Artificial Neural Networks for Predicting Food Antiradical Potential

Abstract

Using an artificial neural network (ANN), the values of the antiradical potential of 1315 items of food and agricultural raw materials were calculated. We used an ANN with the structure of a “multilayer perceptron” (MLP) and with the hyberbolic tangent (Tanh) as an activation function. Values reported in the United States Food and Nutrient Database for Dietary Studies (FNDDS) were taken as input to the analysis. When training the ANN, 60 parameters were used, such as the content of plastic substances, food calories, the amount of mineral components, vitamins, the composition of fatty acids and additional substances presented in this database. The analysis revealed correlations, namely, a direct relationship between the value of the antiradical potential (ARP) of food and the concentration of dietary fiber (r = 0.539) and a negative correlation between the value of ARP and the total calorie content of food (r = −0.432) at a significance level of p < 0.001 for both values. The average ARP value for 10 product groups within the 95% CI (confidence interval) was ≈23–28 equivalents (in terms of ascorbic acid) per 1 g of dry matter. The study also evaluated the range of average values of the daily recommended intake of food components (according to Food and Agriculture Organization—FAO, World Health Organization—WHO, Russia and the USA), which within the 95% CI, amounted to 23.41–28.98 equivalents per 1 g of dry weight. Based on the results of the study, it was found that the predicted ARP values depend not only on the type of raw materials and the method of their processing, but also on a number of other environmental and technological factors that make it difficult to obtain accurate values.

1. Introduction

The level of computing technologies development to date has given a rise to the possibility of accumulating many classes of data, which has led to the need to analyze large amounts of information (big data analysis) accumulated in archives and digital libraries [1,2]. These databases include previously published and currently updated reference materials and tables on the chemical composition of food products, food components and agricultural raw materials [3,4]. It is quite obvious that without modern statistical tools, the analysis of this amount of information, as well as the identification of hidden connections within/between groups in these data, is extremely difficult [5]. Currently, various statistical methods of extrapolation and forecasting are used.

One of the promising methods suitable for these two purposes is the use of artificial neural networks (ANN). They are suitable for clustering, recognizing distribution patterns, and identifying internal connections in data libraries. However, they have been successfully used more than once to calculate previously unknown values [1,6,7,8].

ANN is a matrix where the cells are the “neurons” of this network, and the connections between the cells are the “synapses” [1,2,8]. Synapses are specified correlations between cell values—they can be either positive or negative. Each cell (neuron) can have either one or several synapses, depending on the structure of the ANN. In this case, the cell that has the data entered by the operator as its content is called the “input neuron”, and the cell that displays the total values is called the “output neuron”. The cells connecting the input and output neurons are called “hidden neurons” and contain an algorithm for calculating a specific function, called the “activation function”. This function and the values of synapses can be set either randomly (at the first launch of the ANN) or with the given parameters when compiling the structure of the neural network (before it is launched). In addition to the structure and interconnections of cells, an “increment” parameter is set before starting the network—this parameter affects the amount of change in the values of synapses and, as a result, the speed of network learning. The work of ANN is described in detail in numerous publications, for example [1,9,10,11].

In total, more than 20,000 papers have been published using neural networks at the beginning of 2022 (according to NCBI). By comparison, Google Scholar returns nearly 400,000 results for “Artificial neural network food processing” request.

The use of ANNs in the food industry, as well as in other areas, has been demonstrated many times in all three types of studies [12,13,14].

With the advent of such a method as ANN based analysis, it has been repeatedly used to work with chemometric data (chemical compositions) since the 1990s of the last century [15]. A little later, works related to food processing and analysis of food raw materials appeared, for example, in predicting the nutritional value and composition of seven amino acids in food products using ANN [16]. A little later, another work was carried out to assess the possibility of using ANN to study individual groups of products.

Thus, based on 144 varieties of Scotch whiskey, a new model of sensory characteristics and organoleptic qualities, known to be important signs of authenticity of this group of drinks, was developed. The ANN in this study was also used to eliminate personal preferences of tasting commissions members, which could previously influence the results [17].

Similarly, the possibility of using ANN for the classification of white varietal wines is demonstrated. The most successful use in this study was the ANN architecture in the form of a perceptron. The chemistry data for network training were obtained using a gas chromatograph–mass spectrometer (GC-MS). As a result of the analysis, contributions of each of the groups of volatile substances to the aromatization of wine were segregated. Good convergence of data obtained using ANN and classical statistical methods was also noted [7]. Neural networks were also used to create a model for assessing the rate of aging of wines; in the course of these works, it was found that when comparing linear and non-linear activation functions, the latter are preferable [18].

