The mathematical pathogenetic factors analysis of acute inflammatory diseases development of bronchopulmonary system among infants

Materials and methods. The examination group consisted of 59 infants (average age 13.8 ± 1.4 months) sick with acute inflammatory bronchopulmonary diseases. Also we tested the level of 25-hydroxyvitamin D (25(ОН)D), vitamin D-binding protein, hBPI, cathelicidin LL-37, ß1-defensins, lactoferrin in blood serum with the help of immunoenzymometric analysis. Selection of prognostically important pathogenetic factors of acute bronchopulmonary disease among infants was conducted using ROC-analysis. The procedure for classifying objects was carried out using Hierarchical Cluster Analysis by the method of Centroid-based clustering.

Математический анализ патогенетических факторов развития острых воспалительных заболеваний бронхолёгочной системы у детей раннего возраста Г. А. Леженко, Е. Е.The respiratory diseases are among the most important problems in pediatrics, because so far, they take the first place in the structure of infant morbidity [11].Every year the number of children, who are hospitalized with acute bronchitis increases, which complicates the flow of acute respiratory disease every year [8].Among the factors that raise the risk of heightened respiratory morbidity, are determined these: the mother age, abnormal pregnancy, prematurity, purulent-septic diseases in the neonatal period, prenatal CNS lesions [4].In addition, the risk of infectious and inflammatory diseases of bronchopulmonary system among infants increases due to protein-vitamin deficiency and past diseases (rickets, anemia), environmental pollution, stress in the family, which lower the organism's resistance to respiratory pathogens [12].
Recent studies show the pathogenetic importance of endogenous antimicrobial peptides in the formation of the inflammatory process in various forms of pathology [2,5,14].It is known that antimicrobial peptides act as a first line of defense when respiratory pathology is present [17].The antimicrobial peptides, as a component of innate immunity, act as a natural defense against a wide spectrum of microbes.Considering the representation of antimicrobial peptides in many organs and systems of humans and their multidirectional action, it is certainly interesting to study their pathogenetic role in the development of acute bronchopulmonary disease in infants.
It is known that the production of antimicrobial peptides, including defensins and catelicidin, is strengthened by the presence of vitamin D [15].Currently, there is evidence that 1.25 (OH) 2D regulates the effectiveness of the immune response and has anti-inflammatory effect [3].The connection between vitamin D deficiency and the incidence frequency of respiratory disease is detected [13,23].In Wayse V. and all studies (2004), the increasing of serious lower respiratory tract infections risk among children with subclinical deficiency of vitamin D, was shown [22].
Considering the diversity of the mechanisms of infectious-inflammatory process in bronchopulmonary system formation, significant interest is the associative interaction between the individual sections of pathogenesis, determining the development of acute respiratory infections among infants.One of the possible and most effective ways to study complex systems is the use of factor analysis [10].
The purpose to study the factor structure and to establish the associative interaction of pathogenetic links of acute diseases development of the bronchopulmonary system in infants.

Materials and methods
The examination group consisted of 59 infants (average age 13.8 ± 1.4 months), of which 46 patients were diagnosed with acute bronchitis and 13 patients -community aguared pneumonia.The control group included 20 healthy children, resembling by age.Verification of the diagnosis was conducted in accordance with the criteria for the diagnosis of acute bronchitis (Order of the Ministry of Health of Ukraine № 18 dated December 31, 2005 "The protocol of treatment for children with acute bronchitis") and pneumonia among children (Ministry of Health of Ukraine № 18 dated December 31, 2005 "The protocol for treatment for children with pneumonia").During the collection of the anamnesis, particular attention was paid to the peculiarities of the process of antenatal intranatal and neonatal periods, as well as the form of child feeding.A mandatory complex of examination included chest organs roentgenography, a general blood test examination, general urinalysis, blood chemistry test of glucose, total protein, total bilirubin, thymol test, ALT, AST, electrolytes (potassium, calcium, sodium, phosphorus).Also we tested the level of of 25-hydroxyvitamin D (25(ОН) D), vitamin D-binding protein, bactericidal protein that increases the permeability of cells (hBPI), cathelicidin LL-37, ß1-defensins, lactoferrin in blood serum with the help of immunoenzymometric analysis.
Selection of prognostically important pathogenetic factors was conducted using ROC-analysis of acute bronchopulmonary disease among infants.A zero degree of prediction of the indicator was established at an area under the ROC curve with 0.5 c. u. and less [6].
In order to determine the least possible number of hidden common factors, that affect the most the occurrence of acute diseases of the bronchopulmonary system in children and their factor loads, a factor analysis was conducted.The basis for modeling for the selection of factor complexes Spearman correlation matrix was chosen with the subsequent determination of the vector load of the indicators that were studied.Significant factors in the model were studied using the scree plot criterion and the Kaiser criterion [9].For exponent sampling with a high factor load on the complex (more than 0,6), the method of orthogonal rotation VARIMAX was used.The factor analysis using VARIMAX rotation was performed along taking into account the results of the initial analysis and using it to describe the dispersion of the data array of the main components [9].
The procedure of classifying the objects was conducted using the Hierarchical Cluster Analysis by the method The measure of the distance between the formed clusters was Euclidean distances [9].Received results were processed with using the statistic package of a licensed program Statistica ® for Windows 6.1.RU", serial number AXXR712D833214SAN5 and "SPSS 13.0" for Windows.The differences were considered meaningful, if р < 0.05 for all kinds of analysis.

Results of the research and discussion
Based on the results of the ROC-analysis, 15 potential predictors of the development of acute inflammatory diseases of the bronchopulmonary system, among infants, were selected, which included the age of the child, the course of the antenatal period, the nature of nutrition (natural or artificial), the parameters of the general blood test (the level of red blood cells, hemoglobin, leukocytes, ESR), serum levels of total protein and calcium, and vitamin D, vitamin D-binding protein, bactericidal protein that increases the permeability of cells (hBPI), cathelicidin LL-37, ß1-defensins, lactoferrin.
According to the analysis of the Spearman rank correlation matrix in the group of infants with acute diseases of the bronchopulmonary system, the presence of certain integrations between prenatal, metabolic and immune factors was indicated (Table 1).This way, the pathological flow of mother's pregnancy had an effect on the level of vitamin D-binding protein in the child's blood serum.Also, the associative interaction between cathelicidin and lactoferrin in serum levels and ß1-defensins was indicated.
In order to determine the factors, which that most affect the occurrence of acute diseases of the bronchopulmonary system in infants, as well as their factor loads, the correlation matrix exponents were analyzed with factor analisys.Conducted analysis of correlation integration of 15 indicators, that can influence the development and the flow of acute disease among infants, allowed to determine and rank "latent" factors (the main components) in terms of their effect on the pathological process in the bronchopulmonary system.After the initial analysis, the main components with proper numbers greater than 1.0 were distinguished (Table 2).
The proper number of the first 6 main components exceeded 1.0 and their summary contribution in the total variance was 66.9 %, with the first 4 main components accounting for almost half (48.9 %) of the total load.This indicated that these factors determine the major part of the pathogenetic factors of acute bronchopulmonary pathology in the examined patients.Then, a matrix of factor loads was determined using the principal component method (Table 3).
In accordance to the obtained data, the main factor was determined by the parameters of hemoglobin and erythrocytes (factor load, accordingly, 0.885 and 0.877) among infants with acute bronchopulmonary pathology.Conditionally, the first factor was designated as "the anemia factor".The received data are logical, if we consider the fact that any anemia leads to a decrease in the respiratory function of the blood and the development of oxygen starvation of the tissues, which leads to a more severe and protracted flow of the disease.
In this case, in the clinical picture, the signs of respiratory insufficiency appear to the forefront.This factor explains 13.6 % of the total variance.
The integration of the second factor, which in the total dispersion was 13.0 %, characterized the ESR (factor load 0.812) and the level of leukocytes in the blood (factor load 0.719).This factor we can call "the factor of inflammation".
In the structure of the third factor which was designated as the "the maternal factor" and accounted for 12 % of the total variance, the most load had the indicators of the child's age (0.795) and the antenatal period (0.617).
In the fourth factor, the integration is divided into two parts: negative (total protein: -0.712) and positive (vitamin D: 0.778).It is known that the activation of protein synthesis occurs with the participation of vitamin D, which in addition to participation in the mineral metabolism regulates the effectiveness of the immune response and has an anti-inflammatory effect [3,20].The factor was defined as "the vitamin D supply factor".
The fifth factor was "the immune factor" which was determined by two variables (the lactoferrin and ß1-defensins).These antimicrobial peptides are the main components of nonspecific protection of the respiratory tract and act as the main proteins of natural immunity [1,16].When the expression of antimicrobial peptides is compromised, the risk of developing infectious diseases increases [7].

