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.     

Comparison of interval and Monte Carlo simulation for the prediction of postprandial glucose under uncertainty in type 1 diabetes mellitus

In this paper, the problem of tackling uncertainty in the prediction of postprandial blood glucose is analyzed. Two simulation approaches, Monte Carlo and interval models, are studied and compared. Interval simulation is carried out using modal interval analysis. Simulation of a glucoregulatory model with uncertainty in insulin sensitivities, glucose absorption and food intake is carried out using both methods. Interval simulation is superior in predicting all severe and mild hyper- and hypoglycemia episodes. Furthermore, much less computational time is required for interval simulation than for Monte Carlo simulation.     

A learning automata-based blood glucose regulation mechanism in type 2 diabetes

This paper proposes a learning automata-based mechanism for blood glucose regulation in type 2 diabetics. The proposed mechanism takes into account the past history of the blood glucose level to determine the correct dosage of the insulin. This method uses the learning automata theory to predict the required dosage of insulin and records the patient history in parameters of a Gaussian probability distribution function. The parameters of the distribution function are updated based on the difference between the actual glucose level regulated by the learning automata and the normal range in such a way that the gap between the actual glucose level and the normal one is minimized. As the proposed algorithm proceeds, it can be seen that it converges to the optimal insulin dosage that keeps the glucose level in normal range for a long time. Convergence of the proposed algorithm to the optimal insulin dosage is theoretically proven. A clinical study is conducted to show the performance of the proposed insulin therapy system for regulation of the blood glucose level of type 2 diabetics.     

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.     

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.     

An augmented subcutaneous type 1 diabetic patient modelling and design of adaptive glucose control

In the present work, an augmented subcutaneous (SC) model of type 1 diabetic patients (T1DP) is proposed first by estimating the model parameters with the aid of nonlinear least square method using the physiological data. Next, a nonlinear adaptive controller is proposed to tackle two important issues of intra-patient variability (IPV) and uncertain meal disturbance (MD). The proposed patient model agrees quite well with the responses of one of the most popular existing nonlinear model used in the research of artificial pancreas. Further, the developed adaptive control is shown to be capable of providing desired glycemic control without feed-forward action for meal compensation or safety algorithms to avoid hypoglycemia. Due to the simple structure and capability of handling intra-patient variability of the adaptive controller, it can find immediate applicability in the development of the in-silico artificial pancreas.     

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.     

On an interval prediction of COVID-19 development based on a SEIR epidemic model

In this paper, a new version of the well-known epidemic mathematical SEIR model is used to analyze the pandemic course of COVID-19 in eight different countries. One of the proposed model’s improvements is to reflect the societal feedback on the disease and confinement features. The SEIR model parameters are allowed to be time-varying, and the ranges of their values are identified by using publicly available data for France, Italy, Spain, Germany, Brazil, Russia, New York State (US), and China. The identified model is then applied to predict the SARS-CoV-2 virus propagation under various conditions of confinement. For this purpose, an interval predictor is designed, allowing variations and uncertainties in the model parameters to be taken into account. The code and the utilized data are available on Github.     

Prediction of postprandial blood glucose under uncertainty and intra-patient variability in type 1 diabetes: A comparative study of three interval models

The behavior of three insulin action and glucose kinetics models was assessed for an insulin therapy regime in the presence of patient variability. For this purpose, postprandial glucose in patients with type 1 diabetes was predicted by considering intra- and inter-patient variability using modal interval analysis. Equations to achieve optimal prediction are presented for models 1, 2 and 3, which are of increasing complexity. The model parameters were adjusted to reflect the "same" patient in the presence of variability. The glucose response envelope for model 1, the simplest insulin-glucose model assessed, included the responses of the other two models when a good fit of the model parameters was achieved. Thus, under variability, simple glucose-insulin models may be sufficient to describe patient dynamics in most situations.     

A framework for rule-base evidential reasoning in the interval setting applied to diagnosing type 2 diabetes

A new framework for rule-base evidential reasoning in the interval setting is presented. While developing this framework, two collateral problems such as combining and normalizing interval-valued belief structures from different sources and comparing resulting belief intervals, the bounds of which are intervals, arise. The first problem is solved with the use of the so-called “interval extended zero” method. It is shown that interval valued results of the proposed approach to combining and normalizing interval-valued belief structures are enclosed in those obtained by known methods and possess three desirable intuitively obvious properties of normalization procedure defined in the paper. The second problem is solved using the method for interval comparison based on the Demposter-Shafer theory providing the interval valued results of comparison. The advantages of the proposed framework for rule-base evidential reasoning in the interval setting are demonstrated using the developed expert system for diagnosing type 2 diabetes.     

Interval optimization of dynamic response for structures with interval parameters

This paper presents an interval optimization method for the dynamic response of structures with interval parameters. The matrices of structures with interval parameters are given. Combining the interval extension of function with the perturbation theory of dynamic response, the method for interval dynamic response analysis is derived. The interval optimization problem is transformed into a corresponding deterministic one. Because the mean values and the uncertainties of the interval parameters can be elected as the design variables, more information of the optimization results can be obtained by the present method than that obtained by the deterministic one. The present method is implemented for a truss structure and a frame structure. The numerical results show that the method is effective.     