In addition to the above, ANNs have been used previously to predict the rate of drying of potato slices in the sun. As authors have shown, networks with four neurons in the hidden layer are suitable for such purposes. Despite the apparent simplicity of the ANN architecture, a mathematical model with high predictive ability was created. This made it possible to take into account the environmental parameters, product moisture and heat diffusion in food raw materials, as well as the geometry of potato slices [19].

Similar goals were pursued by authors of a study on the evaluation of the speed and parameters of drying of raw materials of wormwood, suitable for obtaining absinthe. The mathematical model made it possible to optimize temperature conditions, air supply rate, etc. [20].

Resemblant goals were pursued by the authors in assessing the effect of drying products from bananas (Musa nana) under different temperature conditions. It was shown that ANNs created by authors successfully predict the quantitative concentrations of polyphenol compounds with antiradical properties in banana-processing products [21].

Other works were carried out on the study of the rate of drying of grape berries [22], of the relationship between the concentration of nutrients in kiwi fruits and their keeping quality [23], of kinetics of the release of oils from tarragon raw materials during its ultrasonic treatment [24], etc.

No less interesting were works on the use of photo and video images of food raw materials. Thus, for example, a team of authors, in the absence of a spectrophotometer, conducted successful studies to assess the ARA activity of food raw materials. This was achieved by using DPPH, based on a calibration scale built by ANN from cell phone photographs for reaction mixtures with a known number of Trolox units (a synthetic antioxidant). All other reaction mixtures were compared by a neural network with already known color standards, which made it possible to perform a semi-quantitative analysis [25].

A somewhat similar research design was demonstrated when trying to use ANN to assess the end of the fermentation of cocoa beans. The color of beans, obtained by photographic equipment or an electronic scanner, was compared with an assessment of their organoleptic qualities. Based on the values obtained, a dependence was found and an express test was proposed that assesses the degree of readiness for processing by the color of beans from photographs [26].

Note that the use of ANN allows authors to use data of various types in their work. Thus, in one of the publications, when assessing the rate of development of Listeria monocytogenes strains pathogenic for humans on lettuce leaves, data on the chemical composition of the treatment solution, bacteriophage strains, genetic data on Listeria strains, temperature and environment acidity (p_h) were simultaneously analyzed. At the same time, the ANN architecture was by no means complex: there were only four hidden neurons in the inner layer [27].

Previously, we have estimated the ARP of food products and food raw materials [28,29]. However, as we have already pointed out, obtaining large-scale estimates of this parameter is difficult both technically and methodologically. This is due both to the need for constant calibration of the scale for ARP ratings and to the choice of reference substances for chemical analysis. This leads to the fact that the data obtained by different authors for different foodstuffs often cannot be compared with each other (there is no single measurement scale) [30]. In addition, it is known that the composition of food affects the ARP indicators, which will change not only during storage of products, but also during various types of its processing [29]. These complexities make it possible to carry out many routine analyses, which require both a lot of time and equipment from the researcher, which even in this case, does not guarantee the ability to develop a uniform scale for comparing the results obtained by different research teams. For example, earlier in our published data, we indicated that the study of one food sample is carried out in several stages [28,29]. The full extraction stage was carried out by us for one week, using refrigeration units and in an inert gas atmosphere. Then, photocolorimetric analysis followed, requiring from 30 to 40 min to be carried out, the presence of specific equipment and a standardized DPPH solution. The use of an ANN as a method for forecasting allows one to save significant production and time resources.

For example, the reference book on the chemical composition of food products [3] provides data on a little more than 1200 types of food products. Even if we assume that ≈16 samples can be processed in an 8 h day, and it will take at least 1 week to extract them, then at least 75 weeks will be spent on such a volume of analyses with daily data processing (excluding holidays, sick leave, vacations, etc.) or ≈2 years, taking into account the average length of the working week. Thus, the economic and technological expediency of using ANN for carrying out this kind of routine analysis is traced.

All of the above makes it imperative to search for methods that allow one to calculate the ARP of food “in one measurement scale”, and ideally without performing routine chemical reactions, since by now, numerous data on the chemical composition of food have been accumulated. In addition, it will be important to find components that predominantly affect ARP indicators, including for the purposes of food engineering.

Note that the development of such a method for predicting ARP is also dictated by the potential possibility of using this parameter as one of the complex characteristics whose values are necessary to assess the stability, safety, quality of food products and their consumer properties [29].

