There are two major ways to model the microbial activity in the rumen. The first is the material or physical modelling with in vitro systems and the other is mathematical modelling with sets of equations.

The evaluation of the ability of in vitro devices is to mimic in vivo ruminal digestion needs to perform first a typology of the most known and published in vitro procedures. This typology is aimed at clustering them according to their basic function (batch or continuous), to their major targets (studies of food degradation, of microbial proteosynthesis, of volatile fatty acid (VFA) production and profile, of gas production and composition, of outflow influences, of interactions between microbe species … also of prediction of intake of food nutritive value), to their level of time integration (cumulative at a given time or kinetic values), to their actual validity to simulate one or several items of ruminal digestion. Another key of typology of in vitro procedures is also the nature of the active substance, microbes or enzymes.

Rumen mathematical modelling can be variously used in connection with in vitro and in vivo experimentations. At least three main targets can be pursued in this perspective:

To model in vivo ruminal digestion. This aspect already has a long history because the first actual mechanistic model of whole rumen digestion was that of Baldwin et al. (1970). Since this date around a tenth of whole rumen models were proposed. Their current limits are those of the knowledge on rumen digestion: proteosynthesis, VFA production, nutrient absorption, liquid and particle outflows. As far as we are aware, none of these published rumen models was checked against in vitro data. One reason could be that some of them were more or less built from in vitro data.

To model in vitro devices. Surprisingly no such specific model seemed to be published until now. In our opinion it is urgent to develop such models because they could be highly useful: to compare analogies and discrepancies between the various in vitro procedures; to try to build a unique model of in vitro ruminal digestion which could be parameterized according to the type of device; to elucidate intrinsic properties of micro-organisms.

To model both in vitro and in vivo digestion. This way is likely to be the most difficult but it is also potentially the most fruitful. Effectively the use of an intermediate mathematical model of the rumen seems to be a priori the best way to check the major areas of analogy and discrepancy between in vivo and in vitro events. Thus this approach could be an objective mean of validation of in vitro studies.