RobustH∞ glucose control in diabetes using a physiological model

A simple modeling framework for prediction in the human glucose-insulin system

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

Robust nonlinear control of blood glucose in diabetic patients subject to model uncertainties

Recent advances in the artificial pancreas system provide an emerging treatment option for type 1 diabetes. The performance of the blood glucose regulation directly relies on the accuracy of the glucose-insulin modeling. Sorenson model involves the behavior of different organs and offers precise representation. However, the high complexity of such a model makes the controller design procedure a hard task. Therefore, the high-order nonlinear Sorensen model as a popular high-fidelity physiological model is opted in this paper to analyze the glucose-insulin interactions in great detail, and a new robust nonlinear approach to regulate the blood glucose concentration (BGC) in Type-I diabetic patients is proposed. Inspiring the backstepping technique, for designing an acceptable controller, the model is divided into three main subsystems such that in each subsystem, the virtual control input laws are obtained using both Lyapunov stability and input-to-state theorems. Since the measurement of the parameters in the glucose-insulin system is not accurate, parametric uncertainties are defined in the investigated model. Furthermore, owing to the fact that the only measurable state variable is blood glucose, the estimation of inaccessible state variables is an important issue that is properly considered by the unscented Kalman filter (UKF) estimator. The suggested approach is compared to H_∞, robust H_∞, and linear parameter-varying control approaches. The comparison results on 500 simulated patients imply a remarkable superiority of the proposed controller approach to the compared methods in terms of the BGC tracking and the algorithm robustness in the presence of food intake disturbance patterns.

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.

Towards the Integration of an Islet-Based Biosensor in Closed-Loop Therapies for Patients With Type 1 Diabetes

In diabetes mellitus (DM) treatment, Continuous Glucose Monitoring (CGM) linked with insulin delivery becomes the main strategy to improve therapeutic outcomes and quality of patients' lives. However, Blood Glucose (BG) regulation with CGM is still hampered by limitations of algorithms and glucose sensors. Regarding sensor technology, current electrochemical glucose sensors do not capture the full spectrum of other physiological signals, i.e., lipids, amino acids or hormones, relaying the general body status. Regarding algorithms, variability between and within patients remains the main challenge for optimal BG regulation in closed-loop therapies. This work highlights the simulation benefits to test new sensing and control paradigms which address the previous shortcomings for Type 1 Diabetes (T1D) closed-loop therapies. The UVA/Padova T1DM Simulator is the core element here, which is a computer model of the human metabolic system based on glucose-insulin dynamics in T1D patients. That simulator is approved by the US Food and Drug Administration (FDA) as an alternative for pre-clinical testing of new devices and closed-loop algorithms. To overcome the limitation of standard glucose sensors, the concept of an islet-based biosensor, which could integrate multiple physiological signals through electrical activity measurement, is assessed here in a closed-loop insulin therapy. This investigation has been addressed by an interdisciplinary consortium, from endocrinology to biology, electrophysiology, bio-electronics and control theory. In parallel to the development of an islet-based closed-loop, it also investigates the benefits of robust control theory against the natural variability within a patient population. Using 4 meal scenarios, numerous simulation campaigns were conducted. The analysis of their results then introduces a discussion on the potential benefits of an Artificial Pancreas (AP) system associating the islet-based biosensor with robust algorithms.

H∞ controller and observer synthesis with delay and nonlinear perturbation of double diabetes systems

Patient having type 1 diabetes mellitus (having insulin resistance experience) cannot be treated solely by treatment procedure of type 1 patient nor does treatment employed for type 2 diabetes work for such patient. This type of diabetes patient needs a specific insulin injection procedure. For continuous insulin injection, the patient has to be classified as a different group from type 1 and type 2 patient. The patients experiencing both type 1 and 2 are called double diabetes mellitus (DDM) patient. Dynamic behavior of the patient was presented in delay differential equation (DDE). Based on the developed DDE of DDM model, controllers and observers fulfilling H_∞ norm bound are designed for this specific group of diabetes mellitus patient. Also, a nominal controller and a nominal observer are synthesized to check the proposed controller's ability for disturbance rejection, which is the glucose intake. The performance of the designed controller and observer is evaluated for a population of simulated patients. It shows that controller and observer are able to regulate and estimate, respectively, glycaemic for population of double diabetes patients.

