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ANIMAL NUTRITION |
* Department of Animal Science, Cornell University, Ithaca, NY 14853; and
MTT Agrifood Research Finland, Animal Production Research, FI-31600 Jokioinen, Finland
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Abstract |
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 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: effective digestion rate • fiber • gas production • mathematical model • rumen digestion
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INTRODUCTION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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, 2000; Schofield et al., 1994; Cone et al., 1996). Most of the new models are non-first-order models [i.e., the digestion rate (kd) is variable during fermentation]. A limitation of the non-first-order kinetic parameters is that they cannot be used in steady-state rumen models. To overcome these problems, Pitt et al. (1999) derived equations to estimate the effective first-order kd from non-first-order models assuming that rumen is a 1-compartment system with random passage of feed particles.
However, the feed particles are retained selectively in the rumen (Allen and Mertens, 1988), and without the mechanisms of selective retention, it is impossible to attain observed in vivo digestibility of potentially digestible NDF (pdNDF) with realistic passage kinetic parameter values (Ellis et al., 1994; Huhtanen et al., 2006). Huhtanen et al. (2008) demonstrated that using digestion kinetic parameters derived from gas production data fitted with a 2-pool Gompertz model and indigestible NDF (iNDF) concentration estimated by 12-d in situ incubation in a 2-compartment rumen model predicted the in vivo NDF digestibility of grass silages accurately and precisely. Furthermore, they proposed a method for estimating the effective first-order kd from the model-predicted pdNDF digestibility. The model predicted the in vivo digestion rate accurately and precisely. The problem of the 2-compartment Gompertz model and other non-first-order models is that although they fit the data better than simpler models such as the first-order exponential model, the parameter values of these models do not always permit unequivocal comparison of feedstuffs.
The objective of the present study was to evaluate the importance of choice of models in fitting gas production data to estimate the in vivo NDF digestibility and effective first-order digestion rate of grass silages.
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MATERIALS AND METHODS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Feeds
In vitro gas production was measured from isolated neutral detergent residue of 15 primary growth timothy (Phleum pratense)-meadow fescue (Festuca pratensis) silages harvested at different stages of maturity over 3 yr. Details of silages, isolation of NDF, estimation of iNDF concentration, and in vivo digestibility of the silages are described in more detail by Huhtanen et al. (2008) and chemical analyses by Nousiainen et al. (2003a).
The concentration of pdNDF (g/kg of DM) was calculated as NDF (g/kg of DM) – iNDF (g/kg of DM). Because iNDF by definition is indigestible, amount of iNDF ingested in feeds was also used for output. Thus, in vivo digestibility of pdNDF was calculated as follows: [NDF intake (g/d) – NDF output (g/d)]/pdNDF intake (g/d). The concentration of digestible NDF (dNDF; g/kg of DM) was calculated as follows: [NDF intake (g/d) – fecal NDF (g/d)]/DMI (kg/d).
In Vitro Gas Production Measurements
In vitro gas production measurements were made by an automated system described in detail by Huhtanen et al. (2008). In brief, the system consists of 39 serum bottles with a volume of 120 mL. The system is based on pressure transducers (142PC05D, Honeywell Inc., Minneapolis, MN) and solenoid valves (11–15–1-SV-24Q70, Pneutronics, Hollis, NH). The contents of fermentation bottles are stirred intermittently with 15 s of stirring and 30-s pauses using a magnetic stirring plate. Solenoid valves are adjusted to open when the differential pressure in the bottle reaches 2.8 kPa to release accumulated gas (approximately 1.1 mL). The system allows using a relatively large sample size (500 mg), which will decrease the relative contribution of gas from the inoculum and decrease the random errors associated with a small sample size (e.g., those related to attachment of feed particles on the walls of fermentation bottles). Cumulative gas production was recorded every 15 min for the 72-h incubation periods, resulting in 288 recordings per sample. Gas production from each sample was determined in 3 replicated runs.
