J. Anim. Sci. 2005. 83:1102-1115
© 2005 American Society of Animal Science
Non-steady-state modeling of effects of timing and level of concentrate supplementation on ruminal pH and forage intake in high-producing, grazing ewes1
R. Imamidoost and
J. P. Cant2
Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, N1G 2W1 Canada
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Abstract
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A computer model was developed to predict responses of lactating ewes to concentrate supplementation, whether on pasture or stall-fed, given concentrate once per day or in multiple feedings, and suckling multiple lambs. The model considers effects of concentrate supplementation on organic acid production, saliva flow, ruminal pH, and forage intake. The user defines ewe BW, feed composition, and concentrate feeding times and amounts. The reference ewe has free access to forage and water. Upon consumption, forages and concentrates enter into lag pools for 2.0 and 0.24 h, respectively. Carbohydrates then enter ruminal pools of degradable fiber, undegradable fiber, or nonstructural carbohydrate, from which they are degraded or pass to the lower gut. Rapid dissociation of organic acids from carbohydrate fermentation and buffers from rumination are simulated to determine ruminal pH according to the Henderson-Hasselbach equation. The pH, in turn, affects fiber degradation rates. Forage intake continues during daylight hours until ruminal NDF exceeds 1.0% of BW, or organic acid concentration exceeds 130 mM. A circadian pattern of organic acid concentrations and pH of rumen contents with multiple concentrate feedings was simulated by the model with root mean square prediction error of 7.7 and 3.0 to 4.0% of the observed mean, respectively. However, ignoring fermentation of dietary protein may have caused an underestimation of organic acid production rates. The model predicted the increase in total DMI and the substitution effect on forage intake of increasing levels of concentrate supplementation. Simulations suggested that a single concentrate meal daily was best fed in the evening to minimize the substitution effect, and that there was no benefit in forage intake to feeding 2 kg/d concentrate in more than two meals per day.
Key Words: Forage Intake • Modeling • Ruminal pH • Sheep
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Introduction
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The NRC (1985)
provides nutrient recommendations for ewes suckling up to two lambs, but ewes of highly prolific breeds produce more than two lambs per gestation. To produce enough milk to raise three to four lambs, there is a high demand for dietary nutrients, which is often met by feeding high levels of concentrates. A ewe suckling four lambs would be expected to produce more than 4 kg of milk/d during the first month of lactation (Peart et al., 1975). According to the factorial AFRC (1993) model of energy partitioning, a 75-kg ewe producing 4 kg/d milk containing 6.5% fat requires a daily ME intake of 9.2 Mcal/d. At a DMI of 4% of BW, the required ME content of the diet is 3.07 Mcal/kg. Barley grain itself is reported to have a ME content of 3.11 Mcal/kg (NRC, 1985), which leaves little room for inclusion of forage in the diet. A common practice is to allot 500 g of concentrate/d per lamb suckled, which, when four lambs are suckling, can mean that concentrate makes up more than 80% of the ewe’s intake.
Increasing the level of concentrate in a ewe diet increases milk production (Avondo et al., 1995; Zervas et al., 1999); however, high levels of concentrate feeding can cause low ruminal pH (Mould et al., 1983; Carro et al., 2000), which can decrease forage degradability (Mould et al., 1983; Allen, 1997) and induce clinical ruminal acidosis. The level of concentrate feeding is then a question of optimizing costs and benefits. The acidotic cost of concentrate feeding occurs within hours of each meal of concentrate consumed, and so is dependent on the size and frequency of meals. Ruminal pH can range more than 1 pH unit over the course of a day, and it is the time spent under pH 6.0 or 5.6 that is taken to indicate acidosis (Keunen et al., 2002). To address the need for feeding recommendations for high-producing ewes, a dynamic model was constructed to predict the consequences of timing and level of concentrate intake in lactating ewes. The ewe may be pasture-or stall-fed, given concentrate once per day or in multiple feedings, and may be suckling multiple lambs.
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Experimental Procedures
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The general strategy for modeling the rumen was based on the lag approach of Illius and Gordon (1990), the rumination modeling of Argyle and Baldwin (1988), the concepts of Kohn and Dunlap (1998) for calculating ruminal pH, and the constraints on ad libitum intake from Forbes (1993).
The simulated animal is a grazing, lactating ewe with free access to forage and a restricted level of concentrate feeding during the day. Forage and concentrate composition is defined at the beginning of a model run. The user also may set the number of concentrate meals per day, as well as the time and amount fed in each meal. Feed ingredients are described in terms of their nonstructural carbohydrate (Nc), degradable fiber (Df), and undegradable fiber (Uf) contents. It is assumed the animal has free access to water during the day.
