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Short and Medium Term Blood Glucose Prediction Using Multi-objective Grammatical Evolution

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Abstract

In this paper we investigate the benefits of applying a multi-objective approach for solving a symbolic regression problem by means of grammatical evolution. In particular, we continue with previous research about finding expressions to model the glucose levels in blood of diabetic patients. We use here a multi-objective Grammatical Evolution approach based on NSGA-II algorithm, considering the root mean squared error and an ad-hoc fitness function as objectives. This ad-hoc function is based on the Clarke Error Grid analysis, which is useful for showing the potential danger of mispredictions. Experimental results show that the multi-objective approach improves previous results in terms of Clarke Error Grid analysis reducing the number of dangerous mispredictions.

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In this paper we investigate the benefits of applying a multi-objective approach for solving a symbolic regression problem by means of Grammatical Evolution. In particular, we extend previous work, obtaining mathematical expressions to model glucose levels in the blood of diabetic patients. Here we use a multi-objective Grammatical Evolution approach based on the NSGA-II algorithm, considering the root-mean-square error and an ad-hoc fitness function as objectives. This ad-hoc function is based on the Clarke Error Grid analysis, which is useful for showing the potential danger of mispredictions in diabetic patients. In this work, we use two datasets to analyse two different scenarios: What-if and Agnostic , the most common in daily clinical practice. In the What-if scenario, where future events are evaluated, results show that the multi-objective approach improves previous results in terms of Clarke Error Grid analysis by reducing the number of dangerous mispredictions. In the Agnostic situation, with no available information about future events, results suggest that we can obtain good predictions with only information from the previous hour for both Grammatical Evolution and Multi-Objective Grammatical Evolution.
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Self-monitoring of blood glucose (SMBG) and continuous glucose monitoring (CGM) are commonly used by type 1 diabetes (T1D) patients to measure glucose concentrations. The proposed adaptive basal-bolus algorithm (ABBA) supports inputs from either SMBG or CGM devices to provide personalised suggestions for the daily basal rate and prandial insulin doses on the basis of the patients' glucose level on the previous day. The ABBA is based on reinforcement learning (RL), a type of artificial intelligence, and was validated in silico with an FDA-accepted population of 100 adults under different realistic scenarios lasting three simulated months. The scenarios involve three main meals and one bedtime snack per day, along with different variabilities and uncertainties for insulin sensitivity, mealtime, carbohydrate amount, and glucose measurement time. The results indicate that the proposed approach achieves comparable performance with CGM or SMBG as input signals, without influencing the total daily insulin dose. The results are a promising indication that AI algorithmic approaches can provide personalised adaptive insulin optimisation and achieve glucose control - independently of the type of glucose monitoring technology.
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The large patient variability in human physiology and the effects of variables such as exercise or meals challenge current prediction modeling techniques. Physiological models are very precise but they are typically complex and specific physiological knowledge is required. In contrast, data-based models allow the incorporation of additional inputs and accurately capture the relationship between these inputs and the outcome, but at the cost of losing the physiological meaning of the model. In this work, we designed a hybrid approach comprising physiological models for insulin and grammatical evolution, taking into account the clinical harm caused by deviations from the target blood glucose by using a penalizing fitness function based on the Clarke error grid. The prediction models were built using data obtained over 14 days for 100 virtual patients generated by the UVA/Padova T1D simulator. Midterm blood glucose was predicted for the 100 virtual patients using personalized models and different scenarios. The results obtained were promising; an average of 98.31% of the predictions fell in zones A and B of the Clarke error grid. Midterm predictions using personalized models are feasible when the configuration of grammatical evolution explored in this study is used. The study of new alternative models is important to move forward in the development of alarm-and-control applications for the management of type 1 diabetes and the customization of the patient’s treatments. The hybrid approach can be adapted to predict short-term blood glucose values to detect continuous glucose-monitoring sensor errors and to estimate blood glucose values when the continuous glucose-monitoring system fails to provide them.