Arbitrary-order sliding mode-based robust control algorithm for the developing artificial pancreas mechanism

In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed-loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed-loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary-order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n-order controllable canonical system. The proposed control algorithm affirms the finite-time effective stabilisation of the glucose-insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non-linear terms. In addition, the necessary discontinuous terms are filtered-out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature.

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.

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients

This study designs a robust closed-loop control algorithm for elevated blood glucose level stabilisation in type 1 diabetic patients. The control algorithm is based on a novel control action resulting from integrating algebraic meal disturbance estimator with back-stepping integral sliding mode control (BISMC) technique. The estimator shows finite time convergence leading to accurate and fast estimation of meal disturbance. Moreover, compensation of the estimated disturbance in controller provides significant reduction in chattering phenomenon, which is inherent drawback of sliding mode control (SMC). The controller is applied to one of the most reliable models of type 1 diabetic patients, named Bergman's minimal model. The effectiveness and superiority of the designed controller is shown by comparing it to classical SMC and super-twisting sliding mode control. The designed controller is subject to three different cases for detailed analysis of the controller's robustness against meal disturbance. The three cases considered are hyperglycaemia, hyperglycaemia combined with meal disturbance and three meal disturbance. The simulation results confirm superior performance of algebraic disturbance estimator based BISMC controller for all the cases mentioned above.

Connecting Rodent and Human Pharmacokinetic Models for the Design and Translation of Glucose-Responsive Insulin

Despite considerable progress, development of glucose-responsive insulins (GRIs) still largely depends on empirical knowledge and tedious experimentation-especially on rodents. To assist the rational design and clinical translation of the therapeutic, we present a Pharmacokinetic Algorithm Mapping GRI Efficacies in Rodents and Humans (PAMERAH) built upon our previous human model. PAMERAH constitutes a framework for predicting the therapeutic efficacy of a GRI candidate from its user-specified mechanism of action, kinetics, and dosage, which we show is accurate when checked against data from experiments and literature. Results from simulated glucose clamps also agree quantitatively with recent GRI publications. We demonstrate that the model can be used to explore the vast number of permutations constituting the GRI parameter space and thereby identify the optimal design ranges that yield desired performance. A design guide aside, PAMERAH more importantly can facilitate GRI's clinical translation by connecting each candidate's efficacies in rats, mice, and humans. The resultant mapping helps to find GRIs that appear promising in rodents but underperform in humans (i.e., false positives). Conversely, it also allows for the discovery of optimal human GRI dynamics not captured by experiments on a rodent population (false negatives). We condense such information onto a "translatability grid" as a straightforward, visual guide for GRI development.

Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus

Mathematical modelling has established itself as a theoretical tool to understand fundamental aspects of a variety of medical-biological phenomena. The predictive power of mathematical models on some chronic conditions has been helpful in its proper prevention, diagnosis, and treatment. Such is the case of the modelling of glycaemic dynamics in type 2 diabetes mellitus (T2DM), whose physiology-based mathematical models have captured the metabolic abnormalities of this disease. Through a physiology-based pharmacokinetic-pharmacodynamic approach, this work addresses a mathematical model whose structure starts from a model of blood glucose dynamics in healthy humans. This proposal is capable of emulating the pathophysiology of T2DM metabolism, including the effect of gastric emptying and insulin enhancing effect due to incretin hormones. The incorporation of these effects lies in the implemented methodology since the mathematical functions that represent metabolic rates, with a relevant contribution to hyperglycaemia, are adjusting individually to the clinical data of patients with T2DM. Numerically, the resulting model successfully simulates a scheduled graded intravenous glucose test and oral glucose tolerance tests at different doses. The comparison between simulations and clinical data shows an acceptable description of the blood glucose dynamics in T2DM. It opens the possibility of using this model to develop model-based controllers for the regulation of blood glucose in T2DM.

