MODELING IMPULSIVE INJECTIONS OF INSULIN: TOWARDS ARTIFICIAL PANCREAS
MODELING IMPULSIVE INJECTIONS OF INSULIN: TOWARDS ARTIFICIAL PANCREAS
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胰岛素脉冲注射建模：人工胰腺
DOI：
10.1137/110860306
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发表时间：
2012-01-01
影响因子：
1.9
通讯作者：
Guo, Hongjian
中科院分区：
文献类型：
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作者：
Huang, Mingzhan;Li, Jiaxu;Guo, Hongjian
我们提出了两个新的数学模型，脉冲注射胰岛素或其类似物的1型和2型糖尿病。一种模型包括胰岛素的周期性脉冲注射。我们解析地证明了1型糖尿病正的全局渐近稳定周期解的存在性和唯一性，这意味着胰岛素注射引起的扰动不会干扰体内平衡，而是将血糖从病理水平向健康水平修正.我们还表明，该系统是一致永久的2型糖尿病，也就是说，葡萄糖浓度水平是一致有界的上下。另一个模型通过密切监测葡萄糖水平来确定胰岛素注射，当葡萄糖水平达到或超过预定义但可调节的阈值时。我们解析地证明了一阶周期解的存在性和稳定性，这确保了以这种自动化的方式注射的扰动可以保持血糖浓度在控制之下。我们的数值分析证实并进一步增强了我们的模型的实用性和鲁棒性。第一个模型具有临床意义，因为糖尿病患者的葡萄糖水平可以通过调整两个模型参数（注射时间和注射剂量）的值而被控制在期望的水平内。描述了选择这两个参数的方法。第二个模型是，据我们所知，第一次尝试克服一些关键问题的设计与闭环方法的人工胰腺。对于前一种情况，我们的数值分析表明，具有较小胰岛素剂量和更频繁递送的方案更有效，但令人惊讶的是，对于后一种情况，较大剂量更有效。这对胰岛素泵和人工胰腺的设计和开发具有重要意义。
We propose two novel mathematical models with impulsive injection of insulin or its analogues for type 1 and type 2 diabetes mellitus. One model incorporates the periodic impulsive injection of insulin. We analytically show the existence and uniqueness of a positive globally asymptotically stable periodic solution for type 1 diabetes, which implies that the perturbation caused by insulin injection will not disturb homeostasis but amend the glucose from a pathological level toward a healthier level. We also show that the system is uniformly permanent for type 2 diabetes, that is, the glucose concentration level is uniformly bounded above and below. The other model determines the insulin injection by closely monitoring the glucose level when it reaches or passes a predefined but adjustable threshold value. We analytically prove the existence and stability of the order one periodic solution, which ensures that the perturbation by the injection in such an automated way can keep the blood glucose concentration under control. Our numerical analysis confirms and further enhances the usefulness and robustness of our models. The first model has clinical implications in that the glucose level of a diabetic can be controlled within a desired level by adjusting the values of two model parameters, injection period and injection dose. A method for choosing these two parameters is described. The second model is, to the best of our knowledge, the first attempt to conquer some critical issues in the design of an artificial pancreas with closed-loop approach. For the former case, our numerical analysis reveals that a regime with a smaller insulin dose and more frequent deliveries is more efficient and effective, but surprisingly, for the latter case, a larger dose is more effective. This can be significant in the design and development of the insulin pump and artificial pancreas.