-The article presents a fragment of the generalized structural and parametric model of adequate nutrition of a healthy person, describing in a matrix form a priori known data and knowledge about characteristics of a person's condition and their relationship with environmental factors and dietary and nutritional parameters. The algorithm of identification of an abnormal condition of a person and search for the root cause of deviation from norm is shown. To assess the adequacy of diet options in the information technology of its structural optimization, it is proposed to use a quality functional reflecting the weighted average total deviation of actual values of the chemical composition parameters from FAO/WHO norms. The use of information technologies implemented by multicriteria optimization and mathematical programming methods will make it possible to adjust and optimize diets according to various quadratic criteria of minimum deviation from the reference structure of a variety of indicators of nutritional, biological and/or energy value. The resulting set of alternative dietary options shall be structured to establish an optimal diet of a given quality, composition and properties, taking into account biomedical requirements addressing parameters of a certain group of people, structural relationships and limitations at the component, elemental and monostructural levels.
According to the World Health Organization [1], adult overweight and obesity rates are increasing in almost all countries and regions; in 2016, 1.3 billion people were overweight, of whom 650 million (13% of the world population) were obese. Obesity is a serious risk factor for diabetes; cardiovascular diseases (mainly heart disease and apoplectic attack); musculoskeletal disorders (especially osteoarthritis, a degenerative joint disease with severe disabilities); and certain forms of cancer (including endometrium, breast, ovary, prostate, liver, gallbladder, kidney and colon cancer).
According to a WHO report [2], increased attention must be paid to ensuring optimal diet at every stage of human life. It is estimated that 3.7 million lives can be saved by 2025 by allocating necessary resources to address nutrition problems. In the human body, there is practically no organ or system which normal functioning does not depend on nutrition.
The Russian Federation has a number of legislative documents that provide guidelines for the organization and monitoring of the nutritional status of the country's population. Support and promotion of human health is impossible without adequate nutrition. Constant disruption of dietary regimen inevitably leads to pathological changes in vital functions. This is due to the deep influence of nutrition on all biochemical and physiological processes in the human body. It is this fundamental influence that underlies any diet therapy – therapeutic nutrition – for the treatment and prevention of various diseases. When recommending a diet, a nutritionist should use not only biochemistry data (protein, carbohydrate and lipid statuses, immune indicators, biochemical blood analysis), physiology (weight deficit, activity and injury factors), nutrition hygiene (volume, weight, consistency and temperature of food), but also take into account individual parameters (age, anthropometric data).
The mathematical apparatus is widely used in the analysis of nutrition problems [3 - 9], principles of food combinatorics in the design of combined food products [10, 11]. To solve the issue of adequate nutrition, corresponding to the needs and capabilities of the human body and balanced in all indicators of nutritional and biological values it is necessary to process large data sets.
Actual and reliable information on the chemical composition of food products and dishes should be stored in databases. The structure of a database should provide for the division into clusters, for example, “Porridge”, “Soups”, “Vegetables”, etc. Clusters are necessary for the subsequent distribution of food and dishes included in the diet into individual meals according to the time. Along with this, it is necessary to take into account the division into clusters according to different characteristics, for example, allergenicity (does the product contain an allergic component), etc.
This article presents the methodology of construction of the structural and parametric model of adequate nutrition, reflecting the variety of existing known and unknown links between the factors of a person's health condition and characteristics of his/her diet; development of information technologies in the system of healthy adequate nutrition for defined groups of people taking into account the metabolism of nutrients (ethnic affiliation, cultural preferences, health status, lifestyle, and clinical factors) of the available traditional products for the region. Creation (selection) of an individual (personal) diet and dietary regime is carried out on the basis of models and methods of multicriteria structural and parametric optimization and objective evaluation of the adequacy of proposed options with the help of computer technologies of processing and formalization of knowledge with finding optimal solutions.
Structural and parametric modeling of systems [12, 13] of any physical system and social nature is reduced to the development of interaction matrices between the grouped parameters of state and purpose of individual functional blocks of the system similarly to the parametric adjacency matrix. At that, the main task is to find comparable characteristics of the relationship between parameters of a person’s condition of health with the subsequent development of a situational model of the state of the system with the algorithmization of procedures for its identification and forecasting.
The structural and parametric model of adequate nutrition reflects the functional relationship between characteristics (parameters) of a person's condition and his/her diet, reflecting many specific factors and links that determine the goals, purpose and use of developed diets and dietary regimes for specific defined consumer groups.
Classification of population groups in combination with characteristics of physiological condition, anthropometric data, parameters of motor activity and biomedical requirements allows developing the information map of the condition of a person, reflecting his/her parametric description with selected groups of characteristics and properties.
All physiological characteristics can practically be determined in the process of medical examination of a particular person or a specialized group of people. For example, biochemical blood test is necessary to determine carbohydrate, lipid and protein metabolism.
Finding all the indicators within the limits of the permissible norm indicates that a person receives necessary and sufficient amount of food substances, nutrients and energy with food.
The parametric description of a diet contains a set of parameters of food, biological and energy values, as well as indicators of carbohydrate, vitamin and mineral compositions.
