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

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 focusses 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.