DE Seminar: Justin Garrish (UMBC)

Abstract: As glucose enters the bloodstream, e.g. after a meal, the beta cells of the pancreas release the hormone insulin to signal glucose uptake in tissues throughout the body. Since insulin plays a major role in the regulation of glucose concentration, accurate and precise estimation of insulin secretion rate (ISR) 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 C-peptide measurements taken from plasma. We propose a Bayesian hierarchical model (BHM) that takes C-peptide as the output of a common C-peptide dynamics model with ISR as a source term, and the logarithm of ISR as a Gaussian process with a quadratic mean trend. This BHM allows us to infer ISR curves constrained to positive values. Further, the method furnishes a linear approximation of the non-linear transformation from log-ISR to C-peptide that adheres to the constraints, allowing for physiologically accurate and computationally efficient uncertainty quantification. The efficacy of the BHM is demonstrated on a set of data from youth participants with and without cystic fibrosis.