Mathematical Biotechnology

Tara Kerr

MATH345 Mathematics Advanced Project

Autumn 2006

Project Summary In recent times there have been many new developments in food production, including the applications of chemical engineering to processing, packaging and means of enhancing the shelf life of a product. It has yet to be highly studied the effect these new developments have on food metabolism upon its consumption. Measurements and data relating to the human digestive system, and therefore this process, are difficult to collect mainly due to its location in the body and rather invasive means of access. The development of artificial components of the digestive system would provide a means for this data to be collected with considerable ease. In order to construct these artificial components the functioning of actual organs, tissues and the digestive system as a whole must be thoroughly understood. With this knowledge as a motivation, the aim of this project was to analyse certain mathematical models which have potential applications to the human digestive system.

To gain an understanding of the digestive process and exactly which areas of the digestive system these models could be applied to, a detailed overview of the human digestive system was performed. The tissues and organs involved in digestion, their role in digestion as well as some qualitative information relating to the general digestive process was reviewed. Following this, several mathematical models to describe the processes occurring within such organs as the colon (large intestine) were examined.

Some already known mathematical models with a variety of applications are Flow Reactor Models and also Membrane Reactor models. It was the analysis of a Basic Flow Reactor Model, the Basic Flow Reactor Model with two extensions and a Membrane Reactor with a main focus toward the digestive system that comprised the mathematical modelling content of this report.

Finally, a literature review of journal articles, which were thought to relate to the content and aims of this project, was carried out. This involved reviewing a selected number of articles from a previous database search using the word "colon" and "mathematical". The relevance to the content of this project was examined and the mathematical models presented in each article were critically assessed.

Some suggestions on future work, mathematical models and literature reviews, to increase the understanding of this area have also been included in this report.

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Page Created: 10th October 2006.
Last Updated: 2nd December 2009.