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Predicting glucose values on the basis of insulin and food intakes is a difficult task that people with diabetes need to do daily. This is necessary as it is important to maintain glucose levels at appropriate values to avoid not only short-term, but also long-term complications of the illness. Artificial intelligence in general and machine learning techniques in particular have already lead to promising results in modeling and predicting glucose concentrations. In this work, several machine learning techniques are used for the modeling and prediction of glucose concentrations using as inputs the values measured by a continuous monitoring glucose system as well as also previous and estimated future carbohydrate intakes and insulin injections. In particular, we use the following four techniques: genetic programming, random forests, k-nearest neighbors, and grammatical evolution. We propose two new enhanced modeling algorithms for glucose prediction, namely (i) a variant of grammatical evolution which uses an optimized grammar, and (ii) a variant of tree-based genetic programming which uses a three-compartment model for carbohydrate and insulin dynamics. The predictors were trained and tested using data of ten patients from a public hospital in Spain. We analyze our experimental results using the Clarke error grid metric and see that 90% of the forecasts are correct (i.e., Clarke error categories A and B), but still even the best methods produce 5 to 10% of serious errors (category D) and approximately 0.5% of very serious errors (category E). We also propose an enhanced genetic programming algorithm that incorporates a three-compartment model into symbolic regression models to create smoothed time series of the original carbohydrate and insulin time series.
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Objective Recent studies have provided new insights into nonlinearities of insulin action in the hypoglycemic range and into glucagon kinetics as it relates to response to hypoglycemia. Based on these data, we developed a new version of the UVA/PADOVA Type 1 Diabetes Simulator, which was submitted to FDA in 2013 (S2013). Methods The model of glucose kinetics in hypoglycemia has been improved, implementing the notion that insulin-dependent utilization increases nonlinearly when glucose decreases below a certain threshold. In addition, glucagon kinetics and secretion and action models have been incorporated into the simulator: glucagon kinetics is a single compartment; glucagon secretion is controlled by plasma insulin, plasma glucose below a certain threshold, and glucose rate of change; and plasma glucagon stimulates with some delay endogenous glucose production. A refined statistical strategy for virtual patient generation has been adopted as well. Finally, new rules for determining insulin to carbs ratio (CR) and correction factor (CF) of the virtual patients have been implemented to better comply with clinical definitions. Results S2013 shows a better performance in describing hypoglycemic events. In addition, the new virtual subjects span well the real type 1 diabetes mellitus population as demonstrated by good agreement between real and simulated distribution of patient-specific parameters, such as CR and CF. Conclusions S2013 provides a more reliable framework for in silico trials, for testing glucose sensors and insulin augmented pump prediction methods, and for closed-loop single/dual hormone controller design, testing, and validation.
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We study grammars used in grammatical genetic programming (GP) which create algorithms that control the base station pilot power in a femtocell network. The overall goal of evolving algorithms for femtocells is to create a continuous online evolution of the femtocell pilot power control algorithm in order to optimize their coverage. We compare the performance of different grammars and analyse the femtocell simulation model using the grammatical genetic programming method called grammatical evolution. The grammars consist of conditional statements or mathematical functions as are used in symbolic regression applications of GP, as well as a hybrid containing both kinds of statements. To benchmark and gain further information about our femtocell network simulation model we also perform random sampling and limited enumeration of femtocell pilot power settings. The symbolic regression based grammars require the most configuration of the evolutionary algorithm and more fitness evaluations, whereas the conditional statement grammar requires more domain knowledge to set the parameters. The content of the resulting femtocell algorithms shows that the evolutionary computation (EC) methods are exploiting the assumptions in the model. The ability of EC to exploit bias in both the fitness function and the underlying model is vital for identifying the current system and improves the model and the EC method. Finally, the results show that the best fitness and engineering performances for the grammars are similar over both test and training scenarios. In addition, the evolved solutions’ performance is superior to those designed by humans.