Currently, there are many food databases on the Internet, for example: FNDDS (USA), Australian Food Composition Database (Australia), FAO/INFOODS (International Network, Italy); FoodB (Canada); FITsPBiBP (Russia); USDA (USA), etc. In view of the fact that the quality of ANN training depends on the number of parameters entered into it for calculation, the archives that include the data presented by a large number of tabular values for each type of product will be of the greatest value for this kind of research.

For this reason, not every database will fit the objectives of the study. During the comparison, it was found that some of the data presented above are not suitable for a number of reasons: there are gaps and text abbreviations in the volume of values (nonnumerical values that cannot be used for training the ANN), and the absence of the same number of input numerical values. For example, FAO/INFOODS had from ≈80 to ≈320 different cells for different types of products, including empty ones. The FoodB database contained chemical formulas that would be more suitable for searching for individual components using mass spectrometry and chromatography. The Australian Food Composition Database contained blank cells and text notes, and the number of parameters for each product was 54. The FITsPBiBP and USDA databases had a similar structure, where each type of product was represented by a small number of parameters (USDA ≈ 25; FITsPBiBP ≈ 30), while the data format was extremely inconvenient for analysis and required conversion from a columnar form to a lineal one. As it turned out, the FNDDS base was the most suitable for our purposes. It contains 63 parameters of the nutritional value of food products in a common data array, does not contain non-zero cells, and there are no text abbreviations inside the volume of the database array [4].

Thus, the goal of this study is to train the ANN and predict ARP values for the main analyzed food groups based on the chemical composition of the FNDDS (USA) international food and nutrient database.

We have not come across similar works with the use of databases on the nutritional value of food products published earlier. The novelty of the proposed approach lies in the fact that the antiradical activity of the total volume of consumed food components has not been previously assessed in accordance with the accepted international norms of daily intake (FAO and WHO). Research in this area is still significant and relevant.

Similarly, dietary ARAs and frequently consumed representatives of food groups have not been studied. The databases of nutritional content of foodstuffs collected to date allow for such studies to be carried out.

2. Materials and Methods

This study included several stages. The first stage involved the evaluation of the antiradical activity of food products. For this, the photocolorimetric method was used [31]. ARP was determined from the difference between the detected extinction values of mixtures of alcoholic solutions of the stable colored radical DPPH and extracts of food products according to the previously published method [28,29,32]. In total, about 100 types of products, food components and types of agricultural raw materials were analyzed. For antiradical values, a 95% confidence interval (hereinafter CI) was calculated, which was used to train the ANN.

After analyzing the data, a comparison was made of those products that were presented in the FNDDS database and those that were analyzed by us. Twenty-nine indisputably coinciding positions were singled out: wheat and rye bread; milk and dairy products; seafood, fish and products of its processing; cereals; frozen and fresh vegetables; fruits; eggs; cane molasses. For selected positions, the chemical composition of products and the concentration of components were used from the FNDDS database, and the ARP values were substituted according to our own experimental data. Thus, a mixed table was formed, simultaneously containing both the data obtained by us and the values of the chemical composition.

At the second stage, using the data, optimization (training) of the neural network was carried out. The level of deviation from the model values was ≈0.005 (or half a percent). NeuroXL Predictor (v. 3.1.2; OLSOFT software development; Russia, Uzbekistan) program was used to create the ANN structure, which was used in the study (a schematic representation is given at the center of Figure 1). Since in our work the goal was only to obtain two estimates (without complex transformations), we used a neural network built according to the “perceptron” type (with one layer of hidden neurons). The choice of such a structure was justified by the simplicity of calculations, and the use of MLP has been repeatedly justified in the literature and was often used earlier to study problems of similar complexity [1,9,10,33,34,35]. At this stage, we empirically selected ANN parameters according to the number of hidden neurons (structures from 2 to 20 neurons were tested). Preference was given to such an ANN structure, with the use of which it was possible to obtain the best approximation with the least number of training epochs.

The schematic diagram of the internal structure of the ANN used by us to calculate the ARP of food systems is shown schematically in Figure 1. The number of input neurons was equal to the number of cells in the FNDDS database (with the exception of three, which were removed from the calculation, since these substances were not present in the products we studied: alcohol content, and specially added vitamins B₁₂ and tocopherols. All input neurons are schematically combined for visual convenience in one rectangle (see Figure 1) Hyperbolic tangent (Tanh) was used as the activation function of latent neurons. Antiradical activity values within the 95% CI for the output neurons were designated by the term ARP (max–min).

