The effects of diffusion and viscosity on ruminant faecal excretion of markers in a simple compartmental model.

Using equations obtained in a previous analysis, results are computed numerically which illustrate the effects of diffusion and viscosity on faecal excretion patterns of markers in ruminants. Results are first given for plug flow, a velocity gradient produced by viscosity, and diffusion, each mechanism operating alone. Plug flow gives a period during which no marker appears in the faeces, then a sharp increase in faeces marker concentration, followed by rapid washout. A velocity gradient gives a more gradual appearance of marker in the faeces followed by a slower washout. Diffusion alone (although not realistic for ruminant marker kinetics) can give early appearance of marker followed by slow washout. Combining diffusion with a velocity gradient produced by viscosity can give a range of behaviour, depending on the effective diffusion coefficient, D'; an approximate method is used to compute these solutions. Because plug flow with no velocity gradient plus diffusion gives results similar to convective flow with a velocity gradient plus diffusion, we believe it will not be possible to determine the main mechanisms defining marker outflow patterns from observations of marker kinetics alone, and more detailed investigations will be needed. Although estimates of quantities such as mean transit time are unaffected by detailed mechanism, the interpretations of measures such as sigmoidicity, sharpness of the faecal marker concentration v. time curve, and length and nature of the washout tail are highly dependent on mechanism.

A non-linear compartmental model to describe forage degradation kinetics during incubation in polyester bags in the rumen.

A new model for describing forage degradation kinetics during incubation in the rumen using polyester bags is presented. Attention is given to dealing with the problem of deviations from exponential behaviour in the early stages of degradation by devising a function capable of representing exponential or sigmoidal trends. This is achieved by allowing part of the fractional degradation rate to vary with time of incubation, thus enabling responses other than those expected under simple first-order kinetics to be described. Seven sets of data consisting of 620 curves were analysed to study the performance of the new model compared with a commonly used exponential model. The proportion of significantly better fits varied from set to set. The new model deals successfully with sigmoidal behaviour and, thus, provides a means of analysing the degradation profiles of low-quality forage feeds.

On incorporating diffusion and viscosity concepts into compartmental models for analysing faecal marker excretion patterns in ruminants.

Deterministic mathematical equations are derived to describe the pattern of marker excretion in the faeces of ruminants under steady-state conditions when diffusion and viscosity concepts are introduced into a simple two-compartment scheme of the gastrointestinal tract. The basic scheme comprises a pure-mixing pool obeying first-order kinetics and a second compartment exhibiting streamline flow. Introduction of a velocity gradient, longitudinal diffusion or both into the second compartment, even with various simplifying assumptions, yields analytically insoluble equations. The impact of these mechanisms is to be investigated numerically rather than analytically in future work.

Adaptation of compartmental schemes for interpreting isotope dilution data on volatile fatty acid metabolism in the rumen to the non-steady state and for single-dose injection.

A unifying mathematical analysis of the one-pool and three-pool schemes for estimating acetate, propionate and butyrate production in the rumen from isotope dilution data is presented. Emphasis is given to non-steady-state conditions and to the administration of isotope as a single injection. The single-pool representation is also derived as a special case of the three-pool representation by assuming that the external fluxes are directly proportional to their concentrations in the rumen.

A unifying mathematical analysis of methods to estimate rumen volume using digesta markers and intraruminal sampling.

A theoretical exposition of methods for estimating the quantity of digesta in the rumen using digesta-flow markers and intraruminal sampling is given, with emphasis on the kinetic assumptions underlying each method. Single- and dual-marker approaches to estimating volume in steady and non-steady-state are presented.

On the two-compartment model for estimating the rate and extent of feed degradation in the rumen.

An analysis of the compartmental scheme used to determine the rate and extent of ruminal degradation of feeds is presented. Attention is given to the kinetic representation of the degradation of the potentially degradable fraction. Changing the kinetic order of the rate, and introducing indigestible substrate inhibition and microbial activity into its representation, are investigated. This leads to response functions such as the Gompertz and logistic for describing the cumulative disappearance of potentially degradable substrate during in-sacco and in-vitro incubation.

On using a double-exponential model for describing faecal marker concentration curves.

