Glucose-Insulin Control System Impacted By Time and Spatial Variations in Carbohydrate Intestinal Absorption: Analytical Solution and Analysis of Integro-Differential Model

Abstract

Together with protein and fat, carbohydrates are among the macronutrients in the human diet, playing an important role in the anatomy. The process of breaking down carbohydrates into glucose begins in the digestive tract. Glucose is absorbed across the membrane of the small intestine and conveyed to the liver where they are either utilized, or distributed to the more remote parts of the human body. Sugar levels in the bloodstream then increase, triggering secretion of insulin which motivates the body’s cells to absorb glucose for energy. High carbohydrates consumption may contribute to obesity, cardiovascular diseases, and type 2 diabetes. However, it was reported that “the risk of developing type 2 diabetes is lowered as the amount of calories from carbohydrates is increased. Diet that are high in carbohydrates tend to increase the sensitivity of insulin.” Nowadays, some healthcare providers routinely recommend high carbohydrate diet to type 2 diabetics, whose risk of heart disease has been observed to lower. To investigate this paradoxical effects, we construct a 3 compartmental dynamical model of the glucose-insulin control system incorporating the carbohydrate absorption process, described by an exponential function so that the amount absorbed per unit of digested carbohydrate varies with space and time. We arrive at an integro-differential system model, which is analyzed for its stability. Its analytical solution obtained as a traveling wave solution, and the time series of glucose and insulin levels provide valuable insights into the impacts of starch content on the glucose-insulin control system for diabetics or healthy subjects.