The parameters of two main blocks of the system of adequate nutrition – health condition of a person х1÷х16 and his/her diet х17÷х29 in the form of main integral characteristics, indicators of chemical composition and properties are placed along the main diagonal.
If the state parameters are independent or if there is no reliable information about possible relationship between them, the corresponding non-diagonal cells of the matrix remain empty. If there is relationship between the parameters, the non-diagonal elements marked in Fig. 1 by points reflect the presence of links between the parameters of a particular person's condition (height, weight, heart function, etc.) and the characteristics of the nutrition system, both within the group and between groups (non-diagonal blocks). Expert estimates, correlation and multiple regression coefficients; impact estimates found in the result of active experiments, as well as possible functions, ratios and conversion algorithms may characteristics of relationships. be used as formalized
For example, Fig. 1 demonstrates that the metabolism of carbohydrates, heart and lungs functions depend on the intake of vitamin B1; the content of vitamin B6 influences the metabolism of amino acids and fatty acids and the functions of the nervous system; folic acid (folate) influences the maturation of red blood cells, synthesis of DNA and RNA; calcium makes impact on blood clotting, functions of the nervous and muscle systems, heart function; phosphorus influences functions of the muscle and nervous systems; magnesium - energy generation, acid-base balance, etc.
From [14] it was established, for example, that parameters of nutritional value х17÷х19 affect a person's anthropometric data, performance, functions of the central nervous system, immunity and recovery (renewal) of cells. Energy value has an impact on all factors of a person's condition x1÷x16.
Identification of the state of a person's nutrition system comes down to diagnosing the causes of its occurrence, predicting its further state, analyzing and evaluating possibilities of achieving the goal.
The identification algorithm contains (Fig. 2) a block of formation of the situation matrix and the procedure for finding the causes of the anomalous state of the system.
The procedure is a cycle of iteration of independent deviations, within which the maximum element in a line is searched for, its ordinal number p is remembered and transition to the p-th line takes place followed by a new search for the maximum element of this line [13].
To detect possible looping of cause-effect relationships, an array of tl indices of diagonal elements included in the interaction trajectory is formed, and when two elements of this array match, it is followed by a “cycle” signal. In this case, the cause may be inside or outside the cycle circuit. To exit the cause-effect cycle and continue to search for the original cause, the last link of feedback is broken, i.e. element Sgp=0, with its value fg=Sgp and addresses memorized in index arrays Indg1; Indg2. Then when iterating over the elements of the g-th line, the procedure will either stop at the last link of the cycle (if the reason lies within the cycle circuit) or go further through the steps of a new cycle (Fig. 2). When moving to the detection of the causal chain of the next k+1-th consequence, the interrupted link of the j-th cycle of the previous trajectory of the links is restored, i.e. SIndj1, Indj2=fj.
To find the influence of other factors on the next k-th consequence, the first maximum contribution to its deviation is set equal to zero and the next largest element of the k-th line is selected, i.e. the next largest contribution to the k-th consequence.
All abnormal values of indicators are kept in the array of deviations from the norm and based on the knowledge base a person is provided with the initial selection of products in the recommended diet, which compensates for existing deviations taking into account individual characteristics of the patient and social conditions (personal perception of certain product, presence of allergies, as well as availability of specific products due to material or geographical factors).
If there is insufficient compensation for deviations by selecting the desired products and dishes included in the diet, a search should be made for their optimal quantitative ratios (structural optimization) with the possible introduction of additional products and dishes depending on the current deviations of parameters from the norms or the development of an individual combined product that minimizes residual deviations.
The structural and parametric model (Fig. 1) includes the adequacy functional (x30), which assesses the degree of deviation of the current diet from the reference models of a particular type of diet: children, school, student, adult, elderly nutrition, etc. Taking into account the breakdown of many factors into groups of properties, the adequacy functional of the diet is as follows:
m k G
x i0j where zij is the relative deviation of the j-th factor in the i-th group; х , 0 , 0 is the actual, reference and permissible deviation from the norm of the j-th parameter in the i-th group, respectively; , are the factors of significance of the i-th group of factors and the j-th factor in the i-th group, determined by methods of expert estimates or by factor experiment; is the relative deviation of the k-th factor of the critical group, which deviation beyond the tolerance turns the functional to 0.
The functional varies from 1 with full adequacy of the diet to 0 at the limit of the allowable area and turns to 0 when any parameter of the critical group exceeds the maximum allowable value.
Thus, the structural and parametric model of adequate nutrition reveals the structure of links between parameters and factors affecting the health of a particular person, the use of which is necessary to develop or correct certain indicators of the daily diet and recommendations for a person’s dietary regime.
The procedure for assessing the diagnosis of a person’s condition comes down to the formation of the structural and parametric situational model [12] of an abnormal condition of a person and the search for reasons for deviations of his/her condition parameters from the FAO/WHO standards.
Based on the maximum deviation of the parameter of condition from the norm (for example, ∆х7 - function of the nervous system), it is necessary to identify all causes of this deviation (for example, fat, vitamin B6, vitamin B12, calcium, magnesium) and choose the most significant one (e.g. fat). This is followed by a change in diet with a selection of foods and dishes that minimize the identified imbalance with maximizing the functional adequacy of the diet.