Identification of dynamical systems with a robust interval fuzzy model

In this paper we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used. The idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values. This results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. We believe that the fuzzy interval model can be very efficiently used, especially in fault detection and in robust control design.     

Blood glucose level prediction for diabetes based on modified fuzzy time series and particle swarm optimization

Blood glucose control is an essential goal for the patients who have Type‐1 diabetes (T1D). The prediction of the blood glucose levels for the next 30‐minute is crucial. If the predicted blood glucose level is in the critical ranges, and these predictions can be known in advance, then the patients can take the necessary cautions to prevent from it. In this article, we propose a modified fuzzy particle swarm optimization algorithm for the prediction of blood glucose levels of 30‐minute after the last measurement. We form the average and patient‐specific models to predict the blood glucose level of the patients. Both models are tested on two different datasets which contain patients with T1D. The experimental results are evaluated in terms of root mean squared error and Clarke error grid analysis metrics. The results indicate that our proposed modified algorithm is feasible to be applied to the prediction of blood glucose levels. In addition, this approach can assist patients with T1D for their blood glucose control.     

A study of interval metric and its application in multi-objective optimization with interval objectives

The aim of this paper is to discuss the optimality of interval multi-objective optimization problems with the help of different interval metric. For this purpose, we have proposed the new definitions of interval order relations by modifying the existing definitions and also modified different definitions of interval mathematics. Using the definitions of interval order relations and interval metric, the multi-objective optimization problem is converted into single objective optimization problem by different techniques. Then the corresponding problems have been solved by hybrid Tournament Genetic Algorithm with whole arithmetic crossover and double mutation (combination of non-uniform and boundary mutations). To illustrate the methodology, five numerical examples have been solved and the computational results have been compared. Finally, to test the efficiency of the proposed hybrid Tournament Genetic Algorithm, sensitivity analyses have been carried out graphically with respect to genetic algorithm parameters.     

Implementation and evaluation of a decision support system for type II diabetes

A decision support system for the management of oral hypoglycaemic therapy in type II diabetes was evaluated. The ruleset contained therein forms the basis of a prototype computer programme, but in order to assess the robustness of the individual rules, it was decided it was necessary to use a paper-based form of the ruleset. A nurse with no previous experience of managing type II diabetes was trained to use the system and then undertook the exclusive management of half of all new type II diabetics, from a district population of 300 000, over a 16-month period. General practices within this area were divided into two groups, study and control, matching for size, geographical area and standards of existing diabetes care. Patients (n = 102) from the study group practices were then assigned to her care. Those patients (n = 116) in the control group of practices were treated according to their normal procedures. The decision support system for oral hypoglycaemic therapy was based on the following criteria: the current type of treatment (six levels); current glycaemic control (HbA₁ and FBS) — whether improving, steady or worsening; and weight — %IBW, whether rising, steady or falling. Each of these parameters was carefully defined on the basis of established practice and clinical experience. Patients after initial education were seen at their usual clinic by the nurse only, on a monthly basis, until satisfactory glycaemic control was established and thereafter reviewed 3 monthly. She was also responsible for ensuring the organisation of Diabetes Annual Review procedures. The medical records of the control group patients were examined at the end of the study and data on glycaemic control and Annual Reviews extracted. In the study group 98% patients achieved HbA₁ levels within the normal range and all patients had full annual reviews performed. The control practices achieved much poorer degrees of metabolic control (P < 0.01) and completed fewer annual reviews. The study group did not demonstrate a significantly increased frequency of clinical hypoglycaemia consequent upon better blood sugar control. No exceptions to the ruleset, as initially defined, were detected. In conclusion, this decision support system was successful at achieving standards of diabetes control and care equal to or better than conventional structures of diabetes care. Implementation of such a system, on a simple computer platform, could greatly assist and possibly improve diabetes management in general practice.     

Graphs of interval count two with a given partition

We describe a polynomial time algorithm to decide for a given connected graph G and a given partition of its vertex set into two sets A and B  , whether it is possible to assign a closed interval I(u)$I(u)$ to each vertex u of G such that two distinct vertices u and v of G   are adjacent if and only if I(u)$I(u)$ and I(v)$I(v)$ intersect, all intervals assigned to vertices in A   have some length _LA$L_A$, and all intervals assigned to vertices in B   have some length _LB$L_B$ where _LA<_LB$L_A<L_B$. Our result is motivated by the interval count problem whose complexity status is open.     

区间适应值交互式遗传算法神经网络代理模型

为了解决交互式遗传算法的用户疲劳问题,提出区间适应值交互式遗传算法神经网络代理模型．首先,对用户已评价个体的基因型及其适应值进行采样以训练神经网络,使其逼近区间适应值的上下限;然后,利用神经网络代理模型,评价后续的部分进化个体,并不断更新训练数据和代理模型,以保证逼近精度;最后,对算法性能进行了定量分析,并将其应用于服装进化设计系统．分析结果表明,所提算法在减轻用户疲劳的前提下,具有更多找到满意解的机会．