Estimating the extent of degradation of ruminant feeds from a description of their gas production profiles observed<i>in vitro</i>:derivation of models and other mathematical considerations

Dijkstra, J.; Dhanoa, M. S.; López, S.; Bannink, A.

doi:10.1017/s0007114500000180

Cited by 366 publications

(316 citation statements)

References 24 publications

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“…The mathematical form of FRD was defined by the equation 2(dS/dt)/S by France et al (2000), calculated as the negative ratio value of equations (6) and (5), and then expressed as…”

Section: Resultsmentioning

confidence: 99%

Deriving fractional rate of degradation of logistic-exponential (LE) model to evaluate early in vitro fermentation

Wang

Sun

Tang

et al. 2013

Animal

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Water-soluble components of feedstuffs are mainly utilized during the early phase of microbial fermentation, which could be deemed an important determinant of gas production behavior in vitro. Many studies proposed that the fractional rate of degradation (FRD) estimated by fitting gas production curves to mathematical models might be used to characterize the early incubation for in vitro systems. In this study, the mathematical concept of FRD was developed on the basis of the Logistic-Exponential (LE) model, with initial gas volume being zero (LE 0 ). The FRD of the LE 0 model exhibits a continuous increase from initial (FRD 0 ) toward final asymptotic value (FRD F ) with longer incubation time. The relationships between the FRD and gas production at incubation times 2, 4, 6, 8, 12 and 24 h were compared for four models, in addition to LE 0 , Generalization of the Mitscherlich (GM), c th order Michaelis-Menten (MM) and Exponential with a discrete LAG (EXP LAG ). A total of 94 in vitro gas curves from four subsets with a wide range of feedstuffs from different laboratories and incubation periods were used for model testing. Results indicated that compared with the GM, MM and EXP LAG models, the FRD of LE 0 model consistently had stronger correlations with gas production across the four subsets, especially at incubation times 2, 4, 6, 8 and 12 h. Thus, the LE 0 model was deemed to provide a better representation of the early fermentation rates. Furthermore, the FRD 0 also exhibited strong correlations (P , 0.05) with gas production at early incubation times 2, 4, 6 and 8 h across all four subsets. In summary, the FRD of LE 0 model provides an alternative to quantify the rate of early stage incubation, and its initial value could be an important starting parameter of rate.Keywords: mathematical models, rate of gas production, logistic-exponential model, in vitro fermentation ImplicationsThe fractional rate of degradation (FRD) of LE 0 model generally had high correlation with gas production at 2, 4, 6 and 8 h across all four subsets tested, and thus provides a good alternative to reveal the rate of early stage in vitro fermentation. The FRD of LE 0 model would have an implication in quantifying the rate of fermentation and evaluating digestion efficiency of feedstuffs in the rumen, as ruminal retention time of feedstuffs is short. However, further studies are needed to testify whether a higher FRD leads to a higher nutritive value (e.g. volatile fatty acid profile, microbial protein synthesis and feedstuff digestibility) for ruminants.

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“…The mathematical form of FRD was defined by the equation 2(dS/dt)/S by France et al (2000), calculated as the negative ratio value of equations (6) and (5), and then expressed as…”

Section: Resultsmentioning

confidence: 99%

Deriving fractional rate of degradation of logistic-exponential (LE) model to evaluate early in vitro fermentation

Wang

Sun

Tang

et al. 2013

Animal

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“…Kinetic parameters of GP were estimated (mL/g DM) by fitted data in the NLIN option of SAS (2002) according to France et al (2000) as:…”

Section: Calculations and Statistical Analysesmentioning

confidence: 99%

Effects ofSaccharomyces Cerevisiaeat Direct Addition or Pre-incubation onin VitroGas Production Kinetics and Degradability of Four Fibrous Feeds