Upon being consumed, forages and concentrates enter lag pools and subsequently become available to the ruminal environment for microbial degradation. Essentially, ruminal pH is calculated from concentrations of organic acids (Oa) produced in fermentation of dietary carbohydrates and of buffers entering from saliva (Figure 1). Ruminal pH affects fiber digestibility. Ruminal fiber content, organic acid concentration, and day length affect forage intake. In turn, forage and concentrate intake and size of the forage lag pool affect buffer production. The user defines concentrate feeding levels, whereas the forage intake is controlled by feedback mechanisms.
Differential equations describing state variables were written in Advanced Continuous Simulation language (Aegis Simulation, Inc., Huntsville, AL), and were solved using a fourth-order Runge-Kutta algorithm with an integration interval of 0.001 d. Expression of state variables in units of concentration is obtained by dividing the integrated pool size by ruminal volume. Ruminal volume (in liters) is calculated from BW using an allometric equation (Figure 2):
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Figure 2. Plot of ruminal volume of sheep measured by liquid marker dilution and BW ( ; from Bergman et al., 1965; Stokes, 1983; Mees and Merchen, 1985; Judkins and Stobart, 1988; Weston, 1988b; Gunter et al., 1990; Charmley et al., 1991; Martin et al., 2001; López et al., 2003). The solid line represents Eq. [1] from the text: ruminal volume = a BWb, where a = 1.3 (approximate SE = 0.7), and b = 0.37 (approximate SE = 0.11); root mean square prediction error = 8.2% of the observed mean volume.
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 | [1] |
Lag Pools
According to Illius and Gordon (1990), concentrates and forages each enter a lag pool upon consumption. The feed components are not subject to degradation or passage from the rumen during this time. The differential equations for size, in kilograms, of the lag pools for concentrates (CNlag) and forages (Frlag) are:
 | [2] |
and
 | [3] |
where inCn is the instantaneous concentrate intake rate set at 0 or 30 kg/d depending on concentrate meal times defined by the user, and instantaneous intake of forage (inFr) is calculated in the model as either 0 or 4 kg/d (Table 1) when all conditions for forage intake are met (see below). The user defines concentrate meal times and daily concentrate intake (DMICn), and the model simulates the meals numerically as they occur. The rates of concentrate (UinCn) and forage (UinFr) release to the ruminal environment after the lag period are calculated as a simple delay of intake according to Illius and Gordon (1990):
 | [4] |
and
 | [5] |
where Cnlagtime and Frlagtime are the lag time periods for concentrates and forages, respectively. There is usually a longer lag time for forages than for concentrates due to their higher cell wall contents. Varga and Hoover (1983) reported lag times of 0.24 h for barley grain and 0.9 to 4.3 h for forages. Illius and Gordon (1990) used a 2-h lag in their model for feedstuffs with 30 to 50% cell contents. For the pasture and barley grain inputs for behavioral runs of the model, lag times of 2 and 0.24 h, respectively, were used (Table 1
).
Nutrient Pools
After the lag, nutrients become available to microorganisms for degradation and utilization. Feedstuffs are characterized as containing Df, Uf, and Nc. Fiber pools (Df and Uf) are considered for simulation of ruminal fill. In addition, Df and Nc are considered for determining Oa production and ruminal pH (Figure 1). Net Oa production from protein is ignored assuming protein degradation to Oa is balanced by Oa utilization for protein synthesis by microorganisms.
Undegradable fiber is resistant to degradation in the rumen and can be calculated from analytical NDF, NDF-insoluble CP, ADF-insoluble CP, and lignin values according to Weiss et al. (1992). There is no degradation of Uf in the model, so Uf (kg) is calculated from inflow from the delayed lag pool (Eq. [4] and [5]) and passage out of the rumen (UUfpass) as
 | [6] |
where fCnUf and fFrUf are the fractions of Uf in concentrate and forage DM, respectively.
 | [7] |
where kPpass is 40% of the liquid passage rate constant (Table 1).
Degradable fiber is that proportion of NDF that can potentially be degraded by enzymatic activity of microorganisms in the rumen. Thus, Df (kg) is simulated based on input from the delayed lag pools (Eq. [4] and [5]), passage to intestines (UDfpass), and degradation to Oa (UDfDfOa) as
 | [8] |
where fCnDf and fFrDf are fractions of Df, calculated according to Weiss et al. (1992), in concentrate and forage, respectively.