A mathematical and numerical appraisal of the double-exponential model is presented, with particular reference to its ability to reproduce preset values of biological measures such as rumen and whole-tract mean retention times and faecal production rate. A complete, formal mathematical derivation is provided, with consideration given to a solution to the model when the two smallest rate constants are equal. It is concluded that any error introduced by using an approximation in deriving the double-exponential form is negligible in practice, and that the double exponential in logarithmic form is able to determine the relevant biological measures quite satisfactorily and speedily.

Estimating the production of faeces by ruminants from faecal marker concentration curves.

The use of faecal marker concentration curves, in conjunction with compartmental analysis, is examined as a method for predicting faecal output in ruminants. Formulae for faecal production are derived for the various multicompartment models currently used to interpret marker concentration data. A comparison of observed and model-derived estimates of faecal dry matter production using three different markers is given for sheep consuming hay or a mixed diet.

Metabolism of lactic acid isomers in the rumen of silage-fed sheep.

1. Four mature sheep were offered perennial ryegrass (Lolium perenne, cv. S23) silage (885 g dry matter/d) at hourly intervals. The silage was well fermented with a pH of 4.0, a lactic acid content of 139 g/kg dry matter and an organic matter digestibility of 0.766. 2. Continuous intraruminal infusions of 14C-labelled sodium salts of [U-14C]acetic acid, [2-14C]propionic acid, [2-14C]butyric acid and D- and L-[U-14C]lactic acid and an intravenous infusion of [U-14C]glucose were made on separate occasions to estimate the fluxes of rumen acetate, propionate, butyrate and lactate as well as plasma glucose. The data were resolved by the use of appropriate four-compartment (rumen) and three-compartment (rumen-plasma) models. 3. Irreversible loss rate (g C/h) of rumen acetate (5.32 g C/h) was considerably greater than values obtained for propionate (2.58), butyrate (2.80) and lactate (2.91). 4. Total flux of lactate (1.83 mol/d) exceeded the amount of lactate consumed in the diet (1.37 mol/d) indicating a net synthesis of 0.46 mol lactate/d. Approximately 0.90 of total lactate flux was metabolized in the rumen, with 1.00 mol/d converted to acetate, 0.57 to propionate and 0.08 to butyrate. The flux to acetate was significantly (P less than 0.05) greater than that to propionate. Both the D- and L-isomers appeared to have similar metabolic fates. 5. Lactate appeared to make no direct contribution to glucose flux in the animal, but 0.10 of total lactate was converted to glucose through propionate. 6. The results are discussed in relation to overall lactate metabolism, and it is suggested that almost 0.30 of ruminally digested organic matter may be fermented via lactate.

Ytterbium acetate as a particulate-phase digesta-flow marker.

The ability of ytterbium acetabe (Yb acetate) to fulfil the requirements of a particulate-phase digesta-flow marker in a dual-phase marker system, and of the indigestible acid-detergent-fibre fraction of the feed (IADF) to act as a digesta flow marker, were examined using six mature wether sheep given a diet of dried grass (1 kg dry matter (DM)/d). CrEDTA was continuously infused (240 mg chromium/d) into the rumen of all sheep and Yb acetate was also continuously infused (100 mg Yb/d) into the rumen of three of the sheep. At this level of infusion the equilibrium concentration of Yb in rumen, duodenal and ileal digesta and in faeces could be reliably measured by atomic absorption spectrometry. Estimates of faecal DM excretion based on either Yb or IADF did not differ (P greater than 0.05) from that determined by total collection, whereas estimates based on Cr were significantly (P less than 0.05) lower. Urinary excretion accounted for 3.1% of the infused Cr but no Yb was detected in urine. Estimates of ileal DM flow, assuming total marker recovery, were similar (P greater than 0.05) with all three markers, whereas the estimate of duodenal DM flow based on IADF was lower (P less than 0.05) than the estimates based on either Cr or Yb. Compared with the infusion of Cr alone, the infusion of Cr and Yb had no effect (P greater than 0.05) on nutrient flows at the duodenum, ileum and in faeces nor on microbial degradative activity volatile fatty acid production and N metabolism in the rumen. Polyester bag and in vitro studies showed that pre-labelling the dried grass with up to 285 mg Yb/g DM did not affect its susceptibility to microbial degradation. The Yb in rumen, duodenal and ileal digesta was predominantly (greater than 90%) associated with the particulate matter but was not uniformly distributed and its concentration increased as particle size decreased. The use of CrEDTA and Yb acetate as a dual-phase marker system proved more reliable in estimating 'true' duodenal flow than the use of the individual markers when the digesta sample was unrepresentative.