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Although the scientific literature contains numerous reports of the statistical accuracy of systems for self-monitoring of blood glucose (SMBG), most of these studies determine accuracy in ways that may not be clinically useful. We have developed an error grid analysis (EGA), which describes the clinical accuracy of SMBG systems over the entire range of blood glucose values, taking into account 1) the absolute value of the system-generated glucose value, 2) the absolute value of the reference blood glucose value, 3) the relative difference between these two values, and 4) the clinical significance of this difference. The EGA of accuracy of five different reflectance meters (Eyetone, Dextrometer, Glucometer I, Glucometer II, Memory Glucometer II), a visually interpretable glucose reagent strip (Glucostix), and filter-paper spot glucose determinations is presented. In addition, reanalyses of a laboratory comparison of three reflectance meters (Accucheck II, Glucometer II, Glucoscan 9000) and of two previously published studies comparing the accuracy of five different reflectance meters with EGA is described. EGA provides the practitioner and the researcher with a clinically meaningful method for evaluating the accuracy of blood glucose values generated with various monitoring systems and for analyzing the clinical implications of previously published data.
Article
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Glucose sensors often measure s.c. interstitial fluid (ISF) glucose rather than blood or plasma glucose. Putative differences between plasma and ISF glucose include a protracted delay during the recovery from hypoglycaemia and an increased gradient during hyperinsulinaemia. These have often been investigated using sensor systems that have delays due to signal smoothing, or require long equilibration times. The aim of the present study was to define these relationships during hypoglycaemia in a well-equilibrated system with no smoothing. Hypoglycaemia was induced by i.v. insulin infusion (360 pmol.m(-2).min(-1)) in ten non-diabetic subjects. Glucose was sequentially clamped at approximately 5, 4.2 and 3.1 mmol/l and allowed to return to normoglycaemia. Subjects wore two s.c. glucose sensors (Medtronic MiniMed, Northridge, CA, USA) that had been inserted for more than 12 h. A two-compartment model was used to quantify the delay and gradient. The delay during the fall in plasma glucose was not different from the delay during recovery (8.3+/-0.67 vs 6.3+/-1.1 min; p=0.27) and no differences were observed in the ratio of sensor current to plasma glucose at basal insulin (2.7+/-0.25 nA.mmol(-1).l) compared with any of the hyperinsulinaemic clamp phases (2.8+/-0.18, 2.7+/-0.021, 2.9+/-0.21; p=NS). The ratio was significantly elevated following recovery to normoglycaemia (3.1+/-0.2 nA.mmol(-1).l; p<0.001). The elevated ratio suggests that the plasma to ISF glucose gradient was decreased following hypoglycaemia, possibly due to increased skin blood flow. Recovery from hypoglycaemia is not accompanied by a protracted delay and insulin does not increase the plasma to s.c. ISF glucose gradient.
Conference Paper
This study investigates how to improve the predictions of glucose values obtained with genetic programming models. A set of statistical techniques are used to discover glucose profiles that identify similar situations in patients with type 1 diabetes mellitus, and incorporate this knowledge to the models. Glucose time series are divided into 4-hour non-overlapping slots and clustered using the technique based on decision trees called chi-square automatic interaction detection, to classify glucose profiles into groups using two decision variables: day of the week and time slot of the day. The objective is to customize models for different glucose profiles that appear in the patient's day-to-day. Genetic programming models created with glucose values from the original data-set are compared to those of models created with classified glucose values. Significant differences (p-value < 0.05) and associations are observed between the glucose profiles. In general, using classified glucose values in models created with genetic programming, the accuracy of the predictions improves in comparison with those of models created with the original data-set. We concluded that the classification process can be useful to correct and improve habits or clinical therapies in patients, and obtain more accurate models through automatic learning techniques and artificial intelligence.
Conference Paper
Structured grammatical evolution is a recent grammar-based genetic programming variant that tackles the main drawbacks of Grammatical Evolution, by relying on a one-to-one mapping between each gene and a non-terminal symbol of the grammar. It was applied, with success, in previous works with a set of classical benchmarks problems. However, assessing performance on hard real-world problems is still missing. In this paper, we fill in this gap, by analyzing the performance of SGE when generating predictive models for the glucose levels of diabetic patients. Our algorithm uses features that take into account the past glucose values, insulin injections, and the amount of carbohydrate ingested by a patient. The results show that SGE can evolve models that can predict the glucose more accurately when compared with previous grammar-based approaches used for the same problem. Additionally, we also show that the models tend to be more robust, since the behavior in the training and test data is very similar, with a small variance.
