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There are several techniques to study the nutritional value of foods in the rumen. To fulfill the hypotheses of the experimental design, in vivo techniques need sufficient numbers of animals and, therefore, large volumes of plant material (Rodríguez et al. 2020). However, in vitro techniques are less time consuming, require less food as substrate and allow greater control of experimental conditions (Arce et al. 2020). In this regard, Theodorou et al. (1994) proposed a method to study the fermentation kinetics of substrates from the in vitro gas production (IVGP) generated by their fermentation, which is measured in bottles of constant volume and at different times.
There are some programs that specialize in modeling ruminal degradation kinetics. These need a mathematical function to estimate the parameters that describe the IVGP kinetics. This is the case of the NEWAY EXCEL program, version 5.0 (Chen 1997) and the ROMENAL procedure (Correa 2004). Both use the Excel platform and are commonly applied in in situ experiments. One of their disadvantages is that they have a reduced number of mathematical models to describe the IVGP kinetics.
Regardless of the used program, the most common parameters during modeling are: asymptotic IVGP, IVGP rate, Lag phase and inflection point, among others. In relation to the inflection point, it is known that it allows identifying the moment in which the food reached the maximum degradation rate. However, the mathematical models that are most used to describe the IVGP kinetics, having a single inflection point, do not allow knowing the time in which the food stopped degradation. If it is added to this the low availability of computer programs related to IVPG, it is necessary to implement a program specialized in the preprocessing and data analysis of IVGP ruminant foods.
The Microsoft Office Excel 2007 development environment was used, which has a friendly platform, common among researchers, with numerous options, formulas and logical operators that make the implementation process easy. The conversion of the IVGP values in Pascal (Pa) to volume data in mL g-1 incOM was carried out using the equation proposed by Rodríguez et al. (2013):
The estimation of the speed and acceleration of the IVGP was based on the calculation of the mean variation rates (figure 1) of the i-th observations. This is the slope of the secant line to the function that passes through the abscissa points ti and ti+hi. Particularly, in the IVGP experiments, the h value corresponds to the difference between the consecutive sampling times. It is important to highlight that, when the measurements are not taken evenly spaced and the time between IVGP samples is lengthened, h increases and the approximations are less exacts. However, with these concepts it is possible to have an approximate image of the real speed of IVGP, especially when h is small. Similarly, acceleration can be calculated by performing the same procedure at the approximate IVGP point velocities.
Figure 1 Performance of the IVGP of ruminant foods: speed and acceleration calculated by means of the average variation rates
To determine the time in which the maximum and minimum speed of IVGP occurred, the procedures for calculating the critical and inflection points were used, as reported by Pico and Alava (2018) and Jones (2019), who state that there is a local maximum of the function f at point a, if: f´(a) = 0 and f´´(a) < 0 and there is a local minimum at point a, if: f´(a) = 0 and f´´(a) > 0. On the other hand, if f´ is derivationable at point a and f´´(a) = 0, there is an inflection point at a.
To locate the critical points in the IVGP speed curve, estimated from the experimental data, the time intervals between ti and ti + hi were analyzed. When the estimated acceleration at ti was higher than zero, and the estimated acceleration at ti + hi was lower than zero, the velocity was assumed to have a local maximum in the interval between ti and ti + hi. On the other hand, when the estimated acceleration at ti was lower than zero and the estimated acceleration at ti + hi was higher than zero, it was estimated that the velocity had a local minimum in the interval between ti and ti + hi. As shown in figure 1, the velocity was maximum when the acceleration intercepted the abscissa axis, and when the acceleration slope was negative. At this time, there was also an inflection point for the IVGP. This methodology, although it constitutes an approximation, can be applied to other types of experimental observations, and does not require a mathematical model to determine the critical and inflection points of the data set.
To access ProGas v1.1, users must have a computer running Microsoft Windows XP or newer versions of the operating system. In addition, they must have the Microsoft Office 2007 work package or higher versions. Then, they must copy and open the ProGas v1.1 file, in Excel format (.xls). When starting the program, the general sheet appears, from which you can see the names of the rest: enter pressures, accumulated volume, critical points, graphs and help. The only ones that can be edited are the general one and the one for enter pressures. Sheets must be used sequentially.
The general sheet is where the user enters the characteristics of the experiment. That is: name of the experiment, number of treatments that comprise it, number of repetitions, replications and times. In addition, the names of each treatment must be entered, with their respective fresh (g) and incubated (mL) matter.
The functionality (enter pressures) allows the researcher to fill in the pressure values measured with the manometer in Pa at the different sampling times. In addition, the user must fill in the gas production of the controls, and enter the hours in which each measurement was made (figure 2a). Once all these values are filled in, the application calculates the accumulated gas production and applies the conversion equation proposed by Rodríguez et al. (2013). For this, ProGas v1.1 takes into account the IVGP of the corresponding controls. The result is shown in the accumulated table of gas production in mL g-1 incOM, belonging to the accumulated volume sheet (figure 2b). This sheet also shows another table with the average value of IVGP (mL g-1 incOM).
Figure 2 a) Sheet to enter pressures of the ProGas v1.1 program. b) Sheet of accumulative volume of ProGas v1.1 program. Outlet table
The critical points sheet is the special functionality of ProGas v1.1, since it allows a better understanding of the IVGP performance over time (figure 3a). Here the average rates of change are calculated as approximate indicators of those derived from the IVGP. The time at which the critical points were reached is shown, and it is specified if it is a local maximum or minimum. In addition, it provides the two critical points that were most repeated in each treatment. Having an approximation of the time in which the minimum speed of IVGP occurred allows knowing when the food finished the degradation. This can contribute to not extending the sampling time in the experiments, since these estimates are made with the experimental data, and without the need to fit a mathematical model. In addition, they allow better characterization of the food, by providing the duration of each IVGP phase.
The graphic sheet shows the performance of the average accumulated volumes (mL g-1 incOM) of each treatment (figure 3b). Lastly, the help sheet offers an explanation of the application's functionalities to facilitate working with the ProGas v1.1 program.
Figure 3 a) Critical points sheet of the ProGas v1.1 program. Outlet table example b) Graphic sheet of the ProGas v1.1 program. Outlet table example
The proposed program made it possible to prepare the experimental data for subsequent modeling, especially when they were obtained using the IVGP technique, described by Theodorou et al. (1994). In addition, the methodology that was applied to estimate the critical points did not require a mathematical model to calculate the duration of the IVgp phases, which facilitated the description of the degradation kinetics of the evaluated foods.