Estimation of the degradability of dietary protein in the sheep rumen by in vivo and in vitro procedures.

Estimates of degradability of nitrogen in the sheep rumen for a basal hay diet and for soya-bean meal (SBM), groundnut meal (GNM) and fish meal (FM), when given together with the hay, were determined from measurements of duodenal N flow, ammonia kinetics and rumen N disappearance from polyester bags and rumen outflow rate. The ability of various in vitro procedures to predict in vivo N degradability was also examined. Four sheep were given a basal hay diet (800 g dry matter (DM) and 19 g N/d) either alone or supplemented with isonitrogenous amounts (15 g N/d) of SBM, GNM or FM. Duodenal non-ammonia-N flow (g/d) was increased more by FM (8.0) than by GNM (5.9) and SBM (5.8), whilst microbial N flow (g/d) was increased more by SBM (3.9) than by GNM (2.3) and FM (1.6). N degradability values calculated from these results were 0.88, 0.76 and 0.57 for the SBM, GNM and FM respectively. The corresponding value for hay was calculated to be 0.76. The irreversible loss of ammonia in the forestomachs (g N/d) was increased more by SBM (11.9) than by GNM (7.2) and FM (5.8), whilst ammonia outflow from the rumen (g N/d) was increased to a similar extent by all supplements (1.1, 0.9 and 0.8 respectively), as was the amount of microbial N (g/d) synthesized from sources other than rumen ammonia (1.8, 2.0 and 1.9 respectively). N degradability values calculated from these results were 0.84, 0.54 and 0.45 for the SBM, GNM and FM respectively. The fractional rate of N disappearance (/h) when the feedstuffs were incubated in polyester bags in the rumen of sheep receiving the basal hay diet (800 g DM/d) was the highest for SBM (0.145) and lowest for FM (0.037), with the hay (0.082) and GNM (0.071) intermediate, whilst the fractional outflow rates from the rumen (/h) of the three supplements were similar (0.034, 0.038 and 0.030 for SBM, GNM and FM respectively). N degradability values calculated from these results were 0.82, 0.67 and 0.60 for the SBM, GNM and FM respectively; the value for the hay was 0.73. Of a number of in vitro procedures tested, only N solubility in sodium hydroxide and ammonia or total non-protein-N (NPN) production during incubation with rumen fluid in the absence of hydrazine sulphate ranked the supplements, although not the hay, in the same order as in the vivo degradability procedures.(ABSTRACT TRUNCATED AT 400 WORDS)

Nitrogen digestion and metabolism in sheep consuming diets containing contrasting forms and levels of N.

Nitrogen kinetics were studied in six sheep (45-55 kg live weight) consuming either a high-N grass silage or a low-N dried grass made from swards of perennial ryegrass (Lolium perenne). The diets were fed hourly at a level of 600 g dry matter/d and supplied 19.5 and 11.0 g N/d respectively. The amounts of organic matter (OM) consumed and flowing at the duodenum and ileum and excreted in the faeces were similar (P greater than 0.05) with both diets. Each diet supplied 23 g digestible OM/d per kg live weight 0.75, which was sufficient to maintain body-weight. There were no differences (P greater than 0.05) between diets in rumen fluid volume, fractional outflow rate of fluid from the rumen, total concentration of volatile fatty acids or molar proportion of acetate in the rumen. The pH and molar proportion of propionate in rumen fluid were higher (P less than 0.01), and molar proportion of butyrate lower (P less than 0.001) when the silage was given. There was a net loss of N (4.0 g/d) between mouth and duodenum when the silage was consumed but a net gain (5.5 g/d) when the dried grass was consumed. As a result, total non-ammonia-N (NAN) flow at the duodenum did not differ (P greater than 0.05) between diets. Rumen microbial NAN flow at the duodenum, based on 15N as the marker, also did not differ (P greater than 0.05) between diets but the efficiency of microbial N synthesis in the rumen (g/kg OM apparently digested) was higher (P less than 0.05) with the dried grass. When the sheep were consuming silage they had a higher concentration of ammonia in rumen fluid (P less than 0.01), a higher rate of irreversible loss of ammonia from the rumen (P less than 0.05) and a higher rate of absorption of ammonia across the rumen wall (P less than 0.01). The rate of absorption was found to be more closely related to the unionized ammonia concentration in rumen fluid (r2 0.85) than to the total ammonia concentration (r2 0.36). Endogenous N entry into the forestomachs was calculated to be 5.5 g/d when the silage was given and 9.4 g/d when the dried grass was given, of which 1.7 and 3.5 g/d respectively were in the form of urea. Thus, approximately 4-6 g N/d were derived from non-urea materials.(ABSTRACT TRUNCATED AT 400 WORDS)

