=Paper=
{{Paper
|id=Vol-2753/paper20
|storemode=property
|title=Mathematical Modeling and Optimization of Technological Parameters of the Obtaining Process of Hydrogel Medical Dressings
|pdfUrl=https://ceur-ws.org/Vol-2753/short9.pdf
|volume=Vol-2753
|authors=Оleksandr Grytsenko,Petro Pukach,Oleh Suberlyak,Ivan Gaydos,Mykola Kushnirchuk ,Bohdan Berezhnyy
|dblpUrl=https://dblp.org/rec/conf/iddm/GrytsenkoPSGKB20
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==Mathematical Modeling and Optimization of Technological Parameters of the Obtaining Process of Hydrogel Medical Dressings==
https://ceur-ws.org/Vol-2753/short9.pdf
Mathematical Modeling and Optimization of Technological
Parameters of the Obtaining Process of Hydrogel Medical
Dressings
Оleksandr Grytsenkoa, Petro Pukacha, Oleh Suberlyaka, Ivan Gaydosb, Mykola Kushnirchukc,
and Bohdan Berezhnyya
a
Lviv Polytechnic National University, 12, St. Bandera str., Lviv, 79013, Ukraine
b
Technical University in Košice, 74 Mäsiarska, Košice, Slovakia
c
Danylo Halytsky Lviv National Medical University Ogienko str., 5 , Lviv, 79005, Ukraine
Abstract
By using the means of mathematical modeling and optimization, the calculation of the main
technological parameters of the formation method of film hydrogel products based on silver-
filled copolymers of 2-hydroxyethylmethacrylate with polyvinylpyrrolidone was performed.
The technological parameters of the polymerization processes, chemical reduction of silver
ions and centrifugal formation of the film cloth were substantiated. Those are the components
of the technological process, which occurs in one stage in the form of a centrifugal unit. By
using the obtained results, silver-filled films were obtained, which are characterized by
unique properties and can be used in treatment of trophic ulcers of lower limbs.
Keywords 1
Mathematical modeling, technological parameters; hydrogel medical dressings; silver-
containing hydrogels; centrifugal formation, trophic ulcers
1. Introduction
Modern methods of mathematical modeling, synthesis and optimization of technological parameters
of production systems anticipate, in particular, a set of different methods of qualitative [1] and
quantitative [2, 3] nature. Nowadays, the significant success has been achieved in development the
new methods, optimization of synthesis conditions and properties of composite polymers [4-9]. This
is prerequisite for creation materials with unique properties for different fields of application [10-13].
Especially it concerns the composite polymer hydrogels [14-17], among which the most popular in
science and practice are hydrogels filled with (nano) metal particles [18-20].
The uniqueness of such materials is the combination of the properties of a polymer matrix and the
metal-filler. A polymer matrix is characterized by the ability to absorb low molecular substances,
including medicines, to swell in solvents, retain a significant amount of water while being in a highly
elastic state. Depending on the nature of metal, composite hydrogel can acquire electro-conductive,
magnetic and anti-bacterial properties, which significantly expands the fields of its usage [20-23].
Composite metal-hydrogels with antibacterial and antifungal properties are ideal materials in the
medical field for the creation of dressings to treat wounds, burns, ulcers of various kinds, including
venous ulcers of lower limbs [24-26].
The modern practice of the treatment of venous ulcers of lower limbs implies a combination of
various methods for conservative treatment and surgical interventions. Most trophic venous ulcers are
characterized by a high degree of bacterial colonization with high probability of development of
IDDM'2020: 3rd International Conference on Informatics & Data-Driven Medicine, November 19-21, 2020, Växjö, Sweden
EMAIL: ogryts@gmail.com (О. Grytsenko); ppukach@gmail.com (P. Pukach); suberlak@polynet.lviv.ua (O. Suberlyak);
ivan.gajdos@tuke.sk (I. Gaydos); Kolakushnir@i.ua (M. Kushnirchuk); bersebog@gmail.com (B. Berezhnyy)
ORCID: 0000–0001–8578–4657 (О. Grytsenko); 0000-0002-0359-5025 (P. Pukach); 0000-0002-6046-5972 (O. Suberlyak); 0000-0003-
1496-1892 (I. Gaydos); 0000–0002–0589–4045 (M. Kushnirchuk); 0000-0002-9038-126X (B. Berezhnyy)
©️ 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
wound infection. According to many researchers, an important condition, necessary to prevent
recurrence of venous ulcers, is the application of the adequate systemic and local therapy with
antibiotics and antiseptic preparations in combination with lower limb compression [27].
One of the promising methods for the treatment of venous ulcers is considered to be covering (in
order to prevent the development of wound infection) with the sorption hydrogel film materials with
antibacterial properties and the combination of therapy using medical preparations [28].
