ion channels that then trigger stress through calcium transients.

Publication Highlights: