Models for gas production adjustment in ruminant diets containing crude glycerol
V Peripolli, E R Prates, J O J Barcellos, C M McManus, C A Wilbert*, J Braccini Neto, C M Camargo and R B Lopes
Departamento de Zootecnia, Faculdade de Agronomia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil.
vanessa.peripolli@hotmail.com
* Embrapa Suínos e Aves, Concórdia, SC, Brasil.
Abstract
The
objective of this study was to identify the model (Exponential, France,
Gompertz, Logistic and Dual-pool logistic models) that best fits the
cumulative gas production curve in ruminant diets consisted of
the substitution of maize with crude glycerol (0, 4, 8 and 12%). Alfalfa hay
(Medicago sativa) was used as roughage and comprised 60% of the diet.
The criteria used
were the graphic analysis of the observed and estimated curves,
graphic analysis of residues,
mean square error,
coefficient of determination (r²), residual mean absolute
deviation (RMAD),
mean percentage error and relative efficiency.
Dual-pool logistic, Gompertz
and logistic models showed the highest r2 values, as well as the
lowest mean squared error. The France and Gompertz models had the lowest
mean percentage error. The dual-pool logistic model showed the lowest RMAD
and relative efficiency greater than 1.0 in all comparisons, and therefore,
was considered the most efficient of the models evaluated.
Keywords: curve, gas production, in vitro, mathematical models, rumen kinetics
Introduction
The technique of in vitro gas production may describe the kinetics of food ruminal fermentation, in addition of estimating the degradation rate and extent of the food solubles and insoluble fractions by monitoring gas production rates at determined time intervals (Beuvink and Kogut 1993) and quantifying the residues on the final time point (Pell and Schofield 1993).
The mathematical description of gas production curves allows analyzing data and comparing substrates or characteristics of the fermentation environment, thereby providing useful information relative to composition of the substrate and the fermentation of soluble and slowly fermentable substrate fractions (Groot et al 1996).
The mathematical non-linear models commonly used to estimate the kinetics of ruminal fermentation are the exponential models, proposed by Ørskov and McDonald (1979), Mertens and Loften (1980), France et al (1993), Beuvink and Kogut (1993) and the Gompertz model, proposed by Lavrencic et al (1997); the single model proposed by Schofield et al (1994); the dual-pool logistic models proposed by Schofield et al (1994) and Groot et al (1996). The models may assume one, two or more fermentation compartments and/or phases (Groot et al 1996; Huhtanen et al 2008). Therefore, data analyzed by different models may generate different results, and hence, their interpretation demands caution and common sense (Mello et al 2008).
According to Noguera et al (2004), mathematical models have advantages and disadvantages relative to one another. Estimating variations exist between them depending on the experimental conditions and food evaluated. It is therefore essential, prior assessment of the most appropriate model for suitable interpretation of the nutritional value of feedstuffs for ruminants (Beuvink and Kogut 1993) particularly in diets utilizing alternative foods for substituting the conventional ones.
Crude glycerol could be used as an alternative energy source for ruminant feeding, due to its increasing availability and favorable price as a result of the expansion of the biofuel industry, as well as to the increase in grain maize prices.
The objective of the present study was to identify among non-linear mathematical models the one that best fitted biologically the in-vitro cumulative gas production curves in diets based on alfalfa hay and ground maize grain with the addition of increasing levels of crude glycerol in substitution of maize.
Materials and methods
Location
The experiment was carried out in the ruminant sector of Laboratory of
Animal Science, and the chemical analyses were performed at the Animal
Nutrition, both belonging to the Department of Animal Science of the School
of Agronomy of the
Federal University of Rio Grande do Sul (UFRGS), Brazil.
Experimental animals
Two Texel sheep, with 40-kg average body weight and fitted with a rumen fistula, were used as inoculum donor. The animals were kept in a 120-m2 paddock with a shelter during the entire experiment. Alfalfa hay was daily fed at 3% the animals’ body weight. Mineral salt and water were supplied ad libitum. Before the experiment started, the animals were submitted to a 10-day adaptation period to the above described diet. The experimental protocol followed the guidelines of the Ethics Committee on the Use of Animals in Research as Number 18.442 in compliance with Law 11.794.
In-vitro cumulative gas production
The experimental treatments consisted of substituting maize with liquid crude glycerol (0, 4, 8 and 12%) in dry matter basis. Alfalfa hay (Medicago sativa) was used as roughage and comprised 60% of the diet. Table 1 shows the nutritional composition of the ingredients of the experimental diets.