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and
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where the degradation rate constant, kDfOa, ranges from 0 to 100% of the maximum rate constant, depending on ruminal pH. The lower the ruminal pH, the lower the activity of fibrolytic bacteria and rate of fiber degradation (Mouriño et al., 2001). The ruminal pH that is optimal for growth of fibrolytic bacteria is between 6.2 and 6.8 (Mould and Ørskov, 1983), and at pH 5.2, cellulolysis stops (Mouriño et al., 2001). The following equation was parameterized using PROC NLIN of SAS (SAS Inst., Inc., Cary, NC) from the in vitro gas production data of Mouriño et al. (2001) to capture the transition in degradation (Figure 3):
 | [11] |
where pH is calculated in Eq. [30]. Values of kDfOa estimated from serial nylon bag incubations of feed-stuffs in situ have ranged from 0.55 to 6.48 d–1 (Varga and Hoover, 1983; López et al., 1999). For the reference pasture, the value of kDfmax is set at 1.92 d–1 (Table 1), so that 0 < kDfOa < 1.92 d–1.
Nonstructural carbohydrate is mainly composed of starch and soluble carbohydrates, which are readily degraded by enzymatic activity of microorganisms. The Nc content of feedstuffs is calculated as the remainder after analyzed NDF, CP, fat, and ash contents have been subtracted from the DM. The differential equation for Nc (kg) is based on inflow from the delayed lag pools (Eq. [4] and [5]), outflow to the intestine (UNcpass), and degradation to Oa (UNcNcOa) as:
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where fCnNc and fFrNc are the fractions of Nc in concentrate and forage DM, respectively, and
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and
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where kNcOa is the degradation rate constant. Starch degradability depends on the feedstuff and the processing applied to it (Theurer, 1986). Degradation rate constants have ranged from 0.58 to 14.0 d–1 in situ (Offner et al., 2003). A value of 7.2 d–1, measured for barley, is used for the reference starch degradation rate constant (Table 1).
Organic Acids
The production of Oa that dissociate into conjugate base and H+ decreases ruminal pH, which in turn affects the dissociation of Oa. To model the equilibrium between Oa species, two pools were considered for undissociated (OaA) and dissociated (OaD) forms of Oa, respectively.
Organic acid in its undissociated form is produced in the rumen by degrading Df (POaDfOa) and Nc (POaN-cOA) and is removed from the rumen by passage (UOaApass), absorption through the rumen wall (UOaAabs), and dissociation to OaD (UOaAOaD):
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where the fluxes in Eq. [15] are all in moles per day.
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where kpass is the liquid passage rate constant (Table 1). Liquid passage rate from the rumen was 2.30 to 2.69 d–1 in wether lambs (Judkins and Stobart, 1987) and 2.66 to 2.81 d–1 in lactating ewes (Weston, 1988b; Gunter et al., 1990). A value of 2.7 d–1 is used as the reference liquid passage rate constant in the model (Table 1).
For absorption,
 | [17] |
where kOaAabs is 227 d–1 (Table 1) based on steady-state solutions of the model for inputs from 16 experiments in the literature (see below).
The terms POaNcOa and POaDfOa represent total Oa production from Nc and Df respectively, and are based on total acetate, propionate, butyrate, and valerate productions rates as:
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and
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Each mole of glucose fermented can produce 2 mol of acetate, 2 mol of propionate, 1 mol of butyrate, or 1 mol of valerate (Baldwin, 1995). The proportions produced on a net basis from ruminal fermentation of starch and cellulose were calculated from literature data by Murphy et al. (1982). There were different proportionalities for high-forage and high-concentrate diets. Linear extrapolations of the Murphy et al. (1982) constants are used to predict molar yields (Y) of individual VFA per kilogram of Nc or Df fermented:
 | [20] |
where the molecular weight of glucose in Nc (MwNc) and Df (MwDf) is 0.162 kg/mol. The fractions of forage (fDMFr) and concentrate (fDMCn) in the daily DMI are calculated in Eq. [32].
The production of acetate, propionate, butyrate, and valerate is calculated by applying the yield coefficients to rates of Df and Nc degradation (Eq. [10] and [14]) as:
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The OaD is produced from OaA (UOaAOaD) and removed from the rumen with liquid passage (UOaDpass) and absorption across the ruminal wall (UOaDabs).
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where
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and
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with kOaDabs = 1.41 d–1 according to steady-state solutions of the model for inputs from 16 experiments in the literature (see below).