Models and Curve-Fitting
For each NDF residue, a mean gas curve was calculated from the 3 replicates. Eleven different 1-pool, 7 different 2-pool, and three 3-pool models were fitted to the data by the NLIN procedure (SAS Inst. Inc., Cary, NC). The 1-pool models are presented in Table 1. The models included 3 exponential equations EXP0, EX-PDLag, and EXPLPool. Subscripts 0, DLag, and LPool denote absence of lag, discrete lag time, and lag pool. The concepts of discrete lag and lag pool are explained in detail by Mertens (1993a). Groot et al. (1996) proposed an empirical multiphase model, in which B (units, h) describes the time at which 50% of the asymptotic value of gas was produced and C is a dimensionless switching parameter that together with B determines the shape of the curve. The France et al. (1993) equation is a generalization of the Mitscherlich model, which allows accommodating either a sigmoidal or nonsigmoidal shape. The generalized Michaelis-Menten (Gen M-M) model allows the rate of digestion to decrease continuously or to increase first and then decrease and includes a lag time. The logistic (LOG) model assumes that gas production is proportional both to the microbial mass and the digestible substrate (Schofield et al., 1994). Gompertz (GOMP) and Richards (RICH) models are extensively used to describe growth functions. Two different forms of the Gompertz equations as derived by Schofield et al. (1994; GOMPS) and France et al. (2000; GOMPF) were used. A probability function Weibull (Ross, 1976; WEIB) was also included in the analysis. The compartmental interpretation of most of the functions is described in detail by France et al. (2000).
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Rumen Digestion Models
Digestion kinetic parameters derived from the gas production data were used in a dynamic mechanistic model described by Huhtanen et al. (2008) to predict ruminal pdNDF digestibility for a single batch of feed. The amount of pdNDF digested in the rumen was estimated using a model incorporating the selective retention of feed particles in the rumen (Allen and Mertens, 1988). Large forage particles entering the rumen need to be comminuted below a threshold size before they can escape from the rumen. Specific gravity has also been shown to influence the probability of particles to escape from the rumen. Marker kinetic studies (e.g., Pond et al., 1988; Lund et al., 2006) have demonstrated that the release of feed particles from the nonescapable pool to the escapable pool is a time-dependent process; therefore, a gamma time-related function (G2G1) was used to describe this process. The rate constant (kr) was calculated as: kr = (t x 
2)/[1 + (t x )], where = the rate constant (= 2/residence time in the compartment) and t = time. The passage rate from the escapable pool was assumed to be a first-order process. The mean residence time in the rumen was assumed to be 50 h. Distribution of 0.4:0.6 of rumen residence time between the nonescapable and escapable pools was assumed (Huhtanen et al., 2006; Lund et al., 2006).
Model-predicted pdNDF digestibility was used to calculate the effective first-order digestion rate (effective kd) using the equation described by Huhtanen et al. (2006): effective kd = {– [kp + kr] + [(kp + kr)2 + 4 x pdNDF digestibility x krkp/(1 – pdNDF digestibility)]0.5}/2. Values of 0.05 and 0.0333 were used for kp and kr, respectively. Pitt et al. (1999) demonstrated that the function derived to estimate effective kd is independent of intake, which allows using this parameter in continuous rumen models.
Digestibility of cell wall carbohydrates in the rumen is competition between the rates of digestion and passage. The total mass disappearing by digestion is the integral over time from t > lag to
, and total extent of digestion is defined as the total amount degraded divided by the total amount entering the system. For the simple exponential model, the digestibility (D) with a kd and 1-compartment rumen model with first-order passage (kp) can be evaluated by a simple algebraic equation [D = kd/(kd + kp)], but for most models, the integrals are nonanalytical (France et al., 2000) and must be evaluated numerically.
