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Quantitative assessment of metabolic health using dynamical systems informed by Gaussian processes
Garrish, Justin Kirk
Garrish, Justin Kirk
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2025
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2026-11-11
Abstract
As glucose enters the bloodstream after a meal, the beta cells of the pancreas release the hormone insulin to signal glucose uptake by tissues throughout the body. Since insulin plays a major role in the regulation of glucose concentration, accurate and precise estimation of insulin secretion during a response to ingested glucose provides insight into beta cell function. Though insulin secretion cannot be observed in real time during a physiological meal response, mathematical and statistical tools can reconstruct continuous secretion profiles for insulin from discrete measurements taken from plasma.
This work introduces new methods to infer insulin secretion rate with the quantification of uncertainty. We place particular emphasis on the natural integration of dynamical systems and Gaussian processes (GPs) that can be accomplished using Bayesian hierarchical models (BHMs). First, we present a novel BHM that combines an established model of C-peptide dynamics with a GP prior on insulin secretion rate (ISR) to accurately reconstruct ISR and quantify uncertainty from noisy C-peptide measurements. We validate the method by implementation on data from youth with and without cystic fibrosis. Next, we improve upon the GP model of ISR by incorporating additional physiological constraints and discuss the effects on posterior ISR distributions. Finally, we present a novel approach for the estimation of glucose derivatives from noisy glucose observations using variably scaled covariance kernels. Robust estimation of glucose derivatives is necessary for future extensions of ISR inference incorporating explicit glucose dependence, and variably scaled kernels can directly leverage knowledge of the sampling schedule and target function to define covariances flexible enough for implementation in heterogeneous data sets that readily adapt to the sampling schedules of different experimental protocols. Together, these contributions lay a foundation for flexible, physiologically informed inference of insulin secretion dynamics from clinical data.
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