My research focuses on applying mathematical concepts to problems in cardiovascular health. These are a few of my most recent projects:
1. Fluid Dynamics: The development of high-performance computing has created a large push in the area of fluid dynamical modeling. Using a 1D network model, we can simulate blood pressure and flow in downstream vasculature. Healthy patients have been well studied under this modeling framework, but predicting the same waveforms in diseased individuals is non-trivial. Patients with pulmonary hypertension (PH) fall into this category and are the focus of my research. The aim of this project is to use the above model framework to provide noninvasive clinical indicators of disease onset and progression. Model predictions are verified with clinical data obtained from collaborators at the University of Glasgow, Scotland and Duke University.
2. Uncertainty Quantification: Medical imaging is the gold standard for non-invasive medical testing. Frequently, mathematicians will work alongside physicians and medical physicists to obtain patient-specific models. These models are driven based on the 3D renderings that are provided from medical imaging. However, these images are subject to measurement uncertainty, thus creating space for variation in model predictions. Uncertainty quantification techniques help to understand the limits of model predictions and further develop the mathematical models used in cardiovascular health.