Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview

@article{Makroglou2006MathematicalMA,
  title={Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview},
  author={A. Makroglou and Jiaxu Li and Y. Kuang},
  journal={Applied Numerical Mathematics},
  year={2006},
  volume={56},
  pages={559-573}
}
An overview of some of the mathematical models appearing in the literature for use in the glucose-insulin regulatory system in relation to diabetes is given, enhanced with a survey on available software. The models are in the form of ordinary differential, partial differential, delay differential and integro-differential equations. Some computational results are also presented. 

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References

SHOWING 1-10 OF 85 REFERENCES
Mixed graphical models for simultaneous model identification and control applied to the glucose-insulin metabolism.
In this paper a method for model identification of biological systems described by stochastic linear differential equations using a new computational technique for statistical Bayesian inference,Expand
An adaptive plasma glucose controller based on a nonlinear insulin/glucose model
TLDR
An appropriate nonlinear model of the insulin/glucose regulatory system into an adaptive controller should predict the insulin-dependent glucose removal more reliably and hence provide better control over a wide spectrum of insulin signals. Expand
Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin
TLDR
This paper proposes a model which incorporates this time delay explicitly and proves theorems on positivity, boundedness, persistence and global asymptotic stability. Expand
Mathematical modelling of the intravenous glucose tolerance test
TLDR
It is concluded that a global unified model of the glucose-insulin system is both theoretically desirable and practically usable, and that any such model ought to undergo formal analysis to establish its appropriateness and to exclude conflicts with accepted physiological notions. Expand
The intravenous route to blood glucose control.
  • R. Parker, F. Doyle, N. Peppas
  • Medicine, Computer Science
  • IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society
  • 2001
TLDR
Close-loop blood glucose regulation algorithms that use the intravenous route for insulin delivery to insulin-dependent diabetic patients and classical control methods and advanced algorithms using implicit knowledge or explicit models are examined are examined. Expand
The subcutaneous route to insulin-dependent diabetes therapy.
  • R. Bellazzi, G. Nucci, C. Cobelli
  • Medicine
  • IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society
  • 2001
TLDR
The authors review the subcutaneous closed- and partially closed-loop strategies that have been proposed and tested in recent years for insulin-dependent diabetes therapy. Expand
A fully symbolic design and modeling of nonlinear glucose control with Control System Professional Suite (CSPS) of Mathematica.
TLDR
A fully symbolic design and modeling method is presented for blood glucose control of diabetic patients under intensive care using Mathematica based on a modified two-compartment model proposed by Bergman et al. Expand
Mathematical modeling in glucose metabolism and insulin secretion
  • A. Mari
  • Biology, Medicine
  • Current opinion in clinical nutrition and metabolic care
  • 2002
TLDR
Mathematical models in the study of glucose metabolism, insulin secretion and the insulin-glucose interactions are reviewed, with particular emphasis on the methods for the assessment of insulin sensitivity and insulin secretion. Expand
Coefficients of normal blood glucose regulation.
  • V. Bolie
  • Chemistry, Medicine
  • Journal of applied physiology
  • 1961
A previously formulated glucose-insulin feed-back theory was simplified with appropriate assumptions for the purpose of determining which physiological sensitivity coefficients dominate the mathema...
A Model of β -Cell Mass, Insulin, and Glucose Kinetics: Pathways to Diabetes
Abstract Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are β -cell mass, plasma insulinExpand
...
1
2
3
4
5
...