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Equations to describe gas production profiles, obtained using manual or automated systems for in vitro fermentation of ruminant feeds, were derived from first principles by considering a simple three-pool scheme. The pools represented were the potentially degradable and undegradable feed fractions, and accumulated gases. The equations derived and investigated mathematically were the generalized Mitscherlich, generalized Michaelis-Menten, Gompertz, and logistic. They were obtained by allowing the fractional rate of degradation to vary with time. The equations permit the extent of ruminal degradation (hence the supply of microbial protein to the duodenum) to be evaluated, thus linking the gas production technique to animal production. Rumen: Gas production: Mathematical models

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Five lactating dairy cows with a permanent cannula in the rumen were given (kg DM/d) a normal diet (7.8 concentrates, 5.1 hay) or a low-roughage (LR) diet (11.5 concentrates, 1.2 hay) in two meals daily in a two-period crossover design. Milk fat (g/kg) was severely reduced on diet LR. To measure rates of production of individual volatile fatty acids (VFA) in the rumen, 0.5 mCi 1-(14)C-acetic acid, 2-(14)C-propionic acid, or 1-(14)C-n-butyric acid were infused into the rumen for 22 h at intervals of 2 to 6 d; rumen samples were taken over the last 12 h. To measure rumen volume, we infused Cr-EDTA into the rumen continuously, and polyethylene glycol was injected 2 h before the morning feed. Results were very variable, so volumes measured by rumen emptying were used instead. Net production of propionic acid more than doubled on LR, but acetate and butyrate production was only numerically lower. Net production rates pooled across both diets were significantly related to concentrations for each VFA. Molar proportions of net production were only slightly higher than molar proportions of concentrations for acetate and propionate but were lower for butyrate. The net energy value (MJ/d) of production of the three VFA increased from 89.5 on normal to 109.1 on LR, equivalent to 55 and 64% of digestible energy, respectively. Fully interchanging, three-pool models of VFA C fluxes are presented. It is concluded that net production rates of VFA can be measured in non-steady states without the need to measure rumen volumes.