In addition to the number of neurons, the applicability of several activation functions was tested—threshold (Thd), logarithmic (Log), hyperbolic tangent (Tanh), sigmoid (Sig). As in the first case, preference was given to those configurations that had the fewest training epochs. For different configurations, the number of epochs varied from 5.5 to 80 thousand. The training curves for different functions are shown in Figure 2.

In the upper right corner of Figure 2 (inset), there is a fragment of the curve obtained for a neural network with a threshold activation function (Thd) in the hidden layer of neurons. The neural network configuration containing this function in the hidden layer of neurons could not optimize its structure to the desired level of a 0.5% error even after 100 thousand training epochs and was rejected by us. When using the sigmoid (Sig), logarithmic (Log) and hypertangential (Tanh) functions, the neural network achieved the goals of optimizing its structure in about ≈5.5–7.5 thousand training epochs.

The most optimized configuration turned out to be a MLP containing 4 hidden neurons with a hyperbolic tangential function (Tanh) in them (Figure 2).

Along with this, during the data fitting process, it was found that substances with low concentrations (vitamins) strongly influence the appearance of statistical outliers (increased variance). To eliminate this, we coarsened (increased the robustness) the values, changing them within 1% of the initial values (it was permissible, since the ARP data were presented for analysis in the form of 95% CI, and not in the form of point values).

In addition, food products that differ significantly from those product groups that were analyzed by us were removed from the analysis. First, this was performed due to the influence of additional substances, such as anthocyanins, which can significantly change the ARP values of food, while the values of such components themselves are not given in the FNDDS table [4,36,37]. In total, 1315 positions (types of food products) were selected for the ARP prediction. We analyzed the following food groups: bakery products, confectionery, fruits, fish and fish products, pork, vegetables (fresh and processed), eggs, milk and dairy products.

After receiving the predictive data, it was analyzed at the third stage of the study for the presence or absence of correlations. Pearson’s test (r) was used for the analysis. This method is parametric and is often used in scientific research for identical purposes [5]. Along with this, a paired test according to Tukey [5] was also used to identify differences. The statistical significance level p ≤ 0.000833 obtained after applying the Bonferroni correction to the 5% significance level was used for the analysis, since the analysis assumed multiple pairwise comparisons. The concentration values of chemical components of food from the FNDDS table were recalculated per gram of dry matter in the same way as we performed in our experiments [29]. Statistical data analysis was carried out in the Statistica (v.10; StatSoft Inc., Tulsa, OK, USA) application package, as well as in the spreadsheet MS Excel 2010.

3. Results and Discussion

The first point to pay attention to is that when using data with low values (for example, vitamin concentrations) for training, with a simultaneous low level of system robustness, the probability of overfitting of the ANN increases. This manifests itself, for example, in obtaining negative ARP values, which contradicts the chemical meaning and logic of the experiment.

Similar values appeared in two groups of data: on products that differed significantly from those that were analyzed by us (for example, soft drinks, exotic fruits and products of their processing, etc.), as well as on products with vitamin fortification or modified recipes due to the introduction of various kinds of food additives into them. We were forced to leave for analysis only those products and related product groups that we used in training the ANN (a total of 1315 items). At the same time, we were forced to increase the robustness, as mentioned in Section 2, by simulating data noise within 1% of chemical composition values. This approach significantly accelerated learning and obtained adequate results [1,18,38].

Turning to the analysis of the data obtained, we note that the grouping was carried out by us both taking into account the already adopted system in the FNDDS library itself (by product groups), and according to the features, we identified ourselves (by the product processing method).

As a result of training, ARP values were predicted. Next, we carried out pairwise comparisons of data groups with the results predicted by the ANN. We identified in total almost 1.5 dozen components with the concentrations and the ARP values of which there is a correlation. For the analysis, we used only those components that had a Pearson correlation value (r) > 0.25 (at p ≤ 0.000833 according to the Bonferroni statistical correction). The values are presented in

Table 1. Values of statistically significant correlations of the main components of food systems that affect the indicators of the ARP parameter of products predicted by ANN (for generalized data).

No.	Name of the Food System Component	Correlation Value (r) 1
1	Dietary fiber, total	0.539
2	β-cryptoxanthin	0.381
3	Ascorbic acid	0.347
4	Potassium	0.343
5	Folic acid, average	0.312
6	Magnesium	0.281
7	Carbohydrates, total	0.277
8	Philoquinnones (vitamin K)	0.262
9	β-carotene	0.259
10	Cholesterol	−0.257
11	Fats, total	−0.260
12	Fatty acid (C16–C20)	−0.285
13	Food calories, total	−0.432

¹ Note: statistically insignificant values (p ≥ 0.000833) and correlation levels (r < 0.25) are not included in the table.

