A stochastic deconvolution method to reconstruct insulin secretion rate after a glucose stimulus

Abstract
Insulin secretion rate (ISR) is not directly measurable in man but it can be reconstructed from C-peptide (CP) concentration measurements by solving an input estimation problem by deconvolution. The major difficulties posed by the estimation of ISR after a glucose stimulus, e.g., during an intravenous glucose tolerance test (IVGTT), are the ill-conditioning of the problem, the nonstationary pattern of the secretion rate, and the nonuniform/infrequent sampling schedule. In this work, a nonparametric method based on the classic Phillips-Tikhonov regularization approach is presented. The problem of nonuniform/infrequent sampling is addressed by a novel formulation of the regularization method which allows the estimation of quasi time-continuous input profiles. The input estimation problem is stated into a Bayesian context, where the a priori known nonstationary characteristics of ISR after the glucose stimulus are described by a stochastic model. Deconvolution is tackled by linear minimum variance estimation, thus allowing the derivation of new statistically based regularization criteria. Finally, a Monte-Carlo strategy is implemented to assess the uncertainty of the estimated ISR arising from CP measurement error and impulse response parameters uncertainty.