We established experimentally the prospects of using silver-filled film hydrogel products based on
co-polymers of polyvinylpyrrolidone (PVP) with 2-hydroxyethylmethacrylat (HEMA) during the
treatment of venous ulcers [25].
High elasticity, strength, sorption capacity, bactericidal and antifungal properties of the obtained
materials based on co-polymers of polyvinylpyrrolidone with 2-hydroxyethylmethacrylat (pHEMA-
gr-PVP) make them effective to use as hydrogel dressings for medical purposes. A unique porous
structure [17], combined with the existence of hydrophilic functional groups ensures swelling of a
polymer matrix in water and high permeability for dissolved low molecular substances. This, in turn,
determines the suitability of the obtained hydrogel dressings for the preparation treatment by
introducing medicines through the material by the transdermal method [25].
At the same time, due to the ability to absorb and retain moisture, elasticity and stability of the
form in aqueous medium, such materials are compatible with a variety of biological systems.
2. The analysis of previous researchs and problem statement
A new method of obtaining metal-filled hydrogels based on copolymers HEMA with PVP was
proposed, which consist in implementation of polymerization with the simultaneous reduction of
metal ions by using exoeffect of polymerization [29].
The method is especially attractive both from the practical and the scientific point of view, because
the particles of metal are formed at the same time with the formation of a polymer matrix. This
approach makes it possible to achieve a better, uniform distribution of the filler and to obtain the
material with the isotropic properties.
High reactivity and possibility to regulate within wide limits the time of HEMA/PVP compositions
being in liquid state is a prerequisite of their recycling in film products by the method of centrifugal
formation [25]. The technological characteristics [30], cost effectiveness of the centrifugal formation
and low quality of the films, obtained by the other currently existing methods, contribute to this
(casting and filling into glass or polymer form). The samples of hydrogel film materials, obtained by
centrifugal formation, are characterized by various thickness, which does not exceed 1 %, high-
quality surfaces and a complex of physical and mechanical properties.
Centrifugal molding is one method of plastic products production in the bodies of revolution by
the filling of the material in a viscous-flow state into the form that rotates in the same plane.
Centrifugally material is evenly distributed on the inner surface of the form in a continuous layer,
while receiving curing required configuration [31].
The proposed technology is easy to implement into production, does not require sophisticated
apparatus design. One of its advantages is the minimum amount of waste and no need of recycling or
recuperation of solutions of an oxidant and a reducing agent. Such technology is a priority and needs
development, taking into consideration the prospects of the obtained composites.
However, as for any technology, one of the main factors in obtaining high-quality hydrogel film
products is the optimal technological parameters of the technological manufacturing process. At the
same time, the establishment of some optimal technological parameters requires an implementation of
a large amount of experimental studies and needs the use of mathematical modeling and forecasting
methods. Developed methods of optimization provide the use of mathematical apparatus not only on
the stage of analyzing research results, but also during their forecast; that gives an opportunity to
decrease significantly materials and time consuming for providing the experiment occuring [32, 33].
Therefore, the aim of the research was to establish the technological parameters of obtaining hydrogel
films for medical purposes by using the means of mathematical modeling. The films were obtained by
the centrifugal method with the simultaneous formation of a polymer matrix and obtainment of metal-
filler particles.
3. Object of investigation
Lightly crosslinked polymers obtained by radical polymerization of HEMA at the presence of PVP
are selected as a matrix for filling. 2-hydroxyethylmethacrylat (Sigma Chemical Co) and high-purity
polyvinylpyrrolidone (AppliChem GmbH) with MM 12000 were used for co-polymerization. The
initiator of the radical type benzoyl peroxide (BP) was selected as the polymerization initiator. Such
choice was determined by its wide use for the synthesis of pHEMA-gr-PVP co-polymers [20]. HEMA
was distilled in vacuum (residual pressure was 130 N/m2, Tboil=351 K), PVP was dried at 338 K in
vacuum for 2–3 h, BP was re-crystallized from ethanol.
Polymerization was carried out with the initiator of a radical type of BP (Т0=50ºС).
Given that the silver-filled hydrogel is meant for medical purposes, silver deposition was carried
out from argentum nitrate (of chemically pure brand) in the aqueous-ethanol solution. The recovery
process goes on intensively at the temperature of 70 ºC [34] according to the following reaction:
2AgNO3 + C2H5OH → 2Ag↓ + 2HNO3 + CH3СН=O
4. The calculation results of technological parameters of the obtaining
process of hydrogel films
Technological parameters are a set of conditions that ensure the obtainment of a quality product. Each
parameter has a greater or lesser effect, but this influence is interrelated, so in the technology the
optimal set of parameters should be established. Deviation of one of them can lead to changes in
product quality (both in terms of physico-mechanical and performance characteristics, and in terms of
appearance) and process productivity. For the formation of hydrogel films, a centrifugal unit was
designed with the main element of centrifugal mold (Figure 1).