Except for the EXP0, EXPDLag, and EXPLPool models, kd is or can be time-dependent. The kd at each time point can be estimated as the mass digested as a proportion of the mass in the rumen. If the function of cumulative gas production is described as F(t) and the derivative of the function F'(t) = dF/dt describes the mass disappearing at time = t, the kd at each time point (t) can be described as follows: kd = F'(t)/F(t). Estimated gas production parameters from different models were used to compute the value of F at different time points. With the models including discrete lag time, the digestion began at t = lag time, but the release from the non-escapable to the escapable pool commenced at time t = 0. In the model ExpDLag, the retention in the lag pool was included in the rumen nonescapable pool.
The amount of dNDF predicted by the model was calculated as pdNDF (g/kg of DM) x model-predicted pdNDF digestibility. Total NDF digestibility was calculated as model-predicted dNDF/NDF. Single effective first-order digestion rate was calculated from in vivo pdNDF digestibility similarly as from model-predicted pdNDF digestibility described earlier.
The rumen models were constructed using Powersim software (Bergen, Norway). Simulations were run for 120 h with a 0.0625-h integration step and using the Euler integration method.
Statistical Analysis
To evaluate the performance of the models, the goodness of fit was compared using the proportion of variance accounted for (R2) and residual mean squares (RMS) and ranking the models according to RMS. These evaluations were made separately for the 11 one-pool models, the 6 two-pool models, and the 3 three-pool models.
Root mean squared errors (RMSE) between the observed in vivo and model-predicted dNDF and NDF digestibility values and in vivo derived and model-predicted effective kd values were calculated as follows: RMSE = 
(observed – predicted)2/n. Mean square prediction error (MSPE) was divided to components resulting from mean bias, slope bias, and random variation around the regression line (Bibby and Toutenburg, 1977). The significance of the deviation of the intercept from 0 and the slope from 1 was analyzed by t-test.
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RESULTS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The chemical and morphological composition and in vivo digestibility of the silages are shown in Table 2. Due to differences in maturity, the silages showed a large variation in all parameters. The silages were well-preserved as indicated by low pH (4.10) and low concentrations of VFA (22 g/kg of DM) and ammonia N (47 g/kg of total N).
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The proportion of variance explained by the models was in general very high, as for all 15 gas production curves, it was greater than 0.997 (Table 3). The RMSE were 1.1 to 4.3% of the final gas volume. The Gen M-M and Groot models showed the greatest average R2 values, whereas LOG was the worst according to this criterion. The differences between the models were much greater when evaluated on the basis of RMS. The average RMS across the 15 curves was smallest with the Gen M-M model followed by the Groot model. Models LOG and EXP0 clearly had the greatest RMS. The GOMPS model had a smaller RMS than LOG and EXP0, but it was always greater than for the other models. Although the mean RMS was greater for the Groot model compared with Gen M-M, the smallest RMS was observed more often with the Groot model (8/15) than with Gen M-M (4/15). Only the fit to models LOG (11/15) and EXP0 (4/15) resulted in the largest RMS.
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). In many cases, fitting the gas production profiles to the 2-pool EXPDLag model resulted in similar rates for the both pools. The R2 values were above 0.9999 with all other 2-pool models, and RMS was below 1.00 in all cases. For the best models, the RMSE was only 0.32 to 0.70% of the final gas volume. Including a third pool into the Groot, GOMPS, and LOG further decreased RMS.
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Model-predicted asymptotic gas volumes together with observed endpoints are shown in Figure 1. The variation between the models in predicted gas volume was relatively large, ranging from 116.2 mL (LOG) to 130.1 mL (Gen M-M). The differences between the models were highly significant (P < 0.001). Asymptotic extent of gas production was closely associated with potential NDF digestibility (pdNDF/NDF), with R2 values ranging from 0.757 to 0.940 (Table 5). One- and 2-pool Groot and Gen M-M models had the lowest R2 values between potential NDF digestibility and asymptotic gas volume. Including the third pool in the Groot model clearly improved the relationship between potential NDF digestibility and asymptotic gas volume.
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. The residuals were usually greatest during the first 20 h of incubation, but there were differences also during the later phases of incubation.
