Continuous-time interval model identification of blood glucose dynamics for type 1 diabetes

While good physiological models of the glucose metabolism in type 1 diabetic patients are well known, their parameterisation is difficult. The high intra-patient variability observed is a further major obstacle. This holds for data-based models too, so that no good patient-specific models are available. Against this background, this paper proposes the use of interval models to cover the different metabolic conditions. The control-oriented models contain a carbohydrate and insulin sensitivity factor to be used for insulin bolus calculators directly. Available clinical measurements were sampled on an irregular schedule which prompts the use of continuous-time identification, also for the direct estimation of the clinically interpretable factors mentioned above. An identification method is derived and applied to real data from 28 diabetic patients. Model estimation was done on a clinical data-set, whereas validation results shown were done on an out-of-clinic, everyday life data-set. The results show that the interval model approach allows a much more regular estimation of the parameters and avoids physiologically incompatible parameter estimates.     

Development of a multi-parametric model predictive control algorithm for insulin delivery in type 1 diabetes mellitus using clinical parameters

A multi-parametric model predictive control (mpMPC) algorithm for subcutaneous insulin delivery for individuals with type 1 diabetes mellitus (T1DM) that is computationally efficient, robust to variations in insulin sensitivity, and involves minimal burden for the user is proposed. System identification was achieved through impulse response tests feasible for ambulatory conditions on the UVa/Padova simulator adult subjects with T1DM. An alternative means of system identification using readily available clinical parameters was also investigated. A safety constraint was included explicitly in the algorithm formulation using clinical parameters typical of those available to an attending physician. Closed-loop simulations were carried out with daily consumption of 200 g carbohydrate. Controller robustness was assessed by subject/model mismatch scenarios addressing daily, simultaneous variation in insulin sensitivity and meal size with the addition of Gaussian white noise with a standard deviation of 10%. A second-order-plus-time-delay transfer function model fit the validation data with a mean (coefficient of variation) root-mean-square-error (RMSE) of 26 mg/dL (19%) for a 3 h prediction horizon. The resulting control law maintained a low risk Low Blood Glucose Index without any information about carbohydrate consumption for 90% of the subjects. Low-order linear models with clinically meaningful parameters thus provided sufficient information for a model predictive control algorithm to control glycemia. The use of clinical knowledge as a safety constraint can reduce hypoglycemic events, and this same knowledge can further improve glycemic control when used explicitly as the controller model. The resulting mpMPC algorithm was sufficiently compact to be implemented on a simple electronic device.     

Weighting Restriction for Intravenous Insulin Delivery on T1DM Patient via $H_{infty}$ Control

A weighting restriction with frequency components is proposed for the insulin delivery on Type 1 Diabetics Mellitus (T1DM) towards the control of the blood glucose level. The weighting restriction is stated from a model of healthy subjects which includes a rate for insulin delivery. The frequency components are incorporated via a transfer function from the plasma glucose to the free-plasma insulin such that a H _infin-based controller is designed. In this way, the control synthesis involves the frequency components on which a healthy pancreas delivers insulin for the glucose homeostasis. In order to test controller performance, a dynamical model of an actuator is also included in the closed-loop system to add its effects in the closed-loop evaluation of the H _infin -based controller. The actuator is a pump to deliver of an insulin infusion according with the rate computed by the controller. Note that the contribution is particularly focused on T1DM; however, the inclusion of weighting restriction can be used also onto critical care conditions.     

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.     

面向智能血糖管理的餐前胰岛素剂量贝叶斯学习优化方法

餐前胰岛素剂量精准决策是改善糖尿病患者血糖管理的关键. 临床治疗中胰岛素剂量调整一般在较短时间内完成, 具有典型的小样本特征; 数据驱动建模在该情形下无法准确学习患者餐后血糖代谢规律, 难以确保胰岛素剂量的安全和有效决策. 针对这一问题, 设计一种临床经验辅助的餐前胰岛素剂量自适应优化决策框架, 构建高斯过程血糖预测模型和模型有效性在线评估机制, 提出基于历史剂量和临床经验决策约束的贝叶斯优化方法, 实现小样本下餐后血糖轨迹的安全预测和餐前胰岛素注射剂量的优化决策. 该方法的安全性和有效性通过美国食品药品监督管理局接受的UVA/Padova T1DM平台测试结果和1型糖尿病患者实际临床数据决策结果充分验证. 可为餐前胰岛素剂量智能决策及临床试验提供方法基础和技术支持, 也为中国糖尿病患者血糖管理水平的有效改善, 提供了精准医学治疗手段.     