Saliva Production and Ruminal pH
Bicarbonate is the most important buffer in saliva. Therefore, for the sake of simplicity, the bicarbonate system is the paradigm for pH buffering in the rumen. The quantity of buffer in the rumen is determined by inflow from the saliva (PBfSaBf) and from the diet (PBfCnBf; in cases where a buffer like sodium bicarbonate is included in the concentrates), outflow from the rumen (UBfpass), and to buffer acid production (UOaAOaD):
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where
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 | [27] |
The term fSaBf is the concentration of buffer in saliva, and PSa is the rate of saliva production. Ruminant saliva contains 126 mEq/L of HCO3– and 26 mEq/L of PO42– (McDougall, 1948; Bailey and Balch, 1961) for a fSaBf of 0.15 M (Table 1). According to Meot et al. (1997), 18% of saliva is produced during resting, 36% during eating, and 46% during rumination. Daily saliva production in sheep ranges from 6 to 16 L (Carter et al., 1990). Assuming the parotid glands contribute 50% of total saliva production (Meot et al., 1997), we used the parotid secretion rates reported by Meot et al. (1997) to set instantaneous PSa at 7.2, 16.2, and 19.5 L/d during resting, eating, and ruminating, respectively, following Argyle and Baldwin (1988). Rumination was considered to occur when Frlag > 0.01 kg (Eq. [3]) and the ewe was not eating.
For pH modeling, it was assumed, following Kohn and Dunlap (1998), that dissociation of 1 mol OaA (UOaAOaD) is buffered by 1 mol Bf flowing to CO2 + H2O, and that the bicarbonate and Oa systems are always at the equilibrium state described by their respective dissociation constants (KaOa and KaBf), and the CO2 pressure remains at a constant 0.7 atm due to exchange with the gas phase and eructation.
Accordingly, the equalities
 | [28] |
yield the constraint
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where the leading "c" denotes a concentration in moles per liter.
The value of UOaAOaD in Eq. [15], [22], and [25], for which Eq. [29] holds true, is solved by a Newton-Raphson iteration method. From an initial guess, UOaAOaD is modified in successive iterations until Eq. [29] holds true.
The ruminal pH is then calculated according to the Henderson-Hasselbach equations:
 | [30] |
where pKaBf and pKaOa are the pKa values for Bf and Oa, respectively. Both equations yield the same pH value.
Forage Intake
Instantaneous intake of forage inFr = 4.0 kg/d when inCn 
0 kg/d, cOaA + cOaD 0.13 M, actual ruminal capacity (ARC) 0.8 x maximum ruminal capacity (MRC), and time of day is between dawn and dusk. According to Baile (1975), a typical instantaneous rate of good quality roughage intake from a manger by sheep is 15 kg/d. Intake rate measured over 12 to 15 bites of a pasture sward was 6.2 to 11.5 kg/d. These rates exclude nonbiting and nonchewing times that occur during grazing. Sixty-five-kilogram wethers on a grass sward consumed 1 kg/d DM in 8.9 h of grazing (Thomson et al., 1985), which yields an average rate of 2.7 kg/d. Lactating ewes consumed 2.9 kg/d DMI in 16 h of the heaviest grazing times of the day for a rate of 4.4 kg/d (Bermudez et al., 1989). A value of 4.0 kg/d was chosen for the forage intake rate in the model.
Of NDF weights measured at six time points throughout a day in grazing sheep, the maximum ranged from 0.76 to 1.2% of BW depending on the pasture. Values for MRC of 0.9, 1.2, and 1.38 % of BW have been used in past intake models (Mertens, 1987; Poppi et al., 1994; Chilibroste et al., 1997). The MRC value used here is 1.0% of BW (Table 1). Actual ruminal capacity is calculated as:
 | [31] |
Although forage intake commences when ARC = 0.8 MRC, it continues until ARC 
MRC or some other condition on inFr is violated.
Organic acid concentration is a controlling factor to terminate feeding in many models (Forbes, 1993; Chilibroste et al., 1997). Forbes (1993) used a threshold of 130 mM Oa, beyond which sheep stop eating. The same concept and parameter value are used in this model.
Day length was considered a limiting factor on total daily intake simulated from instantaneous rates. According to Bermudez et al. (1989), there is lower intake between the hours of 2400 and 0800 compared with the rest of the day. Such a decrease in feeding activity is common among animals that are more active during the day. Sheep typically commence grazing at dawn and continue for 4 h and then have a second grazing bout in the afternoon until dusk (Thomson et al., 1985). Dawn and dusk are inputs to the model and, for the reference state, we simulated a temperate summer day, with dawn at 0500 and dusk at 2100.