Chapter
One the most relevant application areas of artificial intelligence and machine learning in general is medical research. We here focus on research dedicated to diabetes, a disease that affects a high percentage of the population worldwide and that is an increasing threat due to the advance of the sedentary life in the big cities. Most recent studies estimate that it affects about more than 410 million people in the world. In this chapter we discuss a set of techniques based on GE to obtain mathematical models of the evolution of blood glucose along the time. These models help diabetic patients to improve the control of blood sugar levels and thus, improve their quality of life. We summarize some recent works on data preprocessing and design of grammars that have proven to be valuable in the identification of prediction models for type 1 diabetics. Furthermore, we explain the data augmentation method which is used to sample new data sets. © Springer International Publishing AG, part of Springer Nature 2018.
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Background: Predicting insulin-induced postprandial hypoglycemic events is critical for the safety of type 1 diabetes patients because an early warning of hypoglycemia facilitates correction of the insulin bolus before its administration. The postprandial hypoglycemic event counts can be lowered by reducing the size of the bolus based on a reliable prediction but at the cost of increasing the average blood glucose. Methods: We developed a method for predicting postprandial hypoglycemia using machine learning techniques personalized to each patient. The proposed system enables on-line therapeutic decision making for patients using a sensor augmented pump therapy. Two risk-based approaches were developed for a window of 240 min after the meal/bolus, and they were tested based on real retrospective data from 10 patients using 70 mg/dL and 54 mg/dL as thresholds according to the consensus for Level 1 and Level 2 hypoglycemia, respectively. Due to the small size of the patient cohort, we trained personalized models for each patient. Results: The median specificity and sensitivity were 79% and 71% for Level 1 hypoglycemia, respectively, and 81% and 77% for Level 2. Conclusions: The results demonstrated that it is feasible to anticipate hypoglycemic events with a reasonable false-positive rate. The accuracy of the results and the trade-off between performance metrics allow its use in decision support systems for patients who wear insulin pumps.
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This paper describes our preliminary steps towards the deployment of a brand-new original feature for a telemedicine portal aimed at helping people suffering from diabetes. In fact, people with diabetes necessitate careful handling of their disease to stay healthy. As such a disease is correlated to a malfunction of the pancreas that produces very little or no insulin, a way to enhance the quality of life of these subjects is to implement an artificial pancreas able to inject an insulin bolus when needed. The goal of this paper is to extrapolate a regression model, capable of estimating the blood glucose (BG) through interstitial glucose (IG) measurements, that represents a possible revolutionizing step in constructing the fundamental element of such an artificial pancreas. In particular, a new evolutionary approach is illustrated to stem a mathematical relationship between BG and IG. To accomplish the task, an automatic evolutionary procedure is also devised to estimate the missing BG values within the investigated real-world database made up of both BG and IG measurements of people suffering from Type 1 diabetes. The discovered model is validated through a comparison with other models during the experimental phase on global and personalized data treatment. Moreover, investigation is performed about the accuracy of one single global relationship model for all the subjects involved in the study, as opposed to that obtained through a personalized model found for each of them. Once this research is clinically validated, the important feature of estimating BG will be added to a web portal for diabetic subjects for telemedicine purposes.
Conference Paper
Currently, Diabetes Mellitus Type 1 patients are waiting hopefully for the arrival of the Artificial Pancreas (AP) in a near future. AP systems will control the blood glucose of people that suffer the disease, improving their lives and reducing the risks they face everyday. At the core of the AP, an algorithm will forecast future glucose levels and estimate insulin bolus sizes. Grammatical Evolution (GE) has been proved as a suitable algorithm for predicting glucose levels. Nevertheless, one the main obstacles that researches have found for training the GE models is the lack of significant amounts of data. As in many other fields in medicine, the collection of data from real patients is very complex. In this paper, we propose a data augmentation algorithm that generates synthetic glucose time series from real data. The synthetic time series can be used to train a unique GE model or to produce several GE models that work together in a combining system. Our experimental results show that, in a scarce data context, Grammatical Evolution models can get more accurate and robust predictions using data augmentation.
