Modelling the effects of glucagon during glucose tolerance testing.

From Europe PMC via Jisc Publications RouterHistory: ppub 2019-12-01, epub 2019-12-12Publication status: PublishedBACKGROUND:Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship. RESULTS:Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ). CONCLUSIONS:The models are used to investigate how different degrees of pax'tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted

Optimal input design for identification of compartmental models. Theory and application to a model of glucose kinetics.

The optimal input design problem for the identification of linear compartmental models is studied. The optimality criterion consists in maximizing the achievable precision of parameter estimates. The rationale, theory, and computational methods for solving the problem for the scalar case are presented first. An application to a two-compartment model of glucose kinetics is then shown. The effect on parameter precision of the measurement error structure and of various design factors, such as an equienergy or equidose class of admissible inputs and the time interval for input and measurement, is discussed. The performance of standard classical inputs, e.g. an impulse or an infusion, is also evaluated

On optimality of the impulse input for linear system identification.

The optimal input design for the identification of linear single input-single output systems is considered in the particular situation of continuous time measurement corrupted by white gaussian noise of constant variance. The optimality of the impulse among nonnegative equidose inputs is proven

Generalized Sensitivity Functions in Physiological System Identification.

Parameters of physiological models are commonly associated in an input-output experiment with a specific pattern of the system response. This association is often made on an intuitive basis by traditional sensitivity analysis, i.e., by inspecting the variations of model output trajectories with respect to parameter variations. However, this approach provides limited information since, for instance, it ignores correlation among parameters. The aim of this study is to propose a new set of sensitivity functions, called the generalized sensitivity functions (GSF), for the analysis of input-output identification experiments. GSF are based on information theoretical criteria and provide, as compared to traditional sensitivity analysis, a more accurate picture on the information content of measured outputs on individual model parameters at different times. Case studies are presented on an input-output model and on two structural circulatory and respiratory models. GSF allow the definition of relevant time intervals for the identification of specific parameters and improve the understanding of the role played by specific model parameters in describing experimental data

The minimal model of glucose disappearance: optimal input studies.

The \u201cminimal model\u201d of glucose disappearance provides noninvasive estimates of important metabolic parameters, among them the effect of insulin on glucose uptake. We study here the design of optimal inputs for the identification of the model, i.e., for estimating its parameters with maximum precision. The scalar case is examined first and solved via Pontryagin's maximum principle for two input classes: equienergy and equidose. For the equidose class the vector case is then studied by simulation for clinically realizable glucose inputs in both the normal and the diabetic case. Finally, recent experimental developments proposed for the identification of the model, i.e., a glucose input involving a concomitant drug stimulus and a tracer labeled glucose input, are examined in the context of optimal input design

Optimal equidose inputs and role of measurement error for estimating the parameters of a compartmental model of glucose kinetics from continuous- and discrete-time optimal samples.

The optimal input design for estimating all the parameters of a two-compartment model of glucose kinetics is studied. The problem is solved by simulation for the class of equidose rectangular-shaped inputs with both continuous- and discrete-time optimal samples. The important role of the measurement error in determining the optimal input is analyzed by examining four error structures. With continuous-time measurements the optimal input depends on the measurement error, but rather efficient suboptimal inputs can be obtained with small infusion periods. The impulse input is optimal among the considered error structures with discrete-time optimal samples