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The design and develop of a software to study the speed and acceleration of growing and developing of biological systems in the time (Pro-Vel-Ac) is showed with the objective of support the researchers performed by the experts in the study of the biological systems evolution. For the implementation of this software, Microsoft Office Excel 2007 was used. The estimation of the speed and acceleration was based on the calculation of the average variation rates. The local maximum and minimum were estimated from the mathematical concepts of the calculation of the critical and inflection points of a function. The software has three sheets: data input, analysis and graphs. It is concluded that Pro-Vel-Ac provides the analysis of data because calculate and illustrate its speed and acceleration without needing a mathematical model. Inform about the estimated time in which the critical points of the growing speed occurs. Also, generate a table that summarizes the characteristics of data, allowing knowing the biological process in study.
The biological growing is defined as the increase of an organism’s size or of the parts which is made it until their stabilization in the adulthood (Castro-Ochoa 2020). The biological developing is the process through this a cell turn into a creature made up by an innumerable cells with different functions. This term also make reference to the progression of vital stages an organism pass from fecundation to senescence.
The growing as the developing is the result of complex changes which occurs in live systems. The growing is just quantitative, while the developing can be quantitative and qualitative (Castro-Ochoa 2020).
The biological growing curves have a non linear performance and can have several of the fallowing phases: lag, acceleration, exponential, deceleration, asymptotic and died (Ortega-Monsalve et al. 2021). Generally, sigmoid mathematical models that allow summarizing the observed performance in parameters are used (Rodríguez et al. 2013). However, the analysis of speed and acceleration from the models is a more complex task for the researchers.
In the field of research, different statistical programs to model and processing the data are used. These software needs the choice of a mathematical equation to estimate the model indicators. Later the research should derive the equation once and once again to obtain the performance of the speed and acceleration, respectively. This procedure has as disadvantage that an inadequate selection of the mathematical model involves an incorrect description of the speed and acceleration of the biological phenomenon in study. Another disadvantage is that the mathematical models most common to describe the biological growing have an only local maximum, while speed of the data set can have more than one and even, can have several local minimums.
There was not either an specialized informatics tool, able to calculate and illustrate the speed and acceleration of data without needing a mathematical model, that estimate, in turn, the estimated time in which occurs the maximums, minimums and inflection points of the phenomenon in study. That is why in the Departamento de Bioestadística Aplicada at the Instituto de Ciencia Animal an informatics system to study the speed and acceleration of growing and developing of biological system in time was designed and developed.
The development range Microsoft Office Excel 2007 was used, which has a friendly platform, usual among researchers with numerous options, formula and logical operators that make the implementation process easy. To determine the estimated performance of speed and acceleration of the data set, Pro-Vel-Ac is based on the calculation of the average variation rate (figure 1). This is the slope of the line that passes through the abscissa points t and t+h. The h value corresponds with the absolute value of the difference between the execution time of the measure and the next one. It is important to highlight that when the measurements are not taken evenly spaced and the time between them 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 data, especially when “h” is small. Similarly, acceleration can be calculated by performing the same procedure at the approximate point velocities.
Figure 1 Performance of growing data: speed and acceleration calculated by means of the average variation rates of the studied data footprint
To detrmine the local maximums and minimums, the procedures for calculating the critical and inflection points were used (González and Llamas 2017). They 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”, f´´ (a) = 0 and f´´´ (a) ≠ 0, there is an inflection point at “a”.
To access Pro-Vel-Ac, users must have a computer running Microsoft Windows XP or newer versions of the operating system, Microsoft Excel 97 newer versions. Then, they must copy and open the Pro-Vel-Ac file, in Excel format (xls).
When starting Pro-Vel-Ac the sheet data input appears (figure 2), from which you can see the name of the other sheets analysis and graphs. The only sheet that can be edited is the data input. Here it should introduce the numerical data of the variable to be studied in the time. The measurement unit of the variable should be homogeneous.
Once the values are filled, the application calculates the average variation rates as punctual and approximates indicators of the derivatives from the data set. The first, second, third and fourth derivate of the data are estimated. With these results, Pro-Vel-Ac showed in the speed row, of the analysis sheet (figure 3), the moments in which the critical points of speed were reached and it is specified if it is a local maximum or minimum. These critical points are probable inflection points of the variable under study. In the analysis sheet is also provide a summarize outlet table with some characteristics of the analyzed data: average speed, maximum speed, minimum speed, asymptotic, critical points, among others.
The graphics sheet shows the performance of the speed and acceleration of the growing and developing variable. Figure 4 show an example.
Articles about software or informatics applications were searched, which were not statistical program, and help the researchers in the analysis of biological data of growing and developing. It was showed great availability of informatics tools specialized in the topic of child growing and developing (OMS 2009). In the animal science branch the livestock software SG. (2016), is highlight, which provide the livestock management and, also, control the animal growing. It was also located the Wezoot (2016) software, which unify and analyze the cattle data to improve the production yield. However, these softwares should be buying in the market, and they are only applied to the animal sector. The value of Pro-Vel-Ac lies in which is a general tool that is applied to any biological system in growing and developing in the time.
It is concluded that (Pro-Vel-Ac) provide the analysis of data because calculate and illustrate its speed and acceleration, without needing a mathematical model. It offers the estimated time in which the growing peaks are produced. Also, generate a table that summarizes the characteristics of data, allowing knowing the biological process in study.
