Compartment models for estimating attributes of digesta flow in cattle

1. The basic assumptions involved in one- and two-compartment models with age-independent distributed residence times (exponential, G1) for describing digesta flow are reviewed as the bases for describing families of one- and two-compartment models which assume age-dependent distributions (Gn) of residence times. 2. The two-compartment, age-independent model with exponentially distributed residence times (GIGI) yielded estimates of essentially equal rate parameters when fitted to faecal values for all four cows receiving a diet of 500 g coarsely chopped, sodium hydroxide-treated straw /kg and one of four cows receiving the same diet but with ground and pelleted straw. The incorporation of progressively higher orders of age dependency (G2-G6, Gn) into the faster turnover compartment of two-compartment models (GnG1) resulted in a resolution of equal rate parameters estimated by the G1G1 model and a reduction in standard errors for the rate and the initial concentration parameters. 3. The occurrence of equal rate parameters in two-compartment models indicated an age-dependent process; a process which could equally well be described by a one-compartment, age-dependent compartment having an order of age dependency equal to the sum of these orders in the two-compartment model with equal rate parameters. 4. The age-independent models overestimated time of first appearance in the faeces of a meal's particles. The association of age dependency with the faster turnover compartment resulted in earlier estimates for first appearance of the marked particles; estimates which were more consistent with observed first appearance. 5. The faecal excretion pattern from cows fed on the ground and pelleted straw diet exhibited an age-independent distribution of longer residence times which dominated approximately 80% of the later residence times. Age-dependent, one-compartment models gave a poor fit to such data from these cows fed on ground and pelleted straw. In contrast, age-dependent, one-compartment models provided an excellent fit to data from cows fed on chopped straw; data which indicated that age-independent distributions of residence times were much delayed in appearing or were totally absent. 6. The mean residence time for the slower turnover, age-independent compartment estimated from faecal excretional of stained particles from either diet was similar to that estimated from duodenal concentrations of the stained particles. This suggests that the slower turnover model compartment was confined to preduodenal sites. 7. The mean residence time for the faster turnover, age-dependent compartment estimated from duodenal data was 58–62 % that estimated from faecal data and suggests that the site of this model compartment was both pre- and post-duodenal. 8. It is emphasized that the slow and imperfect mixing of particulate matter that occurs in reticulo-rumen digesta is inconsistent with the assumptions of instantaneous and homogeneous mixing made by models having age-independent distributions of residence times. The use of age-dependent distributed residence times can accommodate such imperfect mixing and is consistent with the existence of age-discriminating processes involved in particle flow from the reticulo-rumen. Age dependency also offers improved precision in estimating parameters of digesta flow via processes having inherent uncertainty in their mixing and age-discriminating mechanisms.