Model individualization for artificial pancreas

Highlights

• Two approaches are proposed for identifying tailored linear models describing the dynamics of patients with type 1 diabetes.

• The first method is a black box identification based on a novel kernel-based nonparametric approach.

• The second is a grey box identification that relies on constrained optimization and requires a pre-defined model structure.

• The individualized models are evaluated in simulation on the adult virtual population of the UVA/Padova simulator.

• The resulting simulation performance is significantly improved with respect to a linear average model.

• The proposed approaches can identify glucose-insulin models for designing individualized control laws for articial pancreas.

Abstract

Background and Objective

The inter-subject variability characterizing the patients affected by type 1 diabetes mellitus makes automatic blood glucose control very challenging. Different patients have different insulin responses, and a control law based on a non-individualized model could be ineffective. The definition of an individualized control law in the context of artificial pancreas is currently an open research topic. In this work we consider two novel identification approaches that can be used for individualizing linear glucose–insulin models to a specific patient.

Methods

The first approach belongs to the class of black-box identification and is based on a novel kernel-based nonparametric approach, whereas the second is a gray-box identification technique which relies on a constrained optimization and requires to postulate a model structure as prior knowledge. The latter is derived from the linearization of the average nonlinear adult virtual patient of the UVA/Padova simulator. Model identification and validation are based on in silico data collected during simulations of clinical protocols designed to produce a sufficient signal excitation without compromising patient safety. The identified models are evaluated in terms of prediction performance by means of the coefficient of determination, fit, positive and negative max errors, and root mean square error.

Results

Both identification approaches were used to identify a linear individualized glucose–insulin model for each adult virtual patient of the UVA/Padova simulator. The resulting model simulation performance is significantly improved with respect to the performance achieved by a linear average model.

Conclusions

The approaches proposed in this work have shown a good potential to identify glucose–insulin models for designing individualized control laws for artificial pancreas.

Introduction

Type 1 Diabetes Mellitus (T1DM), also known as insulin-dependent or juvenile diabetes, is a metabolic disorder characterized by chronic hyperglycemia that occurs when the pancreas is no longer able to produce insulin. Patients affected by T1DM are dependent on exogenous insulin administration to maintain the Blood Glucose (BG) concentration (also called glycemia) within the so called euglycemic range, which spans from 70 mg/dl to 180 mg/dl. Manual insulin administration is complex since there is the need to estimate the insulin dose to inject subcutaneously both during mealtimes and fasting periods. If the injected insulin is underestimated, the patient can experience hyperglycemia, which is generally associated to BG levels higher than 180–200 mg/dl. In addition, symptoms may not start to become noticeable until even higher BG levels, such as 250–300 mg/dl. Chronic hyperglycemia can produce a wide variety of serious complications over a period of years, including damages to kidneys, nervous system, cardiovascular system, retina, feet/legs and nerves (i.e. diabetic neuropathy). On the other hand, if the injected insulin is overestimated, the patient can experience hypoglycemia, which is associated to a BG level lower than 70 mg/dl. Hypoglycemia can cause tachycardia, shakiness, strong headache, sudden mood changes, hunger, sweating, dizziness and nausea, and, if severe, can lead to seizures, loss of consciousness, coma, or death.

The Artificial Pancreas (AP) is a system thought to automate the exogenous insulin supply and is composed of a subcutaneous glucose sensor, which allows Continuous Glucose Monitoring (CGM), a subcutaneous insulin pump, and a control algorithm. Recently, several research projects on AP were supported by the Juvenile Diabetes Research Foundation, the European Commission, and the National Institutes of Health (see Refs. [1], [2], [3], [4], [5], [6], [7], [8], [9]). The core of the AP is the control algorithm, which is in charge of continually estimating the quantity of insulin to inject in the subcutaneous tissue on the basis of the subcutaneous continuous glucose measurements. A detailed description of the state of the art of the considered AP system can be found in Ref. [10], where the adopted control algorithm is a Model Predictive Control (MPC). MPC synthesizes a controller on the basis of a model that describes the dynamics of the process under control (i.e. the biological dynamics of the patient). A complex metabolic model was first introduced in Ref. [11] and then improved in Ref. [12]. This model is highly nonlinear and time-varying and its implementation in a MPC law is computationally demanding. However, as shown in Refs. [13], [14], a linear time-invariant approximation of glucose–insulin interaction is adequate to capture the essential dynamics to design an effective and safe MPC, while guaranteeing reduced complexity and low computational burden in the MPC implementation. This fact was also confirmed by several clinical trials performed in silico [14], [15], [16], [17], [18], [19], [20] and in vivo [7], [9], [21], [22], [23], [24], [25], [26], [27] through MPC synthesized on the basis of a linear model.

Diabetic patients are characterized by a substantial inter-subject variability that may limit the closed-loop control performance achievable by a non-individualized controller. Thus, a significant step forward would be represented by the controller individualization that, however, is very challenging. The control performance could be limited even by the patient intra-subject variability, which would require a recursively adaptive control law [28]. Different approaches can be considered like multivariable adaptive control [29], [30] or run-to-run strategies used for daily adaptation of basal insulin [31], insulin boluses [32], [33], [34], [35], or MPC cost function [36].

In order to synthesize an individualized MPC, a patient-tailored glucose–insulin model is needed. The Nonparametric (NP) approach for linear models identification presented in Ref. [37] was applied to simulated data. An in silico trial was also performed, demonstrating that the MPC synthesized on the basis of the individualized models significantly improves closed-loop control performance. In addition to the NP approach, a parametric identification technique driven by Constrained Optimization (CO) is presented, where the identified models are characterized by a fixed structure that is postulated as prior knowledge. Models identification and test are based on in silico data collected during closed-loop simulations of clinical protocols designed to produce a sufficient input–output excitation without compromising the patient safety. The identified models are evaluated in terms of prediction performance by means of the Coefficient of Determination (COD), FIT, Positive and Negative Max Errors (PME and NME, respectively), and Root Mean Square Error (RMSE). The resulting performance is compared with the performance achieved by the NP models presented in Ref. [37] and with the average linear model used to synthesize the linear MPC introduced in Ref. [19], which was also used in several clinical experiments.