Real-time estimation of plasma insulin concentration from continuous glucose monitor measurements

Abstract

Continuous glucose monitors can measure interstitial glucose concentration in real-time for closed-loop glucose control systems, known as artificial pancreas. These control systems use an insulin feedback to maintain plasma glucose concentration within a narrow and safe range, and thus to avoid health complications. As it is not possible to measure plasma insulin concentration in real-time, insulin models have been used in literature to estimate them. Nevertheless, the significant inter-and intra-patient variability of insulin absorption jeopardizes the accuracy of these estimations. In order to reduce these limitations, our objective is to perform a real-time estimation of plasma insulin concentration from continuous glucose monitoring. Hovorka's glucose-insulin model has been incorporated in an Extended Kalman Filter in which different selected time-variant model parameters have been considered as extended states. The observability of the original Hovorka's model and of several extended models has been evaluated by their Lie derivatives. We have evaluated this methodology with an in-silico study with 100 patients with Type 1 diabetes during 25 hours. Furthermore, it has been also validated using clinical data from 12 insulin pump patients with Type 1 diabetes who underwent four mixed meal studies. Real-time insulin estimations have been compared to plasma insulin measurements to assess performance showing the validity of the methodology here used in comparison with that formerly used for insulin models. Hence, real-time estimations for plasma insulin concentration based on subcutaneous glucose monitoring can be beneficial for increasing the efficiency of control algorithms for the artificial pancreas.

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

“…Hovorka glucose-insulin model [23] and the Extended Kalman Filter (EKF) are used in [35], where real-time estimation of plasma insulin concentration from continuous glucose monitoring (CGM) measurements in subjects with type 1 diabetes is addressed in the context of insulin observers for closed-loop control. The extra equatioṅ…”

“…With regard to variability, different scenarios are devised: natural physiological variability in insulin pharmacokinetics at a given infusion site along the lifetime of the infusion set; and more abrupt changes in insulin pharmacokinetics due to the use of a new infusion site after rotation, with different subcutaneous tissue properties (for instance, affected by lypohypertrophia [18]). Due to the limited duration of the data (5 hours), the above scenarios are characterized in [35] through the observer initialization, since a change in infusion site is expected to imply a larger mismatch between the observer model and the actual behavior. Thus three cases are compared in Figure 4: (i) a population model is used as insulin predictor considering nominal pharmacokinetic parameters in the Hovorka model, which are clearly detuned for this patient (comparator); (ii) pharmacokinetic parameters k e and t maxI are included into the Kalman filter for real-time estimation with initial conditions set to nominal parameters in Hovorka model, far from the actual values (representing the case of a new infusion site); and (iii) is the same case as (ii), but initial conditions of the pharmacokinetic parameters are set to the average of the parameter values estimated for the rest of patients (following a cross-validation procedure), which are closer to the actual values as demonstrated by data (representing performance against variability of the current infusion site along its lifetime, after a longer run of the observer).…”

“…Figure 4. Example of performance of the insulin observer in [35] for a sample patient. Dashed red line represents the case with nominal pharmacokinetic parameters in the Hovorka model; solid blue line the case with real-time adaptation of k e and t maxI with initial values set to nominal values; and solid green line the case with real-time adaptation of k e and t maxI with initial values set to the average of the parameter values estimated for the rest of patients.…”

“…Dashed red line represents the case with nominal pharmacokinetic parameters in the Hovorka model; solid blue line the case with real-time adaptation of k e and t maxI with initial values set to nominal values; and solid green line the case with real-time adaptation of k e and t maxI with initial values set to the average of the parameter values estimated for the rest of patients. Green diamonds represent measurements (adapted from [35]). In particular, for cooperative systems [S7], the relation order is induced by the corresponding positive orthant, which is characterized by a Metzler Jacobian Matrix, that is,…”

A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs

“…where the sets X, W, and V are assumed to be polyhedral and convex. Consider the constrained estimation problem for (1). The estimate of x t given the measurement sequence {y 0 , · · · , y t−1 }, denoted asx t|t−1 , is obtained by the solution of the state equation (1) if the a priori estimates of the initial state x 0|t−1 and the disturbance sequence {w 0 , · · · , w t−1 } are known, ie,x 0|t−1 and {ŵ 0 , · · · ,ŵ t−1 }, respectively,…”