Insulin Estimation and Prediction: A Review of the Estimation and Prediction of Subcutaneous Insulin Pharmacokinetics in Closed-Loop Glucose Control

Abstract

is currently the safest infusion route for a commercial artificial pancreas, as opposed to the endogenous pancreas that secretes insulin directly into portal circulation (the vessels that connect the pancreas and other organs with the liver, which acts as a first blood filter before entering the main circulatory system). Even in approaches with concomitant infusion of glucagon (the socalled dual-hormone artificial pancreas), mechanisms are necessary to avoid an excess of insulin delivery which may lead to late hypoglycemia putting at stake the patient's safety. Independently of how these mechanisms are incorporated into the control schemes, all of them must rely on pharmacokinetic models predicting either circulating plasma insulin or a measure of "insulin-onboard", such as the insulin depot remaining at the subcutaneous tissue before entering circulation. In this article, methods to constrain insulin delivery are reviewed, as well as the subcutaneous insulin pharmacokinetic models and estimators on which they rely upon. A big challenge in the prediction of physiological signals, such as insulin concentration, is the large intra-subject variability that patients suffer. Indeed, in terms of control engineering, a patient is a highly time-varying uncertain plant. The intra-day and day-today patient's behavior change due to circadian rhythms (24-hour rhythmic physiological oscillations driven by the body clock, for instance, daily patterns in insulin sensitivity), and other multiple sources of uncertainty arise in key physiological processes such as meal absorption and subcutaneous insulin absorption. Despite this fact, the use of population models for the prediction of insulin pharmacokinetics, that is, how the infused insulin appears in blood, is still common practice. The impact of variability on the model prediction and its implication in closed-loop performance is analyzed. Nevertheless, large intra-subject variability suggests that real-time state and pharmacokinetic parameters estimation is convenient, even when individualized models are considered. The availability of continuous glucose measurements allows to address this problem should an observable glucose-insulin model be available. Different observer techniques proposed to this purpose are reviewed and discussed. The subcutaneous insulin route The pancreas secretes insulin into the portal vein towards the liver, which acts as a first filter before insulin reaches systemic circulation. In the liver, insulin promotes glucose storage in hepatic cells decreasing glucose production. In the fat and muscle cells, insulin acts as a key that triggers the mobilization of glucose transporters to the cell membrane promoting glucose uptake by the cell. As a result of both actions, plasma glucose concentration decreases. The dynamic lag of insulin action is estimated to be about 30 minutes [3]. An artificial pancreas is a classic closed-loop glucose control system (see Figure 1) that

Sliding-mode disturbance observers for an artificial pancreas without meal announcement

“…where is the controller gain ( = 0.42 L/min) and ˆI * P is the estimated plasma insulin in basal conditions. Unlike in [25], here, the deviation regarding the plasma insulin is employed, to avoid retuning the PD for keeping the steady state conditions of the PD without IFB.…”

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“…Addressing these complexities is crucial for effective artificial pancreas (AP) control. Extensive efforts, including diverse mathematical models and controller design techniques, have been employed to overcome these challenges, as detailed in comprehensive reviews such as [33,34] on existing models and the utilized controllers. MPC and PID are widely applied in APS [35,36].…”