A Fundamental Analysis of Mathematical Modeling of the Gastrointestinal Tract

Rodney van Bentum

Bachelor of Mathematics Advanced (Honours) Project



An increased need for detailed information on the processes contained within the gastrointestinal tract has lead to the creation of mathematical models to analyse experimental data. The digestion of food substances in the gastrointestinal tract (GIT) is a complex process which is controlled by several factors. The flow rate of digesta and the specific pH profile of an animal's stomach significantly impacts the effective breakdown and absorption of nutrients. The creation of mathematical models to analyse these aspects of digestion is very important in understanding and increasing knowledge of the GIT.

The use of mathematical models allows for a greater understanding of the parameters contained within the digesta kinetics of the GIT, enabling insights into the nutrition and feeding strategies of animals. In many agricultural and pharmaceutical case studies, it is of primary importance to know the quantity of nutrients or the specific amount of an oral drug absorbed into the body of an animal. The rate of absorption and the quantity of a particular substance absorbed is directly dependent upon the mean residence time of the substance through the gastrointestinal tract. Thereby it is important to understand model digesta flow kinetics through the gastrointestinal tract. We utilise multicompartmental models to simulate the flow of digesta through the gastrointestinal tract of animals. The problem can be treated as a sequence of reactor `tanks' in series. More classical mathematical models relating to the digestive system of animals and humans, focus on modelling the flow of digesta through the gastrointestinal tract of animals and its affect on animal nutrition and physiology. In literature, there has been a criticism of some of the key assumptions utilised in the modeling framework of these classical models. In this thesis we produce a series of multicompartmental models of the gastrointestinal tract under non-ideal and variable volume conditions. These models present a more realistic framework of the GIT, resolving the key complains about classical digesta flow models.

The application of these multicompartmental models is not wholly restricted to the passage of digesta through the gastrointestinal tract of animals. We produce mathematical models that describe the change in PH associated with the process of digestion in the stomach of animals. Producing a pH profile of the stomach under many different conditions, i.e. varying certain parameter values, is integral to understanding the conditions and processes contained within the stomach. By comparing the results produced by the infinitely fast chemistry pH model with experimental data collected from in vitro studies, we verify that the model is both accurate and relevant. With further research there are many important applications for this model in areas related to nutritional and pharmacological studies. These include calculating the optimal conditions in the stomach for the breakdown of nutrients and specific oral drugs in the stomach or to determine the effect that varying pH has on the rate of digestion in the stomach.

Joanna Herrmann, MIN and Rodney van Bentum. October 2009. In this photograph we have Joanna Herrmann, MIN and Rodney van Bentum. I supervised Jo and Rod's honours projects in 2009. This photograph was taken on the last day of session (30th October) when the honours students were celebrating the end of teaching in the student bar. However, I am not sure why Jo and Rod were celebrating as they had not yet handed in their thesis!

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Page Created: 2nd December 2009.
Last Updated: 2nd December 2009.