=Paper=
{{Paper
|id=Vol-2631/paper32
|storemode=property
|title=Modeling and Predicting the Organochlorine Pesticides Concentration in the Child’s Body Based on their Accumulation in the Mother’s Body
|pdfUrl=https://ceur-ws.org/Vol-2631/paper32.pdf
|volume=Vol-2631
|authors=Violetta Demchenko,Serge Olszewski,Mariia Voronenko,Eva Zaets,Nataliia Savina,Iryna Lurie,Volodymyr Lytvynenko
|dblpUrl=https://dblp.org/rec/conf/momlet/DemchenkoOVZSLL20
}}
==Modeling and Predicting the Organochlorine Pesticides Concentration in the Child’s Body Based on their Accumulation in the Mother’s Body==
https://ceur-ws.org/Vol-2631/paper32.pdf
Modeling and Predicting the Organochlorine Pesticides
Concentration in the Child’s Body Based on their
Accumulation in the Mother’s Body
Violetta Demchenko1[0000-0001-6239-0882], Serge Olszewski2[0000-0003-4499-8485],
Mariia Voronenko3[0000-0002-5392-5125], Eva Zaets1[0000-0002-8503-2487],
Nataliia Savina4[0000-0001-8339-1219], Iryna Lurie 3[0000-0001-8915-728X],
Volodymyr Lytvynenko3[0000-0002-1536-5542]
1
State Institution «Kundiiev Institute of Occupational Health of the National
Academy of Medical Sciences of Ukraine», Kyiv, Ukraine,
2
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
3
Kherson National Technical Unіversity, Kherson, Ukraine,
4
National University of Water and Environmental Engineering
Rivne, Ukraine
chemioh@ukr.net,olszewski.serge@gmail.com,mary_voronenko@i.ua,
eva512@gmail.com, n.b.savina@nuwm.edu.ua, lurieira@gmail.com,
immun56@gmail.com
Abstract. This paper describes the problem of developing a model of a poly-
nomial neural network and applying it to predict the concentrations of
organochlorine pesticides in a child’s body on the basis of their accumulation in
the mother’s body. The results of the use of the developed models showed that
the dependence of the concentration of organochlorine xenobiotics in the
child’s body on its concentration in the mother’s body is non-monotonic. The
developed models of the polynomial neural network allowed us to establish a
critical interval at which an explosive transfer of persistent organochlorine
xenobiotics takes place.
Keywords: Self-Organizing Modeling, Polynomial Neural Network, Model
Validation, Organochlorine Pesticides, Persistent Organic Pollutants,
Biomonitoring of Exposure Environmental Exposure, Pesticides Exposure.
1 Introduction
Environmental pollution by persistent organic pollutants (POPs) is one of the global
environmental concerns. These compounds are very resistant to degradation proc-
esses, they have the ability to bioaccumulate and biomagnify, as a result of which
they can accumulate in significant concentrations in the higher links of food chains
even at low levels in the air, water, and soil. These features served as the basis for the
fact that most of the organochlorine pesticides are classified as POP.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
Environmental pollution with stable organochlorine pesticides (OCPs) is a serious
environmental problem that is closely linked to health issues, as POP adversely af-
fects the human body, having a toxic effect of a broad nature. The most sensitive indi-
cator of assessing the health status of a population and the influence of environmental
factors on it are indicators of the health of newborns, in particular, the prevalence of
congenital malformations.
POP adversely affect human health, they cause changes in the neuroendocrine,
immune systems, reproduction, and embryonic development. POPs affect the carrier’s
health, penetrate the placental barrier and significantly affect the course and outcome
of pregnancy, fetal development and the health of the newborn, entering the baby’s
body as early as the neonatal period of development with the mother’s blood and
percutaneous fluid with amniotic fluid, in which xenobiotics enter breaking the pla-
cental barrier. Subsequently, the baby's load continues in the postnatal period: first,
mainly with breast milk of the mother, and then - due to persistence and global preva-
lence in the environment with a diet. Changes in reproductive health indicators can
sufficiently reflect the state of the environment, characterizing the mutagenicity and
embryotoxicity of factors and their ability to suppress the adaptive mechanisms of the
body.
