Nonlinear Control for Blood Glucose Regulation of Diabetic Patients: An LMI Approach

By Anirudh Nath, Rajeeb Dey and Valentina Emilia Balas

Nonlinear Control for Blood Glucose Regulation of Diabetic Patients: An LMI-Based Approach exposes readers to the various existing mathematical models that define the dynamics of glucose-insulin for Type 1 diabetes patients. After providing insights into the mathematical model of patients, the authors discuss the need and emergence of new control techniques that can lead to further development of an artificial pancreas. The book presents various nonlinear control techniques to address the challenges that Type 1 diabetic patients face in maintaining their blood glucose level in the safe range (70-180 mg/dl).

The closed-loop solution provided by the artificial pancreas depends mainly on the effectiveness of the control algorithm, which acts as the brain of the system. APS control algorithms require a mathematical model of the gluco-regulatory system of the T1D patients for their design. Since the gluco-regulatory system is inherently nonlinear and largely affected by external disturbances and parametric uncertainty, developing an accurate model is very difficult.

• Presents control-oriented modeling of the gluco-regulatory system of Type 1 diabetic patients using input-output data
• Demonstrates the design of a robust insulin delivery mechanism utilizing state estimation information with parametric uncertainties and exogenous disturbance in the framework of Linear Matrix Inequality (LMI)
• Introduces readers to the relevance and effectiveness of powerful nonlinear controllers for the Artificial Pancreas
• Provides the first book on LMI-based nonlinear control techniques for the Artificial Pancreas

• Language: English
• Publisher: Academic Press
• Release date: Aug 13, 2022
• ISBN: 9780323907774

Book preview

1: Introduction

Abstract

A brief description of the artificial pancreas system and its components is provided here. The various challenges of the artificial pancreas, ranging from physiological factors to mathematical models, are discussed thoroughly. Furthermore, the long-term risks of continued postprandial hyperglycemia and the immediate danger of severe hypoglycemia are addressed. Again, a short note on additional safety and other auxiliary algorithms that augment existing control algorithms in the artificial pancreas is included here. The required theoretical background on the basics of the concepts, such as state-space modeling, feedback linearization control technique, and linear matrix inequalities-based robust control techniques, are presented to provide the readers a sufficient background of the methods discussed in this book.

Keywords

Artificial pancreas; type 1 diabetes; glycemic control; safety algorithms; inter-patient variability; intra-patient variability

1.1 Introduction

Diabetes mellitus is one of the primary causes of mortality in the world. Its prevalence at an alarming rate across the globe is a serious issue. Being a global health-related challenge, diabetes mellitus incurs a heavy economic loss to nations. For instance, around 366 million people are suffering from the menace of diabetes mellitus [1]. People who have diabetes cannot effectively utilize the glucose available in the blood plasma for various metabolic processes. The plasma glucose concentration (PGC) is increased when the carbohydrates present in meals is absorbed and converted to glucose. The blood glucose in the body is consumed/utilized in various ways: (i) glucose utilization in the brain, (ii) glucose storage in the liver in the form of glycogen, and (iii) glucose transfer to muscle and adipose tissues [2]. The pancreas is the primary organ responsible for maintaining glucose homeostasis in the body. The pancreas comprises Langerhans' islets containing two essential cells, namely the α-cells and β-cells. While the α-cells are responsible for secreting the endocrine hormone, glucagon, β-cells are responsible for secreting the endocrine hormone, insulin. Glucagon is responsible for increasing the PGC when the glucose level falls below the basal value by converting the stored glycogen in the liver to glucose in the blood. Insulin, on the other hand, is the primary regulator of glucose homeostasis in the human body. It decreases the increased PGC in the blood by enhancing the peripheral glucose utilization in the body [3].

The pathogenesis of diabetes mellitus is related to the insufficient or negligible secretion of insulin. As a result, the PGC remains at an elevated level in the bloodstream. Depending on the nature of insulin secretion in the body, diabetes mellitus can be classified as type 1 diabetes (T1D) and type 2 diabetes (T2D) [3]. Insulin secretion ceases entirely in the case of T1D patients. At the same time, insulin secretion exists in an insufficient amount in T2D patients. The PGC needs to be maintained in the euglycemic range of 70–180 mg/dl [4]. In diabetic patients, the tight control of PGC cannot be accomplished via the open-loop control based on multiple daily insulin injections [5]. Though approximately 5–15% of the total diabetic patients in the World are T1D, the portion of the T1D patients are increasing every year, especially among children and adolescence [5,6].

The persistent elevated PGC in the blood of diabetic patients for a long period gives rise to critical health issues affecting almost all the human body's organ systems. If PGC is persistently above 180 mg/dl, it is called hyperglycemia, and PGC below 70 mg/dl is termed as hypoglycemia, and below 50 mg/dl is known as severe hypoglycemia [7]. Diabetic retinopathy (eye blindness), diabetic nephropathy (kidney failure), diabetic neuropathy (nervous system disorder), cardiac arrest (heart disorder), leg amputation, diabetic ketoacidosis, etc., occur due to prolonged hyperglycemia for a long period [3]. Severe hypoglycemia can be fatal for T1D patients since it may lead to diabetic coma and death if unnoticed [7]. Hence, avoiding hypoglycemia is the primary concern for the blood glucose regulation in T1D patients.

1.2 The artificial pancreas system

Due to the dysfunctional/poor pancreas in T1D patients, glucose homeostasis (or automatic control of glucose) does not occur owing to any secretion of the insulin hormone in the body. Such a situation can be thought of as an open-loop control system. So, researchers have attempted to artificially make the glucose-insulin metabolism automatic such that it resembles a closed-loop configuration. The closed-loop control perspective between glucose-insulin dynamics is shown in Fig.