.

Analyzing the presented table, we can come to one of the first non-trivial conclusions about the relationship between the antiradical capacity of food systems and the amount of dietary fiber in it. At the same time, the correlation of the data has a moderate strength (the only one of identified cases). An explanation for this can be found in the chemical structure of dietary fiber. Most often, these are polymer components containing various functional groups in their molecules, which, apparently, can act as stabilizers of physicochemical parameters of products, as well as structure them, forming a “molecular framework” [39,40]. It can be expected that a similar mechanism underlies the relationship between the concentration of carbohydrates in foods and their ARP.

One of discussed topics related to dietary fiber is the ability to regulate the concentration of microcomponents (dosage) in food with their help, as well as the ability to influence the rate of their absorption in the human intestine from chyme. Conversely, an inverse relationship is known between their concentration in food and the likelihood of oncological diseases of the intestine and cardiovascular pathologies [40,41,42].

According to our data, it seems reasonable to add a number of components during the development of new food products that can both repair the lost ARP (or change the current ARP) and influence the physical/epidemiological properties of the food system. Among such components, we primarily outline dietary fiber and a number of other substances (Table 1). Research work on the enrichment of products from various commodity groups with dietary fiber, in our opinion, is moving in a promising direction. Especially, it is an actuality for those products that are subject to rapid “aging” and loss of their nutritional value [43].

In addition, the analysis of results obtained (Table 1) allows us to note that the revealed weak correlations between the ARP parameters and the concentrations of some vitamins are quite expected. Thus, antiradical properties are peculiar to a number of vitamins: C, K, carotenoids, folic acid, etc. Conversely, the correlation found between the concentrations of potassium and magnesium and the antiradical potential of food is not entirely trivial.

The data obtained (Table 1) also show the promise of using B vitamins for the development of both products with increased ARP and for correcting the nutrition of people with impaired metabolism of folic acid and sulfur-containing amino acids [44].

All significant negative correlations presented were found between ARP and lipophilic components. The only exception is the total calorie content of food. However, knowing that the energy value is more than half dependent on the amount of fat, we can conclude that an increase in the concentration of fatty acids in food contributes to a drop in the ARP value due to the easy oxidation of these components (possibility of rancidity of fats), especially during long-term storage [29].

Conversely, we do not rule out the possibility that the data presented are distributed in this way due to the influence of the nature of the raw materials used to manufacture the product. Thus, for example, vegetable raw materials (showing high levels of ARP) contain elevated concentrations of potassium, magnesium, dietary fiber, ascorbic acid, and carotenoids [40]. On the contrary, animal raw materials are often rich in fats, including those prone to rancidity. Similar uneven distributions of these components revealed both different strength and direction of correlations (Table 1).

In this case, it is reasonable to provide data on processing methods (if mentioned) and commodity groups. The results for the first group are presented in

Table 2. ARP values predicted for products processed by different methods.

No.	Type of Processing	Statistical Parameters 1
		Mean	St. Error	St. Dev (σ)	95% CI
1	Baking	17.16	0.69	14.98	15.82–18.50
2	Conservation	35.89	2.06	20.85	31.85–39.94
3	Boiling	32.39	1.69	31.34	29.07–35.71
4	Drying	39.22	3.52	27.23	32.32–46.11
5	Frying	16.17	0.79	14.34	14.62–17.73
6	Smoking	18.99	3.02	19.57	13.07–24.90
7	Double boiler	20.78	1.95	17.47	16.95–24.61

¹ Note: Mean, average; St. dev, standard deviation; St. error, standard error; 95% CI, 95% confidence interval. Explanation of background color in table in the text below.

. The confidence interval for all values for all products ranged from 22.99 to 27.62 ARP equivalents.