OCPs enter the body of a child even in the neonatal period of development with
maternal blood and percutaneously with the amniotic fluid, into which xenobiotics
enter, overcoming the placental barrier. Subsequently, the effect on the baby contin-
ues in the postnatal period: first, mainly with breast milk of the mother, and then - due
to persistence and global prevalence in the environment with a diet. Earlier, we con-
ducted biomonitoring in the “mother - child” system.
Currently, it is believed that the detection of OCPs in food, air, and water, which
are the main sources of their entry into the human body, is only evidence of its possi-
ble chemical exposure. At the same time, the results of biomonitoring of exposure
(BME), that is, the identification and quantification of xenobiotics in human biologi-
cal environments, is complete evidence of their presence and health risk [1-3]. There-
fore, we conducted a screening with BME-resistant OCPs from among POPs, namely,
those that were determined by us in environmental objects among the adult population
and the children most vulnerable to their negative influence.
2 Problem Statement
The task is to simulate the effect of the content of hexachlorocyclohexane (HCH)
and its isomers and on the composition of the whole blood of the mother and
the blood of her child.
Formally, this problem can be considered as a class of tasks for modeling a
statistical sample that contains information about n observations of m input
variables. The statement of the problem of constructing models from experimental
data can be reduced to searching for the extremum of a certain CR criterion on a
variety of different models :
f * arg min CR( f ) (1)
f
It is clear that (1) does not contain a comprehensive formulation of the problem, so it
is additionally necessary to: specify the type and amount of source information;
specify the class of basic functions (operators) from which the set is formed;
determine the method of generating models f together with a method for estimating
parameters; choose a criterion for comparing models; indicate the CR minimization
method. We refine this statement by assuming that the given sample W = [Xy],
contains n observation points, form the matrix X {xij, i1,...,n; j1,...,m} and the
vector y (y1...ym)T, so n m.
3 Review of the Literature
The results of a study of invasive and non-invasive biological media of the mother
(hair, whole venous blood, placenta, breast milk) and the baby (whole umbilical cord
blood, which is considered the blood of the baby) indicate their multi pollution of
OCPs and their derivatives. There are almost no examples of such complex studies,
with the exception of [4,5]. They are of particular importance for identifying correla-
tive relationships characterizing the processes of xenobiotic transfer from mother to
child. The creation of a mathematical apparatus for their description is of great prog-
nostic value for identifying risks to the health of a nascent child.
In [6], multivariable linear regression models were used to identify the relationship
between the concentration of polychlorinated biphenyls (PCBs), polybrominated di-
phenyl ethers (PBDEs), lead and mercury in maternal blood during pregnancy, and
their content in umbilical cord blood.
In [7], using multiple regression analysis, the relationship between the Kinder In-
fants Development Scale (KIDS) and the levels of 3-phenoybenzoic acid, 3-PBA) of
the maternal urethra was investigated.
In [8], the use of a neural network for determining the concentration of pesticides
in maternal blood during pregnancy and in the umbilical cord blood of a child is de-
scribed. The authors used a combined analysis of prenatal analyzes of mother’s hair
and blood, as well as neonatal tests such as hair, baby’s blood, umbilical cord blood,
and meconium to identify the effects of environmental pesticides on the fetus.
In [9], the concept of developing alternative tools for modelling toxicity and pre-
dicting chemical compounds was described in order to minimize animal tests, costs,
and time associated with registration and risk assessment processes. The concept of
multilevel self-organization for multidimensional modelling, as well as model verifi-
cation, is proposed.In [10], a combined statistical analysis was proposed to identify
the effects of environmental pesticides on the fetus.
Thus, the task of constructing mathematical models for the transmission of POP,
and their metabolites from mother to child becomes relevant. In this paper, to solve
the problem of predicting the transmission of POP and their metabolites from mother
to child, GMDH neural networks are used. It is expected that the use of GMDH-
neural networks will increase the efficiency of the developed model and maintain
sufficient algorithm stability when working with various types of input information.
The purpose of this study is to obtain a model of a polynomial neural network
that reproduces the level of chlorine-containing pesticides such as hexachlorocyclo-
hexane and its isomers to their content in the body of a child of a particular mother.
