Wang, Li, Kuang, 2007

Model Status

This CellML version of the model has been checked in COR and PCEnv. The units are consistent and the model runs to pasrtially recreate the published results. The infusion of glucose and insulin and the insulin response are the same as in the paper, but the glucose oscillations are different - this may be because the time delays in the original model have not been included in the CellML model.

Model Structure

Diabetes is typically classified as type 1, type 2, and gestational diabetes. Patients with type 1 diabetes have an impaired ability to produce insulin, through a loss of pancreatic beta-cells, type 2 diabetics produce insulin, but are relatively insensitive to it, and gestational diabetes can occur during pregnancy if a woman is unable to produce sufficient insulin (insulin demands increase during pregnancy). Common to all these patients is an inability to effectively control their blood glucose concentration. In a healthy individual, an elevated plasma glucose concentration stimulates the pancreatic beta cells to secrete insulin. In turn, this stimulates glucose up take and storage (as glycogen) by the liver and muscles, and inhibits gluconeogenesis (the synthesis of glucose).

As a feature of the metabolic syndrome, and in parallel with the current obesity epidemic, diabetes (in particular type 2) is becoming more common. Extensive research has been carried out on the glucose-insulin endocrine metabolic system, in particular in the search for new and improved therapeutic treatments. Typical current therapies include multiple daily insulin injections or subcutaneous insulin infusion, for example through an insulin pump.

In the paper described here, Wang et al. propose a delay differential equation model to simulate pancreatic insulin secretion with exogenous insulin infusion in response to elevated blood glucose levels in type 1 diabetics. The model parameters were based on experimental measurements taken from healthy individuals, and the results of the model simulations show the existence of a stable periodic solution that corresponds to ultradian insulin secretion oscillations.

Glucose (blue solid line) and insulin (red dotted line) concentrations oscillate over time, with a slight time delay between the peaks as insulin spikes in response to elevated glucose levels.

The complete original paper reference is cited below:

Mathematical modeling and qualitative analysis of insulin therapies, Haiyan Wang, Jiaxu Li, and Yang Kuang, 2007, Mathematical Biosciences . (Full text (HTML) and PDF versions of the article are available to journal subscribers on the Mathematical Biosciences website.) PubMed ID: 17610909