The use of deterministic multicompartmental models to analyse data relating to faecal outflow is long-standing and well established. In a typical experiment an indigestible external marker is added to a food source and the concentration (or mass) of the marker excreted in the faeces of an animal is measured over time. With the aid of an appropriate mathematical model to analyse the data this provides a non-invasive method to estimate digesta passage rate and mean retention time in animals. This allows a greater understanding of digesta kinetics, enabling insights into the nutrition and feeding strategies of animals. For example, the mean residence time can be used to estimate the rate of fermentation of dietary components in the rumen (Dhanoa et al., 1985).
The term gastrointestinal tract, or GIT, refers to the alimentary canal in animals that runs from the mouth through to the anus. If is involved with the absorption and the digestion of food into fuel molecules. In ruminant animals the gastrointestinal tract consists of a four-chambered stomach and an additional caecum to break down cellulose into fuel molecules (Knox et al, 2006). It is important to note that the term `compartment or stomach', used throughout this article, may represent any specific organ in the GIT with a relatively large mean residence time.
Multicompartmental models were first used in this manner by Blaxter et al (1956), who suggested that the ruminant gut (a ruminant is a mammal that digits its food in two steps) is essentially composed of two mixing compartments and a tubular compartment. A two-component model was used by Grovum & Williams (1973) to analyse the concentration of a marker deposited in sheep faeces. Milne et al (1978) used the Grovum & Williams model to analyse the digestion of a range of forages at different times of the year by sheep and red deer. Uden et al (1982) used the model of Grovum & Williams to model the passage of digesta through heifers, sheep, goats, equines and rabbits. The model was found to apply to the excretion of liquids in ruminants, but not to the passage of solids.
Dhanoa et al (1985) developed a multicompartmental model to describe the outflow of digesta along the gastrointestinal tract of ruminants. The individual compartments within such a model are not necessarily identified with specific compartments of the gastrointestinal tract. In a two-compartment model, the compartments simply represent the parts of the gastrointestinal tract with the longest residence times.
The model was used to describe faecal marker excretion. Moore-Colyer et al (2003) used the multicompartmental model developed by Dhanoa et al and various two-compartmental models to described the passage of digesta through the gastrointestinal tract of ponies.
The application of multicompartmental models it not restricted to the passage of digesta through animals. Since the early 1990s there has been a growing interest in developing experimental models of the human gastrointestinal tract (Yoo and Chen, 2006). The two main experimental models to be developed in the 1990s were SHIME (simulator of the human intestinal microbial ecosystem) (Molly et al. 1993) and TIM (TNO's gastrointestinal model) (Havenaar and Minekus, 1996). Applications of such models include simulating the in vivo testing of drugs on animals (including humans!) and the investigation of the viability of the probiotic intake. Information on the behaviour of digesta within the different segments of the gut would allow a clearer understanding of the dynamic interactions between food, enzymes and gut microflora. This would provide insights into improving the design of food supplements for a range of applications. Defects in SHIME and TIM have lead to the development of a new in vitro model that is capable of simulating the digestion process as an exact replica of the actual in vivo model (Yoo and Chen, 2007). Multicompartmental models can be used to analyse data from these experimental systems.
Classic models assume that the digesta contained within the gastrointestinal tract are a homogeneous mixture (Blaxter et al, 1956; Grovum & Williams, 1973). There have been complaints about the use of ideal mixing reactor models to simulate the flow of digesta through the GIT (Dhanoa et al, 1985; Ellis et al, 1994; Moore-Colyer et al, 2003). In (Moore-Colyer et al, 2003) the assumptions of idealized reactor conditions, i.e. constant volume and instantaneous mixing of digesta within the reactor system, are identified as a weakness of deterministic models.
In some applications it is reasonable to allow the reactor volume to change as a function of time. For example, following digestion of food, secretion of pancreatic juices may occur; diluting the tracer. In Nelson et al (2008) the flow of digesta through one- and two-compartment systems in which the volume of each compartment changes over time. For the perspective of chemical reactor engineering, this problem can be treated as a series of semi-batch reactors in series. General solutions were obtained for both the one- and two-compartment problems, in which the change in volume of the stomachs is a general function of time. Special cases were considered that allow explicit solutions.
In (Bentum et al, 2011) ideas from chemical reaction engineering are used to introduce stagnant regions into the classic compartment model. To do this the classic two-compartment digesta flow model was reformulated into a two compartment CSTR model. A segregated reactor model was then obtained by incorporating `non-mixing' stagnant regions into the ideal CSTR model. The ability to incorporate non-ideal mixing into the model allowed for a more accurate representation of the conditions within the gastrointestinal tract. The effect of the stagnant region upon the cumulative digestion curve was investigated. Small changes in the size of the first compartment and the division of the initial digesta ingested between the `well-mixed' and stagnant regions of the first compartment were found to substantially effect the cumulative excretion of digesta.
These problems are a good illustration of the application of the methods of chemical reactor engineering to a situation that, at first sight, does not appear to be a chemical engineering problem.
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The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.cej.2010.10.017.
|Professor X. Dong Chen||2007-Present|
|Dr H.S. Sidhu.||2007-Present|