Blood glucose regulation and control of insulin and glucagon infusion using single model predictive control for type 1 diabetes mellitus

This study elaborates on the design of artificial pancreas using model predictive control algorithm for a comprehensive physiological model such as the Sorensen model, which regulates the blood glucose and can have a longer control time in normal glycaemic region. The main objective of the proposed algorithm is to eliminate the risk of hyper and hypoglycaemia and have a precise infusion of hormones: insulin and glucagon. A single model predictive controller is developed to control the bihormones, insulin, and glucagon for such a development unmeasured disturbance is considered for a random time. The simulation result for the proposed algorithm performed good regulation lowering the hypoglycaemia risk and maintaining the glucose level within the normal glycaemic range. To validate the performance of the tracking of output and setpoint, average tracking error is used and 4.4 mg/dl results are obtained while compared with standard value (14.3 mg/dl).

CarbMetSim: A discrete-event simulator for carbohydrate metabolism in humans

This paper describes CarbMetSim, a discrete-event simulator that tracks the blood glucose level of a person in response to a timed sequence of diet and exercise activities. CarbMetSim implements broader aspects of carbohydrate metabolism in human beings with the objective of capturing the average impact of various diet/exercise activities on the blood glucose level. Key organs (stomach, intestine, portal vein, liver, kidney, muscles, adipose tissue, brain and heart) are implemented to the extent necessary to capture their impact on the production and consumption of glucose. Key metabolic pathways (glucose oxidation, glycolysis and gluconeogenesis) are accounted for in the operation of different organs. The impact of insulin and insulin resistance on the operation of various organs and pathways is captured in accordance with published research. CarbMetSim provides broad flexibility to configure the insulin production ability, the average flux along various metabolic pathways and the impact of insulin resistance on different aspects of carbohydrate metabolism. The simulator does not yet have a detailed implementation of protein and lipid metabolism. This paper contains a preliminary validation of the simulator's behavior. Significant additional validation is required before the simulator can be considered ready for use by people with Diabetes.

The parameter Houlihan: A solution to high-throughput identifiability indeterminacy for brutally ill-posed problems

One way to interject knowledge into clinically impactful forecasting is to use data assimilation, a nonlinear regression that projects data onto a mechanistic physiologic model, instead of a set of functions, such as neural networks. Such regressions have an advantage of being useful with particularly sparse, non-stationary clinical data. However, physiological models are often nonlinear and can have many parameters, leading to potential problems with parameter identifiability, or the ability to find a unique set of parameters that minimize forecasting error. The identifiability problems can be minimized or eliminated by reducing the number of parameters estimated, but reducing the number of estimated parameters also reduces the flexibility of the model and hence increases forecasting error. We propose a method, the parameter Houlihan, that combines traditional machine learning techniques with data assimilation, to select the right set of model parameters to minimize forecasting error while reducing identifiability problems. The method worked well: the data assimilation-based glucose forecasts and estimates for our cohort using the Houlihan-selected parameter sets generally also minimize forecasting errors compared to other parameter selection methods such as by-hand parameter selection. Nevertheless, the forecast with the lowest forecast error does not always accurately represent physiology, but further advancements of the algorithm provide a path for improving physiologic fidelity as well. Our hope is that this methodology represents a first step toward combining machine learning with data assimilation and provides a lower-threshold entry point for using data assimilation with clinical data by helping select the right parameters to estimate.

Glucose-responsive insulin by molecular and physical design

The concept of a glucose-responsive insulin (GRI) has been a recent objective of diabetes technology. The idea behind the GRI is to create a therapeutic that modulates its potency, concentration or dosing relative to a patient's dynamic glucose concentration, thereby approximating aspects of a normally functioning pancreas. From the perspective of the medicinal chemist, the GRI is also important as a generalized model of a potentially new generation of therapeutics that adjust potency in response to a critical therapeutic marker. The aim of this Perspective is to highlight emerging concepts, including mathematical modelling and the molecular engineering of insulin itself and its potency, towards a viable GRI. We briefly outline some of the most important recent progress toward this goal and also provide a forward-looking viewpoint, which asks if there are new approaches that could spur innovation in this area as well as to encourage synthetic chemists and chemical engineers to address the challenges and promises offered by this therapeutic approach.

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.

Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype

We introduce data assimilation as a computational method that uses machine learning to combine data with human knowledge in the form of mechanistic models in order to forecast future states, to impute missing data from the past by smoothing, and to infer measurable and unmeasurable quantities that represent clinically and scientifically important phenotypes. We demonstrate the advantages it affords in the context of type 2 diabetes by showing how data assimilation can be used to forecast future glucose values, to impute previously missing glucose values, and to infer type 2 diabetes phenotypes. At the heart of data assimilation is the mechanistic model, here an endocrine model. Such models can vary in complexity, contain testable hypotheses about important mechanics that govern the system (eg, nutrition's effect on glucose), and, as such, constrain the model space, allowing for accurate estimation using very little data.

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.

Neural network-based model predictive control for type 1 diabetic rats on artificial pancreas system

Artificial pancreas system (APS) is a viable option to treat diabetic patients. Researchers, however, have not conclusively determined the best control method for APS. Due to intra-/inter-variability of insulin absorption and action, an individualized algorithm is required to control blood glucose level (BGL) for each patient. To this end, we developed model predictive control (MPC) based on artificial neural networks (ANNs), which combines ANN for BGL prediction based on inputs and MPC for BGL control based on the ANN (NN-MPC). First, we developed a mathematical model for diabetic rats, which was used to identify individual virtual subjects by fitting to empirical data collected through an APS, including BGL data, insulin injection, and food intake. Then, the virtual subjects were used to generate datasets for training ANNs. The NN-MPC determines control actions (insulin injection) based on BGL predicted by the ANN. To evaluate the NN-MPC, we conducted experiments using four virtual subjects under three different scenarios. Overall, the NN-MPC maintained BGL within the normal range about 90% of the time with a mean absolute deviation of 4.7 mg/dl from a desired BGL. Our findings suggest that the NN-MPC can provide subject-specific BGL control in conjunction with a closed-loop APS. Graphical abstract ᅟ.

Model-Fusion-Based Online Glucose Concentration Predictions in People with Type 1 Diabetes

Accurate predictions of glucose concentrations are necessary to develop an artificial pancreas (AP) system for people with type 1 diabetes (T1D). In this work, a novel glucose forecasting paradigm based on a model fusion strategy is developed to accurately characterize the variability and transient dynamics of glycemic measurements. To this end, four different adaptive filters and a fusion mechanism are proposed for use in the online prediction of future glucose trajectories. The filter fusion mechanism is developed based on various prediction performance indexes to guide the overall output of the forecasting paradigm. The efficiency of the proposed model fusion based forecasting method is evaluated using simulated and clinical datasets, and the results demonstrate the capability and prediction accuracy of the data-based fusion filters, especially in the case of limited data availability. The model fusion framework may be used in the development of an AP system for glucose regulation in patients with T1D.

Higher Order Sliding Mode Control for Blood Glucose Regulation of Type 1 Diabetic Patients

Type 1 diabetes mellitus (T1DM) treatment depends on the delivery of exogenous insulin to obtain near normal glucose levels. This article proposes a method for blood glucose level regulation in type 1 diabetics. The control strategy is based on comparing the first order sliding mode control (FOSMC) with a higher order SMC based on the super twisting control algorithm. The higher order sliding mode is used to overcome chattering, which can induce some undesirable and harmful phenomena for human health. In order to test the controller in silico experiments, Bergman's minimal model is used for studying the dynamic behavior of the glucose and insulin inside human body. Simulation results are presented to validate the effectiveness and the good performance of this control technique. The obtained results clearly reveal improved performance of the proposed higher order SMC in regulating the blood glucose level within the normal glycemic range in terms of accuracy and robustness.

Rational Design of Glucose-Responsive Insulin Using Pharmacokinetic Modeling

A glucose responsive insulin (GRI) is a therapeutic that modulates its potency, concentration, or dosing of insulin in relation to a patient's dynamic glucose concentration, thereby approximating aspects of a normally functioning pancreas. Current GRI design lacks a theoretical basis on which to base fundamental design parameters such as glucose reactivity, dissociation constant or potency, and in vivo efficacy. In this work, an approach to mathematically model the relevant parameter space for effective GRIs is induced, and design rules for linking GRI performance to therapeutic benefit are developed. Well-developed pharmacokinetic models of human glucose and insulin metabolism coupled to a kinetic model representation of a freely circulating GRI are used to determine the desired kinetic parameters and dosing for optimal glycemic control. The model examines a subcutaneous dose of GRI with kinetic parameters in an optimal range that results in successful glycemic control within prescribed constraints over a 24 h period. Additionally, it is demonstrated that the modeling approach can find GRI parameters that enable stable glucose levels that persist through a skipped meal. The results provide a framework for exploring the parameter space of GRIs, potentially without extensive, iterative in vivo animal testing.

