Vicini P, Sparacino G, Caumo A, Cobelli C
Department of Electronics and Informatics, University of Padova, Italy.
Comput Methods Programs Biomed. 1997 Mar;52(3):147-56. doi: 10.1016/s0169-2607(96)01784-1.
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.
了解葡萄糖扰动后内源性葡萄糖生成（EGP）的时间进程，对于理解健康和疾病（如糖尿病）状态下的葡萄糖调节系统至关重要。EGP无法直接测量，因此需要采用间接测量方法。静脉葡萄糖耐量试验（IVGTT）期间EGP的估计可被视为一个输入估计问题，可作为第一类弗雷德霍姆积分方程求解（A. Caumo和C. Cobelli，《美国生理学杂志》，264（1993）E829 - E841）。葡萄糖系统核的时变模型是通过伴随示踪剂实验确定的，EGP则通过采用菲利普斯 - 蒂霍诺夫正则化（反卷积）算法进行重建。然而，所提出的反卷积方法仍存在一些问题，例如如何选择正则化量以及如何处理非均匀/不频繁采样。在此，通过采用一种新的反卷积算法提供了这些问题的解决方案。由于新反卷积方法所基于的随机嵌入，正则化量得以以统计学上合理的方式确定。此外，面对不频繁采样时，可获得EGP的时间连续曲线。该方法被证明在正常和疾病状态下的不同IVGTT实验方案中，都能可靠地用于重建EGP。