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The relationships between the predicted and observed NDF digestibility are shown in Table 6. The R2 values were greater than 0.96 for all other models except for the WEIB model, indicating that the precision of this model was less than that of the other models. The models EXP0, Gen M-M, Groot, and Groot2 underpredicted in vivo NDF digestibility, whereas the LOG model slightly overpredicted it. In most cases, the variation resulting from mean bias or random variation across the regression line had the greatest contribution to the total MSPE.
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. Most models predicted the in vivo-derived effective kd accurately (bias from –0.005 to 0.005) and precisely R2 > 0.80. None of the models was the best according to all criteria (small bias, slope close to 1, intercept close to 0, and high R2), but the models France, RICH, LOG2, GOMP2S, GOMP2F, and WEIB2 performed well according to these criteria.
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DISCUSSION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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) demonstrated that in vivo NDF digestibility could be predicted accurately and precisely by a model in which digestion kinetic parameters were estimated from gas production profiles by the 2-pool Gompertz equation and iNDF concentration by a 12-d in situ incubation. The model described the cumulative gas production profiles very well as indicated by small mean square errors and confidence intervals of the parameter values. However, a disadvantage of this and other models with a time-dependent fractional digestion rate, especially with multiple pool models, is that parameter values are strongly correlated and do not permit unequivocal comparison of feedstuffs. Steady-state rumen models (e.g., Danfær et al., 2006) need first-order digestion rates, which preclude the use of kinetic parameters estimated using models including time-dependent digestion rates. Pitt et al. (1999) proposed equations to estimate effective first-order digestion rates for models including digestion lag and time-dependent digestion rate for 1-compartment rumen models. This approach was extended by Huhtanen et al. (2008) for 2-compartment rumen models. The effective first-order kd was computed from the model-predicted pdNDF digestibility by solving the equation proposed by Allen and Mertens (1988). Gas Production Models
Different versions of simple exponential equations have been applied to gas production studies. Sometimes a parameter describing a rapidly or immediately degradable fraction has been included in models describing cumulative gas production, similarly as for the in situ data (Ørskov and McDonald, 1979). As discussed by France et al. (2000), this often results in negative values at zero time. However, negative gas volumes at zero time are biologically meaningless, and the usefulness of such parameter values in rumen models is questionable.
Including a discrete lag time in the simple first-order equation improved the fit of models markedly. The discrete lag time can be attributed to hydration, removal of digestion inhibitors, or attachment of microbes with the substrate. This model assumes that digestion begins instantaneously after the lag time. Although the discrete lag time does not completely describe the lag phenomena, it provides a simple quantitative measure of lag effects (Mertens, 1993a). Allen and Mertens (1988) proposed a model that describes digestive processes by a 2-step mechanism: the first step is a first-order process involving a change of substrate from unavailable to available form (lag pool), and the second step represents the first-order digestion of the substrate. Biologically, the first step can be interpreted to be related to the same processes as the discrete lag. Although the lag pool model is theoretically more correct than the discrete lag model, it did not fit the data better than the discrete lag model. Mertens (1993a) postulated that a discrete lag time was a necessary addition to the model to adequately describe the digestion processes.
France et al. (1993) proposed a generalized Mitscherlich model, which can accommodate both sigmoid and nonsigmoid shapes. Further, the fractional digestion rate can increase or decrease. An increase in digestion rate with time may reflect an increase in substrate availability, microbial attachment, and increased microbial numbers. France et al. (2000) discussed several factors (e.g., build-up of fermentation products, decreased availability of growth factors) that could result in a decreased fractional digestion rate as the degradation proceeds. The France model fit the data consistently better than the ExpDLag model, but the reductions in RMS were rather small, suggesting that the France model was not able to describe the digestion kinetics of isolated NDF very accurately.