The analysis of the data in Table 2 allows us to see that the way food is processed strongly affects the value of ARP predicted by the neural network. Making pairwise comparisons of the predicted average values (3rd column of Table 2), one can notice the presence of two groups for the following methods: group 1 combines frying, smoking, steaming and baking (green color in the table), and group 2 contains cooking, drying and preservation (yellow color in the table). It can be reasonably assumed that for the first group, low average ARP values are associated with a longer processing time and/or more severe temperature or chemical conditions for processing food raw materials. This ultimately leads to a strong degradation of food ARP. Confirmation of this assumption can be found in the accepted technological approaches currently used in the production of public catering products [45]. Thus, for example, steam treatment is almost two times longer than boiling in water, and frying and baking take place at 160–250 °C, which is also higher than the boiling temperature (≈100 °C). Smoking is associated with the introduction of a large number of smoke substances into the product, which have prooxidative properties and contribute to the oxidation of vitamins and related components of food systems [46,47]. Thus, the distributions of values for different processing methods predicted by the ANN are consistent with previously published data. In addition to comparing the two groups of methods with each other, we also checked for the presence of differentiation within each of the groups. To do this, a pairwise assessment of all the data grouped in Table 2 was carried out using the Tukey test (

Table 3. Pairwise comparison for no difference between the ANN predicted data groups (grouped by type of processing of raw materials).

No.	Method/Number 1	1	2	3	4	5	6	7
1	Baking		<0.001	<0.001	<0.001	0.99	0.99	0.79
2	Conservation	11.49		0.76	0.96	<0.001	<0.001	<0.001
3	Boiling	14.38	2.07		0.24	<0.001	0.0021	<0.001
4	Drying	10.77	1.36	3.26		<0.001	<0.001	<0.001
5	Frying	0.91	11.62	14.01	10.97		0.98	0.58
6	Smoking	0.75	6.16	5.48	6.72	1.15		0.99
7	Double boiler	2.0	6.76	6.25	7.21	2.47	0.63

¹ Note: Under the diagonal are the values of the Tukey test, and above the diagonal are the levels of statistical significance for the obtained values. The numbers of processing methods at the top of the table correspond to the numbering on the left; p values less than <0.05 in bold.

). Similar to the data presented above in Table 3, one can also notice two groups, which combine all the listed methods of processing food raw materials. Conversely, differences within each of these groups are not reliable (p values from 0.24 to 0.99).

Thus, according to the value of the predicted residual ARP in food products, two clearly differentiated clusters can be identified. They differ from each other at statistically significant levels.

However, we do not exclude that the obtained values may partly be of an artifactual nature, primarily due to the existing practices of using certain technological methods for processing various types of food raw materials. In this case, it would be logical to move on to a discussion of the results predicted for different product groups. For division into groups and classification, we used filters already available in the FNDDS database itself [4]. The values are presented in

Table 4. ARP values calculated by the ANN for products and raw materials from different commodity groups.

No.	Product Groups	Statistical Parameters 1
		Mean	St. Error	St. Dev	95% CI
1	Apples, processed products	118.16	28.79	70.52	61.73–174.59
2	Vegetables, cabbage	51.64	1.92	36.13	47.88–55.39
3	Legumes and cereals	41.63	2.15	35.26	37.40–45.85
4	Cheeses and sandwiches	16.36	1.09	15.97	14.22–18.50
5	Eggs and omelets	14.57	0.63	13.36	13.33–15.82
6	Fish, processed products	16.10	0.60	15.61	14.93–17.27
7	Milk, yogurts	31.26	1.92	24.73	27.50–35.03
8	Pasta, noodles and flour dishes	25.94	2.72	19.21	20.61–31.26
9	Pork, bacon	21.57	1.20	16.69	19.21–23.93
10	Marine invertebrates	13.87	1.14	15.65	11.63–16.11

¹ Note: Mean, average; St. dev, standard deviation; St. error, standard error; 95% CI, 95% confidence interval.

.

Analyzing the data presented in Table 4, one can notice that the first group “Apples, processed products” demonstrates the highest ARP value (118.16). The result obtained is not surprising, since this group also includes fresh fruits, with an increased content of both dietary fiber and water-soluble vitamins (ascorbic acid). It leads to an increase in the predicted ARP values for this group. The use of the Tukey test (table not shown) revealed indisputable differences at a statistically significant level only for three product groups: Apples, Legumes and Cereals, and Vegetables (p < 0.001). Despite the fact that the “Milk, yoghurts” group also differs from most other product groups, its statistically significant differences from meat products (bacon, p = 0.91) and from flour dishes, pasta (p = 0.002, which is two times higher than the significance level p = 0.0011 when applying the Bonferroni correction to the values of this test) were not found. However, the “Milk, yoghurts” product group shows statistically significant differences from all other samples (p < 0.001).

Figure 3 shows a histogram of the distribution of the calculated average ARP values for all the studied product groups. The average value for the entire data set was ≈25.3 equivalents.