Оригинальные исследования
In the sixth factor, one variable is defined, precisely the level of calcium in the blood with a factor load of 0.840.The established factor was named as "the calcium exchange factor".Calcium ions have an important place in immune processes.On the one hand, each population of immunocompetent cells has a calcium dependent activation mechanism [21].On the other hand, excessive calcium saturation of cells closes the transmembrane channels and makes the cytomele impermeable [19].Because of this, the deviation of calcium concentration in blood can negatively affect the vital activity and activity of immunocompetent cells and, as a consequence, reduce the resistance of the organism [18].
Thus, the development of acute diseases of the bronchopulmonary system among infants occurs in a dynamic interaction of a number of factors.On the basis of the factor analysis, a formation of a pathological process model was formed, which is associated with 6 different conditions.The data of factor analysis, confirmed a priority contribution to the development of acute bronchopulmonary pathology, the presence of anemia, immune disorders, the state of provision with vitamin D and calcium, and the course of the antenatal period.
Based on the obtained data of factor analysis, a cluster analysis of the main pathogenetic factors was performed.According to the results of hierarchical cluster analysis, 2 clusters were allocated in the sample of pathogenetic factors of development of acute bronchopulmonary pathology among infants (Fig. 1).
The conducted cluster analysis shows that at the initial stage an associative interaction between the indicators of red blood is formed with the subsequent addition of calcium level indices and the total protein of the blood.The level of these components is affected by the unfavorable course of the antenatal period (cluster 1).
Then, based on the results of the cluster grouping, an agglomeration was formed which was made up of lactoferrin, ß1-defensins, vitamin D, the index of ESR and the level of leukocytes in serum (cluster 2).The resulting structure is displayed in a hierarchical tree of different branches and a certain cluster emphasized the initial role of immuno-inflammatory components in the development of respiratory diseases among infants.The recieved line interactions were completed by indicator of child's age, which formed a common agglomerate with these parameters.With all this, the components of the formed clusters not only logically complemented each other, but also indicated their pathogenetic role in the development of the broncho-pulmonary system among infants.
So, the results of conducted factor and cluster analysis were of interest for determination the main indicators when predicting the possibility of developing of acute inflammatory diseases of the bronchopulmonary system in infants.

Сonclusions
1.The highlighted factors allowed to define a group of parameters, that must be influenced to achieve a maximum effect in carrying out preventive and therapeutic measures.
2. When developing therapeutic measures, that are aimed at preventing the occurrence of acute inflammatory diseases of the bronchopulmonary system in infants, first of all, it is necessary to influence the "the anemia factor" The age of the child 0.795 The leukocytes level 0.719 The calcium 0.840 The total protein -0.712 The vitamin D 0.778 The lactoferrin 0.601 The ß1-defensins 0.731 The hemoglobin level 0.858 The red blood cells 0.877 The pathology of the antenatal period 0.617 ESR 0.812

The hemoglobin
The red blood cells

Original research
and "the calcium exchange factor" as well as "the vitamin D supply factor", meaning to correct vitamin D deficiency and carry out measures aimed to prevent the development of anemia.
3. Taking into account the fact that the unfavorable course of the antenatal period is one of the risk factors for the development of acute bronchopulmonary diseases in infants, then those activities, aimed at the prevention and treatment of the pathological course of pregnancy will help stabilize the "the maternal factor" in the future.
The prospects.In the future we plane to analyze the peculiarities of the flow of acute bronchopulmonary diseases among infants, taking into account highlighted pathogenetic factors with the justification of preventive measures aimed at preventing their occurrence.
based clustering.Hierarchical clustering was based on the unification of the most similar objects and was completed by the construction of the dendrogram.

Fig. 1 .
Fig. 1.The cluster analysis dendrogram of leading pathogenetic factors of development of acute inflammatory diseases of the bronchopulmonary system among infants.

Table 1 .
The correlation matrix in the group with acute inflammatory diseases of the bronchopulmonary system in infants

Table 2 .
The factor analysis of indicators that affect the development of acute inflammatory diseases of the bronchopulmonary system among infants

Table 3 .
The calculation of factor loads on indicators that were studied among infants with acute bronchopulmonary pathology