In the Gen M-M model, the kd increases first and decreases later during fermentation (c >1.0) or decreases continuously (c 
1.0). The average value for the c parameter across the 15 gas production curves was 1.69 (range 1.46 to 2.30; i.e., in all cases, the kd increased first and declined thereafter, probably reflecting increased microbial number, substrate accessibility, and microbial attachment at the beginning of incubation, and exhaustion of the rapidly degradable substrate toward the end of fermentation). Compared with other gas production models, the Gen M-M is more flexible (France et al., 2000), and it decreased RMS compared with the previous models. Groot et al. (1996) proposed a modified Gen M-M equation without a discrete lag. This equation has been extensively used by the Dutch workers (Cone et al., 1996, 1997). Omitting the lag parameter from the model increased the RMS, but it was still much smaller than the RMS of the other 1-pool models.
In the RICH and WEIB models, the parameter n influences the pattern of changes in kd with time. When the parameter value is –1.0 (RICH) or 1.0 (WEIB), the kd is constant (i.e., the model is exponential). In the WEIB model, the kd either first increases rapidly and thereafter slowly (n > 1.0) or first decreases rapidly and thereafter slowly (n < 1.0). The effects of parameters n and c on the gas production curve in the WEIB and France models are very similar, and consequently, the RMS values of the 15 gas curves were strongly correlated (R2 = 0.995). In the RICH model, the kd either increases (n > –1.0) or decreases (n < –1.0) with increased digestion time; the changes are more rapid at the early stages of incubation. The parameter n increases the flexibility in curve-fitting with both WEIB and RICH models improving the fit compared with the EXPDLag model. The effects of the n parameter may be attributed to the changes in hydration, microbial attachment and microbial growth, or to chemical and structural changes in cell walls with the advancing fermentation time.
The 1-pool Gompertz model derived by France et al. (2000) fit the data better than the model derived by Schofield et al. (1994). Gompertz and logistic equations as given by Schofield et al. (1994) have an inherent error in that predicted gas volumes are positive at time zero, which is not biologically possible, because the initial gas volume should be zero. In the Gompertz model derived by France et al. (2000), the fractional digestion rate increases with time when the parameter value of c >0, which was interpreted as increased microbial activity per unit of feed. However, in the present study using isolated NDF, the value of parameter c was only marginally different from zero, and the model approached ExpDLag.
The 2-pool models fit the data markedly better than the corresponding 1-pool models except the ExpDLag model, in agreement with the study of Schofield et al. (1994). The RMS with 1-pool models was positively (R2 = 0.65 to 0.85) correlated with the in vivo NDF digestibility, suggesting that 1-pool models did not adequately describe the NDF digestion kinetics of early harvested silages. The 2-pool models assume that the pdNDF is comprised of rapidly and slowly degradable fractions as described by Schofield et al. (1994) and Schofield and Pell (1995). The proportion of the rapidly degradable pool of the total gas produced increased with improved in vivo NDF digestibility, but the proportion of the rapidly degradable pool varied markedly between the models (0.39 in GOMP2, 0.26 in GOMP2FR, 0.15 in Groot2, 0.55 in LOG2, 0.23 in RICH2, and 0.22 in WEIB2).
The Gompertz model derived by Schofield et al. (1994) fit all 15 cumulative gas production profiles better than the model derived by France et al. (2000) when 2-pool models were used despite the positive intercept at time zero with the Schofield et al. (1994) model. However, including the second pool markedly decreased the positive intercept, and it took only 1.5 h to reach zero residual. Including the second pool to the Gompertz model derived by France et al. (2000) presented some biological problems despite the fact that the fit was markedly improved. Predicted asymptotic gas volume was smaller than observed gas volume at 70 to 72 h in many cases (9/15). This was probably due to high values of the parameter c, especially for the rapidly degradable pool but also for the slowly degradable pool. For example, the fractional digestion rates of the slow pool increased up to 0.15 to 0.20 per hour toward the end of fermentation period.