|
Table 1. Dry matter (DM), organic matter (OM), crude protein (CP), neutral detergent fiber (NDF) and acid detergent fiber (ADF), crude energy (CE) and glycerol contents of the ingredients in the experimental diets |
|||||||
|
Ingredients |
DM |
OM |
CP |
NDF |
ADF |
CE (MJ/kg) |
Glycerol (%) |
|
(%) |
……….% DM..……… |
||||||
|
Alfalfa hay |
88.5 |
88.3 |
19.2 |
54.4 |
30.6 |
18.6 |
- |
|
Ground maize |
88.8 |
99.1 |
8.53 |
16.0 |
3.46 |
18.7 |
- |
|
Crude glycerol* |
81.4 |
- |
0.11 |
- |
- |
14.5 |
80.0 |
|
*methanol content lower than 45 mg/L |
|||||||
In-vitro cumulative gas production was measured using the technique of automatic in-vitro gas production (ANKOM Gas Production System). One day before the incubation to each 250 ml fermentation bottle, 1g composite sample consisting of 60% alfalfa hay and ground maize was placed. Crude glycerol substituting 0, 4, 8, and 12% of the total maize (40%) on the dry matter basis were individually added to the flasks, according to experimental treatment, and the flasks were then kept in an oven at 39ºC. On incubation day 100 ml of a mixture containing culture medium (Goering and Van Soest 1975), which was previously heated and maintained at 39ºC, and saturated with CO2 for approximately 15 minutes before being added to the bottles. After the addition of the mixture, bottles were saturated with CO2 for approximately 30 seconds, immediately closed, and maintained in the incubator at 39ºC until the inoculum was added.
Two hours after the animals received the morning meal, ruminal liquid and part of solid ruminal material were collected. The objective of collecting solid material was to also collect microorganisms attached to the substrate. The collected materials were homogenized in a food processor at a 1:1 ratio (1 part of liquid to 1 part of solid). The homogenized material was then filtered through four layers of gauze and maintained under constant CO2 gas flow, always keeping the temperature near 39ºC before and during the addition of the material to the bottles. A volume of 25 ml of inoculum was added to each bottle using a 50 ml glass syringe. The bottles were then placed in an incubator at 39ºC for 48 hours.
In-vitro cumulative gas pressure was automatically measured every 10 minutes. The gas production was determined for each sample in four repeated runs. The gas production curves obtained in each run were very reproducible (repeatability estimated by RELM method = 0.79).
In order to transform pressure into volume data, the following equation recommended by the manufacturer was applied: Vx =VjPpsi x 0.068004084, where: Vx = volume at 39ºC in ml; Vj = head space of the digestion bottle in ml; Ppsi = cumulative pressure recovered by the software.
Gas production data were expressed in ml of gas produced per gram of organic matter incubated.
The models were fit to the cumulative gas production data and was presented in Table 2.
Goodness of fit of the models
The criteria adopted to verify the goodness of fit of the models were the coefficient of determination (r2), mean square error (MSE), residual mean absolute deviation (RMAD), graphic analysis of observed and predicted curves, graphic analysis of residues, mean percentage error (MPE), and relative efficiency (RE).
The MSE was obtained by analysis of variance, using the PROC NLIN of SAS (SAS Inst., Inc., Cary, NC; Version 9.5), dividing the sum of squared errors (SSE) by the number of observations because the models presented different number of parameters to be estimated.
The r² values resulted from the division of the sum of squares of the model (SSM) by the sum of total squares (STS). RMAD was calculated as the sums of difference between the observed and predicted values, divided by the number of observations.
The PROC CORR of SAS (SAS Inst., Inc., Cary, NC; Version 9.5) was used for r², RMAD, graphic analysis of observed and predicted curves and graphic analysis of residues.
The relative efficiency
was calculated as 
where MSE is the mean square error, and RE (i/j) indicates the
efficiency of model i relative to model j.
The parameters of the models were estimated using the iterative method of Marquardt inserted in the NLIN procedure of SAS (SAS Inst., Inc., Cary, NC; Version 9.5).
The values of the mean squared error (MSE), coefficient of determination (r2), residual mean absolute deviation (RMAD) and mean prediction error (MPE), obtained from fitting the data of organic matter gas production to the tested models, were submitted to analysis of variance (PROC GLM) and the means were compared by the test of Tukey at the level of 5% error probability.
Results
No difference was observed in the initial hours in the gas production profiles, only differences in total gas production are observed (Figure 1).
The exponential (A) and France (B) models were less effective in gas production fitting to the curves in the beginning of incubation (0 to 5 hours) at all crude glycerol levels as they underestimated gas production. The exponential model yielded negative values, which is biologically impossible (Figure 1). Moreover, these models presented exponential growth during the incubation period, when, in fact, gas production curves are usually sigmoidal, as those produced by the Gompertz (C), logistic (D) and dual-pool logistic (E) models. These models presented three phases: an initial phase with no or slow gas production, exponential phase of rapid gas production, and asymptotic with gas production reduction. Different from Gompertz model, the logistic e dual-pool logistic models overestimated gas production during the initial period of incubation (0 to 2 hours) at all crude glycerol levels evaluated.
The exponential and France model underestimated gas production in the transition between the end of the exponential phase and the beginning of the asymptotic phase, specifically between 12 and 24 hours of incubation, whereas the logistic model overestimated gas production during this phase. The Gompertz and duo-pool logistic models best estimate at all stages of gas production.
| A: | A: |
 |
 |
| B: | B: |
 |
 |
| C: | C: |
 |
 |
| D: | D: |
 |
 |
| E: | E: |
 |
 |
| Figure 1. Observed and predicted curves of
cumulative gas production (ml/g incubated OM) and residual
dispersion during the incubation period as determined by the
exponential (A), France (B), Gompertz (C), logistic (D) and dual-pool logistic (E) models when increasing crude glycerol levels (0, 4, 8, and 12%) were included in the diet |
|