Figure 2: Installation for centrifugal molding of composite films from polymer hydrogels
The developed obtainment method of silver-filled hydrogel films by polymerization with
simultaneous reduction of Ag+ ions anticipates the production of films in one stage on one equipment.
The peculiarity of the method is that during the time of formation of the final product – the time
between loading the reaction composition to removing the final product, in centrifugal form occur
three processes at the same time, which differ in their nature – chemical (synthesis of polymer matrix
due to copolymerization of HEMA with PVP and Ag(0) formation by reduction of Ag+ ions) and
physical (obtaining a film cloth by centrifugal molding). Each process must be carried out under
certain conditions, which form a set of technological parameters of the technological obtainment
process of hydrogel films.
As kinetic investigations of speed of ions reduction have shown the main parameters of the process
are the duration of the induction period of reduction (τi.r.), duration of reduction (τr.t.), the reduction
temperature (Tr) [28]. A start time of gel formation (τs.f.), a duration of gel effect area (τ d.e.) and the
maximum exothermic temperature (Tmax) [28, 29] were used for a characteristic of the
copolymerization process HEMA with PVP [26, 27]. τs.f., τd.e., Tmax parameters have been taken on
the base of thermometric polymerization research [28, 29].
In our case, it is important that the duration of the Ag+ reduction process approaches to the
duration of gel effect area of the polymerization reaction with a minimum start time of gel formation
and a maximum Tmax. The duration of molding is determined by the duration of polymerization,
which depends in our case mainly on the formulation of the original reaction composition and is
established by the experimental method.
It needs to choose compositions, which polymerize with the maximum heat liberation, the
minimum induction period and with the maximum gel effect area according to the technological
features of obtaining metal-filled hydrogels by proposed method.
Experimentally, the optimal content of the initial composition components in which achieves the
necessary parameters of the exothermic process could not be found. Therefore, for investigation the
simultaneous influence of initial composition components on the exothermic process parameters, it
was used the optimization of the experiment by means of simplex-lattice planning Scheffe in order to
reduce the experimental expenses amount [35]. The result of the research is a multifactor
mathematical model in the form of a polynomial of a given degree. The necessary condition in the
simplex method is to provide at each experimental point a condition fulfillment ΣХ i=1, where Хi 0 –
the concentration of the i-th component in the composition. During the research of the mixtures
properties, which depend only on three components, the factor space is an equilateral triangle and for
the system, the ratio is executed: Х1+Х2+Х3=1 [35]. The vertices of the triangle correspond to the
pure substances, the sides – to the double systems. In our case, not the whole concentration triangle
was investigated, but only its local part, which is a simplex with vertices А 1(72% HEMA; 8% PVP;
20% Н2О); А2 (56% HEMA; 24% PVP; 20% Н2О); А3 (56% HEMA; 8% PVP; 36% Н2О) (Figure
2а). Let’s indicate Х1 denote – HEMA, wt.%; Х2 – PVP, wt.%; Х3 – Н2О, wt.%.
a
b
Figure 2: Triangles for the research of «composition-technological parameters» diagrams: a - local
area of research; b - equal values lines of parameters of the exothermic process
The optimization was carried out for exothermic parameters – the start time of the gel formation
(τs.f., min), gel-effect area (τd.e., min) and the maximum exothermic temperature (Tmax, ºС). In Table 1,
conditions and results of experiments in the form of pseudo-components and on a natural scale have
been presented. The average results y1e (Tmax, ºС), y2e (τs.f., min) and y3e (τd.e., min) were obtained by
two parallel experiments.