Large variation between the models in the proportions of the rapidly and slowly degradable pools despite very good fit to the data may indicate that there are not 2 easily distinguishable pdNDF pools described by the cumulative gas production profiles but rather several cell wall fractions differing in the rate of digestion. Depending on the model structure, the division between the rapidly and slowly degradable pools can be rather arbitrary. Differences in kd have been reported between stems and leaves (Chaves et al., 2006) and also between individual cell wall polysaccharides (Mertens, 1993b). In vitro NDF digestion of various forages also demonstrated a fast- and a slow-digesting pool (Van Soest et al., 2005). Including a second pool for the exponential models did not improve the fit much, in contrast to the other 2-pool models. With the exponential model, the small improvement in the fit is likely because the data generated by summing 2 exponential functions produce a curve shaped very much like a single-pool exponential function (Schofield et al., 1994).
Including a third pool in the model further decreased the RMS, and the fit was almost perfect, with the average RMSE being 0.20, 0.15, and 0.27% of the mean asymptotic gas production for models GOMP3S, Groot3, and LOG3, respectively. However, none of the models were able to identify a gas pool that could result from the microbial turnover. The proportion of the third gas pool characterized with the longest lag time and slow rate decreased with improved in vivo NDF digestibility. This is in contrast to what could be assumed from the greater energy supply and increased microbial growth from early-harvested silages. Most likely, this pool represents the gas production both from slowly digestible fiber and microbial turnover.
Cone et al. (1997) suggested that the 3 phases of gas production can be related to the fermentation of soluble and insoluble substrates, and microbial turnover. In their study with sugars, the gas production from the pool assumed to represent microbial turnover was below 10% of the total gas volume (i.e., much less than the gas production from the third pool in the present study). Our data indicate that despite the very good fit of the models, multipool models do not accurately and consistently identify feed entities characterized by differences in degradation kinetics. The pools estimated by the multipool models should therefore be viewed as purely mathematical constructs that may or may not correspond to chemical entities (Schofield, 2000). Furthermore, the declining robustness with increased number of pools is inherent in the nonlinear curve-fitting procedure, and when the number of parameters is increased, the possibility of encountering a local minimum increases.
Relationship Between Potential NDF Digestibility and Gas Production
The close relationship between the extent of potential NDF digestibility and total volume of gas produced indicates that isolated NDF used in the present study was a relatively homogenous substrate. Differences in VFA pattern in fermentation or changes in partitioning of carbon between VFA production and microbial synthesis would influence the amount of gas produced per unit of fermented substrate. However, the large variation between the models in the predicted asymptotic gas volumes suggests that it is not possible to estimate pdNDF from the gas volume. The models LOG, GOMP, and LOG2 predicted lower asymptotic gas production than the observed values (mean 70 to 72 h). Because some gas production still occurred at 72 h (mean 0.12 mL/h), these models were not able to describe the gas production profiles correctly. On contrary, the measured value at 70 to 72 h was proportionally only 0.927 to 0.938 of that predicted by the models EXP0, Groot, Gen M-M, and Groot2. Assuming a digestion rate of 0.05 or 0.06 per hour, proportionally 0.973 to 0.987 of pdNDF will be digested during 72 h. This together with the distinct time-related pattern of changes in the residuals after 40 to 50 h of incubation (discussed later) suggests that these models overestimated the asymptotic value of gas production. Overestimation of the asymptotic gas volume by the EXP0 model is related to its inability to describe the lag phenomenon. The kd decreases at later stages of fermentation in the Groot and Gen M-M models, which although theoretically sound may lead to overestimation of the asymptotic gas volume as the time-related pattern of residuals suggests. To at least partly overcome this problem, the length of the incubation period may be extended. Another solution is to increase the number of pools as lower asymptotic gas volume with the model Groot3 (123.2 mL) compared with Groot1 (128.1 mL) and Groot2 (128.8 mL) indicates. However, rather than attempting to estimate the potential extent of NDF digestion from asymptotic gas production, extended ruminal in situ incubation is likely to be a more reliable method as indicated by the close empirical relationship between iNDF concentration in grass or legume silages and in vivo OM digestibility (Nousiainen et al., 2003b; Rinne et al., 2006).
