Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] 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.Comment: Accepted for publication in PLOS ON

Consistency of compact and extended models of glucose-insulin homeostasis: The role of variable pancreatic reserve

Published compact and extended models of the glucose-insulin physiologic control system are compared, in order to understand why a specific functional form of the compact model proved to be necessary for a satisfactory representation of acute perturbation experiments such as the Intra Venous Glucose Tolerance Test (IVGTT). A spectrum of IVGTT’s of virtual subjects ranging from normal to IFG to IGT to frank T2DM were simulated using an extended model incorporating the population-of-controllers paradigm originally hypothesized by Grodsky, and proven to be able to capture a wide array of experimental results from heterogeneous perturbation procedures. The simulated IVGTT’s were then fitted with the Single-Delay Model (SDM), a compact model with only six free parameters, previously shown to be very effective in delivering precise estimates of insulin sensitivity and secretion during an IVGTT. Comparison of the generating, extended-model parameter values with the obtained compact model estimates shows that the functional form of the nonlinear insulin-secretion term, empirically found to be necessary for the compact model to satisfactorily fit clinical observations, captures the pancreatic reserve level of the simulated virtual patients. This result supports the validity of the compact model as a meaningful analysis tool for the clinical assessment of insulin sensitivity

Data-Driven Disturbance Estimation and Control with Application to Blood Glucose Regulation

A data-driven control approach for nonlinear systems is proposed, called data-driven estimation and control (D2EC), which combines a disturbance estimator and a nonlinear control algorithm. The estimator provides a signal representing the unknown disturbances affecting the plant to control. This signal is used by the control algorithm to improve its performance. A real-data study is presented, concerned with the regulation of blood glucose concentration in type 1 diabetic patients. Preliminary tests of the D2EC approach are also carried out using a diabetic patient simulator, obtained from a revised version of the well-known University of Virginia/Padova model. Both the real-data and the simulator-based studies indicate that the proposed approach has the potential to become an effective tool in the context of diabetes treatment and, more in general, in the biomedical field, where accurate first-principle models can seldom be found and relevant disturbances are present

Optimal H∞ insulin injection control for blood glucose regulation in diabetic patients

The theory of H/sup /spl infin// optimal control has the feature of minimizing the worst-case gain of an unknown disturbance input. When appropriately modified, the theory can be used to design a &quot;switching&quot; controller that can be applied to insulin injection for blood glucose (BG) regulation. The &quot;switching&quot; controller is defined by a collection of basic insulin rates and a rule that switches the insulin rates from one value to another. The rule employed an estimation of BG from noisy measurements, and the subsequent optimization of a performance index that involves the solution of a &quot;jump&quot; Riccati differential equation and a discrete-time dynamic programming equation. With an appropriate patient model, simulation studies have shown that the controller could correct BG deviation using clinically acceptable insulin delivery rates. <br /

Commuted PD controller for nonlinear systems: glucose–insulin regulatory case

As an option to deal with insulin-dependent disease, a recently commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value; hence, avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled systemPeer ReviewedPostprint (published version

Challenges and Opportunities in Design of Control Algorithm for Artificial Pancreas

With discovery of the insulin, Type-1 diabetes converted from a fatal and acute to a chronic disease which includes micro-vascular complications which range from Kidney disease to stroke and micro-vascular complications such as retinopathy, nephropathy and neuropathy. Artificial pancreas is a solution to improve the quality of life for people with this very fast growing disease in the world and to reduce the costs. Despite technological advances e.g., in subcutaneous sensors and actuators for insulin injection, modeling of blood glucose dynamics and control algorithms still need significant improvement. In this paper, we investigate challenges and opportunities for development of efficient algorithm for designing robust artificial pancreas. We discuss the state of the art and summarize clinical and in silico assessment results. We contrast conventional integer order system approach with a newly proposed fractal control and summarize its benefits

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., H(inf)) 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 H(inf) 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