4 Materials and Methods
In the general case, the process of constructing models from experimental data (1)
includes, first of all, the following main stages:
Fig. 1. General research scheme
4.1 Data
Table 1 comparatively shows the results of capillary gas-liquid chromatography with
electron capture background γ-hexachlorocyclohexane (γ – HCH) and its isomers (α-
HCH, β-HCH) in the whole blood of the mother and her newborn.
Table 1. The content of HCH isomers in the blood of mother and child.
Pair number α-HCH β-HCH γ -HCH ∑ HCH
«Mother-Child» Child Mother Child Mother Child Mother Child Mother
1 0,46 0,27 3,82* 3,57* 2,04 1,53 2,11 17,97
2 0,44 0,08 3,01* 0,29 2,20 0,19 0,91 7,43
3 0,81 0,08 2,61* 0,15 2,74 0,19 1,73 12,59
4 0,58 0,18 2,92* 0,91* 1,33 0,34 0,67 12,08
5 0,41 0,09 1,35* 0,58* 0,67 0,33 1,54 11,58
6 0,72 0,35 2,57* 2,72* 4,81 0,58 1,90 38,08
7 0,60 0,14 0,51* 3,82* 0,71 0,22 4,91 4,51
8 0,35 0,09 0,82* 0,48* 1,10 0,12 2,27 17,92
9 0,73 0,99 0,54* 0,69* 19,93 0,13 3,00 16,66
10 0,86 0,20 0,34* 0,34* 0,22 0,19 1,85 6,04
11 0,39 0,17 2,70* 0,18 0,95 0,19 2,66 22,49
12 0,78 0,38 1,22* 0,53* 1,19 0,35 3,83 18,59
13 0,34 0,12 1,45* 0,46* 0,81 0,35 3,27 24,72
14 0,09 0,07 0,84* 0,31* 1,88 0,13 2,60 13,86
15 0,27 0,17 1,04* 0,54* 0,71 0,15 1,81 15,00
16 0,35 0,12 0,80* 0,40* 0,51 0,14 2,21 12,39
17 0,27 0,12 1,12* 1,96* 1,95 0,26 3,05 14,37
18 0,15 0,21 0,78* 0,64* 0,29 0,20 2,99 17,59
19 0,57 0,05 0,46* 0,28 0,25 0,13 3,55 6,16
20 0,95 0,18 0,54* 0,47* 0,21 0,25 2,54 4,16
21 1,57 0,32 0,65* 0,27 0,49 0,23 1,31 3,77
22 0,15 0,08 1,22* 0,38* 2,47 0,26 1,63 13,67
23 2,23 0,20 0,91* 0,40* 0,39 0,34 1,25 7,57
24 1,16 0,33 0,56* 0,61* 0,41 0,40 0,67 5,35
25 0,27 0,16 0,54* 0,45* 0,44 0,27 2,19 20,31
26 0,57 0,22 0,33* 1,01* 0,43 0,32 10,70 10,06
Note: * - exceeding the reference value
4.2 Method
This method is based on a selection procedure that implements the process of sequen-
tial testing of models from a variety of candidates in accordance with the selected
criterion. Using training with a teacher, the Group method of data handling (GMDH)
allows you to find the functional dependence of the output variable on the most sig-
nificant arguments at the system input. Most GMDH algorithms use polynomials as
support functions. At the same time, it is possible to use other types of nonlinear de-
pendencies, for example, finite-difference, logistic, harmonic, etc. In accordance with
the work of [11-13] method GMDH is the basis of mathematical support for direct
modelling of complex systems with a small amount of experimental data. It can be
expected that GMDH models will allow to obtain sufficiently accurate approxima-
tions for quantitative prediction of the content of organochlorine toxicants in the
body. In general terms, the relationship between input and output variables is repre-
sented by the Volterra functional series, the discrete analog of which is the Kolmo-
gorov-Gabor polynomial [14,15] with a general appearance:
N N N
yi n w wij z j n w z n z j n ... (2)
i 0 i1 j 1 j2 j1 ij1 j2 j1 21
1
N N
... w z n z j n ...z n ,
j 1 j2 j1 jk jk 1 ij1... jk j1 21 jk
1
where wij is the parameters of the polynomial to be evaluated, z j n is the discrete
values of the vector argument z z1 , z2 ,..., z N , N is the dimension of the vector of
T
parameters.
