Sparacino G, Cobelli C
Dipartimento di Elettronica ed Informatica, Universita di Padova, Italy.
IEEE Trans Biomed Eng. 1996 May;43(5):512-29. doi: 10.1109/10.488799.
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.
胰岛素分泌率（ISR）在人体中无法直接测量，但可以通过解卷积解决输入估计问题，从C肽（CP）浓度测量值中重建。在葡萄糖刺激后，例如在静脉葡萄糖耐量试验（IVGTT）期间估计ISR时，主要困难在于问题的病态性、分泌率的非平稳模式以及不均匀/不频繁的采样方案。在这项工作中，提出了一种基于经典菲利普斯-蒂霍诺夫正则化方法的非参数方法。通过对正则化方法的一种新颖表述来解决不均匀/不频繁采样的问题，该表述允许估计近似时间连续的输入曲线。将输入估计问题置于贝叶斯框架中，其中葡萄糖刺激后ISR的先验已知非平稳特征由一个随机模型描述。通过线性最小方差估计来处理解卷积，从而可以推导出基于统计的新正则化准则。最后，实施蒙特卡罗策略来评估由CP测量误差和脉冲响应参数不确定性引起的估计ISR的不确定性。