These data confirm the need for evaluation and research of the daily antiradical capacity of food. Currently, there are standards for daily human needs for food components (for example, Codex Alimentarius, recommendations of national academies of medical sciences, etc.). Taking into account the data presented in them, it seems possible to estimate this capacity by conducting preliminary studies on the structure of foodstuffs preferentially consumed by the population. However, knowing that according to the FNDDS database, the average moisture content of products for the studied groups is ≈67%, it is possible to calculate the average capacity of a 100 g portion of a randomly consumed product from the above list of food groups. This capacity, based on a dry weight of 33.1 g, is 837.43 equivalents (761–914 equivalents within the 95% CI). No less important in this case will be the method of processing (cooking) food, which is taken into account to a certain extent when compiling diets for the treatment of a number of pathological conditions.

Evaluation of antiradical daily capacity requires additional research. However, taking the standards of human daily needs for food components [3], we recalculated these values and brought them to the same form as the data in the FNDDS table. The results of the ANN prediction for these data are shown in

Table 5. ARP values predicted by the ANN per gram of dry matter according to recommended daily human requirements taken from the Codex Alimentarius and recommendations according to Russian and American Academies of Sciences, WHO and FAO [3].

No.	Recommendation According to	Daily Calorie (Kcal)	Predicted Values per Gram at 95% CI (Mean)
1	American Academy of Sciences	2000	21.43–26.90 (24.17)
2	American Academy of Sciences	2500	21.52–26.91 (24.22)
3	Codex Alimentarius (WHO and FAO)	2300	30.02–35.92 (32.97)
4	Research Institute of the Russian Academy of Medical Sciences	2500	20.69–26.21 (23.45)

.

ARP values predicted according to the data of the Academy of Sciences of Russia and the USA do not differ from each other within the 95% confidence interval. A slight decrease in the values in the first case (ceteris paribus) is apparently a consequence of the presence of polyunsaturated fatty acids in the recommendations of the Federal Research Center for Nutrition and Biotechnology.

Here, we are faced with one of the contradictions: An increase in the proportion of fatty acids in food according to the ANN is inversely related to ARP values, which reduces the shelf life and stability of food systems. However, polyunsaturated fatty acids improve the nutritional properties of food. In this contradiction, in our opinion, two mutually exclusive trends in the modern food market can be traced—the unification of raw material parameters in mass production, and, conversely, attempts to develop individualized approaches to human nutrition [48,49].

As for the predictive data obtained on the basis of positions taken from the Codex Alimentarius, their higher value is primarily a consequence of the fact that, in this literary source, mainly the amount of proteins is normalized (they account for more than 90% of the dry weight of the recommended average daily components). These proteins have sufficient ARP [29], but since the total amount of plastic substances specified in the code is lower, the total ARP value of all daily food consumed will also be lower. Thus, for example, the total potential for data on the average daily human requirement according to the American Academy of Sciences is from 10.0 to 15.7 thousand equivalents within the 95% CI (for the minimum and maximum calorie values from Table 5). According to the Russian Academy of Sciences, the total potential varies from 12.3 to 15.6 thousand equivalents. However, the data obtained on the basis of the Codex Alimentarius are an order of magnitude less—from 1.6 to 1.9 thousand equivalents—first due to the absence of a number of items, such as fats, carbohydrates, dietary fiber, etc., which reduces the total dry weight (as noted above) used for calculations.

In view of the fact that an excess of free radicals has a pathogenic effect on human health, and in some conditions contributes to an even greater chronicity and severity of the course of the disease, it would be most optimal to divide all the studied foods in relation to reference values (average daily recommendations). To do this, we average the values of confidence intervals given in Table 5. They are 23.41–28.98 equivalents per gram of dry weight. As a result, all products are divided into three groups: products with a low ARP value (below the 95% CI), with a moderate value (falling into the 95% CI) and with high potentials (above the 95% CI). The low ARP group accounts for ≈69.6 to 71.7% of the studied items: eggs, omelets, fish, meat products, marine invertebrates, rolls made from them, cheeses, some types of boiled and fried vegetables (for example, potatoes), highly processed canned food from vegetable raw materials, some types of pasta and macaroni. Average ARP values for this group are ≈9.7 equivalents per gram dry weight of the product (Figure 3).

The second group includes slightly less than 2% of all positions (depending on the type of processing): a part of fish products, canned food and vegetables, some sports nutrition products, and only one type of meat products Mean values for this group were 25.6 equivalents. The last group accounted for approximately 29.5 to 31.4% of all positions. These include fresh fruits and vegetables, in which, due to high concentrations of certain vitamins (for example, ascorbic acid, B vitamins, etc.), there is an increase in the values of predicted antiradical properties. Thus, it can be expected that low-processed food and fresh food raw materials are most likely to fall into the third group of products with a high ARP.