Elghandour

Vázquez-Chagoyán

Salem

et al. 2014

Italian Journal of Animal Science

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The objective of this study was to evaluate the effects of Saccharomyces cerevisiae on in vitro gas production (GP) kinetics and degradability of corn stover, oat straw, sugarcane bagasse and sorghum straw. Feedstuffs were incubated with different doses of yeast [0, 4, 8 and 12 mg/g dry matter (DM)] at direct addition or 72 h pre-incubation. Rumen GP was recorded at 2, 4, 6, 8, 10, 12, 14, 24, 30, 48, 54 and 72 h of incubation. After 72 h, rumen pH and methane were determined and contents were filtrated for DM, neutral (NDF) and acid detergent fibre (ADF) degradability. Fibrous species×method of application×yeast interactions occurred (P<0.001) for all measured ruminal GP parameters and degradability. The direct addition or 72 h pre-incubation of S. cerevisiae with corn stover improved (P<0.05) GP and methane and decreased (P<0.05) the lag time (L) and NDF degradability (NDFD). The direct addition of S. cerevisiae to oat straw increased (P<0.05) rate of GP (c) and decreased (P<0.05) asymptotic GP (b). However, 72 h pre-incubation increased (P<0.05) c with linearly decreased b, DM degradability (DMD) and NDFD. Applying S.cerevisiae for 72 h pre-incubation decreased (P<0.001) methane emission. The direct addition or 72 h pre-incubation of S. cerevisiae to sorghum straw increased (P<0.05) b, c, L, DMD and NDFD. Overall, the effect of dose varied among different feedstuffs and different application methods. Results suggested that the direct addition of S. cerevisiae could support and improve ruminal fermentation of lowquality forages at 4 to 12 g/kg DM.

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“…The runs were replicated three times. Fermentation kinetics were cha racterized by fi tting the data to the model of France et al (2000) to derive curve para meters, which then were predicted by NIRS. This common approach involves two errors, one related to curve fi tting and one resulting from NIRS cali bra tion.…”

Section: Gas Productionmentioning

confidence: 99%

“…Near infrared refl ectance spectroscopy of gas production kinetics NIRS prediction equations were developed separately for ear and stover for (i) the curve parameters of the model proposed by France et al (2000), i.e. parameter A (asymptotic gas production, ml), c (fractional rate of fermentation, h -1 ), and L (lag time, h), and (ii) the gas produced in 10 different incubation intervals (3-5, 3-7, 5-12, 7-12, 5-16, 7-16, 12-16, 12-24, 24-72 and 16-72 h).…”

Section: Gas Productionmentioning

confidence: 99%

“…Table 1. Mathematical treatments for calibrating gas production kinetics with approach I (parameters A, c, L according to model by France et al, 2000), and approach II (gas produc tion in different incubation intervals) 3 number of data points used during fi rst smoothing of the spectrum; 4 number of data points used during second smoothing of the spectrum…”

Section: Gas Productionmentioning

confidence: 99%

See 1 more Smart Citation

Prediction of gas production kinetics of maize stover and ear by near infrared reflectance spectroscopy

Kruse¹,

Herrmann²,

Loges³

et al. 2008

J. Anim. Feed Sci.

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This study was conducted to evaluate the potential of NIRS to predict gas production (GP) kinetics for maize ear and stover. Two approaches were applied to characterize GP kinetics: 1. describing GP profi les by fi tting an exponential model and 2. by calculating GP for various incubation intervals. In the fi rst approach, NIRS pre dic tion equations could explain a high proportion of variability related to the fermen ta tion rate (c), the asymptotic GP (A), and the lag phase (L) of ear samples in the calibration sub set (R²: 0.81-0.87), while for stover predictive ability was inferior. Validation showed satisfactory results only for the fermentation rate (R²: 0.81-0.88). In the se cond approach NIRS calibration was acceptable for GP in several incubation inter vals, but validation showed satisfactory results for intervals 3-7, 7-12, and 7-16 h of sto ver samples only (R²>0.74). Further research is required to elucidate potential sources of error before obtaining robust NIRS equations.

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Estimating the extent of degradation of ruminant feeds from a description of their gas production profiles observedin vitro:derivation of models and other mathematical considerations

Cited by 366 publications

References 24 publications

Deriving fractional rate of degradation of logistic-exponential (LE) model to evaluate early in vitro fermentation

Deriving fractional rate of degradation of logistic-exponential (LE) model to evaluate early in vitro fermentation

Effects ofSaccharomyces Cerevisiaeat Direct Addition or Pre-incubation onin VitroGas Production Kinetics and Degradability of Four Fibrous Feeds

Prediction of gas production kinetics of maize stover and ear by near infrared reflectance spectroscopy

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