As the objective function a hierarchy of quadratic criteria
of the minimum deviation from the reference structure of a
variety of indicators of food, biological and/or energy values
presented in a generalized form as an adequacy criterion is
used:
n m
B k0 b kj y j min (
y mjin y j y mjax ; j 1, m (
As criteria or limitations one can also use digestibility, action selectivity, adequacy of chemical composition and energy value of nutrition to the volume of diet and agerelated needs of human body, etc. as follows: - protein digestibility criterion m j b j y j P 0 j 1
m j1b j y j 2 min (5) where π0 is protein digestibility in a reference product, mg. of tyrosine/g. of protein; πj is digestibility of the j-th component protein, mg. of tyrosine/g. of protein; - protein nutrition adequacy criterion
PBA
AZOT M 100 % max
under
AZOT M AZOT BAL BELOK VVED 4 max (7)
6 .25
where PBA is protein activity indicator (%); AZOTM is blood
urea nitrogen (g); AZOTOB is total nitrogen (g); AZOTBAL is
nitrogen balance (g/day); BELOKVVED is introduced protein;
(6)
- albumin deficiency criterion
n
alb 0 alb i 2 min (8)
i 1
where n is number of patient observations; alb0 is standard
albumin levels in a patient’s blood; 30 (g/l) ≤ alb0 ≤ 35 (g/l)
mild deficiency; 25 (g/l) ≤ alb0 ≤ 30 (g/l) - moderate
deficiency; alb0 < 25 (g/l) - severe deficiency; albi is albumin
levels in a patient’s blood at the i-th observation (g/l);
- transferrin deficiency criterion
n
Trf 0 Trf i 2 min (9)
i 1
where n is number of patient observations; Trf0 is standard
transferrin levels in a patient’s blood; 1.8 (g/l) ≤ Trf0 ≤ 2.0
(g/l) - mild deficiency; 1.6 (g/l) ≤ Trf0 ≤ 1.8 (g/l) - moderate
deficiency; Trf0 < 1.6 (g/l) - severe deficiency; Trfi is
transferrin levels in a patient’s blood at the i-th observation
(g/l);
- lymphocytes deficiency criterion
n
Lmf 0 Lmf i 2 min (
In (7) - (
and proposed rations' parameters is reduced to multicriteria optimization with the formation of a Pareto-optimal set of solutions according to the above formalized criteria.
The algorithm of diet structured optimization by partial criteria:
n
B k0 b kj y j min; k 1, m (
j 1
includes a sequential determination of the imbalance by the
k-th element under limitations (
In case of redundancy, the structural shift is vice versa.
By redistribution of mass fractions of the selected product
pair to and we obtain a new improved value of
the partial criterion (5). The size of redistribution of mass
fractions of components is selected based on the limitation
(
The procedure continues until all the possibilities of
redistributing the mass fractions of the components are
exhausted, resulted in obtaining an alternative diet with a
minimum deviation of the k-th element from the specified
standard value in the adequate nutrition assortment
structure. The choice of the optimal alternative from the
found Pareto-optimal solutions set corresponds to the
minimum value of the global adequacy criterion (
In order to support a healthy lifestyle and maintain health, it is necessary to develop a decision support system for the development and correction of adequate dietary regimes taking into account human metabolism. The authors propose the creation of a computer system of optimization of the current diet and preparation of a new diet for a person (user) based on the principles of adequate nutrition, mathematical methods and information technologies.
The information basis of the system is a database (DB) of products and dishes, being most common and sold in large cities and metropolises. The construction of multidimensional parametric models begins with the creation and filling of a database (DB) of reference information necessary both for constructing parametric and mathematical models of healthy food products and for assessing adequacy.
The database structurally displays physical and chemical parameters of raw materials, products of animal and plant origin, optimization criteria and adequacy assessment, recommendations and norms of food nutrients and energy consumption, ensuring the selection of raw materials that meet the specified requirements.
The structure of the information subsystem has been developed - a database of the main physicochemical characteristics of food products, such as calorie content, vitamin quantitative composition, chemical composition (proteins, fats, carbohydrates, and minerals), fatty acid compositions, and essential amino acids per unit mass of products, which is presented in Fig. 3.
With each day, the integration of nutritional science with engineering sciences, in particular with food technology, is increasing, which creates opportunities for the development of new progressive methods and techniques for developing products with a given chemical composition, specialized products, as well as personalization of diets [15]. Application of information technologies implemented by methods of mathematical programming allows optimizing diets according to different criteria and making an informed decision in determining optimal composition of the diet, taking into account all specified properties and limitations. Analysis of the structural and parametric model of adequate nutrition of a healthy person in a matrix form allows assessing the diagnostics of a person's condition, revealing abnormal conditions and reasons for their occurrence.
This article is published as part of scientific research theme No. 0585-2019-0008 under the state assignment of the federal state budgetary scientific institution ‘V.M. Gorbatov’s Federal Research Centre for Food Systems’ of RAS.