Insulin dosage optimization based on prediction of postprandial glucose excursions under uncertain parameters and food intake

Considering the difficulty in selecting correct insulin doses and the problem of hyper- and hypoglycemia episodes in type 1 diabetes, dosage-aid systems are very useful for these patients. A model-based approach to this problem must unavoidably consider uncertainty sources such as large intra-patient variability and food intake. In the present study, postprandial glucose is predicted considering this uncertain information using modal interval analysis. This approach calculates a safer prediction of possible hyper- and hypoglycemia episodes induced by insulin therapy for an individual patient's parameters and integrates this information into a dosage-aid system. Predictions of a patient's postprandial glucose at 5-h intervals are used to predict the risk for a given therapy. Then the insulin dose and injection-to-meal time with the lowest risk are calculated. The method has been validated for three different scenarios corresponding to preprandial glucose values of 100, 180 and 250 mg/dl.     

Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems

A continuous-time system cannot be recovered solely from its uniformly sampled discrete-time model through the zero-order hold discretization or step-invariant transformation, but our studies indicate that it can be recovered uniquely from its non-uniformly sampled discrete-time model. In this paper, we discuss some related issues of non-uniformly sampled systems, including model derivation, controllability and observability, computation of single-rate models with different sampling periods, reconstruction of continuous-time systems, and parameter identification of non-uniformly sampled discrete-time systems. A numerical example is also given for illustration.     

Artificial pancreas for type 1 diabetes: Closed-loop algorithm based on Error Dynamics Shaping

The present study evaluates Error Dynamics Shaping (EDS) as an alternative closed-loop strategy for subcutaneous insulin delivery in type 1 diabetes. EDS uses the energy-based principle of damping to ensure a robust stability of closed-loop systems despite strong unknown disturbances. It benefits from intuitive tuning criteria and provides explicit state feedback control laws requiring few computational resources. Using FDA approved UVa T1DM simulator, the robustness of an EDS controller against meal profile variability was tested in one scenario over a day and three scenarios over a week with meal variability. No hypoglycaemia was recorded and hyperglycaemias kept limited. In silico, EDS controller proved effective in achieving normoglycaemia and robust to meal disturbances.     

Parameters estimation of systems with delayed and structured entries

This paper deals with on-line identification of continuous-time systems with structured entries. Such entries, which may consist of inputs, perturbations or piecewise polynomial (time varying) parameters, can be defined as signals that can be easily annihilated. The proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients. Application to delayed and switching hybrid systems are proposed. Numerical simulations with noisy data but also experimental results on a delay process are provided.     

Stability of sampled-data piecewise-affine systems under state feedback

This paper addresses stability of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. The paper presents conditions under which the trajectories of the sampled-data closed-loop system will exponentially converge to a neighborhood of the origin. Moreover, the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure, in particular, related to the sampling period. Finally, it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous-time PWA state feedback controller can be recovered by the emulated controller.     

Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes

Current insulin therapy for patients with type 1 diabetes often results in high variability in blood glucose concentrations and may cause hyperglycemic/hypoglycemic episodes. Closing the glucose control loop with a fully automated electro-mechanical pancreas will improve the quality of life for insulin-dependent patients. An adaptive control algorithm is proposed to keep glucose concentrations within normoglycemic range and dynamically respond to glycemic challenges. A model-based control strategy is used to calculate the required insulin infusion rate, while the model parameters are recursively tuned. The algorithm handles delays associated with insulin absorption, time-lag between subcutaneous and blood glucose concentrations, and variations in inter/intra-subject glucose–insulin dynamics. Simulation results for simultaneous meal and physiological disturbances are demonstrated for subcutaneous insulin infusion.     

