Technical note: an algebraic method for calculating fecal output from a pulse dose of an external marker

Fecal 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 lambs given a pulse dose of ytterbium-labeled forage. Lambs were fed one of four diets (as-fed basis): 100% alfalfa hay, 100% prairie hay, 50:50 alfalfa:sorghum grain, and 50:50 prairie hay:sorghum grain. For the one-compartment model, fecal output was calculated as the dose of Yb (micrograms) divided by the initial concentration in the compartment (micrograms of Yb/gram of DM) multiplied by the age-dependent rate constant (hours-1). For the algebraic method, fecal output was calculated as the dose of Yb divided by the area under the marker excretion curve ([micrograms of Yb/gram of fecal DM].hours), both with the full complement of fecal samples and with fecal samples collected at 12-h intervals. Fecal output estimated by the three methods did not differ (P > .15) from measured fecal output (total collection). Marker retention time calculated from the one-compartment, age-dependent model was numerically greater (P > .10) than retention time calculated algebraically (sum of concentration x time divided by sum of concentrations weighted for collection interval) for lambs fed all four diets. These results suggest that the area under the marker excretion curve generated from a pulse dose of Yb-labeled forage will provide estimates of fecal output that do not differ from those calculated from a one-compartment, age-dependent model.