On the mathematics of digesta flow kinetics

A unifying mathematical analysis of the use of compartmental models with and without time lags is given, with particular reference to the use of such models for digesta movement along the gastro-intestinal tract of the ruminant. First the generalized compartmental model without time lags is developed, and then it is shown how discrete time lags may be incorporated into this formalism. The important relationship between distributed lags, especially the gamma-distributed time lags, and the equivalent compartmental scheme, is emphasized. It is shown how distributed time lags can be included in a general compartmental model. The treatment covers, as special cases, some widely used models, and shows their relationship to each other and to other possible models. Finally a compartmental interpretation is outlined for a recently proposed double-exponential model.