Proportions of forage (fDMFr) and concentrate (fDMCn) in the total daily DMI were used in Eq. [20] to calculate proportions of individual Oa produced in microbial fermentation:
 | [32] |
where DMICn is the daily concentrate intake defined by the user (Eq. [2]) and DMIFr is the rolling average inFr over the past day:
 | [33] |
In total,
 | [34] |
Parameters of Oa Absorption
Short-chain fatty acids can be absorbed across the ruminal epithelium in both associated and dissociated forms (Bugaut, 1987; Kramer et al., 1996), although the transport mechanisms are different for the two forms. First-order rate constants for OaA and OaD absorption, kOaAabs (Eq. [16]), and kOaDabs (Eq. [23]) were calculated from 16 measures of BW, nutrient intake, total concentration of Oa in the rumen (cOaT), and ruminal pH (Mees and Merchen, 1985; Judkins and Stobart, 1988; Weston, 1988b; Gunter et al., 1990; Charmley et al., 1991; Chiofalo et al., 1992; Hadjipanayiotou and Photiou, 1995; Carro et al., 2000; Martin et al., 2001; Castro et al., 2002). Differential Eq. [2], [3], [6], [8], [12], [15], [22], and [25] were set to zero to solve the model in steady state for each of the 16 input sets, using the parameter values given in Table 1. Given, from Eq. [30], that cOaA = cOaT/(1 + 10pH – pKaOa), Eq. [15] and [22], respectively, were rearranged to calculate rate constants as
 | [35] |
and
 | [36] |
The value of UOaAOaD at steady state for use in Eq. [35] and [36] was calculated from Eq. [25] as the difference between production (PBfSaBf) and passage (UBf-pass) of Bf.
Model Analysis
Behavior of the model was analyzed by simulating three different concentrate-feeding levels: 1) free grazing with no supplemental concentrate (FR); 2) free grazing with one concentrate meal of 1 kg of barley grain at 2200 daily (CN1); 3) and free grazing with two concentrate meals of 1 kg of barley grain each at 1000 and 2200 daily (CN2). Chemical analyses of mixed-grass–legume pasture and barley grain (Table 2) were obtained from NRC (1996). All parameter values used in the simulations are presented in Table 1. Simulations were run for 11 d, and results from d 11 are presented. Initial values of the state variables have little effect on the d-11 results, but the values used in all simulations were Cnlag(0) = 0.0 kg, Frlag(0) = 0.0 kg, Uf(0) = 0.15 kg, Df(0) =0.439 kg, Nc(0) = 0.129 kg, OaA(0) = 0.001 mol, OaD(0) =0.062 mol, Bf(0) = 0.087 mol.
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Table 2. Chemical composition of mixed-grass–legume pasture and barley input for behavioral analysis of the modela
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To evaluate model predictions of circadian patterns of ruminal pH and Oa concentration, and substitution of forage intake by concentrate, three experiments from the literature were simulated. Inputs of BW, concentrate meal times and sizes, forage and concentrate composition, and milk composition were taken from the publications, if provided. All parameter values used in the simulations were those listed in Table 1 unless otherwise noted. Simulations were run for 11 d, and results from d 11 are presented. Mean square prediction error (MSPE) was decomposed into error due to mean bias, due to deviation of the regression from one, and due to unexplained variance (Bibby and Toutenburg, 1977).
Leng and Leonard (1965) fed twelve 75-g meals of alfalfa chaff hourly to adult sheep from 0800 to 1900 daily, and measured Oa concentration in ruminal fluid samples taken hourly from ruminal fistulas. The experiment was simulated by scheduling forage meals as for concentrate and setting the intake rate to 4.0 kg/d (DM basis). Crude protein content of the alfalfa was 16.4% (DM basis), and all other chemical composition inputs were taken from NRC (1996).
Istasse et al. (1986) investigated the effect of frequency of concentrate feeding on ruminal pH in adult sheep, measured at 2-h intervals throughout a day. The sheep were fed hay ad libitum and a barley-based concentrate at 1.86 times the hay intake in two or four equally spaced meals per day. The value of DMICn was set to 1.02 and 1.09 kg/d for the two treatments, respectively, and DMIFr was predicted by the model. Ash and CP contents of the hay were given in the publication and remaining feed composition inputs were taken from NRC (1996) for mature timothy hay and barley.
Concentrate was fed at 0, 480, and 960 g/d (DM basis) in a single meal at 0900 to 64-kg ewes nursing twins in early lactation and ad libitum intakes from a perennial ryegrass sward were measured by chromic oxide dilution (Milne et al., 1981). The experiment was simulated with chemical composition of ryegrass and barley taken from NRC (1996) to represent the forage and concentrate, respectively.
