My research focuses on applying mathematical concepts to cardiovascular health problems such as heart transplants, pulmonary hypertension, and heart failure. In particular, I am interested in the implementation of different sensitivity analysis techniques such as Morris screening and derivative-based global sensitivity analysis to understand the parameter regimes for which the addition of model compartments plays a role and to aid in the interpretation of results using data from healthy and unhealthy patients. Additionally, I hope to further my understanding of machine learning and its applications to model selection and clustering hypertensive patients into their respective PH groups.
Here are a few of my most recent projects:
- Longitudinal tracking and uncertainty quantification. Heart transplant patients are tracked for up to a year post-transplantation with periodic right-heart catheterizations (RHCs) in order to identify complications and guide treatment. The objective of this project was to identify patients at risk for heart failure following heart transplantation. To do so, we used a systems-level differential equations model analogous to an electrical circuit determining a set of identifiable parameters that were estimated, fitting the model to data. Simulations with the estimated parameters allowed us to calculate physiological markers, including vascular resistance, ventricular power, and beat-to-beat estimates of ventricular pressure and volume. Results allowed us to distinguish between patients with full recovery and those at risk of organ rejection. My contribution was twofold: 1) longitudinally analyzing patients throughout recovery and 2) quantifying the uncertainty of model predictions of left ventricular pressure and volume for two subsets of parameters. Longitudinal tracking included estimating left and right ventricular pressure-volume loops and power output. Uncertainty quantification analysis included setting up MCMC simulations using the Delayed Rejection Adaptive Metropolis algorithm to predict parameter distributions. Sampling from the posterior distributions and comparing the results to the estimated parameters.
- Modeling dynamic waveforms, data assimilation, and sensitivity analysis: One-dimensional models have matched model predictions of pulmonary hemodynamics to time-series waveforms measured in-vivo. For this project, we proposed a lumped parameter model to implement local and global sensitivity analyses in order to estimate physiological parameters using both static systolic/diastolic data and time-series waveforms. The local sensitivity analysis showed that the parameters associated with the timing of systole and diastole in the right ventricle and atria were most influential on model predictions. Global sensitivity analysis using Sobol indices agreed with the local measures and revealed that there was a non-influential set of parameters that could be fixed. Results from data assimilation showed that the inclusion of dynamic data not only changes the combinations of potential parameter subsets but that we can also match the waveforms to model predictions. Additionally, we applied the information criterion to select the smallest parameter subset that still provides accurate assimilations.
- Modeling ventricular interaction: Ventricular interaction has been modeled using a nonlinear end-diastolic pressure-volume relation which gives rise to a differential-algebraic equation that is difficult to solve under certain parameter regimes. We want to study whether a linearized model, much simpler to solve, provides similar results to the nonlinear model.
- A parametric study guided towards a good set of nominal parameters for both models being compared
- Simultaneously sampling all parameters within a 10% range indicated that the linear model reacts like the nonlinear model with minor differences in septal volume
- In progress: Synthesize a database of control and hypertensive patients, run sensitivity analyses and parameter inference on each dataset, utilize machine learning training a model to classify and cluster control and hypertensive patients based on biological markers and indicators of disease.
Research project at Oak Ridge National Laboratory
Machine learning and graphical user interface: The overall goal of this project was to develop a graphical user interface, motivated by the level of uncertainty that exists in identifying newly developed materials in a laboratory, and automating data analysis. Individually manually assessing each material data sample is extremely time-consuming, therefore we used machine learning algorithms and mathematics to change this. A brief overview can be found below:
- Use machine learning algorithms and mathematics to automate material classification.
- Synthetic data generation of thousands of training data samples per model/classification
- Apply weighted k-nearest neighbors to identify the top four models/classifications for specific material data in question
- Allow the user to change initial parameter values, optimize the parameters to the data, and generate confidence intervals bounds for with we are confident that the true parameter value lies
I encourage you to visit my GitHub: https://github.ncsu.edu/alcolung