A Model of the Kinetics of Insulin in Man (original) (raw)
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Models for the Study of Whole-Body Glucose Kinetics: A Mathematical Synthesis
ISRN Biomathematics, 2013
The maintenance of blood glucose homeostasis is complex and involves several key tissues. Most of these tissues are not easily accessible, making direct measurement of the physiological parameters involved in glucose metabolism difficult. The use of isotope tracer methodology and mathematical modeling allows indirect estimates ofin vivoglucose metabolism through relatively noninvasive means. The purpose of this paper was to provide a mathematical synthesis of the models developed for describing glucose kinetics. As many of the models were developed using dogs, example data from the canine literature are presented. However, examples from the human and feline literature are also given in the absence of dog data. The glucose system is considered in both the steady and nonsteady states, and the models are examined by grouping them into schemes consisting of one, two, and three glucose compartments. Noncompartmental schemes are also considered briefly.
Mathematical modeling of the glucose–insulin system: A review
Mathematical Biosciences, 2013
Mathematical modeling of the glucose-insulin feedback system is necessary to the understanding of the homeostatic control, to analyze experimental data, to identify and quantify relevant biophysical parameters, to design clinical trials and to evaluate diabetes prevention or disease modification therapies. Much work has been made over the last 30 years, and the time now seems ripe to provide a comprehensive review. The one here proposed is focused on the most important clinical/experimental tests performed to understand the mechanism of glucose homeostasis. The review proceeds from models of pancreatic insulin production, with a coarser/finer level of detail ranging over cellular and subcellular scales, to short-term organ/tissue models accounting for the intra-venous and the oral glucose tolerance tests as well as for the euglycemic hyperinsulinemic clamp, to total-body, long-term diabetes models aiming to represent disease progression in terms of b-cell population dynamics over a long period of years.
Enhanced modelling of the glucose–insulin system and its applications in insulin therapies
Journal of Biological Dynamics, 2009
It is well known that Michaelis-Menten kinetics is suitable for the response function in chemical reaction, when the reaction rate does not increase indefinitely when an excess of resource is available. However, the existing models for insulin therapies assume that the response function of insulin clearance is proportional to the insulin concentration. In this paper, we propose a new model for insulin therapy for both type 1 and type 2 diabetes mellitus, in which the insulin degradation rate assumes Michaelis-Menten kinetics. Our analysis shows that it is possible to mimic pancreatic insulin secretion by exogenous insulin infusions, and our numerical simulations provide clinical strategies for insulin-administration practices.
Dose-response characteristics of insulin action on glucose metabolism: a non-steady-state approach
American journal of physiology. Endocrinology and metabolism, 2000
The traditional methods for the assessment of insulin sensitivity yield only a single index, not the whole dose-response curve information. This curve is typically characterized by a maximally insulin-stimulated glucose clearance (Cl(max)) and an insulin concentration at half-maximal response (EC(50)). We developed an approach for estimating the whole dose-response curve with a single in vivo test, based on the use of tracer glucose and exogenous insulin administration (two steps of 20 and 200 mU x min(-1) x m(-2), 100 min each). The effect of insulin on plasma glucose clearance was calculated from non-steady-state data by use of a circulatory model of glucose kinetics and a model of insulin action in which glucose clearance is represented as a Michaelis-Menten function of insulin concentration with a delay (t(1/2)). In seven nondiabetic subjects, the model predicted adequately the tracer concentration: the model residuals were unbiased, and their coefficient of variation was simila...
Biosystems, 2001
This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the b-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations.
Insulin Control of Glucose Metabolism in Man
Journal of Clinical Investigation, 1975
During the glucose clamp experiments plasma insulin levels reached a plateau of 95±8 /U/ml. Over the entire range of insulin levels studied, glucose losses were best correlated with levels of insulin in a slowly equilibrating insulin compartment of a three-compartment insulin model. A proportional control by this compartment on glucose utilization was adequate to satisfy the observed data. Insulin also rapidly decreased the endogenous glucose production to 33% of its basal level (0.58 mg/ kg per min), this suppression being maintained for at least 40 min after exogenous insulin infusion was terminated and after plasma insulin concentrations had returned to basal levels. The change in glucose utilization per unit change in insulin in the slowly equilibrating insulin compartment is proposed as a new measure for insulin sensitivity. This defines insulin effects more precisely than previously used measures, such as plasma glucose/plasma insulin concentration ratios. Glucose clamp studies and the modeling of the coupled kinetics of glucose and insulin offers a new and potentially valuable tool to the study of altered states of carbohydrate metabolism.
Kinetic Models for Plasma Disappearance of Insulin in Normal Subjects
Acta Pharmacologica et Toxicologica, 2009
Ahstraci: Three theoretical kinetic models for plasma disappearance of insulin were examined in six normal men. The models allowed for the existence of non-saturable and/or saturable mechanisms. Constant infusion of porcine insulin at different rates was uscd to achieve different levels of steady state plasma insulin concentrations. while normoglycaemia was secured by a glucose clamp technique. Appropriate validation procedures demonstrated that one of the three models was superior to the others in describing the relationship between the exogenous insulin infusion rate I,, and the steady state plasma insulin concentration C: I,, =-Icnd + kl.C/(kl+C), where Iend is the endogenous post-hepatic insulin delivery rate. Thus, only saturable mechanism(s) could be demonstrated. The median value of k2 (the maximal insulin disappearance rate) and k, (the plasma insulin concentration at which the insulin disappearance rate is half maximal) were 7.31 nmol.rnin.-' and 3.89 nmol.l-'. The median value of kz/kj (the clearance rate of insulin for infinitesimal plasma insulin concentrations) was 25.0 ml.kg-'min. ~ 1. Thus, at physiological levels of plasma insulin concentrations the metdbohc clearance rate of insulin is higher than insulin clearance estimates previously reported in studies based on the assumption of first order kinetics. Key-wvrds; Porcine insulinkinetics of insulin disappearanceinsulin degradationsaturation kineticsfirst order kincticshumans.
Letters in Biomathematics, 2018
A basic model highlighting the counter-regulatory roles of insulin and glucagon is proposed to start a series of models designed to explore continuous rein control and major aspects of glucose metabolism. The three-by-three dynamical system uses black boxes to model unit processes such as the dependencies of insulin secretion rate and the glucagon secretion rate on blood glucose concentration. The dependency of basal conditions on insulin resistance and any defects in insulin or glucagon secretion are shown. Since overproduction of hepatic glucose exists early in the history of diabetes, it is important that mathematical models should account for this effect by inclusion of the dynamical equation governing glucagon concentration as this illustrative model does. All solutions are consistent with gross features of the metabolic process. The model is examined for explicit and implicit assumptions affecting its validity which determines that the first extension to the model should account for glucose storage and the release of stored glucose.
A mathematical model for insulin kinetics III. Sensitivity analysis of the model
Journal of Theoretical Biology, 1990
A non-linear mathematical model involving four variables and several constants incorporating beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term had beeen applied in earlier papers to various forms of diabetes mellitus. In this paper, we examine the response of the system to variations in the parameters and to initial conditions using sensitivity analysis. It is found that such a method leads to results that are consistent with clinical findings. Further, it is suggested that such an analysis could help in making some predictions regarding future directions in the therapy of diabetes mellitus. 255 0022-5193/90/022255 + 09 $03.00/0