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Results and Discussion
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Parameterization of Oa Absorption
An important component of pH regulation in the rumen is the absorption of H attached to OaA (Allen, 1997). There has been some question as to the rate of absorption of Oa in the dissociated form, and it has often been called negligible (Dijkstra et al., 1993; Allen, 1997), although Kramer et al. (1996) demonstrated that OaD were absorbed by a system that required Cl–. At a pH above the pKa for Oa of 4.8, the predominant form of Oa is OaD, and at pH 6.5, the concentration of OaD is 50 times that of OaA. In preliminary modeling, assigning zero absorption to OaD forced a low ruminal pH to obtain realistic Oa absorption rates, and Bf content of saliva was inadequate to maintain Bf presence in the rumen. Accordingly, as in Pitt et al. (1996), first-order rate constants for both OaA and OaD absorption were estimated by solving the model in steady state. Because of the high relative concentration of OaD, values for kOaDabs (–0.7 to 3.22 d–1) were two orders of magnitude lower than for kOaAabs (82 to 1,460 d–1), which may account for the tendency to discount OaD absorption. Pitt et al. (1996) reported only three- to ten-fold differences in absorption coefficients for OaA and OaD, but their parameters yield a faster rate of OaD absorption than of OaA absorption, which is not consistent with observations (Ash and Dobson, 1963). According to the steady-state model solutions, on average, 84% of Oa absorbed were in the OaA form and 25% of Oa produced passed out of the rumen with the liquid flow as opposed to being absorbed across the rumen wall. Previous estimates of passage of Oa range from 15 to 40% of net production (Dijkstra et al., 1993; Allen, 1997).
In two cases, a negative number was obtained for kOaDabs. In these cases, the expected rate of OaD production, calculated as the difference between production and passage of Bf (Eq. [25]), was lower than the expected rate of OaD passage, calculated with Eq. [23] from the observed cOaT and pH. Because there is error in prediction of rates of Bf production and liquid passage out of the rumen, kOaDabs values were calculated from many sets of observations and averaged.
There seemed to be an effect of ruminal pH on efficiency of OaA absorption, wherein kOaAabs increased exponentially beyond pH 6.5 (Figure 4). The increase may have been an artifact of the extremely low concentration of OaA relative to OaD at such pH or may have been a consequence of consistent deviations in other parameter values, such as PSa or kpass, at higher pH. Alternatively, some aspect of OaA transport, such as proton donation from the ruminal epithelium (Bugaut, 1987), could be upregulated at high pH. Because the model was constructed to simulate the high-producing ewe experiencing periods of low ruminal pH, Oa absorption parameters used (Table 1) were averages of the nine estimates from pH 6.5 (Figure 4). Means ± SE were 227 ± 27 d–1 and 1.41 ± 0.38 d–1 for kOaAabs and kOaDabs, respectively.
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Figure 4. Plots of first-order rate constants for absorption of associated (kOaAabs) and dissociated organic acids (kOaDabs) across the ruminal wall calculated from steady-state solutions of the model for observations of BW, nutrient intake, total concentration of organic acids in the rumen, and ruminal pH in peer-reviewed publications.
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Model Behavior
The simulated ewe, with 24-h access to mixed pasture, had two bouts of grazing during the day (Figure 5), as is commonly observed (Thomson et al., 1985). Supplementing concentrate, either at morning or night, decreased the length of the subsequent grazing bout. Actual ruminal capacity increased during each meal and decreased gradually at other times (Figure 6). Forage intake and degradation rates are lower than those of concentrates, so ARC and Oa concentration in the rumen increased more slowly than CN1 and CN2. The first grazing bout of the day on FR was terminated by the ARC limit of 0.70 kg of NDF. The second bout was terminated at dusk at 2100. Grazing commenced at dawn at 0500 and again when ARC = 0.8 x MRC.
For CN1, the concentrate meal at 2200 caused an increase in Oa concentration and ruminal pH dropped (Figure 6). Because low ruminal pH reduces Df degradation rate (Eq. [11]), ARC decreased more slowly during the night, and the fill restriction on forage intake was hit earlier in the day (Figure 6). The break between grazing bouts and the duration of the second were of the same length as for FR. Due to Oa absorption from the ruminal wall and passage to the lower gut, Oa concentration decreased gradually after the concentrate meal, and the pH returned to FR levels by 1200.
The addition of a second concentrate meal at 1000 caused ruminal fill to be higher throughout the day, which led to shorter grazing times and a long break between the two daily bouts (Figure 5). Although daily forage intake was decreased with concentrate supplementation, total DMI and, therefore, ME intake, was increased in CN1 and CN2 ewes (Figure 7).
