A mathematical modelling of gastrointestinal tract : an effect of randomness in gastric emptying

Abstract

The gastrointestinal (GI) tract is a hollow muscular tube within the human body. The digestive system in the GI tract consists of mechanical and chemical processes for breaking down ingested food. The digested food is mixed and churned with enzymes and acids that transform it into a semi-liquid, called chyme. The process by which the chyme in the stomach is transported into the duodenum is known as gastric emptying (GE). In the duodenum, the digestion of the carbohydrate and other nutrients in the food is completed and gives a mixture containing glucose. Glucose can then be absorbed into the blood system and carried to the tissues and organs of the body. Observations in several studies have revealed that the rate of GE affects the plasma glucose concentration. In this thesis, a stochastic differential equation model of the GI tract is developed by incorporating a stochastic model of GE into a broader model of the glucose-insulin system. The main purposes of this work are to compare the simulated plasma glucose and insulin concentrations in a group of people with normal glucose tolerance (NGT) with a group of people with impaired glucose tolerance (IGT) and to examine the relationship between the plasma glucose concentration and the gastric half-emptying time in the two groups. The simulation results show differences between NGT and IGT groups in plasma glucose and insulin levels, which closely agree with published clinical data. Also, the relationship between the simulated plasma glucose concentrations at 60 120, and 180 minutes and the rate of gastric emptying is in good agreement with clinical observations. In conclusion, the impact of gastric emptying from both groups differ and are time-dependent.