A multicompartmental model to describe marker excretion patterns in ruminant faeces.

A multicompartmental model, which assumes first-order kinetics, is proposed to describe digesta flow along the gastrointestinal tract of ruminants. Solution of the model yields a multiplicative equation, containing a single-exponential term and a double-exponential term, for describing faecal outflow rate. The logarithmic transformation of the equation was fitted to eighty-two excretion curves obtained after the administration of marker into the rumen of cattle and sheep, and compared with other published models. It was found to be superior to the other models in that it fitted all the data sets successfully.

On the mathematics of digesta flow kinetics.

A unifying mathematical analysis of the use of compartmental models with and without time lags is given, with particular reference to the use of such models for digesta movement along the gastro-intestinal tract of the ruminant. First the generalized compartmental model without time lags is developed, and then it is shown how discrete time lags may be incorporated into this formalism. The important relationship between distributed lags, especially the gamma-distributed time lags, and the equivalent compartmental scheme, is emphasized. It is shown how distributed time lags can be included in a general compartmental model. The treatment covers, as special cases, some widely used models, and shows their relationship to each other and to other possible models. Finally a compartmental interpretation is outlined for a recently proposed double-exponential model.

The effect of formaldehyde or glutaraldehyde application to lucerne before ensiling on silage fermentation and silage N digestion in sheep.

The primary growth of lucerne (Medicago sativa) was ensiled after treatment with either formic acid alone (4.1 litres/t; silage F) or with formic acid and either formaldehyde (30.5 g/kg crude protein (nitrogen X 6.25; CP); silage FF), glutaraldehyde (44.2 g/kg CP; silage FG) or a mixture of the two aldehydes at approximately half their individual application rates (silage FFG). Compared with formic acid alone, both formaldehyde and glutaraldehyde reduced protein breakdown and carbohydrate fermentation during ensiling. The extent of protein protection afforded within the silo was similar for the two aldehydes, whereas formaldehyde was more effective in restricting carbohydrate fermentation. The effect of treatment FFG on silage fermentation was confounded by the silo bag bursting and the development of a clostridial-type fermentation. All aldehyde treatments reduced silage soluble-N content but N disappearance when the silages were incubated in polyester bags in the rumen was high for all silages and reductions due to the aldehydes were small. Silage digestion was studied in four mature sheep each fitted with a rumen cannula and re-entrant cannulas in the proximal duodenum and distal ileum. The apparent digestibility of organic matter (OM) in the whole tract was reduced (P less than 0.05) to a similar extent by both aldehydes, whereas rumen OM digestion was reduced (P less than 0.05) more by glutaraldehyde than by formaldehyde. The effects on digestion appeared to be due to the action of the aldehydes on the foods rather than to any adverse influences of the aldehydes on the metabolism of the rumen microbes because, although rumen ammonia levels were lower (P less than 0.05) when the aldehyde-treated silages were given, rumen casein-degrading activity, the degradation of different feedstuffs when incubated in polyester bags in the rumen and microbial N flow at the duodenum did not differ (P greater than 0.05) between silages. All aldehyde treatments decreased (P less than 0.05) the apparent digestibility of N in the whole tract. Silage N degradability in the rumen was also decreased (P less than 0.05) from 0.82 for silage F to 0.67, 0.60 and 0.62 for silages FF, FG and FFG respectively, and consequently non-ammonia-N (NAN) flow at the duodenum increased (P less than 0.05). The aldehydes did not adversely affect the apparent digestibility of NAN in the small intestine, and net NAN absorption from the small intestine increased from 8.8 g/d with silage F to 11.4, 15.3 and 14.2 g/d with silages FF, FG and FFG respectively.(ABSTRACT TRUNCATED AT 400 WORDS)

A comparison of methods for the estimation of microbial nitrogen in duodenal digesta of sheep.

