Compartment models for estimating attributes of digesta flow in cattle

Abstract

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 (GnGl) resulted in a resolution of equal rate parameters estimated by the GlGl 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 ageindependent distribution of longer residence times which dominated approximately 80 YO 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 preand 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 ...

Kinetics of digestion of low-quality forage grazed by beef cattle fed supplements containing increasing levels of rumen undegradable protein

“…(10) N is the order of time dependency of the gamma function (Pond et al, 1988). The total and partial rumen-fill (RF) effects of the potentially degradable (RF(D)) and indigestible (RF(I)) fiber fractions were calculated based on the standardized estimates of parameters A p and I p .…”

The effect of dietary carbohydrate composition on apparent total tract digestibility, feed mean retention time, nitrogen and water balance in horses

“…The DE content of the four different diets was calculated as GE intake with feed − energy excreted in faeces, and the N balance was calculated as N intake − N excreted in faeces − N excreted in urine. Faecal Yb excretion curves were fitted to different nonlinear models describing a single age-dependent mixing compartment (Gamma distribution; Gn, n = 2 to 4) and a two-compartment model with an age-dependent first compartment and an age-independent second compartment (G4G1) using the NLIN procedure in SAS ® (Version 9.2, SAS Institute Inc., Cary, NC, USA) as described by Pond et al (1988) and Moore et al (1992). The two-compartment G4G1 model has previously been proposed as the best model to describe faecal excretion of markers compared with onecompartment (Gn; n = 1 to 4) and other two-compartment models (GnG1; n = 1 to 3) (Moore-Colyer et al, 2003;Rosenfeld et al, 2006), but in the present study the G4G1 model failed to converge in 6 out of the 16 faecal excretion data sets, and therefore only the one-compartment G2, G3 and G4 models were further evaluated.…”

“…The two-compartment G4G1 model has previously been proposed as the best model to describe faecal excretion of markers compared with onecompartment (Gn; n = 1 to 4) and other two-compartment models (GnG1; n = 1 to 3) (Moore-Colyer et al, 2003;Rosenfeld et al, 2006), but in the present study the G4G1 model failed to converge in 6 out of the 16 faecal excretion data sets, and therefore only the one-compartment G2, G3 and G4 models were further evaluated. The following equations were used (Pond et al, 1988):…”

“…where F is the fractional concentration of Yb, C the initial concentration of Yb, λ the rate parameter for the gammadistributed residence time, t the time after dose of marker The effect of diet on digestion and passage rate in horses and 0.59635, 0.47454 and 0.40857 are constants given for each model as described by Pond et al (1988). However, time delay (TD) was incorporated into the equations and t was substituted with (t − τ), where τ is the time post-dosing to the first appearance of Yb in faeces.…”

“…However, time delay (TD) was incorporated into the equations and t was substituted with (t − τ), where τ is the time post-dosing to the first appearance of Yb in faeces. The compartmental mean retention time (CMRT) and TMRT were then calculated as (Pond et al, 1988):…”