Ability of mathematical models to predict faecal output with a pulse dose of an external marker in sheep and goat

Abstract

Faecal output estimates derived from a one-compartment, Gamma-2, age-dependent model were compared with estimates derived algebraically by computing the area under the marker excretion curve for adult sheep and goats given a pulse dose of chromium sesquioxide (Cr₂O₃). Animals were fed one of three diets (as fed basis): 100% alfalfa hay, 64:36 alfalfa hay: barley grain, and 50:50 alfa1fa hay: concentrate mixture. For the one-compartment model, faecal output was calculated as the dose of chromium sesquioxide divided by the initial concentration in the compartment (milligrams of Cr₂O₃/gram of DM) multiplied by the age-dependent rate constant (per hours). For the algebraic method, faecal output was calculated as the dose of Cr₂O₃ divided by the area under the marker excretion curve ([milligrams of %/gram of faecal DM].hours), both with the full complement of faecal samples and with faecal samples collected at 12-h intervals. Faecal output estimated by the three methods did not differ (P<0.48) from measured faecal output (total collection). Marker retention time calculated from the one-compartment, age-dependent model was greater (P<0.05) than retention time calculated algebraically (sum of concentration × time divided by sum of concentrations weighted for collection interval) for animals fed all three diets. No interaction was found for species × diet or species × method of prediction (P<0.05). These results suggest that the area under the marker excretion curve generated from a pulse dose of Cr₂O₃ will provide estimates of faecal output that do not differ from those calculated from a one-compartment, age-dependent model.