Prediction of NDF Digestibility
As indicated earlier, using the gas production kinetic data in a rumen model predicted the in vivo NDF digestibility both accurately and precisely. The good performance of the model can be attributed to the following 3 factors: (1) separation of NDF into iNDF and pdNDF, (2) using digesta passage models including selective retention of feed particles in the rumen, and (3) an accurate and precise prediction of kd by a gas production system (Huhtanen et al., 2008). Because the digestible neutral detergent solubles can be estimated accurately and precisely by the Lucas test (Huhtanen et al., 2006), especially if forage-type specific equations are used, this model can be used to estimate both the D-value (concentration of digestible OM in DM) and kinetic parameters needed in the mechanistic dynamic models.
Good performance in the curve-fitting was not always translated to accurate and precise predictions of the in vivo NDF digestibility values. The France and RICH models were the best 1-pool models in predicting NDF digestibility; these models had a small MSPE and bias, the intercept was not significantly different from 0, and the slope was not different from 1. Although the use of kinetic parameters estimated by the 1-pool LOG and GOMP models resulted in accurate and precise estimates of NDF digestibility, much poorer fit and underestimation of the asymptotic gas volume preclude acceptance of these models. The Gen M-M and Groot1 models fit the data much better than the other 1-pool models, but they were less accurate in predicting the NDF digestibility than the other 1-pool models except for EXP0. This may result from the time-related patterns of the residuals (observed observed – predicted predicted) of gas production curves. Investigating the residuals from approximately 50 h of incubation onwards showed a clear time-related pattern (Figure 2
); with advancing incubation time, the residuals decreased consistently, suggesting an overestimation of the asymptotic gas volume, and consequently underestimation of the parameters describing kd. The LOG model showed an opposite pattern of time-related residual, which resulted in underestimated extent and overestimated rate of digestion. In the present study, the mean extent and rate of gas production of the 15 silages were strongly and negatively correlated (R2 = 0.95; data not shown). Because the extent of digestion was determined separately using 12-d in situ incubation, biased estimates of the extent of gas production lead to biased rate estimates and, consequently, biased digestibility estimates.
Both the Gen M-M and Groot1 models resulted in a significant slope bias (i.e., the digestibility of low digestibility silages was underestimated more than that of high-digestibility silages). It is possible that the assumption of decreased kd with increased fermentation time with these models was not correct, or that the effect was too strong. In agreement with our data, Dhanoa et al. (2000) observed a negative bias with the model Gen M-M compared with the France model in the extent of rumen digestion, whereas LOG tended to overestimate the extent of digestion. Dhanoa et al. (2000) compared several models in estimating the extent of rumen digestion from gas production profiles using measured values for potentially digestible fraction but assumed the rumen as a 1-compartment system.
Surprisingly, the EXP0 model was as accurate in predicting the in vivo NDF digestibility as the models Gen M-M and Groot despite the fact that the fit of gas production data was much better with the latter 2 models. This may be related to the time-related pattern of residuals during late stages of incubation with the Gen M-M and Groot models. It seems that large residuals during early stages of fermentation (<20 h) have a relatively small effect on the predicted dNDF, if the sum of the negative and positive residuals is equal. During early stages of fermentation when both under- and overfitting occur, the feed particles are mainly in the rumen nonescapable pool and not eligible for passage, whereas time-related patterns during later stages of fermentation markedly influence the asymptotic value and consequently the kd. For example, it can be calculated from the duodenal excretion pattern of internally labeled lucerne ADF-15N that only 10% of the cumulative marker excretion at the duodenum was recovered from dairy cows during the first 10 h after dosing (Huhtanen and Hristov, 2001). Consistent with this, Ellis et al. (1994) demonstrated that the effect of lag time on digestibility is smaller when estimated using an appropriate 2-compartment rumen model rather than a 1-pool model.
The dNDF estimates of the WEIB model had lower correlations with the other models and also a greater random error. This appears to be related to the strong relationship (R2 = 0.78) between the residual of dNDF estimates with the value of parameter n. With parameter values above 1.0, dNDF was underestimated, and with values below 1.0, it was overestimated.
