Tests on a virtual patient for an observer-based, closed-loop control of plasma glycemia P. Palumbo G. Pizzichelli S. Panunzi P. Pepe A. De Gaetano Abstract— Exogenous insulin administration is the basic way to face the widespread disease of Diabetes Mellitus. To this aim, closed-loop approaches, though theoretically realizable accord- ing to the control theory results and to the recent technology concerning continuous glucose measurements and affordable insulin infusion pumps, require a careful and thorough testing ground on a virtual environment before arranging an in-vivo clinical setting of experiments. In this work, a model-based control law for the plasma glycemia, recently published by the same authors, is evaluated by closing the loop on a virtual patient, whose model equations are different from the ones used to synthesize the control law. That means: a minimal model of the glucose-insulin system to design the insulin therapy, and a different, more detailed, comprehensive model to test in silico the control scheme. Uncertainties on the blood glucose measurements, as well as malfunctioning on the insulin delivery devices are considered, according to the standard technology, in order to obtain an effective benchmark for the closed-loop control and to show in fact the robustness of the proposed approach. I. I NTRODUCTION The term “diabetes” comprises a group of metabolic disorders characterized by hyperglycemia resulting from defects in insulin secretion, insulin action, or both. In one category (Type 1 diabetes), there is an absolute deficiency of insulin secretion caused by an autoimmune pathologic process occurring in the pancreatic islets. Individuals with this extensive beta-cell destruction, and therefore no residual insulin secretion, require insulin for survival. In the other, much more prevalent category (Type 2 diabetes), the cause is a combination of resistance to insulin action and inadequate compensatory insulin secretory response. These individuals have therefore insulin resistance and usually have relative (rather than absolute) insulin deficiency, in the face of increased levels of circulating insulin. Exogenous insulin administration is a basic procedure to cope with most malfunctioning of the endogenous insulin feedback action (in Type 1 diabetes only exogenous insulin is available, while in Type 2 exogenous insulin comple- ments pancreatic production). Glucose control strategies are mainly actuated by subcutaneous or intravenous injections or infusions. Control of glycemia by means of subcutaneous insulin injections is by far more widespread than control by means of intravenous insulin, since the dose is habitu- ally administered by the patients themselves (see [1] and P. Palumbo, G. Pizzichelli, S. Panunzi and A. De Gaetano are with the Istituto di Analisi dei Sistemi ed Informatica ”A. Ruberti”, Consiglio Nazionale delle Ricerche (IASI-CNR), BioMatLab - UCSC - Largo A. Gemelli 8, 00168 Roma, Italy. P. Pepe is with the Dipartimento di Ingegneria Elettrica e dell’Informazione, Universit´ a degli Studi dell’Aquila, 67040 Poggio di Roio, L’Aquila, Italy. references therein). However, only open loop or semiclosed loop control strategies can be used in this situation, mainly due to the problem of accurately modeling the absorption of the hormone from the subcutaneous depot into the plasma circulation (see [20] for a critical review of subcutaneous absorption models and [7] for a model of intra/inter sub- ject variability of the absorption of subcutaneous insulin preparations). On the other hand, the use of intravenous insulin administration, delivered by automatic, variable speed pumps under the direct supervision of a physician, provides a wider range of possible strategies and ensures a rapid delivery with negligible delays. As a matter of fact, control algorithms based on intravenous insulin administration are directly applicable so far only to problems of glycemia stabilization in critically ill subjects, such as in surgical Intensive Care Units after major procedures. A closed loop control strategy may be implemented ac- cording to a model-less or to a model-based approach. The first approach does not use a mathematical model of the glucose-insulin system, and provides an arbitrary (while possibly very effective) control rule for insulin infusion rate, based on experimental data: recent papers on this topic are mainly devoted to the application of PID controllers aiming to mimic the pancreatic glucose response (see e.g. [5], [32], [14], [19]). Clearly, before applying these empirical therapies in a clinical setting, they need to be tested on a virtual environment, usually provided by a total-body comprehensive model of the glucose-insulin system, which details about the many organs and tissues involved in the insulin dependent/independent glucose uptake as well as in the endogenous/exogenous insulin administration [8], [31], [9]. On the other hand a model-based approach presupposes sufficiently detailed knowledge of the physiology of the system under investigation. The advantages of a model- based approach are evident since, by using a glucose/insulin model, the control problem may be treated mathematically and optimal strategies may be determined. Clearly, the more accurate the model, the more effective is the control law. Recently, model-based glucose controls have been proposed, based on nonlinear models such as the Minimal Model, [2], [33], or more exhaustive compartmental models, [8], [31], [16], (e.g. Model Predictive Control in [15], Parametric Programming in [10], Neural Predictive Control in [34], H ∞ control in [28], non-standard H ∞ control in [6], [30]). It has to be stressed that most of these approaches are based on the approximation of the original nonlinear model, provided by linearization, discretization and model reduction (balanced truncation). In most of the above mentioned papers, insulin 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA, December 12-15, 2011 978-1-61284-799-3/11/$26.00 ©2011 IEEE 6936