Handling Parameter Variations during the Treatment of Type 1 Diabetes Mellitus: In Silico Results

María F Villa Tamayo,Michelle A Caicedo Alvarez,Pablo S Rivadeneira

doi:10.1155/2019/2640405

Abstract

Type 1 diabetic patients need a strict treatment to regulate blood glucose concentration in a target range. Despite the development of different control strategies, the model parameter variations, given by physiological changes, can generate an inaccurate treatment and in consequence hyperglycemia and hypoglycemia episodes. Therefore, it is necessary to use control techniques that compensate such effects and maintain the control goals. Here, the effect of parametric variations is examined by the sensitivity analysis from which the most influential parameters in glycemia dynamics are detected. Based on that, an offset-free MPC strategy for impulsive systems is given for the first time in literature and simulated for type 1 diabetes treatment. This scheme along with the impulsive zone MPC with artificial variables reestablishes the normoglycemia behavior since the parameter variations are adequately rejected. However, only parametric variations up to 50% from their nominal values are well compensated, which suggests that more robust formulations are needed to ensure a greater rejection of physiological variations.

Highlights

Type 1 diabetes mellitus (T1DM) is an autoimmune disease in which the pancreatic β-cells are destroyed, causing inability to secrete insulin and regulate blood glucose (BG) in the body
The development of the offset-free model predictive control (MPC) strategy applied to T1DM treatment consists of four fundamental subsections: the model to describe the interaction between glucose, insulin, and carbohydrates; the appropriate MPC formulation to maintain glycemia in the target zone; the sensitivity analysis of the influence of the parameters in the glycemia dynamics; and an extended MPC formulation considering the offset-free problem
Different MPC strategies for discrete and impulsive systems, applied to the T1DM treatment problem, are compared. These strategies are the standard discrete MPC [24], the discrete zone MPC (ZMPC) with slack variable [26], the discrete ZMPC with artificial variables [28, 29], and the adaptation of the same formulations for impulsive systems: Impulsive MPC (iMPC) [30], impulsive ZMPC (iZMPC) [22], and iZMPC-AV [10]; the description of each formulation can be seen in the appendix

Summary

Introduction

Type 1 diabetes mellitus (T1DM) is an autoimmune disease in which the pancreatic β-cells are destroyed, causing inability to secrete insulin and regulate blood glucose (BG) in the body It leads to secondary pathophysiological alterations in many systems and can be the cause of nephropathy, blindness, or even nontraumatic amputations of lower extremities [1]. One of the most common treatments is functional insulin therapy It consists of daily insulin injections according to glycemia measurements and carbohydrate intake with the objective of maintaining normoglycemia (70 mg/dl ≤ BG ≤ 180 mg/dl). AP attempts to emulate the natural behavior of the pancreas by the use of an insulin pump, continuous glucose monitoring, and closed-loop control strategies This system aims to avoid hypoglycemia (BG < 70 mg/dl) and hyperglycemia (BG > 180 mg/dl) events, which result in complications in the patient with T1DM [2]

Objectives

Methods

Results