The bulk of my thesis work focused on developing a 1D, arterial network model for patients with Hypoplastic Left Heart Syndrome (HLHS). These patients are born with an underdeveloped left heart and aorta, requiring three surgeries to reconstruct the vasculature into a univentricular system called the Fontan circuit. Patients require lifelong monitoring and treatment, suffering from reduced cardiac output leading to liver disease, higher risk of stroke, and the eventual need for heart transplantation. Current disease assessment is done through 4D-MRI of the chest and neck, but other full body scans are usually not performed until signs of Fontan breakdown present themself.

My patient-specific model allows us to use information from the imaged region to predict downstream hemodynamics outside of the imaged region including pressure, flow, wave intensity, and wall shear stress, allowing clinicians to examine cardiac function throughout the body without the need for a full body 4D-MRI. The goal for this model is to be used in real-time clinical decision making for treatments and surgical interventions.

Patient-specific modeling requires models be calibrated to patient data. Patient data can be in the form of demographic data, physiological data such as bodyweight and height, and hemodynamic data such as flow waveforms extracted form 4D-MRI. I have developed an efficient parameter inference pipeline that takes multiple datasets for multiple patients into account to calibrate our 1D arterial network model for Fontan patients. 

As we expand this pipeline, we are working towards developing a statistical emulator using the basis of this parameter inference method that can be used in real-time clinical decision making for Fontan patients.

My most recent work with Dr. Beatrice Riviere focuses on developing a 1D-3D advection-diffusion model to investigate blood perfusion into the liver. By incorporating the discontinuous-Galerkin method, we are able to construct a CFD model that not only predicts blood perfusion into the tissue of the liver, but the diffusion of medications used for cancer treatment as well.

When constructing patient-specific models, we often look to medical imaging data. This data comes with multiple sources of uncertainty; patient motion during scanning, user expertise for extracting the patient geometry, complex anatomy, and image resolution to name a few. All impact the quality of the image and the size/shape of the vascular network extracted from the image. Vascular dimensions radii and length have a large impact on hemodynamic predictions from CFD models. 

To limit the impact of these sources of uncertainty on our hemodynamic predictions, we have developed a framework that develops high-fidelity labeled tress and provides hemodynamic predictions with uncertainty within expected measurement error. We continue to work to understand and improve methodologies to quantify geometric uncertainty and its role in CFD modeling.

I have always had a strong interest in statistics and appreciate its added value to applied mathematics. I have experience from two REUs in biostatistics labs.

The first is constructing statistical networks to investigate demographic and genetic influence on the development and progression of Alzheimer's disease. This research was performed with Dr. Paola Sebastiani.

The second is investigating the robustness of current statistical methods being used by NIEHS to determine if a toxin has harmful effects in rodent studies. 

Current statistical interests include construction of statistical emulators for parameter inference, frequentist and bayesian methods for uncertainty quantification, statistical changepoints, and statistical analysis of large datasets.