Mathematical modelling of root causes of hyperglycemia and hypoglycemia in a diabetes mellitus patient

Abstract

The rapid increase of diabetes patients in the world has attracted many researchers’ efforts to find the best way of managing the disease. However, lack of clear etiology in some types of the diseases such as Idiopathic Type 1 Diabetes hinders the effort. Here we present a mathematical model that demonstrates some possible causes of hyperglycemia and hypoglycemia. Sufficient and necessary conditions for hyperglycemia and hypoglycemia were newly formulated to guide the screening of the diabetes’s root causes. Apart from insulin resistance and insufficient insulin secretion, our study reveals that other factors such as abnormalities in hepatic glucose absorption, endogenous glucose production, glucagon resistance, and beta-cells responsiveness can possibly cause hyperglycemia or hypoglycemia. In an attempt to quantify an influence of each parameter to plasma glucose, it was observed that sensitivity indices of parameters with respect to plasma glucose do vary with plasma glucose concentration; however, plasma glucose was frequently observed to be most sensitive to insulin-dependent glucose uptake rate. The new established conditions for hyperglycemia and hypoglycemia cast some light on the etiological studies of the diseases; they call for more empirical research work on the disease’s etiology beyond insulin resistance and inadequate insulin secretion.

Keywords

• Hyperglycemia necessary and sufficient condition
• PRCC sensitivity analysis
• Beta-cell responsiveness
• Glucagon resistance