Current Projects

The following projects are considered graduate or postdoctoral level projects. In rare cases, undergraduate students may also contribute to these. If you are an undergraduate student interested in one of these projects, please email Dr. Colebank.

(1) Scientific machine learning and statistical based emulation for digital twins

Computational models are a corner stone of the digital twin pipeline. However, the most accurate, high-fidelity simulation tools require infeasible computation time, especially for clinical, bedside care. Thus, emulation (or surrogate modeling) can be used in place. This project requires innovation in how emulation is carried out, as well as significant mathematical investigations into whether the emulator structure and design can efficiently solve inverse problems and quantify uncertainty.

Students working on this project will:

Develop new emulation methods driven by neural networks, Gaussian processes, and other scientific machine learning methods;
Identify optimal experimental designs for both the training of emulators as well as the solution of inverse problems dictated by sparse, noisy, data; and
Develop a emulator-driven framework for uncertainty quantification under the aforementioned solution to noisy inverse problems.

(2) Image based models of cerebral blood flow

The cerebral circulation is distinct component of the cardiovascular system, and rapidly responds to changes in cerebral oxygen and energy requirements via neurological innervation. However, multiple diseases (e.g., stroke, cerebral ischemia) have been linked to a reduced ability to regulate cerebral blood flow. Most notably, few studies have identified how heart function, vasomotor tone, and cerebral perfusion are altered with psychosocial stress.

This project combines medical imaging data from patients with and without a history of cerebral vascular disease with a one-dimensional, pulse-wave propagation model of blood flow. Students working on this project will:

Work on developing a pipeline for image-to-domain transformations for the blood flow model;
Adapt existing stress-strain relationships to include the role of vasomotor tone; and
Develop new ODE-PDE coupling methods to combine heart function, cerebral blood flow, and cerebral perfusion.

(3) Inverse problems and uncertainty quantification for multiscale models

Mathematical, computational simulators often accrue numerous, uncertain parameters that are unique to a particular dataset or (physiological) system. This requires the solution of an inverse problem (i.e., the calibration of models to data), which is often ill-posed, with issues ranging from parameter non-identifiability, slow methods for model calibration (e.g., Markov chain Monte Carlo, MCMC), and model discrepancy. Addressing all of these issues in multiscale models adds extra complexity, given the multiple spatial and/or temporal scales.

This project will develop new methods for handling inverse problems in both the frequentist and Bayesian framework. In addition, new sensitivity metrics are necessary to understand parameter interactions and covariance structure, as well as identifiability methods for multiscale problems. Students working within this project will:

Implement cutting edge methods for the solution of Bayesian inverse problems;
Develop robust methods for determining parameter identifiability under flexible experimental designs;
Innovate on existing methods for handling model form discrepancy; and
Identify optimal strategies for emulation-informed inverse problems.

(4) Multiscale models of neuroendocrine-inflammatory-cardiovascular function

Multiple stimuli, including environmental factors, psychosocial stress, and diet, trigger a cascade of maladaptive signaling cascades between the neuroendocrine system (e.g., the hypothalamic-pituitary-adrenal (HPA) axis), the inflammatory system (i.e., pro- and anti-inflammatory cytokines, macrophages, etc), and the cardiovascular system. This cascade of events can operate on the order of seconds to minutes (e.g., acute-stress leading to fight-or-flight response), minutes to hours (e.g., circadian disruption), or days-to months (e.g., inflammatory driven vascular and/or cardiac remodeling). These systems-level reactions occur across multiple populations, including those serving in high-stress environments (e.g., combat zones or intensive care units) as well as individuals suffering from social determinants of health and socioeconomic distress.

To these complex, multiscale phenomena, we can combine mathematical models with experimental or clinical data. These models span multiple time-scales (usually requiring nonlinear, delay-differential equations), and spatial scales, requiring innovative mathematical methodologies. In addition, these models typically have numerous parameters that may adapt over time. Students working on this project will:

Develop new, multiscale mathematical models of the neuoendocrine, inflammatory, and cardiovascular system, as well as their intricate interactions;
Implement and devise appropriate methods for identifying influential and identifiable parameters in complex, multiscale systems; and
Innovate on existing calibration methods (e.g., Bayesian inference under model discrepancy) to match these complex models to multimodal data.

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