Ruminal pH
Predicted Oa concentration throughout a day in sheep fed 0.9 kg/d forage followed the same pattern as that observed by Leng and Leonard (1965), but at approximately half the concentration (Figure 8); 98% of the MSPE was due to a mean bias. Daily production of Oa was measured by Leng and Leonard (1965) at 5.4 mol/d, whereas the simulated value was 4.2 mol/d. The simulated volume of the rumen may have been higher than in the sheep of Leng and Leonard (1965); neither volume nor BW was reported. Additionally, rate of liquid passage out of the rumen may have been too high. Increasing DMI of alfalfa chaff from 0.69 to 1.03 kg/d resulted in an increase in the rate constant for liquid passage from 2.30 to 2.82/d (Ulyatt et al., 1984). The value for kpass of 2.7 d–1 used here was obtained from lactating ewes with an elevated consumption of water and DM (Weston, 1988b; Gunter et al., 1990), so the sheep at maintenance of Leng and Leonard (1965) could reasonably be expected to manifest a slower fractional passage. Setting BW = 50 kg and kpass = 1.2 d–1 resulted in predictions of Oa concentration similar to those observed (Figure 8; root MSPE = 7.7% of the observed mean) and a net Oa production rate of 5.1 mol/d. In modeling ruminal water dynamics, Argyle and Baldwin (1988), like us, also used a constant fractional liquid passage rate for all simulation conditions. To improve predictions of cOa, the rate constant for liquid passage may need to be the dependent variable in some mathematical function, or the approach of Dijkstra et al. (1996), where kpass was inputted as a diet-specific variable, may be warranted. The model of Dijkstra et al. (1996) predicted nonsteady Oa concentrations in the rumen of dairy cows at the end of grazing and starvation periods in three different experiments with a root MSPE of 32% of the observed mean (Chilibroste et al., 2001).
To simplify the calculation of Oa production rate, the production of Oa from protein fermentation and the partitioning of degraded carbohydrate use to microbial growth, maintenance, and energy spilling were not considered. The consequences of the simplifying assumptions were explored by estimating, from 16 sets of steady-state organic matter and nonammonia microbial and feed N intakes and duodenal flows in sheep (Ivan et al., 1996; Perez et al., 1996; Faichney et al., 1997; Rogers et al., 1997; Poncet and Remond, 2002), rates of Oa production from fermentation of protein and of carbohydrates used in microbial growth and nongrowth processes. The stoichiometries of Oa production, according to Dijkstra et al. (1996), are 15.67 mmol/g protein degraded, 6.75 mmol/g carbohydrate used in microbial protein synthesis from ammonia, 8.35 mmol/g carbohydrate used in protein synthesis from peptides, and 10.64 mmol/g remaining carbohydrate degraded. On average, Oa production calculated from the observed carbohydrate and N balances across the rumen, assuming 50% of the microbial protein flow was synthesized from peptides, was 0.59 ± 0.05 mol/d higher than with the assumption that all degraded carbohydrate and no protein was converted to Oa (Eq. [10], [14], and [18] to [21]). On the other hand, Allen (1997) suggested a simple stoichiometry of 7.44 mmol/g of OM fermented, which yielded an average ± SE Oa production that was 0.21 ± 0.06 mol/d lower than with Eq. [10], [14], and [18] to [21] on the data set. Thus, although it seems that Oa production may be underestimated by ignoring protein fermentation, the bias was considered too small and ill defined to warrant the additional complexity of predicting rates of microbial growth. Dijkstra et al. (1996) presented 36 additional algebraic equations to accomplish the task. In construction of a nonsteady-state nutrient supply model, microbial growth equations would be needed.
Using the parameter values of the reference ewe (Table 1), but setting the daily concentrate intake and meal times equal to those of Istasse et al. (1986) and taking feed composition from NRC (1996), resulted in predictions of a circadian pattern of ruminal pH similar to those observed (Figure 9). Root MSPE were 4.0 and 3.0% of the mean observed pH for the twice and four times daily feeding treatments, with 96 and 79% of the errors, respectively, due to unexplained variance. Predicted DMI for the whole day was 2.07 kg (85.5 g/kg of BW) on both treatments, whereas observed DMI was 67.1 g/kg (Istasse et al., 1986). The overprediction of forage intake may have influenced absolute pH predictions but not the circadian pattern. It has long been recognized that fluctuations in ruminal pH that occur throughout a day can adversely affect intake and well being of the ruminant animal. Continuous pH recording is the current state-of-the-art method in subacute ruminal acidosis diagnosis (Keunen et al., 2002). If analytical techniques have advanced to the point of measuring pH continuously, then there is a need to simulate pH continuously to test hypotheses of pH regulation and its consequences. Previously, Pitt and Pell (1997) simulated identical, sequential periods of pH fluctuation by calculating a steady-state pH empirically from effective NDF content of the diet and the deviation from that mechanistically based on the change in Oa concentrations, a constant saliva concentration, and the stoichiometry of dissociation. Argyle and Baldwin (1988) used an empirical regression equation to relate pH to Oa concentrations that were simulated by solving differential equations numerically. Here, we have presented a first attempt to formulate prediction equations entirely mechanistically according to the rate:state formalism. The approach can be easily incorporated into other models of ruminal digestion that also follow rate:state principles. The approach also allows for simulation of responses to concentrate meals unequally distributed in size and time throughout a day.