Using the matrix of planning, conditions and results of the experiment (Тable 1) the coefficients of
the polynomial are calculated and the regression equations are derived [36]:
𝑦1 = 123.44 + 63.75𝑋2 − 71.25𝑋3 − 203.13𝑋2 𝑋3 − 445.31𝑋22 − 117.19𝑋32 , (1)
2 2 (2)
𝑦2 = 33.13 − 184.38𝑋2 + 7.5𝑋3 + 109.38𝑋2 𝑋3 + 312.5𝑋2 − 15.63𝑋3 ,
𝑦3 = 40.39 − 50.63𝑋2 + 28.75𝑋3 − 234.38𝑋2 𝑋3 − 62.5𝑋22 − 23.44𝑋32 , (3)
The obtained equations give a possibility to predict the parameters change character of the
exothermic copolymerization process HEMA with PVP – a start time of gel formation (y1), a gel-
effect area (y2) and the maximum exothermic temperature (y3) for any composition of the initial
composition. According to the obtained regression equations, the isolines of the exothermic parame-
ters change were plotted depending on each component content of the original composition (Figure
2b). The obtained lines of equal parameters values provide a quick search for a totality of values of
the components concentrations in the reaction composition, which makes a possible to obtain the
optimal technological conditions, that are necessary for the metal deposition during the polymerize-
Table 1
Conditions and results of experiments
Natural variables
№ y1е y 2е y3е
X1 X2 X3
1 0.72 0.08 0.20 103.5 23.00 37.00
2 0.56 0.24 0.20 84.40 13.00 18.20
3 0.56 0.08 0.36 79.00 24.20 36.50
4 0.64 0.16 0.20 96.80 16.00 28.00
5 0.64 0.08 0.28 92.00 23.70 36.90
6 0.56 0.16 0.28 84.00 17.40 26.40
tion. The main technological parameters of the centrifugal molding are rotational frequency of mold,
molding pressure and centrifugal force. The frequency of mold rotation depends on the quality,
physical and mechanical properties of the film. Rotational frequency affects the magnitude of the
centrifugal force, and accordingly, the molding pressure and density of the film. In this work, the
functional connection was established, which make it possible to determine these parameters and the
relationship between them.
In order to form high-quality surface films the working rotational frequency of mold nw must be
greater than critical (ncr):
𝑛𝑤 > 𝑛𝑐𝑟 . (4)
It is established that the critical frequency of rotation of the centrifugal mold depends only on its
geometric dimensions:
g (5)
ncr > √ 2 ,
4π R
where R – radius of the inner mold surface (outer radius of the product), m.
Besides, on the basis of conducted calculations, mathematical equations were derived to calculate
the pressure acting on the outer surface of the film and on the centrifugal force:
4ρπ2 n2 (R3 − R31 ) (6)
𝑃= ,
3𝑅
2ρπlω2 (R3 − R31 ) (7)
𝐹𝐶 = ,
3
where: ρ – density of the composition, kg/m3; n – rotational frequency of mold, rev/min; R – outer
diameter of the film, m; R1 – inner diameter of the film, m; l – work length of designed mold, m; ω –
angular velocity, s-1.
5. Implementation of the obtained results
By using the received results, experimental samples of composite hydrogel films were obtained
(Figure 3). Hydrogel film material samples, obtained by centrifugal molding have attracted the
attention by the isopachic not exceeding 1%, high surface quality and by complex of physico-
mechanical properties.
The medical-biological studies of the resulting film products were carried out under the laboratory
conditions at the Department of Microbiology of Danylo Halytskyi Lviv National Medical University.
A comparative analysis of the results of medical-biological tests of the obtained materials and non-
filled hydrogel films regarding the used micro-organisms revealed that non-filled films do not show
any bactericidal and antifungal properties. The film products that contain silver particles block the
growth of bacteria and fungi (Table 2) [25].
Based on the obtained silver-filled films, we developed hydrogel medical dressings, clinical testing
of which was successfully carried out at the surgical department of the Lviv hospital at ZT PAT
"Ukrainian Railway" in the treatment of venous ulcers of lower limbs. It was established that the use
Figure 3: Experimental sample of hydrogel film
Table 2
Bactericidal and antifungal activity of silver-filled hydrogel films, obtained based on copolymers of
HEMA with PVP
Duration of storage of Magnitude of the zone of inhibition of microorganism growth, mm
hydrogel films S. aureus S. epidermidis Str. viridans Е. соlі С. albicans
1 month 12, 10, 9 12, 8, 9 11, 11, 9 3, 3, 0 11, 11, 7
18 months 5, 4, 8 5, 4, 5 11, 8, 8 – 0, 4, 2
of the silver-filled hydrogel films improves the treatment results, accelerates cleaning, granulation and
healing trophic ulcers and, as a result, reduces the duration of patients staying at hospital. Due to its
unique properties, the developed materials can be also used for the treatment of burn and post-
operative wounds.
6. Conclusions
The basic technological parameters of formation processes of a film hydrogel cloth by a centrifugal
method are calculated. The technological parameters of the polymerization processes, chemical
reduction of silver ions and the centrifugal method were established. They compile the technological
parameters of the technological obtainment process of hydrogel dressings for medical purposes. Using
the Scheffe’s simplex-lattice planning method, the optimization of the experiment was made to
forecast the polymerization parameters of HEMA/PVP compositions, which define the technological
regime of metals’ chemical precipitation.
The results of the clinical studies showed sufficient clinical effectiveness of using the developed
hydrogel dressings for medical purposes based on hydrogels, containing silver particles. Such
materials in combination with the integrated therapy help to increase the speed and intensity of
treatment of trophic venous ulcers of lower limbs.
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