Diagnosis of hypoglycemic episodes using a neural network based rule discovery system

Hypoglycemia or low blood glucose is dangerous and can result in unconsciousness, seizures and even death for Type 1 diabetes mellitus (T1DM) patients. Based on the T1DM patients’ physiological parameters, corrected QT interval of the electrocardiogram (ECG) signal, change of heart rate, and the change of corrected QT interval, we have developed a neural network based rule discovery system with hybridizing the approaches of neural networks and genetic algorithm to identify the presences of hypoglycemic episodes for TIDM patients. The proposed neural network based rule discovery system is built and is validated by using the real T1DM patients’ data sets collected from Department of Health, Government of Western Australia. Experimental results show that the proposed neural network based rule discovery system can achieve more accurate results on both trained and unseen T1DM patients’ data sets compared with those developed based on the commonly used classification methods for medical diagnosis, statistical regression, fuzzy regression and genetic programming. Apart from the achievement of these better results, the proposed neural network based rule discovery system can provide explicit information in the form of production rules which compensate for the deficiency of traditional neural network method which do not provide a clear understanding of how they work in prediction as they are in an implicit black-box structure. This explicit information provided by the product rules can convince medical doctors to use the neural networks to perform diagnosis of hypoglycemia on T1DM patients.     

Parameter and delay estimation of continuous-time models using a linear filter

Linear filter methods have been used in the field of continuous-time identification over a considerable time period. Due to the effectiveness and simplicity of the approach, they have found widespread applications and drawn much interest from the system identification community. However, the estimation of time delay along with continuous-time model parameters has remained an unsolved problem although there are some simple step response based methods. In this paper, a new linear filter method is introduced for simultaneous parameter and delay estimation of continuous-time transfer function models. The proposed method estimates the time delay along with other model parameters in an iterative way through simple linear regression. In addition, the estimated delay is not necessarily an integer multiple of the sampling interval. The applicability of the developed procedure is demonstrated by simulations as well as a laboratory scale experimental example.     

A multicompartment model for open-loop control of glucose in insulin-dependent diabetics

This paper describes a model that has been developed for individually adjusted therapy management in insulin-dependent diabetics. The multicompartment model considers all relevant aspects of glucose kinetics and its dependence on insulin. The structure of the model reflects that of the physiological system. Its parameters can be classified into (a) general parameters that are independent of the individual, (b) classifying parameters that are related systematically to the individual, and (c) distinguishing parameters. Classifying parameters allow a very convenient adjustment to relevant features of the individual like sex, age, body weight and length. The model can be employed in open-loop control for the calculation of insulin dosages. It allows the prediction of the system's behaviour as well as the consideration of predictable disturbance variables, e.g. food intake and physical exercise.     

Neural predictive controller for closed-loop control of glucose using the subcutaneous route: A simulation study

The objective of this study was to develop and evaluate a strategy for closed-loop control of glucose using subcutaneous (s.c.) glucose measurement and s.c. infusion of monomeric insulin analogues. The method was based on off-line identification of the glucoregulatory system using neural networks and a nonlinear model predictive controller. Numerical studies on system identification and closed-loop control of glucose were carried out using a comprehensive model of glucose regulation. The proposed control strategy was robust against noise and time delays, and enabled stable control also for slow time variations of the controlled process. In conclusion, closed-loop control of glucose is feasible using the s.c. route and a neural predictive controller.     

具有不稳定初始状态的连续时间系统辨识

针对传统辨识方法不适用于具有不稳定初始状态的连续时间系统的问题,提出一种全新的状态估计辨识法.首先,用状态空间模型中状态变量的初始值表征系统初始状态,并将状态变量的初始值看作待辨识参数的一部分.然后,用粒子群优化算法获得所有参数的最优估计.该方法在测试开始前不需要任何过程数据,对测试信号无任何要求,可直接用于闭环辨识.仿真实验证明该算法是有效的.     

Frequency-domain identification of continuous-time ARMA models from sampled data

The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.