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Figure 9. Observed (; from Istasse et al., 1986) and predicted (solid line) ruminal pH throughout a day in adult sheep given ad libitum access to hay and 1.02 kg/d concentrate in meals at 0900 and 2100 (top panel) or 1.09 kg/d in meals at 0300, 0900, 1500, and 2100 (bottom panel). The black horizontal bars indicate predicted forage intake > 0. Simulations were run with fFrDf = 0.582, fFrUf = 0.124, fFrNc = 0.161, fCnDf = 0.146, fCnUf = 0.027, fCnNc = 0.652, and all other parameter values as given in Table 1. See Tables 1 and 2 for abbreviations. The root mean square prediction errors were 4.0% (top panel) and 3.0% (bottom panel) of the mean observed pH.
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Forage Intake
Simulation of the so-called substitution effect of concentrate supplementation on forage intake (Figure 7) was a consequence of slower ARC decline at decreased ruminal pH (Figure 6). Freer et al. (1997) predicted substitution by simulating a selective intake behavior, in which grazing sheep consume the feed or herbage components of highest digestibility first, followed by less and less digestible components until MRC or an ME requirement is reached. Using the feedback from low ruminal pH resulted in predicted forage intakes that were within 10% of values observed by Milne et al. (1981) and the magnitude of depression at 0.96 kg/d concentrate was 0.58 kg/d compared with 0.56 kg/d observed (Figure 10). Simulation of results from a single experiment does not constitute a test of intake prediction accuracy of the model. An intake accuracy test would require a larger set of data from several different experiments. The response analysis in Figure 10 merely indicates that the model responds appropriately to the perturbation of concentrate supply and can therefore be used to predict responses in novel situations. Of course, such predictions may not be correct.
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Figure 10. Observed (black bars; from Milne et al., 1981) and predicted (white bars) daily intakes of forage (DMIFr) in grazing, lactating ewes given 0, 0.48, or 0.96 kg concentrate once daily at 0900. Simulations were run with BW = 64 kg, fFrDf = 0.380, fFrUf = 0.068, fFrNc = 0.187, fCnDf = 0.141, fCnUf = 0.028, fCnNc = 0.551, and all other parameter values as given in Table 1. See Tables 1 and 2 for abbreviations.
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Based on simulations of a single, 2-kg concentrate meal at different times throughout a day, forage intake was greatest when the meal was at 1800 (Figure 11). A concentrate meal in the evening had the least affect because of the long time available for recovery before grazing commenced again at dawn. When the 2 kg concentrate was fed in one to 12 equally spaced meals throughout the day, there was a predicted increase in forage intake up to two meals per day but a decrease thereafter (Figure 11). The average ruminal pH, calculated from the area under the predicted pH curve, was improved by increased frequency of feeding the concentrate, but inserting concentrate meals into the grazing time interfered with forage intake. These two opposing forces essentially cancelled each other out beyond two meals per day. Several experiments have demonstrated no effect of feeding frequency beyond two meals per day on forage intake (Sutton et al., 1985; Weston, 1988a; Chestnutt and Wylie, 1995). Weston (1988a) noted that infusion of buffer into the rumen decreased the substitution effect of wheat supplementation by 0.32 kg/d. Setting PBfCnBf (Eq. [23]) equal to 1.63 mol/d to mimic the infusion of Weston (1988a) increased the predicted forage intake by 0.25 kg/d at two concentrate meals per day (Figure 11).
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Implications
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A model that mechanistically predicts the nonsteady state of acid concentrations in the rumen can be used to test hypotheses of ruminal pH regulation and voluntary forage intake and to optimize concentrate supplementation strategies for high-producing ewes. Predicting rates of absorption of organic acids from the rumen suggested that approximately 84% of acids produced were absorbed in the undissociated form. The increase in absorption coefficient for undissociated acids at high ruminal pH suggests that some aspect of absorption remains unaccounted for and should be the subject of further investigation. The rate:state pH model presented here could be integrated with protein degradation and microbial growth models to generate further predictions of postabsorptive nutrient supply and performance responses to timing and level of concentrate supplementation.
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Footnotes
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1 Financial support was provided by the Gartshore Memorial Research Fund, the Ontario Ministry of Agriculture and Food, and NSERC Canada. 
2 Correspondence—phone: 519-824-4120, ext. 56222; fax: 519-836-9873; e-mail: jcant{at}uoguelph.ca).
Received for publication March 25, 2004.
Accepted for publication January 28, 2005.
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Literature Cited
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Abstract
Introduction
where a = 102% (approximate SE = 2), b = 5.92 (approximate SE = 0.02), and c = 38 (approximate SE = 8); root mean square prediction error = 6.8% of the observed mean rate constant.
) infusion of 1.63 mol/d of buffer into the rumen. All other parameters and variables were as given in Tables 1