Institut Universitari d'Automàtica i Informàtica Industrial, Universitat Politècnica de València, Spain.
Comput Methods Programs Biomed. 2012 Dec;108(3):993-1001. doi: 10.1016/j.cmpb.2012.05.012. Epub 2012 Jun 27.
Insulin therapy in type 1 diabetes aims to mimic the pattern of endogenous insulin secretion found in healthy subjects. Glucose-insulin models are widely used in the development of new predictive control strategies in order to maintain the plasma glucose concentration within a narrow range, avoiding the risks of high or low levels of glucose in the blood. However, due to the high variability of this biological process, the exact values of the model parameters are unknown, but they can be bounded by intervals. In this work, the computation of tight glucose concentration bounds under parametric uncertainty for the development of robust prediction tools is addressed. A monotonicity analysis of the model states and parameters is performed. An analysis of critical points, state transformations and application of differential inequalities are proposed to deal with non-monotone parameters. In contrast to current methods, the guaranteed simulations for the glucose-insulin model are carried out by considering uncertainty in all the parameters and initial conditions. Furthermore, no time-discretisation is required, which helps to reduce the computational time significantly. As a result, we are able to compute a tight glucose envelope that bounds all the possible patient's glycemic responses with low computational effort.
1 型糖尿病的胰岛素治疗旨在模拟健康受试者中内源性胰岛素分泌的模式。葡萄糖-胰岛素模型广泛应用于新的预测控制策略的开发中，以将血浆葡萄糖浓度维持在狭窄范围内，避免血液中葡萄糖水平过高或过低的风险。然而，由于这个生物过程的高度可变性，模型参数的确切值是未知的，但它们可以被区间限制。在这项工作中，针对开发鲁棒预测工具，研究了在参数不确定性下计算葡萄糖浓度紧边界的问题。对模型状态和参数进行了单调性分析。提出了临界点分析、状态变换和微分不等式的应用，以处理非单调参数。与当前的方法不同，通过考虑所有参数和初始条件的不确定性，对葡萄糖-胰岛素模型进行了有保证的模拟。此外，不需要时间离散化，这有助于大大减少计算时间。结果，我们能够计算出一个紧密的葡萄糖包络，该包络可以在低计算开销下限制所有可能的患者血糖反应。