Including the second pool in the Groot model did not improve the accuracy, and random variation increased. The residuals of the gas production curve showed a similar pattern as the corresponding 1-pool model. However, including a third pool in the Groot model decreased the bias markedly. The second pool in the WEIB model decreased the random variation markedly, and the model performed similarly to the France, GOMP2S, and RICH2 models. The third pool in the LOG and GOMP models had minimal effects on the accuracy and precision of NDF digestibility estimates.
Prediction of the Effective First-Order Digestion Rate
The ultimate goal of using the in vitro gas production system is to produce reliable parameter values for the effective first-order kd of pdNDF to be used in mechanistic dynamic rumen models. Because of many methodological problems of the in situ technique and strong evidence of underestimation of the in vivo rates of pdNDF digestion (for a review, see Huhtanen et al., 2006), we used kd estimates calculated from in vivo pdNDF digestibility to validate the method. Digestion rates estimated by a gravimetric in vitro method were greater than those determined in situ (Bossen et al., 2008), which also suggests that in vitro techniques may allow a more accurate estimation of the true intrinsic kd (ultimate limit to digestion imposed by cell wall characteristics) than the in situ technique. The studies comparing particle-associated enzyme activities within the in situ bags and in the surrounding rumen digesta (Nozière and Michalet-Doreau, 1996; Huhtanen et al., 1998) showed much lower activities within the bags, which is consistent with lower kd with the in situ compared with in vitro or in vivo techniques.
The 1-pool RICH model was the best model in predicting in vivo first-order kd of NDF in terms of small RMSE and bias, high R2 value, and the slope close to 1. However, the France, EXPDLag, GOMP2S, and WEIB2 models were almost as good. Also, all 3-pool models performed well. Accurate predictions of the in vivo values by the Groot equation appeared to require 3 pools to be used. It is possible that the compartmental retention time varied between the feeds, but this variation would have the same influence on both model-predicted and in vivo-derived estimates. The estimated effective kd can be used in steady-state rumen models, and it results in the same pdNDF digestibility as estimated for a single feed batch using time-related digestion rates estimated from the gas production curves.
Pitt et al. (1999) presented a formal derivation for several models with variable digestion rates for estimating the effective kd including the effects of digestion lag. They assumed rumen as a single-compartment system without selective retention of particles, and both passage and lag time had an influence on the estimated effective kd. However, in the 2-compartment system, the proportion of pdNDF disappearing by passage is smaller during the early residence time compared with a 1-compartment system, but for later residence times, the reverse is true. Due to the slow disappearance via passage during early residence times, a digestion lag time would have a smaller effect on the digestibility in the 2-compartment compared with 1-compartment system (Ellis et al., 1994).
Conclusions
Two-pool models could be fit better to gas production data than 1-pool models, indicating that pdNDF in grass silage cannot be considered as a homogenous substrate. The best fit was not always translated into improved accuracy of the in vivo predictions. There was no evidence of benefits from using 2-pool gas production models in terms of predicting the in vivo parameters despite markedly better fit of the data. It seems that large residuals during early stages of fermentation (<20 h) have a relatively small effect on the predicted NDF digestibility, if the sum of the negative and positive residuals is equal. On the other hand, time-related patterns during the later stages of fermentation markedly affect the asymptotic value and consequently the first-order digestion rate. When the first-order digestion rate for mechanistic rumen models is to be estimated, an investigation of the pattern of residuals during later stages of fermentation is important in addition to fitting criteria. The 1-pool models France and RICH and the 2-pool models GOMPS, RICH, and WEIB had good fit of data, no time-related pattern or residuals, and they predicted the in vivo NDF digestibility and digestion rate accurately and precisely. Also, the model EXPDLag predicted the in vivo data accurately despite greater RMS in curve-fitting. A more unequivocal comparison of feedstuffs is an important advantage of 1-pool models.
1 Corresponding author: pjh87{at}cornell.edu
Received for publication January 22, 2008. Accepted for publication May 30, 2008.
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