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Background and objective: The inter-subject variability characterizing the patients affected by type 1 diabetes mellitus makes automatic blood glucose control very challenging. Different patients have different insulin responses, and a control law based on a non-individualized model could be ineffective. The definition of an individualized control law in the context of artificial pancreas is currently an open research topic. In this work we consider two novel identification approaches that can be used for individualizing linear glucose-insulin models to a specific patient. Methods: The first approach belongs to the class of black-box identification and is based on a novel kernel-based nonparametric approach, whereas the second is a gray-box identification technique which relies on a constrained optimization and requires to postulate a model structure as prior knowledge. The latter is derived from the linearization of the average nonlinear adult virtual patient of the UVA/Padova simulator. Model identification and validation are based on in silico data collected during simulations of clinical protocols designed to produce a sufficient signal excitation without compromising patient safety. The identified models are evaluated in terms of prediction performance by means of the coefficient of determination, fit, positive and negative max errors, and root mean square error. Results: Both identification approaches were used to identify a linear individualized glucose-insulin model for each adult virtual patient of the UVA/Padova simulator. The resulting model simulation performance is significantly improved with respect to the performance achieved by a linear average model. Conclusions: The approaches proposed in this work have shown a good potential to identify glucose-insulin models for designing individualized control laws for artificial pancreas.
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Diabetes is a worldwide epidemic that carries a high cost in consumption of health care resources and is associated with increased morbidity and mortality. Nursing care of patients with diabetes is complex and can be challenging. Evidence-based guidelines regarding diabetes management are lengthy and do not always readily translate into hands on nursing care. The nurse must complete a thorough assessment of patients with diabetes, collaborate with the interprofessional team to achieve individual treatment goals, and prevent and effectively manage hypoglycemia. The nurse must begin discharge planning upon admission due to the complex nature of diabetes and the need for patient education and referrals related to diabetes self-management education. Effective management of patients with diabetes requires nurses to be well informed of evidence-based guidelines related to diabetes care.
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The mathematical models used in simulation must be reliable and trustworthy enough to describe the real systems with an appropriate accuracy. This simulation process is specially important in marine environment due to the changing environmental conditions, to the cost of the infrastructure needed to carry out tests, and to the need of calibration, deployment and recovery of the marine systems. If a reliable mathematical model of the vehicle is available, a part of the experimental tests can be avoided. In this paper we present a system identification technique based on genetic programming, the symbolic regression, to be applied on marine systems. In this sense, we show that it is possible to obtain a mathematical model of a ship for control purposes without the need of describing or knowing the model structure in advance, i.e., the identification itself provides the model structure that better describes the system. Thus, we can define a reliable black-box model that is computed in a simple way and where no many experimental data are needed. The model obtained is tested with additional data and manoeuvres to show its good performance and prediction ability.
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Online prediction of glucose concentration is of importance for blood glucose control in diabetes. For conventional modeling methods, model identification has to be repeated with sufficient data collected for each subject. This may cause repetitive cost and burden for patients and clinician and requires a lot of modeling efforts. Here, a rapid model development strategy is proposed using the idea of model migration for new subjects. First, a base model is obtained which can be empirically identified from any subject or constructed by priori knowledge. Then parameters of inputs in the base model are properly revised based on a small amount of data from new subjects. These issues are investigated by developing auto-regressive models with exogenous inputs (ARX) based on thirty in silico subjects. Some important issues relating to model adjustment performance are also checked, referring to the data used for model parameter adjustment and the interaction of two inputs, etc. The rapid modeling method is compared with subject-dependent models developed based on a large number of data with respect to on-line short-term (30min) glucose prediction accuracy.
