Optimal Design of Clinical Tests for the Identification of Physiological Models of Type 1 Diabetes Mellitus

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen's model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

On the use of continuous glucose monitoring systems to design optimal clinical tests for the identification of type 1 diabetes models

The identification of individual parameters of detailed physiological models of type 1 diabetes can be carried out by clinical tests designed optimally through model-based design of experiments (MBDoE) techniques. So far, MBDoE for diabetes models has been considered for discrete glucose measurement systems only. However, recent advances on sensor technology allowed for the development of continuous glucose monitoring systems (CGMSs), where glucose measurements can be collected with a frequency that is practically equivalent to continuous sampling. To specifically address the features of CGMSs, in this paper the optimal clinical test design problem is formulated and solved through a continuous, rather than discrete, approach. A simulated case study is used to assess the impact of CGMSs both in the optimal clinical test design problem and in the subsequent parameter estimation for the identification of a complex physiological model of glucose homeostasis. The results suggest that, although the optimal design of a clinical test is simpler if continuous glucose measurements are made available through a CGMS, the noise level and formulation may make continuous measurements less suitable for model identification than their discrete counterparts.

Control-relevant models for glucose control using a priori patient characteristics

One of the difficulties in the development of a reliable artificial pancreas for people with type 1 diabetes mellitus (T1DM) is the lack of accurate models of an individual's response to insulin. Most control algorithms proposed to control the glucose level in subjects with T1DM are model-based. Avoiding postprandial hypoglycemia ( 60 mg/dl) while minimizing prandial hyperglycemia ( > 180 mg/dl) has shown to be difficult in a closed-loop setting due to the patient-model mismatch. In this paper, control-relevant models are developed for T1DM, as opposed to models that minimize a prediction error. The parameters of these models are chosen conservatively to minimize the likelihood of hypoglycemia events. To limit the conservatism due to large intersubject variability, the models are personalized using a priori patient characteristics. The models are implemented in a zone model predictive control algorithm. The robustness of these controllers is evaluated in silico, where hypoglycemia is completely avoided even after large meal disturbances. The proposed control approach is simple and the controller can be set up by a physician without the need for control expertise.

Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch

How to design a clinical test aimed at identifying in the safest, most precise and quickest way the subject-specific parameters of a detailed model of glucose homeostasis in type 1 diabetes is the topic of this article. Recently, standard techniques of model-based design of experiments (MBDoE) for parameter identification have been proposed to design clinical tests for the identification of the model parameters for a single type 1 diabetic individual. However, standard MBDoE is affected by some limitations. In particular, the existence of a structural mismatch between the responses of the subject and that of the model to be identified, together with initial uncertainty in the model parameters may lead to design clinical tests that are sub-optimal (scarcely informative) or even unsafe (the actual response of the subject might be hypoglycaemic or strongly hyperglycaemic). The integrated use of two advanced MBDoE techniques (online model-based redesign of experiments and backoff-based MBDoE) is proposed in this article as a way to effectively tackle the above issue. Online model-based experiment redesign is utilised to exploit the information embedded in the experimental data as soon as the data become available, and to adjust the clinical test accordingly whilst the test is running. Backoff-based MBDoE explicitly accounts for model parameter uncertainty, and allows one to plan a test that is both optimally informative and safe by design. The effectiveness and features of the proposed approach are assessed and critically discussed via a simulated case study based on state-of-the-art detailed models of glucose homeostasis. It is shown that the proposed approach based on advanced MBDoE techniques allows defining safe, informative and subject-tailored clinical tests for model identification, with limited experimental effort.

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.