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 towards the creation of a computational infrastructure and modeling needs to create a Cardiac Digital Twin.

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Research Pillars:

1. Mathematical Foundations (The Theory):

Developing foundational theory to improve computational methods

  1. Finite Elements: The mathematical theory that describes how numerical solutions can be computed for many PDEs.
  2. Isogeometric Analysis: While similar to FE, IGA directly links geometry to the PDE. This requires a mathematical expansion to differential geometry and topology which can typically be ignored in standard FE.
  3. Scientific Machine Learning: Scientific machine learning is the integration of machine learning into scientific computing frameworks to leverage rigor with approximation power and speed.

2. Computational Implementation (The Engine):

Building GPU-native frameworks for high-speed scientific simulation.

  1. Neural Network Finite Element: This method showcases a combination of traditional finite elements with modern machine learning for solving a family of parameterized PDEs simultaneously.
  2. Computational Geometry: Here, we look into computationally describing the complex shape of the heart. While IGA focuses on solving the PDE, here we focus on the mesh creation.
  3. Inverse Problems: To create patient-specific models, we need to calibrate them.

3. Clinical Translation (The Impact)

Bridging the gap between simulation and the medical action.

  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: