Model predictive control of glucose concentration in type I diabetic patients: An in silico trial

Glucose Rate-of-Change and Insulin-on-Board Jointly Weighted Zone Model Predictive Control

We present design and evaluation of closed-loop insulin delivery using zone model predictive control (MPC) featuring an adaptive weighting scheme to address prolonged hyperglycemia due to changes in insulin sensitivity, underdelivery from profile mismatch, and meal composition. In the MPC cost function, the penalty on predicted glucose deviation from the upper zone boundary is weighted by a joint function of predicted glucose rate-of-change (ROC) and insulin-on-board (IOB). The asymmetric weighting gradually increases when glucose ROC and IOB were jointly low, independent of glucose magnitude, to limit hyperglycemia while aggressively reduces for negative glucose ROC to avoid hypoglycemia. The proposed controller was evaluated using two simulation scenarios: an induced resistance scenario and a nominal scenario to highlight the performance over a reference zone MPC with glucose ROC weighting only. The continuous adaption scheme resulted in consistent improvement for the entire glucose range without incurring additional risk of hypoglycemia. For the induced resistance and no feedforward bolus scenario, the percent time in 70-180 mg/dL was higher (53.5% versus 48.9%, p<0.001) with larger improvement in the overnight percent time in tighter glucose range 70-140 mg/dL (70.9% versus 52.9%, p<0.001). The results from extensive simulations, as well as clinical validation in three different outpatient studies demonstrate the utility and safety of the proposed zone MPC.

Prediction of Blood Risk Score in Diabetes Using Deep Neural Networks

Improving the prediction of blood glucose concentration may improve the quality of life of people living with type 1 diabetes by enabling them to better manage their care. Given the anticipated benefits of such a prediction, numerous methods have been proposed. Rather than attempting to predict glucose concentration, a deep learning framework for prediction is proposed in which prediction is performed using a scale for hypo- and hyper-glycemia risk. Using the blood glucose risk score formula proposed by Kovatchev et al., models with different architectures were trained, including, a recurrent neural network (RNN), a gated recurrent unit (GRU), a long short-term memory (LSTM) network, and an encoder-like convolutional neural network (CNN). The models were trained using the OpenAPS Data Commons data set, comprising 139 individuals, each with tens of thousands of continuous glucose monitor (CGM) data points. The training set was composed of 7% of the data set, while the remaining was used for testing. Performance comparisons between the different architectures are presented and discussed. To evaluate these predictions, performance results are compared with the last measurement (LM) prediction, through a sample-and-hold approach continuing the last known measurement forward. The results obtained are competitive when compared to other deep learning methods. A root mean squared error (RMSE) of 16 mg/dL, 24 mg/dL, and 37 mg/dL were obtained for CNN prediction horizons of 15, 30, and 60 min, respectively. However, no significant improvements were found for the deep learning models compared to LM prediction. Performance was found to be highly dependent on architecture and the prediction horizon. Lastly, a metric to assess model performance by weighing each prediction point error with the corresponding blood glucose risk score is proposed. Two main conclusions are drawn. Firstly, going forward, there is a need to benchmark model performance using LM prediction to enable the comparison between results obtained from different data sets. Secondly, model-agnostic data-driven deep learning models may only be meaningful when combined with mechanistic physiological models; here, it is argued that neural ordinary differential equations may combine the best of both approaches. These findings are based on the OpenAPS Data Commons data set and are to be validated in other independent data sets.

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

Data-Driven Robust Control for a Closed-Loop Artificial Pancreas

We present a fully closed-loop design for an artificial pancreas (AP) that regulates the delivery of insulin for the control of Type I diabetes. Our AP controller operates in a fully automated fashion, without requiring any manual interaction with the patient (e.g., in the form of meal announcements). A major obstacle to achieving closed-loop insulin control are the "unknown disturbances" related to various aspects of a patient's daily behavior, especially meals and physical activity. Such disturbances can significantly affect the patient's blood glucose levels. To handle such uncertainties, we present a data-driven, robust, model-predictive control framework in which we capture a wide range of individual meal and exercise patterns using uncertainty sets learned from historical data. These uncertainty sets are then used in the insulin controller to achieve automated, precise, and personalized insulin therapy. We provide an extensive in silico evaluation of our robust AP design, demonstrating the potential of the approach. In particular, without the benefit of explicit meal announcements, our approach can regulate glucose levels for large clusters of meal profiles learned from population-wide survey data and cohorts of virtual patients, even in the presence of high carbohydrate disturbances.

Model free sliding mode controller for blood glucose control: Towards artificial pancreas without need to mathematical model of the system

BACKGROUND

The mechanism of glucose regulation in human blood is a nonlinear complicated biological system with uncertain parameters and external disturbances which cannot be imitated accurately by a simple mathematical model. So to achieve an artificial pancreas, a method that does not need a model is necessary.

METHODS

In this paper, a model free third order terminal sliding mode controller is developed and applied to blood glucose regulation system. So in this paper, a data driven control method is proposed which doesn't need a pre specified mathematical model of the system. The proposed method uses a third order terminal sliding mode controller to overcome the problem in finite time without chattering. It also uses a disturbance estimation technique to reject external disturbances. The sliding mode algorithm is equipped with a regression algorithm to release its need to model of the system. It is proved theoretically that the method is stable and the error converges to zero. In order to determine the parameters needed in this method, an algorithm is provided.

RESULTS

Simulation studies are carried out with different scenarios and compared with Model Free Adaptive Control method. At the first scenario, the proposed method is applied to a virtual type- 1 diabetic patient without considering of external disturbances. The blood glucose level of 110 mg/dl is considered as the goal and it is illustrated that the desired glucose concentration is obtained. It is illustrated that the proposed method shows better performance against Model Free Adaptive Controller. Then in the next scenario, blood glucose of the patient is controlled in presence of three meal times during a day with different values of carbohydrate. The maximum of the blood glucose in this scenario is obtained as 168.5 mg/dl and the minimum of it stays on 85.5 Mg/dl. So the patient blood glucose level is almost within acceptable range (70-180 mg/dl) unlike the Model Free Adaptive Controller. In the last scenario, 22 tests are done for different patients (by randomly varying simulator parameters in ± 40% range) and the control performance is evaluated by the well-known Control Variability Grid Analysis CVGA. For all of them, the blood glucose remains in the green zone (safe region) of the CVGA .

CONCLUSION

Simulation results show that the proposed method acts robustly and can overcome uncertainties and external disturbances. The blood glucose level remains in safe region in all case. So the proposed method can be used in an artificial pancreas.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

Model individualization for artificial pancreas

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.

Design of an online-tuned model based compound controller for a fully automated artificial pancreas

This paper deals with the development of a control algorithm that can predict optimal insulin doses without patients' intervention in fully automated artificial pancreas system. An online-tuned model based compound controller comprising an online-tuned internal model control (IMC) algorithm and an enhanced IMC (eIMC) algorithm along with a meal detection module is proposed. Volterra models, used to develop IMC and eIMC algorithms, are developed online using recursive least squares (RLS) filter. The time domain kernels, computed online using RLS filter, are converted into frequency domain to obtain Volterra transfer function (VTF). VTFs are used to develop both IMC and eIMC algorithms. The compound controller is designed in such a way that eIMC predicts insulin doses when the glucose rate increase detector of meal detection module is positive, otherwise conventional IMC takes the control action. Experimental results show that the compound controller performs robustly in the presence of higher and irregular amounts of meal disturbances at random times, very high actuator and sensor noises and also with the variation in insulin sensitivity. The combination of compound control strategy and meal detection module compensates the shortcomings of both slow subcutaneous insulin action that causes postprandial hyperglycemia, and delayed peak of action that causes hypoglycaemia. Graphical Abstract A fully-automated artificial pancreas system containing glucose sensor, insulin pump and control algorithm. Block diagram showing the control algorithm i.e., online-tuned compound IMC comprising enhanced IMC, conventional IMC and meal detection module, developed in the present work.

Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

The Glucose-Insulin-Glucagon nonlinear model accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

Postprandial fuzzy adaptive strategy for a hybrid proportional derivative controller for the artificial pancreas

This paper presents a support fuzzy adaptive system for a hybrid proportional derivative controller that will refine its parameters during postprandial periods to enhance performance. Even though glucose controllers have improved over the last decade, tuning them and keeping them tuned are still major challenges. Changes in a patient's lifestyle, stress, exercise, or other activities may modify their blood glucose system, making it necessary to retune or change the insulin dosing algorithm. This paper presents a strategy to adjust the parameters of a proportional derivative controller using the so-called safety auxiliary feedback element loop for type 1 diabetic patients. The main parameters, such as the insulin on board limit and proportional gain are tuned using postprandial performance indexes and the information given by the controller itself. The adaptive and robust performance of the control algorithm was assessed "in silico" on a cohort of virtual patients under challenging realistic scenarios considering mixed meals, circadian variations, time-varying uncertainties, sensor errors, and other disturbances. The results showed that an adaptive strategy can significantly improve the performance of postprandial glucose control, individualizing the tuning by directly taking into account the intra-patient variability of type 1 patients. Graphical Abstract title: Postprandial glycaemia improvement via fuzzy adaptive control A fuzzy inference engine was implemented within a clinically tested artificial pancreas control system. The aim of the fuzzy system was to adapt controller parameters to improve postprandial blood glucose control while ensuring safety. Results show a significant improvement over time of the postprandial glucose response due to the adaptation, thus demonstrating the usefulness of the fuzzy adaptive system.

Glycemic Control of People With Type 1 Diabetes Based on Probabilistic Constraints

The objective of the paper is to develop an open loop insulin infusion profile, which is capable of controlling the blood glucose level of people with Type 1 diabetes in the presence of broad uncertainties such as inter-patient variability and unknown meal quantity. For illustrative purposes, the Bergman model in conjunction with a gut-dynamics model is chosen to represent the human glucose-insulin dynamics. A recently developed sampling based uncertainty quantification approach is used to determine the statistics (mean and variance) of the evolving states in the model. These statistics are utilized to define chance constraints in an optimization framework. The solution obtained shows that under the assumptions made on the distribution of the model parameters, all possible glucose trajectories over time satisfy the desired glycemic control goals. The solution is also validated on the FDA approved Type 1 Diabetes Metabolic Simulator suggesting that the proposed algorithm is highly suitable for human subjects.

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

Velocity-weighting & velocity-penalty MPC of an artificial pancreas: Improved safety & performance

A novel Model Predictive Control (MPC) law for the closed-loop operation of an Artificial Pancreas (AP) to treat type 1 diabetes is proposed. The contribution of this paper is to simultaneously enhance both the safety and performance of an AP, by reducing the incidence of controller-induced hypoglycemia, and by promoting assertive hyperglycemia correction. This is achieved by integrating two MPC features separately introduced by the authors previously to independently improve the control performance with respect to these two coupled issues. Velocity-weighting MPC reduces the occurrence of controller-induced hypoglycemia. Velocity-penalty MPC yields more effective hyperglycemia correction. Benefits of the proposed MPC law over the MPC strategy deployed in the authors' previous clinical trial campaign are demonstrated via a comprehensive in-silico analysis. The proposed MPC law was deployed in four distinct US Food & Drug Administration approved clinical trial campaigns, the most extensive of which involved 29 subjects each spending three months in closed-loop. The paper includes implementation details, an explanation of the state-dependent cost functions required for velocity-weighting and penalties, a discussion of the resulting nonlinear optimization problem, a description of the four clinical trial campaigns, and control-related trial highlights.

Extremum Seeking Control for Personalized Zone Adaptation in Model Predictive Control for Type 1 Diabetes

Zone model predictive control has proven to be an effective closed-loop method to regulate blood glucose for people with type 1 diabetes (T1D). In this paper, we present a universal model-free optimization scheme for adapting the zone for T1D patients individually. The adaptation is based on a clinical glycemic risk index named relative regularized glycemic penalty index (rrGPI), which is calculated from glucose measurements by a continuous glucose monitor. The scheme's objective is to minimize rrGPI by simultaneously modulating a controller's blood glucose target zone's upper bound and lower bound. The adaptation mechanism is based on extremum seeking control, in which the zone boundaries are driven by gradient estimation obtained by continuously sinusoidally modulating and demodulating the rrGPI readings. To improve the adaptation method's robustness against uncertainties, a decaying feedback gain and a vanishing dither signal are employed. in-silico trials suggested that the personalized optimized zone can be reached within a week of adaptation. Both for announced and unannounced meals, the proposed method outperforms the fixed zone [80, 140] mg/dL, which has been employed in the authors' clinical trials. It is also shown that the developed method has strong robustness against real-life uncertainties.

Event-Triggered Model Predictive Control for Embedded Artificial Pancreas Systems

OBJECTIVE

The development of artificial pancreas (AP) technology for deployment in low-energy, embedded devices is contingent upon selecting an efficient control algorithm for regulating glucose in people with type 1 diabetes mellitus. In this paper, we aim to lower the energy consumption of the AP by reducing controller updates, that is, the number of times the decision-making algorithm is invoked to compute an appropriate insulin dose.

METHODS

Physiological insights into glucose management are leveraged to design an event-triggered model predictive controller (MPC) that operates efficiently, without compromising patient safety. The proposed event-triggered MPC is deployed on a wearable platform. Its robustness to latent hypoglycemia, model mismatch, and meal misinformation is tested, with and without meal announcement, on the full version of the US-FDA accepted UVA/Padova metabolic simulator.

RESULTS

The event-based controller remains on for 18 h of 41 h in closed loop with unannounced meals, while maintaining glucose in 70-180 mg/dL for 25 h, compared to 27 h for a standard MPC controller. With meal announcement, the time in 70-180 mg/dL is almost identical, with the controller operating a mere 25.88% of the time in comparison with a standard MPC.

CONCLUSION

A novel control architecture for AP systems enables safe glycemic regulation with reduced processor computations.

SIGNIFICANCE

Our proposed framework integrated seamlessly with a wide variety of popular MPC variants reported in AP research, customizes tradeoff between glycemic regulation and efficacy according to prior design specifications, and eliminates judicious prior selection of controller sampling times.

Periodic zone-MPC with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes. AUTOMATICA : THE JOURNAL OF IFAC, THE INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL 2016;71:237-246. [PMID: 27695131 PMCID: PMC5040369 DOI: 10.1016/j.automatica.2016.04.015]

A novel Model Predictive Control (MPC) law for an Artificial Pancreas (AP) to automatically deliver insulin to people with type 1 diabetes is proposed. The MPC law is an enhancement of the authors' zone-MPC approach that has successfully been trialled in-clinic, and targets the safe outpatient deployment of an AP. The MPC law controls blood-glucose levels to a diurnally time-dependent zone, and enforces diurnal, hard input constraints. The main algorithmic novelty is the use of asymmetric input costs in the MPC problem's objective function. This improves safety by facilitating the independent design of the controller's responses to hyperglycemia and hypoglycemia. The proposed controller performs predictive pump-suspension in the face of impending hypoglycemia, and subsequent predictive pump-resumption, based only on clinical needs and feedback. The proposed MPC strategy's benefits are demonstrated by in-silico studies as well as highlights from a US Food and Drug Administration approved clinical trial in which 32 subjects each completed two 25 hour closed-loop sessions employing the proposed MPC law.

Tackling problem nonlinearities & delays via asymmetric, state-dependent objective costs in MPC of an artificial pancreas

The design of a Model Predictive Control (MPC) law for an Artificial Pancreas (AP) that automatically delivers insulin to people with type 1 diabetes mellitus is considered. An MPC law was recently proposed that exploits the simplicity of linear dynamical models, but is in two ways a 'nonlinear' departure of standard linear MPC, while circumnavigating the complexity of cumbersome, fully nonlinear MPC approaches. The first of two issues focused on is the nonlinearity of the control problem, and it is demonstrated how this can be tackled via asymmetric objective functions. The second issue is controller induced hypoglycemia resulting from the large delay in actuation and sensing. The proposed MPC strategy employs an asymmetric, state-dependent objective function that leads to a nonlinear optimization problem. The result is an AP controller with significantly elevated safety and comparable control performance. The contribution of this paper is a detailed in-silico analysis of the proposed control law, and a clinical demonstration of the benefits of asymmetric objective functions.

A Review of Emerging Technologies for the Management of Diabetes Mellitus

OBJECTIVE

High prevalence of diabetes mellitus (DM) along with the poor health outcomes and the escalated costs of treatment and care poses the need to focus on prevention, early detection and improved management of the disease. The aim of this paper is to present and discuss the latest accomplishments in sensors for glucose and lifestyle monitoring along with clinical decision support systems (CDSSs) facilitating self-disease management and supporting healthcare professionals in decision making.

METHODS

A critical literature review analysis is conducted focusing on advances in: 1) sensors for physiological and lifestyle monitoring, 2) models and molecular biomarkers for predicting the onset and assessing the progress of DM, and 3) modeling and control methods for regulating glucose levels.

RESULTS

Glucose and lifestyle sensing technologies are continuously evolving with current research focusing on the development of noninvasive sensors for accurate glucose monitoring. A wide range of modeling, classification, clustering, and control approaches have been deployed for the development of the CDSS for diabetes management. Sophisticated multiscale, multilevel modeling frameworks taking into account information from behavioral down to molecular level are necessary to reveal correlations and patterns indicating the onset and evolution of DM.

CONCLUSION

Integration of data originating from sensor-based systems and electronic health records combined with smart data analytics methods and powerful user centered approaches enable the shift toward preventive, predictive, personalized, and participatory diabetes care.

SIGNIFICANCE

The potential of sensing and predictive modeling approaches toward improving diabetes management is highlighted and related challenges are identified.

An Improved PID Algorithm Based on Insulin-on-Board Estimate for Blood Glucose Control with Type 1 Diabetes

Automated closed-loop insulin infusion therapy has been studied for many years. In closed-loop system, the control algorithm is the key technique of precise insulin infusion. The control algorithm needs to be designed and validated. In this paper, an improved PID algorithm based on insulin-on-board estimate is proposed and computer simulations are done using a combinational mathematical model of the dynamics of blood glucose-insulin regulation in the blood system. The simulation results demonstrate that the improved PID algorithm can perform well in different carbohydrate ingestion and different insulin sensitivity situations. Compared with the traditional PID algorithm, the control performance is improved obviously and hypoglycemia can be avoided. To verify the effectiveness of the proposed control algorithm, in silico testing is done using the UVa/Padova virtual patient software.

Velocity-weighting to prevent controller-induced hypoglycemia in MPC of an artificial pancreas to treat T1DM

The design of a Model Predictive Control (MPC) strategy for the closed-loop operation of an Artificial Pancreas (AP) to treat type 1 diabetes mellitus is considered. The contribution of this paper is to propose a velocity-weighting mechanism, within an MPC problem's cost function, that facilitates penalizing predicted hyperglycemic blood-glucose excursions based on the predicted blood-glucose levels' rates of change. The method provides the control designer some freedom for independently shaping the AP's uphill versus downhill responses to hyperglycemic excursions; of particular emphasis in this paper is the downhill response. The proposal aims to tackle the dangerous issue of controller-induced hypoglycemia following large hyperglycemic excursions, e.g., after meals, that results in part due to the large delays of subcutaneous glucose sensing and subcutaneous insulin infusion - the case considered here. The efficacy of the proposed approach is demonstrated using the University of Virginia/Padova metabolic simulator with both unannounced and announced meal scenarios.

The significance of LPV modeling of a widely used T1DM model

The paper investigates the specificity of Linear Parameter Varying (LPV) modeling and robust controller design on a widely used Type 1 Diabetes Mellitus model. LPV systems can be seen as an extension of linear time invariant systems, which allows us to extend some powerful control methodologies to the highly nonlinear and uncertain models of the human metabolism. Different LPV models are proposed with their own advantages and disadvantages. The possible choices are separately analyzed for both controller and observer design perspective.

Personalized tuning of a reinforcement learning control algorithm for glucose regulation

Artificial pancreas is in the forefront of research towards the automatic insulin infusion for patients with type 1 diabetes. Due to the high inter- and intra-variability of the diabetic population, the need for personalized approaches has been raised. This study presents an adaptive, patient-specific control strategy for glucose regulation based on reinforcement learning and more specifically on the Actor-Critic (AC) learning approach. The control algorithm provides daily updates of the basal rate and insulin-to-carbohydrate (IC) ratio in order to optimize glucose regulation. A method for the automatic and personalized initialization of the control algorithm is designed based on the estimation of the transfer entropy (TE) between insulin and glucose signals. The algorithm has been evaluated in silico in adults, adolescents and children for 10 days. Three scenarios of initialization to i) zero values, ii) random values and iii) TE-based values have been comparatively assessed. The results have shown that when the TE-based initialization is used, the algorithm achieves faster learning with 98%, 90% and 73% in the A+B zones of the Control Variability Grid Analysis for adults, adolescents and children respectively after five days compared to 95%, 78%, 41% for random initialization and 93%, 88%, 41% for zero initial values. Furthermore, in the case of children, the daily Low Blood Glucose Index reduces much faster when the TE-based tuning is applied. The results imply that automatic and personalized tuning based on TE reduces the learning period and improves the overall performance of the AC algorithm.

Comparative assessment of glucose prediction models for patients with type 1 diabetes mellitus applying sensors for glucose and physical activity monitoring

The present work presents the comparative assessment of four glucose prediction models for patients with type 1 diabetes mellitus (T1DM) using data from sensors monitoring blood glucose concentration. The four models are based on a feedforward neural network (FNN), a self-organizing map (SOM), a neuro-fuzzy network with wavelets as activation functions (WFNN), and a linear regression model (LRM), respectively. For the development and evaluation of the models, data from 10 patients with T1DM for a 6-day observation period have been used. The models' predictive performance is evaluated considering a 30-, 60- and 120-min prediction horizon, using both mathematical and clinical criteria. Furthermore, the addition of input data from sensors monitoring physical activity is considered and its effect on the models' predictive performance is investigated. The continuous glucose-error grid analysis indicates that the models' predictive performance benefits mainly in the hypoglycemic range when additional information related to physical activity is fed into the models. The obtained results demonstrate the superiority of SOM over FNN, WFNN, and LRM with SOM leading to better predictive performance in terms of both mathematical and clinical evaluation criteria.

In Silico Closed-Loop Control Validation Studies for Optimal Insulin Delivery in Type 1 Diabetes

This study presents a general closed-loop control strategy for optimal insulin delivery in type 1 Diabetes Mellitus (T1DM). The proposed control strategy aims toward an individualized optimal insulin delivery that consists of a patient-specific model predictive controller, a state estimator, a personalized scheduling level, and an open-loop optimization problem subjected to patient-specific process model and constraints. This control strategy can be also modified to address the case of limited patient data availability resulting in an "approximation" control strategy. Both strategies are validated in silico in the presence of predefined and unknown meal disturbances using both a novel mathematical model of glucose-insulin interactions and the UVa/Padova Simulator model as a virtual patient. The robustness of the control performance is evaluated under several conditions such as skipped meals, variability in the meal time, and metabolic uncertainty. The simulation results of the closed-loop validation studies indicate that the proposed control strategies can potentially achieve improved glycaemic control.

Model-based control of plasma glycemia: Tests on populations of virtual patients

Closed-loop devices delivering medical treatments in an automatic fashion clearly require a thorough preliminary phase according to which the proposed control law is tested and validated as realistically as possible, before arranging in vivo experiments in a clinical setting. The present note develops a virtual environment aiming to validate a recently proposed model-based glucose control law on a solid simulation framework. From a theoretical viewpoint, the artificial pancreas has been designed by suitably exploiting a minimal set of delay differential equations modeling the glucose-insulin regulatory system; on the other hand, the validation platform makes use of a different, multi-compartmental model to build up a population of virtual patients. Simulations are carried out by properly addressing the available technological limits and the unavoidable uncertainties in real-time continuous glucose sensors as well as possible malfunctioning on the insulin delivery devices. The results show the robustness of the proposed control law that turns out to be efficient and extremely safe on a heterogenous population of virtual patients.

An iterative learning strategy for the auto-tuning of the feedforward and feedback controller in type-1 diabetes

This paper proposes a scheme for the control of the blood glucose in subjects with type-1 diabetes mellitus based on the subcutaneous (s.c.) glucose measurement and s.c. insulin administration. The tuning of the controller is based on an iterative learning strategy that exploits the repetitiveness of the daily feeding habit of a patient. The control consists of a mixed feedback and feedforward contribution whose parameters are tuned through an iterative learning process that is based on the day-by-day automated analysis of the glucose response to the infusion of exogenous insulin. The scheme does not require any a priori information on the patient insulin/glucose response, on the meal times and on the amount of ingested carbohydrates (CHOs). Thanks to the learning mechanism the scheme is able to improve its performance over time. A specific logic is also introduced for the detection and prevention of possible hypoglycaemia events. The effectiveness of the methodology has been validated using long-term simulation studies applied to a set of nine in silico patients considering realistic uncertainties on the meal times and on the quantities of ingested CHOs.

State Estimation with Sensor Recalibrations and Asynchronous Measurements for MPC of an Artificial Pancreas to Treat T1DM

A novel state estimation scheme is proposed for use in Model Predictive Control (MPC) of an artificial pancreas based on Continuous Glucose Monitor (CGM) feedback, for treating type 1 diabetes mellitus. The performance of MPC strategies heavily depends on the initial condition of the predictions, typically characterized by a state estimator. Commonly employed Luenberger-observers and Kalman-filters are effective much of the time, but suffer limitations. Three particular limitations are tackled by the proposed approach. First, CGM recalibrations, step changes that cause highly dynamic responses in recursive state estimators, are accommodated in a graceful manner. Second, the proposed strategy is not affected by CGM measurements that are asynchronous, i.e., neither of fixed sample-period, nor of a sample-period that is equal to the controller's. Third, the proposal suffers no offsets due to plant-model mismatches. The proposed approach is based on moving-horizon optimization.

MPC Design for Rapid Pump-Attenuation and Expedited Hyperglycemia Response to Treat T1DM with an Artificial Pancreas

The design of a Model Predictive Control (MPC) strategy for the closed-loop operation of an Artificial Pancreas (AP) for treating Type 1 Diabetes Mellitus (T1DM) is considered in this paper. The contribution of this paper is to propose two changes to the usual structure of the MPC problems typically considered for control of an AP. The first proposed change is to replace the symmetric, quadratic input cost function with an asymmetric, quadratic function, allowing negative control inputs to be penalized less than positive ones. This facilitates rapid pump-suspensions in response to predicted hypoglycemia, while simultaneously permitting the design of a conservative response to hyperglycemia. The second proposed change is to penalize the velocity of the predicted glucose level, where this velocity penalty is based on a cost function that is again asymmetric, but additionally state-dependent. This facilitates the accelerated response to acute, persistent hyperglycemic events, e.g., as induced by unannounced meals. The novel functionality is demonstrated by numerical examples, and the efficacy of the proposed MPC strategy verified using the University of Padova/Virginia metabolic simulator.