According to the Stone – Weierstrass theorem, it is shown that at some degrees of
arguments arbitrarily high approximation accuracy can be achieved.
Equation (3) underlies the so-called polynomial neural network [16-19]. However, for
practical use, a nonlinear polynomial transformation of the argument vector into a
vector of polynomials is used:
T
z N z , z ,...,M z M (3)
1 2
Here it is important that each of the polynomials i z depends only on the input
signal and other components of the polynomial extension and does not contain free
parameters. The latter favourably distinguishes polynomial networks from popular
and widely used radial-base neural networks. In addition, polynomial networks are
characterized by high learning speeds, due to the fact that their output signal depends
linearly on the parameters. Finally, we have:
M
yi n w wij j z n , i 1, 2,..., N
(4)
i0 j 1
The consideration procedure used in GMDH is the gradual complication of partial
models, ie. models with fewer components are followed by more complex models.
In practice, the described procedure of the GMDH algorithm is only a stage of a
more complex scheme. Here we will consider two main schemes, called multistage
combinatorial GMDH and GMDH-type neural networks.
In fig. 2 presents the results of experimental studies of the content of HCH isomers
in the blood of the mother and her newborn child.
a) b)
Fig. 2. Comparison of the content of γ- and β -HCH in the blood of mother and child for indi-
vidual pairs "mother-child": a) - β-HCH; b) - γ-HCH, mother and β-HCH, child. In both dia-
grams: columns 1 are the results of measurements in the mother's blood, columns 2 are the
results in the child's blood
The results of studies of the mother's body are presented separately for γ- and β-
HCH, for the child considered only β-HCH as the most dangerous, potential carcino-
gen: diagram a) is a comparison of β-HCH in the blood of mother and child (separate
pairs "mother-child"); diagram b) is a comparison of the content of γ-HCH detected in
the mother's body with the amount of β-HCH detected in the body of the child.
Despite the natural functional relationship between the data samples for mother
and her child, there is due to the large number of uncontrolled parameters of biologi-
cal objects very stochastic nature of the relationship between the measured values in
the pair "mother-child" with sample variance for β-HCH and for γ-HCH in the
mother. Comparative analysis of experimental data suggests that samples of β-HCH
content for mother and her child are less correlated than samples of γ-HCH of mother
and β-HCH of the child. Thus, the coefficient of cross-correlation between samples of
β-HCH content for the mother and her child, while the coefficient of cross-correlation
between samples of γ-HCH content for the mother and β-HCH content for her child.
In addition, the small size of the experimental samples greatly complicates the con-
struction of prognostic models for the diagnosis of the expected content of or-
ganochlorine toxicants in the body of the newborn child based on the analysis of the
mother on the basis of experimental data.
The lack of a reliable theoretical basis for the above system on the mechanisms of
intrauterine transfer of organochlorine toxicants into the body of the child and in-
creased requirements for accurate prediction necessitates the use of modern, often
quite complex approaches, among which we can note the method based on artificial
neural networks necessary approximating and extrapolating properties. It is clear that
without taking into account the specifics of a particular task, it is impossible to choose
or synthesize a neural network architecture that is best suited for this case.
5 Results and Discursion
Implementation and training of a polynomial neural network with training and test
samples of 90% and 10% of the total data set, respectively, was carried out in the
environment GMDH shell 3.1.4. The optimization criterion was chosen to be the
minimum standard deviation between the results of model calculations and experi-
mental data. As a model argument, we took the content of organochlorine toxicants in
the mother's body. The result of the simulation was the calculation of the predicted
amount of the corresponding substance in the body of the unborn child.
As a result of studying the polynomial neural network, we obtained a system of equa-
tions, which will be called the GMDH model.