Recently, studies on the epidemiological relationship between the component composition of food systems and the presence (absence) of chronic diseases in humans have been regularly published [40,41,50]. This topic is closely related to food engineering, but as mentioned above, massive amounts of data complicate the analysis of the influence of food factors both on each other and on human health. Nevertheless, knowing the average ARP values of various food groups and the recommended average daily values, one can make an approximate prediction of the insufficiency/excess of the antiradical potential during long-term human consumption of certain foods (food habits, diets, fast food, highly processed food, etc.).

On the basis of the predictive data presented by us, it could be assumed that antiradical properties of food are mainly influenced by processing methods and the type of a raw material, which in principle makes it possible to take into account only the average chemical composition of food components. However, this approach clearly simplifies the forecasting problem.

To date, evidence has accumulated of a decrease in the nutritional value of foods for at least the last 50 years. Reductions in concentrations (statistically significant) of both mineral (Cu, Zn, etc.) and organic food substances (ascorbic acid, niacin, etc.) are detected by a value from 10% to more than 50% for different components [51]. There is no common explanation of this. Ecological and agricultural reasons (soil depletion, etc.) are indicated; conversely, it is noted that modern plant hybrids produce a larger percentage of carbohydrates in relation to proteins—the “dilution effect” (including due to an increase in carbon dioxide in earth’s atmosphere) [51]. As additional reasons for the decline in nutritional value, one can note the deep processing of raw materials and changes in technological approaches, etc. [50].

Definitely, this problem is complex, but there is a general trend—an intensive fight against absolute hunger, and not so active work to eliminate relative hunger (difficulties in unifying/individualizing nutrition). Such “simple” decisions in the long run can lead to more nutritional problems (obesity, diabetes, etc., including due to a drop in food ARP) than is currently understood.

However, for the purposes of forecasting, such inconsistencies in the parameters of the chemical composition once again complicate the possibilities of their implementation. Moreover, concentration estimates for some components from different literary sources give a spread of tens of times (from 1400% to more than 20,000% for a number of micronutrients) [51], which significantly reduces the accuracy of predictive estimates even with the use of the ANN.

4. Conclusions

In the context of urbanization and a number of other modern challenges (for example, disruption of logistics routes and production during the COVID-19 pandemic, and the chronicity of certain diseases in the population in different countries of the world), activities aimed at improving and developing new types of diets and individual nutrition become relevant. Another applied aspect of this direction is the development of new technological approaches to food security, which will be extremely difficult to implement without the use of mathematical data processing tools, such as artificial neural networks.

In rapidly changing socio-economic and environmental situations, it is important for the customer to receive feedback in a timely manner. This becomes practically impossible without the creation of systems for monitoring the nutrition of a person or his local populations with the function of automated issuance of recommendations or adjustments in food intake.

Ultimately, the researcher must have not only the chemical composition of food products at his disposal, but also information on all procedures associated with the cultivation and processing of primary agricultural raw materials, including genetic passports for breeds and varieties, data on environmental growing conditions or cultivation technologies characteristics, etc.

Currently, the number of papers containing conclusions based on meta-analyses of data from other authors has increased, which in turn does not exclude the possibility of technical or substantive errors, primarily due to an increase in the volume of literature sources that need to be cited.

In the longer term, researchers conducting data from meta-analyses, as well as conventional studies, may face the “data redundancy nightmare”, making it extremely difficult to collect the entire volume of values, or having to sacrifice the accuracy of predictions. However, in any case, the complication of systems and the accumulation of values (including those of the ARP) will push researchers to use neural networks, including to identify new interdisciplinary connections.

Our results have shown the possibility of isolating the contribution of individual components to ARP values, which is important when creating new food products that prevent free radical pathologies (enrichment of foods with dietary fiber, cryptoxanthin, potassium, etc.). In addition to the above, a high contribution of B vitamins to the ARP was noted, which will make it possible to use these components to correct the nutrition of people with disorders of the folate cycle and sulfur-containing amino acids (methionine, cysteine, cystine and homocysteine).

We believe that by now there is a need to develop new systems in human food security, i.e., an approach to obtaining recommendations calculated using ANN, taking into account data on the chemical composition, the ecological situation of growing food raw materials, the risks of developing individual intolerances (including genetically determined), and epidemiological data on diseases caused by the consumption of certain types of food. It is also equally advisable to take into account the data on the relationship between food ARP and the epidemiology of diseases with a free radical mechanism of origin, where the results obtained by us in this study can be applied.