基于血糖综合控制效果对胰岛素注射时间及剂量的优化选择研究

Studies on the Optimization Selection of Injection Timings and Injection Doses Based on the Integrated Control Effect of Glucose

构建一类数学模型研究胰岛素治疗中血糖的有限时间控制问题.首先依据临床治疗情景,建立了基于血糖综合控制效果的目标函数,然后研究两种治疗模式下胰岛素的最优注射策略.为了解决最优脉冲控制中的技术难题,应用一种时间尺度变换的方法,求出了目标函数关于两类控制参数(注射时间和注射剂量)的梯度表达式.最后借助于数值模拟,获取了两种不同治疗模式下胰岛素的最优注射时间和注射剂量.结果表明:基于血糖的综合控制效果,注射时间的优化选择比注射剂量的优化选择更加重要.

A mathematical model is proposed to study the plasma glucose control for insulin therapy in a limited time.The objective function based on the integrated control effect of glucose is given according to the clinical treatment situation,and two different optimal injection strategies are investigated.To solve the technical problem in optimal impulsive control,a time rescaling method is applied and the gradient formulas of the objective function with respect to two control parameters(injection doses and injection timings)are obtained.In addition,using numerical simulations,the optimal injection doses and injection timings for each injection strategy are given.The results show that the optimal injection timing control is superior to the optimal injection dose control.