Ståhl F, Johansson R
Department of Automatic Control, Lund University, SE22100 Lund, Sweden.
Math Biosci. 2009 Feb;217(2):101-17. doi: 10.1016/j.mbs.2008.10.008. Epub 2008 Oct 30.
Insulin-Dependent Diabetes Mellitus (IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. Daily compensation of the deficiency requires 4-6 insulin injections to be taken daily, the aim of this insulin therapy being to maintain normoglycemia - i.e., a blood glucose level between 4 and 7mmol/l. To determine the quantity and timing of these injections, various different approaches are used. Currently, mostly qualitative and semi-quantitative models and reasoning are used to design such a therapy. Here, an attempt is made to show how system identification and control may be used to estimate predictive quantitative models to be used in design of optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin-glucose interaction. The insulin subsystem aims to describe the absorption of injected insulin from the subcutaneous depots and the glucose subsystem the absorption of glucose from the gut following a meal. These subsystems were modeled using compartment models and proposed models found in the literature. Several black-box models and grey-box models describing the insulin/glucose interaction were developed and analyzed. These models were fitted to real data monitored by an IDDM patient. Many difficulties were encountered, typical of biomedical systems: Non-uniform and scarce sampling, time-varying dynamics and severe nonlinearities were some of the difficulties encountered during the modeling. None of the proposed models were able to describe the system accurately in all aspects during all conditions. However, all the linear models shared some dynamics. Based on the estimated models, short-term blood glucose predictors for up to two-hour-ahead blood glucose prediction were designed. Furthermore, we explored the issues that arise when applying prediction theory and control to short-term blood glucose prediction.
胰岛素依赖型糖尿病（IDDM）是一种慢性病，其特征是胰腺无法产生足够量的胰岛素。每日弥补这种不足需要每天注射4至6次胰岛素，这种胰岛素疗法的目的是维持血糖正常——即血糖水平在4至7毫摩尔/升之间。为了确定这些注射的剂量和时间，人们使用了各种不同的方法。目前，大多使用定性和半定量模型及推理来设计这样的疗法。在此，我们试图展示如何利用系统识别和控制来估计用于设计最佳胰岛素治疗方案的预测定量模型。该系统被分为三个子系统，即胰岛素子系统、葡萄糖子系统和胰岛素 - 葡萄糖相互作用。胰岛素子系统旨在描述皮下注射部位注射胰岛素的吸收情况，而葡萄糖子系统描述进食后肠道对葡萄糖的吸收情况。这些子系统使用房室模型和文献中找到的模型进行建模。开发并分析了几个描述胰岛素/葡萄糖相互作用的黑箱模型和灰箱模型。这些模型与一名IDDM患者监测到的实际数据进行拟合。遇到了许多生物医学系统常见的困难：采样不均匀且稀少、动态时变以及严重的非线性是建模过程中遇到的一些困难。所提出的模型在所有情况下都无法在各个方面准确描述该系统。然而，所有线性模型都有一些共同的动态特性。基于估计的模型，设计了用于提前两小时预测血糖的短期血糖预测器。此外，我们探讨了将预测理论和控制应用于短期血糖预测时出现的问题。
