Dynamic modeling of free fatty acid, glucose, and insulin: an extended "minimal model"

The mathematical models for patients with diabetes proposed in the literature since the late 1970s are mainly glucocentric (glucose-based); hence, the contribution of free fatty acid (FFA) metabolism in the body and its glucose-insulin interactions have been largely ignored. However, approximately 90% of the muscle energy is derived from FFA metabolism when the body is at rest. Furthermore, significant interactions exist among FFA, glucose, and insulin. With the long-term goal of developing a closed-loop glucose control system, a model of the major energy-providing substrate dynamics is required.

The Bergman minimal model was extended to include plasma FFA dynamics, and its interaction with glucose and insulin dynamics, with a primary focus on patients with Type 1 diabetes. Differential equations were developed for plasma FFA concentrations and "remote" FFA effects on glucose uptake, as well as "remote" insulin effects on plasma FFA concentrations. Parameters for the model were estimated from experimental data provided in the scientific literature.

The minimal model was extended in order to capture three major metabolic aspects: the antilipolytic effect of insulin; the lipolytic effect of prolonged hyperglycemia; and the impairing effect of FFA on glucose uptake rate. The dynamic fit of glucose, FFA, and insulin profiles is consistent with published data.

The extended minimal model successfully captured the plasma FFA concentration behavior, the plasma insulin and glucose concentrations, and the physiological interactions that exist among these species. This more comprehensive description of energy-providing substrate dynamics may provide a novel simulation test-bed for analysis of patients with insulin dependent diabetes and controller design.