1型糖尿病血糖浓度的多目标优化调控

Raya Abushaker, Y. Sardahi, Ahmad M. Alshorman
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引用次数: 0

摘要

1型糖尿病是一种慢性疾病,其中胰腺β细胞不能充分产生胰岛素,从而导致葡萄糖浓度升高。在实践中,外部胰岛素输送是治疗这种疾病的唯一方法。为此,本文提出了胰岛素输送的多目标优化控制方法。考虑到三个相互冲突的目标:最小化低血糖和高血糖的风险,减少注射胰岛素的量。在调整闭环系统参数(包括线性二次型调节器(LQR)和估计器收敛速度的设计细节)时,这些目标同时最小化。LQR设置参数的下界和上界由Bryson规则确定,考虑标称葡萄糖范围(70 - 160 mg/dL)和最大和最小泵注速率(0.0024 - 15 mU/min)。选取估计器收敛速度的下界和上界,使估计器收敛速度快于闭环系统的最快模式。在计算机模拟方面,采用常用的模型之一Bergman最小模型来模拟i型糖尿病患者的葡萄糖-胰岛素动力学。非支配排序遗传算法(non- dominant sorting genetic algorithm, NSGA-II)是求解多目标优化问题中应用最广泛的算法之一。得到并分析了Pareto集合及其图像Pareto front的最优解。结果表明,MOP解决方案引入了许多最优选项,决策者可以从中选择实施。此外,在高初始血糖水平下,Bergman模型的参数变化和外部干扰;优化控制性能测试表明,无论初始葡萄糖浓度高,该系统都能快速将葡萄糖水平降至所需值,可以有效地为不同的患者工作,并且对不规则的零食或膳食具有鲁棒性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multi-Objective Optimal Regulation of Glucose Concentration in Type I Diabetes Mellitus
Type I diabetes is a chronic disease in which insulin is not adequately produced by the pancreatic β-cells, which leads to a high glucose concentration. In practice, external Insulin delivery is the only method to deal with this disease. To this end, a multi-objective optimal control for insulin delivery is introduced in this paper. Three conflicting objectives are considered: minimizing the risk of hypoglycemia and hyperglycemia, and reducing the amount of injected insulin. These objectives are simultaneously minimized while tuning the closed-loop system parameters that include the design details of the linear-quadratic regulator(LQR) and estimator speed of convergence. The lower and upper bounds of the LQR setup parameters are determined by Bryson's rule taking into account the nominal glucose range (70 – 160 mg/dL) and maximum and minimum pump infusion rates (0.0024 –15 mU/min). The lower and upper bounds of the estimator convergence speed are chosen such that the estimator is faster than the fastest mode of the closed-loop system. For computer simulations, Bergman's minimal model, which is one of the commonly used models, is employed to simulate glucose-insulin dynamics in Type-I diabetic patients. The non-dominated sorting genetic algorithm (NSGA-II) solves the optimization problem, one of the widely used algorithms in solving multi-objective optimization problems (MOPs). The optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained and analyzed. The results show that the MOP solution introduces many optimal options from which the decision-maker can choose to implement. Furthermore, under high initial glucose levels, parametric variations of Bergman's model, and external disturbance; the optimal control performance is tested to show that the system can bring glucose levels quickly to the desired value regardless of high initial glucose concentrations, can efficiently work for different patients, and is robust against irregular snacks or meals.
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