A mathematical model of glucose metabolism in hospitalized patients with diabetes and stress hyperglycemia

Abstract

The human body employs several mechanisms to regulate the concentration of glucose in the bloodstream. The rates of glucose uptake and release from specific organs within the body are modulated directly by the concentrations of metabolites and hormones, and indirectly by the autonomic nervous system. The negative feedback relationship between glucose and the anabolic hormone, insulin, dominates the process of glycemic regulation. The binding of insulin to its receptor begins a cascade of intracellular events that increases glucose uptake into the liver and peripheral tissue and reduces glucose release from the liver. However, this mechanism can be overwhelmed during the acute stress typified by a moderate surgical procedure. Cellular damage and tissue trauma cause a surge in catabolic hormones and cytokines, leading to insulin resistance and marked hyperglycemia. The focus of this study is the mathematical descriptions of the processes that regulate glucose production and uptake. Such descriptions model the complex relationships between metabolites and hormones and their effects on glycemia. Descriptive models that are accurate and robust have the potential to guide the development of tools designed to manage glycemia in hospitalized patients with diabetes and stress-induced hyperglycemia. Specifically, we investigate the validity of a glucose metabolism model published by John Sorensen in a 1985 doctoral thesis. The model is a set of 22 first-order time-invariant nonlinear differential equations describing the interaction of glucose, insulin and glucagon and their effect on organ-level glucose uptake and release. We modified the model to incorporate recent experimental data, including data we have collected in clinical trials. The model was expanded to include a description of epinephrine and its effects on glycemia.