Using meta-differential evolution to enhance a calculation of a continuous blood glucose level

We developed a new model of glucose dynamics. The model calculates blood glucose level as a function of transcapillary glucose transport. In previous studies, we validated the model with animal experiments. We used analytical method to determine model parameters. In this study, we validate the model with subjects with type 1 diabetes. In addition, we combine the analytic method with meta-differential evolution. To validate the model with human patients, we obtained a data set of type 1 diabetes study that was coordinated by Jaeb Center for Health Research. We calculated a continuous blood glucose level from continuously measured interstitial fluid glucose level. We used 6 different scenarios to ensure robust validation of the calculation. Over 96% of calculated blood glucose levels fit A+B zones of the Clarke Error Grid. No data set required any correction of model parameters during the time course of measuring. We successfully verified the possibility of calculating a continuous blood glucose level of subjects with type 1 diabetes. This study signals a successful transition of our research from an animal experiment to a human patient. Researchers can test our model with their data on-line at https://diabetes.zcu.cz.

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.

Switched LPV Glucose Control in Type 1 Diabetes

OBJECTIVE

The purpose of this paper is to regulate the blood glucose level in Type 1 Diabetes Mellitus patients with a practical and flexible procedure that can switch among a finite number of distinct controllers, depending on the user's choice.

METHODS

A switched linear parameter-varying controller with multiple switching regions, related to hypo-, hyper-, and euglycemia situations, is designed. The key feature is to arrange the controller into a framework that provides stability and performance guaranty.

RESULTS

The closed-loop performance is tested on the complete in silico adult cohort of the UVA/Padova metabolic simulator, which has been accepted by the U.S. Food and Drug Administration in lieu of animal trials. The outcome produces comparable or improved results with respect to previous works.

CONCLUSION

The strategy is practical because it is based on a model tuned only with a priori patient information in order to cover the interpatient uncertainty. Results confirm that this control structure yields tangible improvements in minimizing risks of hyper- and hypoglycemia in scenarios with unannounced meals.

SIGNIFICANCE

This flexible procedure opens the possibility of taking into account, at the design stage, unannounced meals and/or patients' physical exercise.

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.

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.

Reducing risks in type 1 diabetes using H∞ control

A control scheme was designed in order to reduce the risks of hyperglycemia and hypoglycemia in type 1 diabetes mellitus (T1DM). This structure is composed of three main components: an H∞ robust controller, an insulin feedback loop (IFL), and a safety mechanism (SM). A control-relevant model that is employed to design the robust controller is identified. The identification procedure is based on the distribution version of the UVA/Padova metabolic simulator using the simulation adult cohort. The SM prevents dangerous scenarios by acting upon a prediction of future glucose levels, and the IFL modifies the loop gain in order to reduce postprandial hypoglycemia risks. The procedure is tested on the complete alic>in silico adult cohort of the UVA/Padova metabolic simulator, which has been accepted by the Food and Drug Administration (FDA) in lieu of animal trials.

A computational proof of concept of a machine-intelligent artificial pancreas using Lyapunov stability and differential game theory

BACKGROUND

This study demonstrated the novel application of a "machine-intelligent" mathematical structure, combining differential game theory and Lyapunov-based control theory, to the artificial pancreas to handle dynamic uncertainties.

METHODS

Realistic type 1 diabetes (T1D) models from the literature were combined into a composite system. Using a mixture of "black box" simulations and actual data from diabetic medical histories, realistic sets of diabetic time series were constructed for blood glucose (BG), interstitial fluid glucose, infused insulin, meal estimates, and sometimes plasma insulin assays. The problem of underdetermined parameters was side stepped by applying a variant of a genetic algorithm to partial information, whereby multiple candidate-personalized models were constructed and then rigorously tested using further data. These formed a "dynamic envelope" of trajectories in state space, where each trajectory was generated by a hypothesis on the hidden T1D system dynamics. This dynamic envelope was then culled to a reduced form to cover observed dynamic behavior. A machine-intelligent autonomous algorithm then implemented game theory to construct real-time insulin infusion strategies, based on the flow of these trajectories through state space and their interactions with hypoglycemic or near-hyperglycemic states.

