双激素人工胰腺葡萄糖动力学的低阶非线性动物模型
Low-Order Nonlinear Animal Model of Glucose Dynamics for a Bihormonal Intraperitoneal Artificial Pancreas
摘要：
目的：设计用于调节血糖水平的人工胰腺（AP）需要可靠的控制方法。模型预测控制是一种很有前途的控制方法。然而，基于模型的控制方法需要计算简单且可识别的数学模型，其精确地表示葡萄糖动态，这由于葡萄糖稳态的复杂性而具有挑战性。方法：在这项工作中，推导出一个简单的模型来估计1型糖尿病（T1DM）受试者的血糖浓度。模型中的新特征是腹膜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。采用剖面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，并指导模型降阶以改善参数的辨识。结果如下：获得并校准了具有10个参数的降阶模型，显示出与来自猪的实验数据的良好拟合，其中在腹膜内腔中递送胰岛素和胰高血糖素推注。结论：一个简单的模型与幂律动力学可以准确地代表葡萄糖动力学提交腹腔注射胰岛素和胰高血糖素。发现该降阶模型具有局部实用性和结构可辨识性。重要性：所提出的模型有助于在动物试验中进行基于腹膜内双激素模型的闭环控制。
英文摘要：
Objective: The design of an Artificial Pancreas (AP) 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 (T1DM). 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. The reduced model was found to exhibit local practical as well as structural identifiability. Importance: The proposed model facilitates intraperitoneal bi-hormonal model-based closed-loop control in animal trials.
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