An integrated mathematical model of the dynamics of blood glucose and its hormonal control

Cobelli, Claudio; Federspil, Giovanni; Pacini, Giovanni; Salvan, Anne-Marie; Scandellari, C.

doi:10.1016/0025-5564(82)90050-5

Cited by 168 publications

(80 citation statements)

References 32 publications

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“…It is observed in Figure 4A that the plasma glucose concentration grows with the glucose infusion rate, with the maximum value at the higher glucose infusion rate reaching twice the value at the lower rate. At the higher Among them, the integrated mathematical model, which was suggested by Cobelli et al 32 is the most well-known. In that study, the whole-body glucose regulation system is divided into the three subsystems: glucose subsystem, insulin subsystem and glucagon subsystem.…”

Section: Whole-body Glucose Regulation Modelmentioning

confidence: 99%

Mathematical model for glucose regulation in the whole-body system

Kang

Han

Choi

2012

Islets

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Section: Whole-body Glucose Regulation Modelmentioning

confidence: 99%

Mathematical model for glucose regulation in the whole-body system

Kang

Han

Choi

2012

Islets

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“…In this case a complete parametric identification step should be conducted on the model used to design the control law [36], according to appropriate data sets generated by the model working as the patient model (e.g. [10], [18], [43]). …”

Section: Remarkmentioning

confidence: 99%

“…Model-based glucose control has been mainly developed for the Ackerman's linear model [1] (e.g. adaptive control [30], optimal control [46,13], ∞ control [20]); more recently, different approaches have been proposed, based on nonlinear models such as the Minimal Model [5,47], or more exhaustive compartmental models [10,43,18] (e.g. Model Predictive Control [38], nonlinear Model Predictive Control [17], Neural Predictive Control [48], ∞ control [39], non-standard ∞ control [7,40], feedback linearization [32,31]).…”

mentioning

confidence: 99%

Robust closed-loop control of plasma glycemia: A discrete-delay model approach

Palumbo

Pepe

Panunzi

et al. 2008

2008 47th IEEE Conference on Decision and Control

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Abstract. The paper investigates the problem of tracking a desired plasma glucose evolution by means of intra-venous insulin administration. A modelbased approach is followed. A recent model of the glucose/insulin regulatory system which consists of discrete-delay nonlinear differential equations is used. A disturbance is added to the insulin kinetics in order to model uncertainties concerning both the insulin delivery rate and the mechanism actuating the insulin pump. A feedback control law which yields input-to-state stability of the closed loop error system with respect to the disturbance is provided. Such control law depends on the glucose and insulin measurements at the present and at a delayed time. In silico simulations validate the theoretical results.

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“…Glucose-insulin metabolism has been extensively investigated with many models describing the effect of insulin supply on glucose metabolism [22][23][24][25] and conversely the effects of a controlled glucose supply on insulin dynamics [26]. More complex models have also been proposed [27][28][29]43] which although detailed are still limited to glucoseinsulin metabolism. There are also models focusing on the metabolism of a variety of lipoproteins in the body and the transport of and conversion between them [30].…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

et al. 2014

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the post prandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin, and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility.In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

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An integrated mathematical model of the dynamics of blood glucose and its hormonal control

Cited by 168 publications

References 32 publications

Mathematical model for glucose regulation in the whole-body system

Mathematical model for glucose regulation in the whole-body system

Robust closed-loop control of plasma glycemia: A discrete-delay model approach

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

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