RESULTS

This technique was tested on 2 simulated participants over a total of fifty-five 24-hour days, with no hypoglycemic or hyperglycemic events, despite significant uncertainties from using actual diabetic meal histories with 10-minute warnings. In the main case studies, BG was steered within the desired target set for 99.8% of a 16-hour daily assessment period. Tests confirmed algorithm robustness for ±25% carbohydrate error. For over 99% of the overall 55-day simulation period, either formal controller stability was achieved to the desired target or else the trajectory was within the desired target.

CONCLUSIONS

These results suggest that this is a stable, high-confidence way to generate closed-loop insulin infusion strategies.

Analysis of three T1DM simulation models for evaluating robust closed-loop controllers

This work compares three well-known models and simulators in terms of their use in the analysis and design of glucose controllers for patients with Type 1 Diabetes Mellitus (T1DM). The objective is to compare them in practical scenarios which include: model uncertainty, time variance, nonlinearities, glucose measurement noise, delays between subcutaneous and plasma levels, pump saturation, and real-time controller implementation. The pros and cons of all models/simulators are presented. Finally, the simulators are tested with different robust controllers in order to identify the difficulties in the design and implementation phases. To this end, three sources of uncertainty are considered: nonlinearities, time-varying behavior (intra-patient) and inter-patient differences.

Applicability results of a nonlinear model-based robust blood glucose control algorithm

INTRODUCTION

Generating optimal control algorithms for an artificial pancreas is an intensively researched problem. The available models are all nonlinear and rather complex. Model predictive control or run-to-run-based methodologies have proven to be efficient solutions for individualized treatment of type 1 diabetes mellitus (T1DM). However, the controller has to ensure safety and stability under all circumstances. Robust control methods seek to provide this safety and guarantee to handle even the worst-case situations and, hence, to generalize and complement results obtained by individualized control algorithms.

METHODS

Modern robust (e.g., Hinf) control is a linear model-based methodology that we have combined with the nonlinear model-based linear parameter varying technique. The control algorithm was designed on the high-complexity modified nonlinear glucose-insulin model of Sorensen, and it was compared step-by-step with linear model-based Hinf control results published in the literature. The applicability of the developed algorithm was tested first on a control cohort of 10 healthy persons' oral glucose tolerance test results and then on a large meal absorption profile adapted from the literature. In the latter case, two preliminary virtual patients were generated based on 1-1 week real continuous glucose monitor measurements.

RESULTS

We have found that the algorithm avoids hypoglycemia (not caused by physical activity or stress) independently from the considered absorption profiles.

CONCLUSION

Use of hard constraints proved their efficiency in fitting blood glucose level within a defined interval. However, in the future, more data of different T1DM patients will be collected and tested, including dynamic absorption model and in silico tests on validated simulators.

A closed-loop artificial pancreas using a proportional integral derivative with double phase lead controller based on a new nonlinear model of glucose metabolism

BACKGROUND

Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed.

METHODS

A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose-insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70-180 mg/dl).

RESULTS

Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively.

CONCLUSION

The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia.

Safety auxiliary feedback element for the artificial pancreas in type 1 diabetes

The artificial pancreas aims at the automatic delivery of insulin for glycemic control in patients with type 1 diabetes, i.e., closed-loop glucose control. One of the challenges of the artificial pancreas is to avoid controller overreaction leading to hypoglycemia, especially in the late postprandial period. In this study, an original proposal based on sliding mode reference conditioning ideas is presented as a way to reduce hypoglycemia events induced by a closed-loop glucose controller. The method is inspired in the intuitive advantages of two-step constrained control algorithms. It acts on the glucose reference sent to the main controller shaping it so as to avoid violating given constraints on the insulin-on-board. Some distinctive features of the proposed strategy are that 1) it provides a safety layer which can be adjusted according to medical criteria; 2) it can be added to closed-loop controllers of any nature; 3) it is robust against sensor failures and overestimated prandial insulin doses; and 4) it can handle nonlinear models. The method is evaluated in silico with the ten adult patients available in the FDA-accepted UVA simulator.