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Dynamics of glucose and insulin concentration connected to the β-cell cycle: model development and analysis.

Gallenberger M, zu Castell W, Hense BA, Kuttler C - Theor Biol Med Model (2012)

Bottom Line: This work focus on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the β-cell cycle.Furthermore, the presented model allows the simulation of pathological scenarios.Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Biomathematics and Biometry, Helmholtz Zentrum München, German Research Center for Environmental Health, Neuherberg, Germany. martina.gallenberger@helmholtz-muenchen.de

ABSTRACT

Background: Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β-cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β-cell cycle for the development of diabetes mellitus.

Methods: This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the β-cell cycle. The interplay of glucose, insulin, and β-cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability.

Results: Our model shows the connection of glucose and insulin concentrations to the β-cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the β-cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose-insulin regulatory system showed in biological experiments.

Conclusions: This work focus on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the β-cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

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Related in: MedlinePlus

Solution of the complete model over 96 hours. The simulation presents an experimental situation with high glucose infusion over 96h. The parameter p6 of glucose production was increased up to. The β‐cell mass increases due to the persisting hyperglycemia. With the adaption of β‐ cell mass, seen in Figure6a) the glucose‐insulin regulatory system is able to reach euglycemia, i.e. the stable steady state. Other parameters and initial values for this simulation are given in Tables1 and2, respectively. The solution of the complete model (9) was achieved numerically using Matlab ODE45.
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Figure 6: Solution of the complete model over 96 hours. The simulation presents an experimental situation with high glucose infusion over 96h. The parameter p6 of glucose production was increased up to. The β‐cell mass increases due to the persisting hyperglycemia. With the adaption of β‐ cell mass, seen in Figure6a) the glucose‐insulin regulatory system is able to reach euglycemia, i.e. the stable steady state. Other parameters and initial values for this simulation are given in Tables1 and2, respectively. The solution of the complete model (9) was achieved numerically using Matlab ODE45.

Mentions: Parameters of model (9) used for the simulations shown in Figures5 and6 in Section ’Simulation’. The parameter values are based on biological experiments of[4,20,31,32].


Dynamics of glucose and insulin concentration connected to the β-cell cycle: model development and analysis.

Gallenberger M, zu Castell W, Hense BA, Kuttler C - Theor Biol Med Model (2012)

Solution of the complete model over 96 hours. The simulation presents an experimental situation with high glucose infusion over 96h. The parameter p6 of glucose production was increased up to. The β‐cell mass increases due to the persisting hyperglycemia. With the adaption of β‐ cell mass, seen in Figure6a) the glucose‐insulin regulatory system is able to reach euglycemia, i.e. the stable steady state. Other parameters and initial values for this simulation are given in Tables1 and2, respectively. The solution of the complete model (9) was achieved numerically using Matlab ODE45.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585463&req=5

Figure 6: Solution of the complete model over 96 hours. The simulation presents an experimental situation with high glucose infusion over 96h. The parameter p6 of glucose production was increased up to. The β‐cell mass increases due to the persisting hyperglycemia. With the adaption of β‐ cell mass, seen in Figure6a) the glucose‐insulin regulatory system is able to reach euglycemia, i.e. the stable steady state. Other parameters and initial values for this simulation are given in Tables1 and2, respectively. The solution of the complete model (9) was achieved numerically using Matlab ODE45.
Mentions: Parameters of model (9) used for the simulations shown in Figures5 and6 in Section ’Simulation’. The parameter values are based on biological experiments of[4,20,31,32].

Bottom Line: This work focus on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the β-cell cycle.Furthermore, the presented model allows the simulation of pathological scenarios.Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Biomathematics and Biometry, Helmholtz Zentrum München, German Research Center for Environmental Health, Neuherberg, Germany. martina.gallenberger@helmholtz-muenchen.de

ABSTRACT

Background: Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β-cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β-cell cycle for the development of diabetes mellitus.

Methods: This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the β-cell cycle. The interplay of glucose, insulin, and β-cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability.

Results: Our model shows the connection of glucose and insulin concentrations to the β-cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the β-cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose-insulin regulatory system showed in biological experiments.

Conclusions: This work focus on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the β-cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

Show MeSH
Related in: MedlinePlus