Obtained as a result of the construction of the neural network, the explicit form of
the GMDH model for predicting the amount of β-HCH in the child's body based on
the results of the mother's analysis is represented by a system of equations:
y x 0.009 2.159 x3 x 1.0033 x 2 x
0.06332 x 3.1362 x 1.03222 x
2 x 0.381 0.992 x 0.527 x3 x 0.186 x
2
0.3933 x ;
2
3 x 0.299 0.2406 x 0.35342 x ;
(5)
4 x 1476.090 1386 x 1161606 x 5 x
11392962 x 1417425 x ;
x 3.523 0.737 x x 8.835 x
5 7 6 6
6.43762 x ;
6 x 1.772 0.113x 2 1.5887 x 1.64972 x ;
7 x 1.235 0.024 x 0.023x .
2
The results of forecasting according to the obtained model are presented in Fig. 3.
It shows the dependence of the concentration of β-HCH in the body of the child on
the concentration of β-HCH in the mother.
Fig. 3. Dependence of β-HCH content in the child's blood on the content of β-HCH in the
mother's blood. Points 1 indicate the results of experimental measurements. Curve 2 corre-
sponds to the calculations for the GMDH model.
Individual points 1 correspond to the experimentally established pairs of values of the
concentration of β-HCH in the body of the mother and her child. The concentration of
the toxicant in the mother's body was chosen as the independent variable. Solid curve
2 represents the results of the values of the concentration of β-HCH in the blood of
the child calculated according to the GMDH model based on its concentration in the
mother's blood.
Both experimental points and numerical approximation indicate the nonmonotonic
nature of these dependencies. In the range of concentrations of the studied xenobiotic
in the mother's body from 0.15 to 0.39 μg / l, there is a rapid decrease in its concentra-
tion in the body of the child from 3.10 to 0.86 μg / l. In the range of concentrations
from 0.65 to 1.51 μg / l there is a sharp peak with a half-width of 0.28 μg / l, the
maximum of which is the concentration of the toxicant in the mother 0.88, and
reaches a concentration of 2.89 μg / l in the child. A further increase in the concentra-
tion of β-HCH in the mother from 1.51 to 3.81 μg / l is accompanied by a monotonous
decrease in its concentration in the child to 0.51 μg / l.
The explicit form of the GMDH model for predicting the amount of β-HCH in the
child's body based on the results of measurements of the amount of γ-HCH in the
mother's body is represented by a system of equations:
y x 0.001 0.01012 x 2 x 0.987 2 x ;
2 x 0.497 0.3399 x 3 x 1.8903 x ;
x 0.061 0.272x 0.996 x ;
3 4
x 0.008 0.046 2 x 1.053 x ;
4 10 5
5 x 0.660 0.24110 x 0.53810 x 6 x 2.0306 x ;
(6)
6 x 0.573 0.3709 x 7 x ;
7 x 1.252 0.11611 x 1.2158 x 0.6828 x ;
2 2
x 0.568 8.110 x x 3.893 2 x 4.264 2 x ;
8 11 9 11 9
x 0.378 1.843 x 3.541 x x 2.277 2 x ;
9 12 12 10 10
10 x 3.197 6.30612 x 11 x 2.01012 2 x 7.22911 x 0.436112 x ;
11 x 2.063 33.610 x 77.317 x ;
2
12 x 1.019.
The results of forecasting according to the obtained model are presented in Fig. 4. It
shows the dependence of the concentration of β-HCH in the child on the concentra-
tion of γ-HCH in the mother. Individual points 1 correspond to the experimentally
established pairs of values of the concentration of γ-HCH in the mother and β-HCH in
her child. The concentration of the toxicant in the mother's body was chosen as the
independent variable. The solid curve 2 represents the results of the values of the
concentration of β-HCH in the child's body calculated according to the GMDH model
based on the concentration of γ-HCH in the mother's body.
Both experimental points and numerical approximation indicate the non-monotonic
nature of these dependencies. In the range of γ-HCH concentrations from 0.12 to 0.85
μg / l, there is a peak concentration of β-HCH. Its half-width is 0.04 μg / l, the maxi-
mum concentration of γ-HCH is 0.15 μg / l, and reaches a value of 0.95 μg / l. Denote
this peak by the letter A.
Fig. 4. Dependence of β-HCH content in the child's body on γ-HCH content in the mother's
body. Points 1 indicate the results of experimental measurements. Curve 2 corresponds to the
calculations for the GMDH model.