Monitoring Artificial Pancreas Trials Through Agent-based Technologies: A Case Report

The increase in the availability and reliability of network connections lets envision systems supporting a continuous remote monitoring of clinical parameters useful either for overseeing chronic diseases or for following clinical trials involving outpatients. We report here the results achieved by a telemedicine infrastructure that has been linked to an artificial pancreas platform and used during a trial of the AP@home project, funded by the European Union. The telemedicine infrastructure is based on a multiagent paradigm and is able to deliver to the clinic any information concerning the patient status and the operation of the artificial pancreas. A web application has also been developed, so that the clinic staff and the researchers involved in the design of the blood glucose control algorithms are able to follow the ongoing experiments. Albeit the duration of the experiments in the trial discussed in the article was limited to only 2 days, the system proved to be successful for monitoring patients, in particular overnight when the patients are sleeping. Based on that outcome we can conclude that the infrastructure is suitable for the purpose of accomplishing an intelligent monitoring of an artificial pancreas either during longer trials or whenever that system will be used as a routine treatment.

Artificial pancreas: model predictive control design from clinical experience

BACKGROUND

The objective of this research is to develop a new artificial pancreas that takes into account the experience accumulated during more than 5000 h of closed-loop control in several clinical research centers. The main objective is to reduce the mean glucose value without exacerbating hypo phenomena. Controller design and in silico testing were performed on a new virtual population of the University of Virginia/Padova simulator.

METHODS

A new sensor model was developed based on the Comparison of Two Artificial Pancreas Systems for Closed-Loop Blood Glucose Control versus Open-Loop Control in Patients with Type 1 Diabetes trial AP@home data. The Kalman filter incorporated in the controller has been tuned using plasma and pump insulin as well as plasma and continuous glucose monitoring measures collected in clinical research centers. New constraints describing clinical knowledge not incorporated in the simulator but very critical in real patients (e.g., pump shutoff) have been introduced. The proposed model predictive control (MPC) is characterized by a low computational burden and memory requirements, and it is ready for an embedded implementation.

RESULTS

The new MPC was tested with an intensive simulation study on the University of Virginia/Padova simulator equipped with a new virtual population. It was also used in some preliminary outpatient pilot trials. The obtained results are very promising in terms of mean glucose and number of patients in the critical zone of the control variability grid analysis.

CONCLUSIONS

The proposed MPC improves on the performance of a previous controller already tested in several experiments in the AP@home and JDRF projects. This algorithm complemented with a safety supervision module is a significant step toward deploying artificial pancreases into outpatient environments for extended periods of time.

Periodic-zone model predictive control for diurnal closed-loop operation of an artificial pancreas

BACKGROUND

The objective of this research is an artificial pancreas (AP) that performs automatic regulation of blood glucose levels in people with type 1 diabetes mellitus. This article describes a control strategy that performs algorithmic insulin dosing for maintaining safe blood glucose levels over prolonged, overnight periods of time and furthermore was designed with outpatient, multiday deployment in mind. Of particular concern is the prevention of nocturnal hypoglycemia, because during sleep, subjects cannot monitor themselves and may not respond to alarms. An AP intended for prolonged and unsupervised outpatient deployment must strategically reduce the risk of hypoglycemia during times of sleep, without requiring user interaction.

METHODS

A diurnal insulin delivery strategy based on predictive control methods is proposed. The so-called "periodic-zone model predictive control" (PZMPC) strategy employs periodically time-dependent blood glucose output target zones and furthermore enforces periodically time-dependent insulin input constraints to modulate its behavior based on the time of day.

RESULTS

The proposed strategy was evaluated through an extensive simulation-based study and a preliminary clinical trial. Results indicate that the proposed method delivers insulin more conservatively during nighttime than during daytime while maintaining safe blood glucose levels at all times. In clinical trials, the proposed strategy delivered 77% of the amount of insulin delivered by a time-invariant control strategy; specifically, it delivered on average 1.23 U below, compared with 0.31 U above, the nominal basal rate overnight while maintaining comparable, and safe, blood glucose values.

CONCLUSIONS

The proposed PZMPC algorithm strategically prevents nocturnal hypoglycemia and is considered a significant step toward deploying APs into outpatient environments for extended periods of time in full closed-loop operation.