title: 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.
authors.affiliation: Dipartimento di Elettronica ed Informatica, Universita di Padova, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Sparacino
authors.forename: C
authors.initials: C
authors.lastname: Cobelli
mesh_terms: D002096:C-Peptide / Q000097:blood / Q000187:drug effects; D016001:Confidence Intervals; D005947:Glucose / Q000008:administration & dosage*; D005951:Glucose Tolerance Test / Q000379:methods / Q000706:statistics & numerical data; D006801:Humans; D007328:Insulin / Q000378:metabolism*; D000078790:Insulin Secretion; D016018:Least-Squares Analysis; D008297:Male; D008954:Models, Biological; D009010:Monte Carlo Method; D012636:Secretory Rate / Q000187:drug effects; D013268:Stimulation, Chemical; D013269:Stochastic Processes; D013997:Time Factors
chemical_list: D002096:C-Peptide; D007328:Insulin; D005947:Glucose