Today, diagnostic decisions about pre-diabetes or diabetes are made using static threshold rules for the measured plasma glucose. In order to develop an alternative diagnostic approach, dynamic models as the Minimal Model may be deployed. We present a novel method to analyze the identifiability of model parameters based on the interpretation of the empirical observability Gramian. This allows a unifying view of both, the observability of the system's states (with dynamics) and the identifiability of the system's parameters (without dynamics). We give an iterative algorithm, in order to find an optimized set of states and parameters to be estimated. For this set, estimation results using an Unscented Kalman Filter (UKF) are presented. Two parameters are of special interest for diagnostic purposes: the glucose effectiveness S(G) characterizes the ability of plasma glucose clearance, and the insulin sensitivity S(I) quantifies the impact from the plasma insulin to the interstitial insulin subsystem. Applying the identifiability analysis to the trajectories of the insulin glucose system during an intravenous glucose tolerance test (IVGTT) shows the following result: (1) if only plasma glucose G(t) is measured, plasma insulin I(t) and S(G) can be estimated, but not S(I). (2) If plasma insulin I(t) is captured additionally, identifiability is improved significantly such that up to four model parameters can be estimated including S(I). (3) The situation of the first case can be improved, if a controlled external dosage of insulin is applied. Then, parameters of the insulin subsystem can be identified approximately from measurement of plasma glucose G(t) only.

译文

:今天,有关糖尿病前期或糖尿病的诊断决策是使用针对所测血浆葡萄糖的静态阈值规则制定的。为了开发替代的诊断方法,可以部署动态模型(如最小模型)。我们提出了一种新的方法来分析模型参数的可识别性,它基于经验可观察性格拉姆式的解释。这样就可以对系统状态的可观察性(带有动态性)和系统参数的可识别性(不带有动态性)两者进行统一查看。我们给出一个迭代算法,以便找到一组最佳的状态和参数进行估算。对于该集合,给出了使用无味卡尔曼滤波器(UKF)的估计结果。为了诊断目的,特别需要关注两个参数:葡萄糖有效性S(G)表征血浆葡萄糖清除的能力,胰岛素敏感性S(I)量化从血浆胰岛素对间质胰岛素子系统的影响。在静脉葡萄糖耐量试验(IVGTT)期间将可识别性分析应用于胰岛素葡萄糖系统的轨迹显示以下结果:(1)如果仅测量血浆葡萄糖G(t),则血浆胰岛素I(t)和S(G )可以估算,但S(I)不能估算。 (2)如果另外捕获血浆胰岛素I(t),可识别性将大大提高,从而可以估计多达四个模型参数,包括S(I)。 (3)如果采用控制剂量的胰岛素,可以改善第一种情况。然后,仅可以通过测量血浆葡萄糖G(t)大致识别出胰岛素子系统的参数。

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