Estimation of endogenous glucose production after a glucose perturbation by nonparametric stochastic deconvolution

The knowledge of the time course of endogenous glucose production (EGP) after a glucose perturbation is crucially important for understanding the glucose regulation system in both healthy and disease (e.g. diabetes) states. EGP is not directly accessible, and thus an indirect measurement approach is required. The estimation of EGP during an intravenous glucose tolerance test (IVGTT) can be posed as an input estimation problem solvable as a Fredholm integral equation of the first kind (A. Caumo and C. Cobelli, Am. J. Physiol., 264 (1993) E829-E841). The time-varying model of the kernel of the glucose system was identified from a concomitant tracer experiment, and EGP was reconstructed by employing the Phillips-Tikhonov regularization (deconvolution) algorithm. However, the proposed deconvolution approach left some issues open, e.g. how to choose the amount of regularization and how to deal with nonuniform/infrequent sampling. Here, a solution to these problems is provided by resorting to a new deconvolution algorithm. Thanks to the stochastic embedding into which the new deconvolution method is stated, the amount of regularization is determined in a statistically sound manner. In addition, in face of infrequent sampling, a time continuous profile of EGP is obtained. The method is shown to work reliably for reconstructing EGP in different IVGTT experimental protocols, both in normal and disease states.