MPC based Artificial Pancreas: Strategies for individualization and meal compensation

Abstract

This paper addresses the design of glucose regulators based on Model Predictive Control (MPC) to be used as part of Artificial Pancreas devices for type 1 diabetic patients. Two key issues are deeply investigated: individualization, needed to cope with intersubject variability, and meal compensation, interpreted as a disturbance rejection problem. The individualization is achieved either by tuning the cost function, based on few well known clinical parameters (MPC1) or through the use of an individual model obtained via system identification techniques and an optimal tuning of the cost function based on real-life experiments (MPC2). The in silico tests, performed on 4 different scenarios using a simulator equipped with 100 patients, show that the performances of MPC1 are very promising, supporting its current use in an in vivo multicenter trial on 47 patients that is being carried out within the European Research Project AP@home. At the same time, further improvements are achieved by MPC2, showing that there is scope for in vivo experimentation of control strategies employing individually estimated patient models.

Introduction

Diabetes is a pathology that involves glucose regulation and can be divided in two main types: type 1, or insulin dependent, and type 2 or insulin resistant. The first one is characterized by the destruction of the beta cells in the pancreas, responsible for the insulin production, and, as a consequence, by the complete dependency of the patient on external insulin administration. In type 2 diabetic patients, there are an alteration of insulin secretion and a reduction of sensitivity to this hormone. A good glucose regulation, with glucose levels in the range 70–140 mg/dl, is mandatory for both types of diabetes because low blood glucose levels, hypo-glycemia, can lead to coma and, if not treated, to death. Conversely, high blood glucose levels, hyper-glycemia, maintained for too long can lead to the onset of long term problems such as cardiovascular diseases, chronic renal failures and retinal damages.

Scientific research devoted to diabetes is motivated by its prevalence, the estimated increase of new cases in the future and also because, with its complications, it imposes heavy charges on individuals, families, health systems, and countries. The World Health Organization (WHO), estimates that more than 346 million people worldwide have diabetes, a number destined to more than double by 2030. Diabetes is a major cause of death and in 2004 an estimated 3.4 million people died from consequences of high blood sugar (World Health Organization).

Research addresses several issues (Cobelli et al., 2009, Cobelli et al., 2011) and has different objectives: prevent the diffusion of the pathology, optimize therapy and develop automatic devices for regulating glucose in diabetic patients. The first example of device, developed in 1970s, for glucose regulation is the Biostator® that used glucose measurements, obtained with an intravenous sensor, to suggest insulin values, injected with an intravenous pump (Albisser et al., 1974, Clemens et al., 1977, Marliss et al., 1977). This method is too invasive and not suitable for outpatient use. For this reason, of great interest are devices employing a subcutaneous glucose sensor and a subcutaneous insulin pump. The integration of these two components with a control algorithm is called Artificial Pancreas (AP). A new era for the AP started in 1999 when the MiniMed introduced a commercial continuous glucose monitoring (CGM) system. Since then, several research project studied and experimented AP systems, starting from the MiniMed AP project (Steil, Rebrin, Darwin, Hariri, & Saad, 2006), with an acceleration caused by the launch of research projects funded by the JDRF, the European Commission and the NIH (El-Khatib et al., 2010, Hovorka et al., 2004, Hovorka et al., 2010, Kovatchev et al., 2010, Weinzimer et al., 2008). Among the most notable results is the approval by the Food and Drugs Administration (FDA) of a large scale in silico simulator developed by the University of Padova and the University of Virginia (Kovatchev, Breton, Dalla Man, & Cobelli, 2008) as a substitute to animal trials in the preclinical testing of AP control strategies.

Designing a control algorithm for the sc to sc glucose–insulin system is challenging because the system is characterized by significant interindividual variability, time varying dynamics, nonlinear phenomena and time delays due to the absorption of insulin from the subcutaneous level to the blood and, on reverse, of glucose from the blood to the subcutaneous level. Moreover the glucose profile depends on the insulin delivered, bounded from zero to a maximal value given by the pump, but also on very important disturbances such as meals and physical exercises that could be predicted to some extent.

The objective of the control algorithm is to keep the glucose levels within an optimal range (70–140 mg/dl). In the literature, several algorithms have been presented starting from PID schemes such as the work of Marchetti et al., 2006, Steil et al., 2006.

One of the most promising approaches to glucose regulation is Model Predictive Control. Three examples of MPC glucose regulation are the study of Parker, Doyle, and Peppas (1999), that considers a linear model identified with step responses and the work of Hovorka et al. (2004) that relies on a nonlinear time varying model whose parameters are adapted via Bayesian estimation and Magni et al. (2007) that is based on a mean linear model with an individualized cost function. Other interesting approaches are presented in Bequette, 2005, Dua et al., 2006, Grosman et al., 2010, Hovorka, 2005a, Hovorka, 2005b, Magni, Raimondo, et al., 2009, Magni, Forgione, et al., 2009, Patek et al., in press. So far, encouraging pilot results have been reported using Proportional-Integral-Derivative (PID) control (Steil et al., 2006, Weinzimer et al., 2008) and MPC strategies (Dassau et al., 2010, Hovorka et al., 2010, Kovatchev et al., 2010). In the technological implementation of the Artificial Pancreas, the control algorithm can be embedded in a modular architecture, (Patek et al., in press), including a safety module that checks the insulin suggested by the algorithm and approves or reduces this value.

The results illustrated in this article have been obtained in silico, using a simulator equipped with a cohort of virtual subjects that span sufficiently well the interindividual variability of key metabolic parameters in the general population of diabetic patients. In particular, the in silico experiments were performed using the glucose–insulin simulator developed by the University of Padova and University of Virginia (see Dalla Man, Rizza, & Cobelli, 2007). Underlying this simulator there is a high-order nonlinear model, characterized by several physiological parameters and incorporating all available knowledge about system functionality so as to be able to provide realistic glucose–insulin simulations in diabetes.

The paper is organized as follows. Section 2 is devoted to discussing the structure of the control system. The main contribution is the analysis of alternative feedback–feedforward schemes that exploit conventional therapy in order to improve the effectiveness of meal compensation. The novel scheme proposed in this paper combines a feedforward action derived from conventional therapy with feedforward action optimized by the MPC based on a meal absorption model. In Section 3, a general framework for controller individualization is described that hinges on two models, one for control design purposes and the other for tuning the cost function. Three possible implementations of this framework are discussed in Section 4. The first control strategy is an ideal one as it assumes availability of an accurate model of the true patient. The second one pursues individualization without assuming knowledge of individual patient dynamics, but exploiting only the knowledge of standard clinical parameters obtainable from screening questionnaires. The third control strategy individualizes the regulator on the basis of an individual linear model identified from real life experiments. The comparison of the three control strategies is carried out in silico in Section 5 considering four different scenarios: nominal, randomly perturbed meals, randomly perturbed insulin sensitivity and perturbation of basal insulin delivery. Some conclusions end the paper.