摘要翻译：
目的：设计一种调节血糖水平的人工胰腺需要可靠的控制方法。模型预测控制是一种有前途的血糖控制方法。然而，基于模型的控制方法需要计算简单和可辨识的数学模型来准确地表示葡萄糖的动态变化，这是由于葡萄糖稳态的复杂性而带来的挑战。方法：在本工作中，推导出一个简单的模型来估计1型糖尿病受试者的血糖浓度。模型中的新特征是腹腔内胰岛素吸收的幂律动力学和单独的胰高血糖素敏感性状态。采用轮廓似然法和基于灵敏度矩阵奇异值分解的方法来评估参数的可辨识性，并指导模型降阶以提高参数的辨识性。结果：建立了一个包含10个参数的简化模型，与猪腹腔注射胰岛素和胰高血糖素的实验数据吻合较好。结论：一个简单的幂律动力学模型可以准确地反映胰岛素和胰高血糖素腹腔注射时的葡萄糖动力学。重要性：简化模型的参数没有发现缺乏局部、实际或结构可识别性。
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英文标题：
《Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal
  Intraperitoneal Artificial Pancreas》
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作者：
Claudia Lopez-Zazueta, {\O}yvind Stavdahl, Anders Lyngvi Fougner
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最新提交年份：
2020
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  Objective: The design of an Artificial Pancreas to regulate blood glucose levels requires reliable control methods. Model Predictive Control has emerged as a promising approach for glycemia control. However, model-based control methods require computationally simple and identifiable mathematical models that represent glucose dynamics accurately, which is challenging due to the complexity of glucose homeostasis. Methods: In this work, a simple model is deduced to estimate blood glucose concentration in subjects with Type 1 Diabetes Mellitus. Novel features in the model are power-law kinetics for intraperitoneal insulin absorption and a separate glucagon sensitivity state. Profile likelihood and a method based on singular value decomposition of the sensitivity matrix are carried out to assess parameter identifiability and guide a model reduction for improving the identification of parameters. Results: A reduced model with 10 parameters is obtained and calibrated, showing good fit to experimental data from pigs where insulin and glucagon boluses were delivered in the intraperitoneal cavity. Conclusion: A simple model with power-law kinetics can accurately represent glucose dynamics submitted to intraperitoneal insulin and glucagon injections. Importance: The parameters of the reduced model were not found to lack of local practical or structural identifiability.
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PDF链接：
https://arxiv.org/pdf/2011.04636