In the range of concentrations of γ-HCH from 0.18 to 0.23 μg / l, there is a sharp peak
concentration of β-HCH with a half-width of 0.01 μg / l, the maximum of which is the
concentration of the toxicant in the mother 0.19 μg / l and reaches the concentration of
β-HCH in the child's body 2.9 mcg/liter. Denote this peak by the letter B.
In the range of γ-HCH concentrations from 0.23 to 0.67, there is a gentle peak con-
centration of β-HCH with a half-width of 0.05 μg / l, the maximum of which is the
value of γ-HCH 0.26 μg / l and reaches the value of β-HCH in the child 0.96 μg / l
with an average baseline value of 0.86 μg / l. Let it be called "peak C".
The difference between the concentration of β-HCH in the child from the concen-
tration of γ-HCH in the mother from a similar dependence for the concentration of β -
HCH in the mother is the presence of a second sharp peak ("peak D") concentration of
β-HCH with a half-width of 0.01 μg / l. in the range of γ-HCH values from 0.32 to
0.36 μg / l, similar to peak B. Its maximum is at a concentration of γ-HCH 0.34 μg / l
and reaches a value of 2.87 μg / l.
Further increase in the concentration in the mother from 0.36 to 0.40 μg / l is ac-
companied by a monotonic decrease in the concentration of β-HCH in the body of the
child from 0.88 to 0.74 μg / l.
Since the difference in the concentration of flat peaks β-HCH A and C from the
mean value of the baseline is 0.09 and 0.10 μg / l, which is within the statistical error
of experimental data, their reliability requires additional studies to increase the size of
the statistical sample. In the framework of the presented work, they cannot be consid-
ered meaningful. That is, only peaks B and D may be of scientific interest.
For the indicator of extrapolation and prognostic capabilities of the model chose
the relative error, calculated as the difference between experimental and calculated
data normalized to the variance of the sample of the amount of β-HCH in the child's
body:
n x n (7)
n , n 1,2,..., N
y2
here x n is the result of the analysis of the child's body, n is the result of calcula-
tions on the systems of equations (4, 5), representing the corresponding model, y2 is
the variance of the sample analysis of the child, N is the number of studied mother-
child pairs. In fig. Figure 5 shows the results of calculating the relative error of the
GMDH model calculated by the formula (7).
As can be seen from the above estimates, the relative error of the constructed mod-
els on average does not exceed the statistical error of experimental studies.
An additional indicator of the quality of the model can be considered the coeffi-
cient of cross-correlation between the calculated and experimental data. Thus, for the
dependence of the concentration of β-HCH in the child's body on the concentration of
β-HCH in the mother's body, the mutual correlation between model and experimental
data is 0.9209, and for the dependence of β-HCH concentration in the child's body on
the concentration of γ-HCH in the mother's body is 0.9379.
Fig. 5. Relative error of GMDH model for different mother-child pairs. Graph a) corresponds to
the simulation of the dependence of the content of β-HCH in the child's blood on the content of
β-HCH in the mother's blood, graph b) corresponds to the dependence of the content of β-HCH
in the child's blood on the content of γ-HCH in the mother's blood.
6 Conclusion
As a result of the work were:
• Numerical models based on a polynomial neural network for approximation and
prediction of β-HCH concentration in the child's body based on data on the accumula-
tion of β- and γ-HCH in the mother's body, due to the state of background contamina-
tion with persistent organochlorine compounds from among stable POPs, namely
drinking water, air and food.
• The error of the models did not exceed the variance of the linear regression in
the samples of experimental data. The correlation coefficients between the calculated
and experimentally obtained data series were 0.9209 for the concentration of β-HCH
and 0.9379 for the concentration of γ-HCH in the mother.
• Experimental studies and approximation results have shown that the dependence
of the concentration of organochlorine xenobiotic in the child's body on its concentra-
tion in the mother's body is non-monotonic. In particular, it was found that there are
critical concentrations of the toxicant in the mother's body at which there is an explo-
sive transfer of stable organochlorine xenobiotics into the child's body. For β-HCH in
the mother, the range of such critical concentrations is in the range of 0.60 ÷ 1.16 μg /
l. For γ-HCH the intervals of critical concentrations are two and they are localized in
the range of 0.18 ÷ 0.20 and 0.33 ÷ 0.35 μg / l.
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