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

Near-optimal feedback control for postprandial glucose regulation in type 1 diabetes

This paper is focused on feedback control of postprandial glucose levels for patients with type 1 Diabetes Mellitus. There are two important limitations that make this a challenging problem. First, the slow subcutaneous insulin pharmacokinetics that introduces a significant lag into the control loop. Second, the positivity constraint on the control action, meaning that it is not possible to remove insulin from the body. In this paper, both issues are explicitly considered in the design process using the internal model control framework, to derive a near-optimal feedback controller. Optimality is understood here as minimizing the blood glucose peak after a meal intake and, at the same time, preventing glucose values below a prescribed threshold. It is shown how the proposed controller approaches the optimal closed-loop performance as a limit case. The theoretical results are supported by a numerical example and the feasibility of the overall strategy under uncertainties is illustrated using an extended version UVa/Padova metabolic simulator.

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).

Parameter estimation of a meal glucose-insulin model for TIDM patients from therapy historical data

The effect of meal on blood glucose concentration is a key issue in diabetes mellitus because its estimation could be very useful in therapy decisions. In the case of type 1 diabetes mellitus (T1DM), the therapy based on automatic insulin delivery requires a closed-loop control system to maintain euglycaemia even in the postprandial state. Thus, the mathematical modelling of glucose metabolism is relevant to predict the metabolic state of a patient. Moreover, the eating habits are characteristic of each person, so it is of interest that the mathematical models of meal intake allow to personalise the glycaemic state of the patient using therapy historical data, that is, daily measurements of glucose and records of carbohydrate intake and insulin supply. Thus, here, a model of glucose metabolism that includes the effects of meal is analysed in order to establish criteria for data-based personalisation. The analysis includes the sensitivity and identifiability of the parameters, and the parameter estimation problem was resolved via two algorithms: particle swarm optimisation and evonorm. The results show that the mathematical model can be a useful tool to estimate the glycaemic status of a patient and personalise it according to her/his historical data.

Control Limitations in Models of T1DM and the Robustness of Optimal Insulin Delivery

BACKGROUND

In insulin therapy, the blood glucose level is constrained from below by the hypoglycemic threshold, that is, the blood glucose level must remain above this threshold. It has been shown that this constraint fundamentally limits the ability to lower the maxima of the blood glucose level predicted by many mathematical models of glucose metabolism. However, it is desirable to minimize hyperglycemia as well. Hence, a desirable insulin input is one that minimizes the maximum glucose concentration while causing it to remain above the hypoglycemic, or higher, threshold. It has been shown that this input, which we call optimal, is characterized by glucose profiles for which either each maximum of the glucose concentration is followed by a minimum or each minimum is followed by a maximum.

METHODS

We discuss the implication of this inherent control limitation for clinical practice and test, through simulation, the robustness of the optimal input to a number of different model and parameter uncertainties. We further develop guidelines on how to design an optimal insulin input that is robust to such uncertainties.

RESULTS

The optimal input is in general not robust to uncertainties. However, a number of strategies may be used to ensure the blood glucose level remains above the hypoglycemic threshold and the maximum blood glucose level achieved is less than that achieved by standard therapy.

CONCLUSIONS

An understanding of the limitations on the controllability of the blood glucose level is important for future treatment improvements and the development of artificial pancreas systems.

A Methodology to Compare Insulin Dosing Recommendations in Real-Life Settings

BACKGROUND

We propose a methodology to analyze complex real-life glucose data in insulin pump users.

METHODS

Patients with type 1 diabetes (T1D) on insulin pumps were recruited from an academic endocrinology practice. Glucose data, insulin bolus (IB) amounts, and self-reported alcohol consumption and exercise events were collected for 30 days. Rules were developed to retrospectively compare IB recommendations from the insulin pump bolus calculator (IPBC) against recommendations from a proposed decision aid (PDA) and for assessing the PDA's recommendation for exercise and alcohol.

RESULTS

Data from 15 participants were analyzed. When considering instances where glucose was below target, the PDA recommended a smaller dose in 14%, but a larger dose in 13% and an equivalent IB in 73%. For glucose levels at target, the PDA suggested an equivalent IB in 58% compared to the subject's IPBC, but higher doses in 20% and lower in 22%. In events where postprandial glucose was higher than target, the PDA suggested higher doses in 25%, lower doses in 13%, and equivalent doses in 62%. In 64% of all alcohol events the PDA would have provided appropriate advice. In 75% of exercise events, the PDA appropriately advised an IB, a carbohydrate snack, or neither.

CONCLUSIONS

This study provides a methodology to systematically analyze real-life data generated by insulin pumps and allowed a preliminary analysis of the performance of the PDA for insulin dosing. Further testing of the methodological approach in a broader diabetes population and prospective testing of the PDA are needed.

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.

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.

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

In this paper, the problem of predicting blood glucose concentrations (BG) for the treatment of patients with type 1 diabetes, is addressed. Predicting BG is of very high importance as most treatments, which consist in exogenous insulin injections, rely on the availability of BG predictions. Many models that can be used for predicting BG are available in the literature. However, it is widely admitted that it is almost impossible to perfectly model blood glucose dynamics while still being able to identify model parameters using only blood glucose measurements. The main contribution of this work is to propose a simple and identifiable linear dynamical model, which is based on the static prediction model of standard therapy. It is shown that the model parameters are intrinsically correlated with physician-set therapy parameters and that the reduction of the number of model parameters to identify leads to inferior data fits but to equivalent or slightly improved prediction capabilities compared to state-of-the-art models: a sign of an appropriate model structure and superior reliability. The validation of the proposed dynamic model is performed using data from the UVa simulator and real clinical data, and potential uses of the proposed model for state estimation and BG control are discussed.

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.

Brain mass estimation by head circumference and body mass methods in neonatal glycaemic modelling and control

INTRODUCTION

Hyperglycaemia is a common complication of stress and prematurity in extremely low-birth-weight infants. Model-based insulin therapy protocols have the ability to safely improve glycaemic control for this group. Estimating non-insulin-mediated brain glucose uptake by the central nervous system in these models is typically done using population-based body weight models, which may not be ideal.

METHOD

A head circumference-based model that separately treats small-for-gestational-age (SGA) and appropriate-for-gestational-age (AGA) infants is compared to a body weight model in a retrospective analysis of 48 patients with a median birth weight of 750g and median gestational age of 25 weeks. Estimated brain mass, model-based insulin sensitivity (SI) profiles, and projected glycaemic control outcomes are investigated. SGA infants (5) are also analyzed as a separate cohort.

RESULTS

Across the entire cohort, estimated brain mass deviated by a median 10% between models, with a per-patient median difference in SI of 3.5%. For the SGA group, brain mass deviation was 42%, and per-patient SI deviation 13.7%. In virtual trials, 87-93% of recommended insulin rates were equal or slightly reduced (Δ<0.16mU/h) under the head circumference method, while glycaemic control outcomes showed little change.

CONCLUSION

The results suggest that body weight methods are not as accurate as head circumference methods. Head circumference-based estimates may offer improved modelling accuracy and a small reduction in insulin administration, particularly for SGA infants.