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Since the discovery of insulin, great progress has been made to improve the accuracy and safety of automated insulin delivery systems to help patients with type 1 diabetes achieve their treatment goals without causing hypoglycaemia. In recent years, bioengineering technology has greatly advanced diabetes management, with the development of blood glucose meters, continuous glucose monitors, insulin pumps and control systems for automatic delivery of one or more hormones. New insulin analogues have improved subcutaneous absorption characteristics, but do not completely eliminate the risk of hypoglycaemia. Insulin effect is counteracted by glucagon in non-diabetic individuals, while glucagon secretion in those with type 1 diabetes is impaired. The use of glucagon in the artificial pancreas is therefore a logical and feasible option for preventing and treating hypoglycaemia. However, commercially available glucagon is not stable in aqueous solution for long periods, forming potentially cytotoxic fibrils that aggregate quickly. Therefore, a more stable formulation of glucagon is needed for long-term use and storage in a bi-hormonal pump. In addition, a model of glucagon action in type 1 diabetes is lacking, further limiting the inclusion of glucagon into systems employing model-assisted control. As a result, although several investigators have been working to help develop bi-hormonal systems for patients with type 1 diabetes, most continue to utilize single hormone systems employing only insulin. This article seeks to focus on the attributes of glucagon and its use in bi-hormonal systems.
Conference Paper
. We describe a Genetic Algorithm that can evolve complete programs. Using a variable length linear genome to govern how a Backus Naur Form grammar definition is mapped to a program, expressions and programs of arbitrary complexity may be evolved. Other automatic programming methods are described, before our system, Grammatical Evolution, is applied to a symbolic regression problem. 1 Introduction Evolutionary Algorithms have been used with much success for the automatic generation of programs. In particular, Koza's [Koza 92] Genetic Programming has enjoyed considerable popularity and widespread use. Koza's method originally employed Lisp as its target language, and others still generate Lisp code. However, most experimenters generate a homegrown language, peculiar to their particular problem. Many other approaches to automatic program generation using Evolutionary Algorithms have also used Lisp as their target language. Lisp enjoys much popularity for a number of reasons, not least...
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To conduct a meta-analysis of the metabolic and psychosocial impact of continuous subcutaneous insulin infusion (CSII) therapy on adults, adolescents, and children. Studies were identified and data regarding study design, year of publication, sample size, patient's age, diabetes duration, and duration of CSII therapy were collected. Means and SDs for glycohemoglobin, blood glucose, insulin dosages, and body weight for CSII and comparison conditions were subjected to meta-analytic procedures. Data regarding pump complications and psychosocial functioning were reviewed descriptively. A total of 52 studies, consisting of 1,547 patients, were included in the meta-analysis. Results indicate that CSII therapy is associated with significant improvements in glycemic control (decreased glycohemoglobin and mean blood glucose). A descriptive review of potential complications of CSII use (e.g., hypoglycemia, diabetic ketoacidosis [DKA], pump malfunction, and site infections) suggests a decreased frequency of hypoglycemic episodes but an increased frequency of DKA in studies published before 1993. CSII therapy is associated with improved glycemic control compared with traditional insulin therapies (conventional therapy and multiple daily injections) and does not appear to be associated with significant adverse outcomes. Additional studies are needed to further examine the relative risks of CSII therapy, including the potential psychosocial impact of this technologically advanced therapy.
Article
A clinically important task in diabetes management is the prevention of hypo/hyperglycemic events. In this proof-of-concept paper, we assess the feasibility of approaching the problem with continuous glucose monitoring (CGM) devices. In particular, we study the possibility to predict ahead in time glucose levels by exploiting their recent history monitored every 3 min by a minimally invasive CGM system, the Glucoday, in 28 type 1 diabetic volunteers for 48 h. Simple prediction strategies, based on the description of past glucose data by either a first-order polynomial or a first-order autoregressive (AR) model, both with time-varying parameters determined by weighted least squares, are considered. Results demonstrate that, even by using these simple methods, glucose can be predicted ahead in time, e.g., with a prediction horizon of 30 min crossing of the hypoglycemic threshold can be predicted 20-25 min ahead in time, a sufficient margin to mitigate the event by sugar ingestion.
Identification for control: from the early achievements to the revival of experiment design*. Eur
  • M Gevers
Insulin pump therapy
  • J Weissberg-Benchell
  • J Antisdel-Lomaglio
  • R Seshadri
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