Computational study of an augmented minimal model for glycaemia control

Modeling Glucagon Action in Patients With Type 1 Diabetes

The dual-hormone artificial pancreas is an emerging technology to treat type 1 diabetes (T1D). It consists of a glucose sensor, infusion pumps, and a dosing algorithm that directs hormonal delivery. Preclinical optimization of dosing algorithms using computer simulations has the potential to accelerate the pace of development for this technology. However, current simulation environments consider glucose regulation models that either do not include glucagon action submodels or include submodels that were proposed without comparison to other candidate models. We consider here nine candidate models of glucagon action featuring a number of possible characteristics: insulin-independent glucagon action, insulin/glucagon ratio effect on hepatic glucose production, insulin-dependent suppression of glucagon action, and the effect of rate of change of glucagon. To assess the models, we use measurements of plasma insulin, plasma glucagon, and endogenous glucose production collected from experiments involving eight subjects with T1D who receive four subcutaneous glucagon boluses. We estimate each model's parameters using a Bayesian approach, and the models are contrasted based on the deviance information criterion. The model achieving the best fit features insulin-dependent suppression of glucagon action and incorporates effects of both glucagon levels and its rate of change.

Pharmacokinetics modeling of exogenous glucagon in type 1 diabetes mellitus patients

BACKGROUND

Insulin-induced hypoglycemia is as a critical barrier in the treatment of type 1 diabetes mellitus patients and may lead to unconsciousness, brain damage, or even death. Clinically, glucagon is used as a rescue drug to treat severe hypoglycemic episodes. More recently, in a bihormonal closed-loop glucose control, glucagon has been used subcutaneously along with insulin for protection against hypoglycemia. In this context, small doses of glucagon are frequently administered. The efficacy and safety of such systems, however, require precise information on the pharmacokinetics of the glucagon transport from the administrative site to the circulation, which is currently lacking. The goal of this work is to address this need by developing and validating a mathematical model of exogenous glucagon transport to the plasma.

MATERIALS AND METHODS

Eight pharmacokinetic models with various levels of complexity were fitted to nine clinical datasets. An optimal model was chosen in two consecutive steps. At Step 1, all models were screened for parameter identifiability (discarding the unidentifiable candidates). At Step 2, the remaining models are compared based on Bayesian information criterion.

RESULTS

At Step 1, two models were removed for higher parameter fractional SDs. Another three were discarded for location of their optimal parameters on the parameter search boundaries. At Step 2, an optimal model was selected based on the Bayesian information criterion. It has a simple linear structure, assuming that glucagon is injected into one compartment, from where it enters a pool for a slower release into a third, plasma compartment. In the first and third compartments, glucagon is cleared at a rate proportional to its concentration.

CONCLUSIONS

A linear kinetic model of glucagon intervention has been developed and validated. It is expected to provide guidance for glucagon delivery and the construction of preclinical simulation testing platforms.

A Generic Integrated Physiologically based Whole-body Model of the Glucose-Insulin-Glucagon Regulatory System

Models of glucose metabolism are a valuable tool for fundamental and applied medical research in diabetes. Use cases range from pharmaceutical target selection to automatic blood glucose control. Standard compartmental models represent little biological detail, which hampers the integration of multiscale data and confines predictive capabilities. We developed a detailed, generic physiologically based whole-body model of the glucose-insulin-glucagon regulatory system, reflecting detailed physiological properties of healthy populations and type 1 diabetes individuals expressed in the respective parameterizations. The model features a detailed representation of absorption models for oral glucose, subcutaneous insulin and glucagon, and an insulin receptor model relating pharmacokinetic properties to pharmacodynamic effects. Model development and validation is based on literature data. The quality of predictions is high and captures relevant observed inter- and intra-individual variability. In the generic form, the model can be applied to the development and validation of novel diabetes treatment strategies.

A composite model of glucagon-glucose dynamics for in silico testing of bihormonal glucose controllers

BACKGROUND

The utility of simulation environments in the development of an artificial pancreas for type 1 diabetes mellitus (T1DM) management is well established. The availability of a simulator that incorporates glucagon as a counterregulatory hormone to insulin would allow more efficient design of bihormonal glucose controllers. Existing models of the glucose regulatory system that incorporates glucagon action are difficult to identify without using tracer data. In this article, we present a novel model of glucagon-glucose dynamics that can be easily identified with standard clinical research data.

METHODS

The minimal model of plasma glucose and insulin kinetics was extended to account for the action of glucagon on net endogenous glucose production by incorporating a new compartment. An existing subcutaneous insulin absorption model was used to account for subcutaneous insulin delivery. The same model of insulin pharmacokinetics was employed to model the pharmacokinetics of subcutaneous glucagon absorption. Finally, we incorporated an existing gastrointestinal absorption model to account for meal intake. Data from a closed-loop artificial pancreas study using a bihormonal controller on T1DM subjects were employed to identify the composite model. To test the validity of the proposed model, a bihormonal controller was designed using the identified model.

RESULTS

Model parameters were identified with good precision, and an excellent fitting of the model with the experimental data was achieved. The proposed model allowed the design of a bihormonal controller and demonstrated its ability to improve glycemic control over a single-hormone controller.

CONCLUSIONS

A novel composite model, which can be easily identified with standard clinical data, is able to account for the effect of exogenous insulin and glucagon infusion on glucose dynamics. This model represents another step toward the development of a bihormonal artificial pancreas.

Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted "minimal model" and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.

Model Predictive Control of blood glucose in Type 1 diabetes: the Principal Dynamic Modes approach

This computational study demonstrates the efficacy of regulating blood glucose in Type 1 diabetics with a Model Predictive Control strategy, utilizing a nonparametric / Principal Dynamic Modes model. For this purpose, a stochastic glucose disturbance signal is introduced and a simple methodology for predicting its future values is developed. The results of our simulations confirm that the proposed algorithm achieves very good performance, is computationally efficient and avoids hypoglycaemic events.