Mathematical Modeling and Numerical Simulation of Glucose-Insulin System for Diabetic Therapeutic Management

摘要

The pathogenesis of diabetes is still not understood and various potential causes are usually investigated through complex in vitro or in vivo experimentation. A mathematical model able to describe insulin-glucose kinetics during simple clinical tests such as insulin and glucose tolerance test was developed. This model can quantify in individual patients, macroscopic physiological process that may be associated with the development of diabetic disease and the model was validated with numerically significant group of subjects. Eighty seven subjects participated in the study. The gut-blood system was modeled as an infinite number of continuous stirred tanks in series. The model was solved using Laplace transformation. The model quantifies the amount of insulin needed for the administration of individuals at different times to keep the glucose level in check. Statistical analysis shows that there was no statistical difference (p<0.05) between the measured and simulated mean plasma insulin levels and the corresponding plasma glucose levels.