1. Six sheep, each fitted with a rumen cannula and re-entrant cannulas in the proximal duodenum and distal ileum, were given two diets (600 g dry matter (DM)/d) consisting of either grass silage (32.1 g nitrogen/kg DM) or dried grass (18.3 g N/kg DM). A net loss of N occurred between mouth and duodenum with the silage diet, indicating extensive ruminal degradation of dietary N, compared with a net gain on the dried-grass diet. Consequently, despite higher N intakes when silage was given, N flow at the duodenum was similar for both diets. 2. The proportion of microbial N in duodenal digesta N was estimated using diaminopimelic acid (DAPA), [35S]methionine (35S), 15N-enriched non-ammonia-N (15NAN) and amino acid profiles (AAP) as microbial markers. Isotopic labelling of rumen micro-organisms was achieved by intraruminal infusions of Na2 35SO4 and (15NH4)2SO4. 3. A comparison of all methods was made based on the marker concentrations in microbial fractions isolated by differential centrifuagation of strained rumen contents. With both diets, DAPA gave the highest estimates and AAP the lowest. Estimates based on 35S and 15NAN were intermediate and did not differ significantly (P greater than 0.05). 4. For the 15NAN, 35S and AAP methods, the effect of site of sampling of the microbial fraction, i.e. from rumen contents or duodenal digesta, was examined and in all instances mean estimates based on duodenally-derived microbes were higher. However, the differences were significant for only 15NAN with both diets (P less than 0.001), for 35S with the dried grass (P less than 0.05), and for AAP with the silage (P less than 0.05). Estimates based on duodenally-derived microbes were higher (P less than 0.05) using 15 NAN than those obtained using 35S with both diets. 5. Depending on the method used for estimating microbial N, estimates of the efficiency of microbial N synthesis in the rumen (g microbial N flow at duodenum/kg organic matter apparently digested in the rumen) ranged between 16 and 38 for the silage diet and 10 and 46 for the dried grass diet. Similarly, estimates of feed N degradability in the rumen ranged between 0.62 and 0.97 for the silage and 0.00 and 0.93 for the dried grass.

Glutathione peroxidase activity and erythrocyte stability in calves differing in selenium and vitamin E status.

1. Glutatione peroxidase activity (EC 1.11.1.9) and erythrocyte stability were measured in Friesian bull calves which were given for 36 weeks semi-purified diets either adequate or low in selenium or vitamin E or both. 2. Dietary Se or vitamin E content had no effect on growth rate and haematlogical values. None of the calves exhibited clinical deficiency symptoms and serum aspartate amino transferase (EC 2.6.1.1) and creatine phosphokinase (EC 2.7.3.2) activities remained normal. Heart and skeletal muscles of all calves appeared macroscopically and microscopically normal ato autopsy. 3. Glutathione peroxidase activity in plasma, blood and other tissues, except the testis, was significantly lower in calves receiving low dietary Se but was independent of dietary vitamin E content. 4. Plasma vitamin E levels decreased rapidly and to very low levels in calves given low vitamin E diets irrespective of the Se content of the diet. 5. A low dietary vitamin E intake increased the susceptibility of erythrocytes to auto- and peroxidative haemolysis whereas a low Se intake in the presence of adequate vitamin E did not. However, erythrocytes from calves receiving low Se and low vitamin E were more susceptible to peroxidative haemolysis than erythrocytes from calves receiving low vitamin E and adequate Se. The effect of dietary vitamin E content on osmotic haemolysis induced by hypotonic saline was variable. 6. The results suggest that measurement of blood glutathione peroxidase activity and the susceptibility of erythrocytes to auto- or peroxidative haemolysis could be used for the differential diagnosis of subclinical Se and vitamin E deficiency in ruminants.