=Paper= {{Paper |id=Vol-2763/CPT2020_paper_s5-4 |storemode=property |title=Mathematical Justification of the Wound suturing by Wound Contractors of new Generation |pdfUrl=https://ceur-ws.org/Vol-2763/CPT2020_paper_s5-4.pdf |volume=Vol-2763 |authors=Sergey Izmaylov,Andrey Rotkov,Vladimir Beschastnov,Sergey Rotkov,Evgeny Popov,Egor Lukoanychev }} ==Mathematical Justification of the Wound suturing by Wound Contractors of new Generation== https://ceur-ws.org/Vol-2763/CPT2020_paper_s5-4.pdf
  Mathematical justification of the wound suturing by wound contractors
                             of new generation
              S.G. Izmaylov1, A.I. Rotkov1, V.V. Beschastnov1, S.I. Rotkov2.3, E.V. Popov2, E.E. Lukoanychev1
                                                    rotkov@nngasu.ru
                                         1
                                           GKB No. 35, Nizhny Novgorod, Russia;
           2
             Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, Russia;
                 3
                   ANO "Research Center for Physical and Technical Informatics", Nizhny Novgorod, Russia

     Frequent cases of man-made disasters, terrorist attacks and military conflicts lead to an increase in the number of victims. Significant
soft tissue defects are known to result from gunshot wounds. So, as a result of mine-blasting injuries, defects in the skin and underlying
tissues more than 10 cm in diameter are formed in 71.1% of cases. The prerequisite for the uncomplicated course of the wound process
is to achieve an adequate comparison of the edges of the wound without excessive tension. To close such extensive wounds, various
technical means are used: sutures on pads, various types of dermatotension. We have developed various models of wound contractors
(RC) for treatment of wounds. With the help of the RC, a complete reposition and good adaptation of the edges of the wound is created.
The wound closure method using these RC almost completely eliminates tissue cutting and limits the sawing effect to a minimum. This
is explained by the effects of elastic forces reducing to zero when matching soft tissues and suturing. The use of hardware methods for
suturing wounds requires the development of mathematical models of various types of wounds and surgical sutures. These models should
provide a simulation of living tissues of the wound edges behavior to achieve the best results in the treatment of wounds by RC advanced
technologies. The purpose of this study is to mathematically justify RC with the parallel holding of spokes. Another purpose is to develop
a mathematical model of the wounds suturing by hardware technology.
     Key words: wound suturing, wound contractors, spoke adaptation and reposition contractors, branch, adaptation and reposition
apparatus.

                                                                         (SPARC-III) that we developed to bring the edges of the
1. Introduction                                                          granulating wound closer in the animals of the main group.
    The mathematical justification of the spoke adaptation-              This device for converging the wound edges is protected
repositional contractors (SPARC) and methods for                         by Patent for invention No. 2214797, filed January 8, 2002
suturing wounds was carried out by standard formulas and                 and published on October 27, 2003 in Bulletin No. 30 S.
methods adopted in mechanics [1-3]. Mathematical                         G. Izmaylov, V. V. Beschastnov, A. A. Bodrov, M. N.
calculation and formulas derivation were consulted by the                Kiselev, M.N. Kudykin. (A positive FIPS decision on the
assistant professor of the Department of Theoretical                     grant of a patent of the Russian Federation dated 01/18/02.
Mechanics of Kazan State University Tazyukova F.Kh.                      On the application for invention No. 2002100973). The
The wound mathematical model was developed together                      device contains two branches (Fig. 1), a rack-and-pinion
with Professor E.V. Popov and Professor S.I. Rotkov.                     drive and spokes, characterized in that the spokes are made
    The experimental part of the work was performed on                   in the form of curved surgical spokes, comprising 1/2 - 5/8
18 outbred dogs, weighing 14.5 ± 0.7 kg, which were                      of the diameter of the circle and installed with the
divided into two groups: experimental (hardware method                   possibility of fixation by presoft tissueated branches made
of suturing) and control (traditional method of suturing).               of two corrugated plates on internal surfaces. In this case,
An extensive granulating wound was modeled according                     one of the plates is removable, and in the end part of the
to the method of V.I. Struchkov (1975) in our                            other, a turnkey 3- or 4-sided groove is made for
modification.                                                            alternately turning the branch in the cylindrical sockets of
    In order to reduce the morbidity of stitched tissues, we             the rack-and-pinion drive, which is equipped with screw
used a spoke (Sp) adaptation-reposition apparatus (ARA)                  clamps for turning the branches, which can be fixed by
                                                                         rails to each other.




  Fig. 1. General view of SPARC -III for rapprochement of the edges of a granulating wound in a prefabricated form with removable
                                 branches and spokes made in the form of curved surgical needles




Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY
4.0)
     The ARA was removed after suturing in the 1st series         method (Ramazanov R.M., 1983; Izmailov S.G., 1994).
of the experimental group of animals, and in the 2nd series,      The thickness of the tissues in the area of the wound
it remained on the wound for up to 3 days. In this case, the      sutured edges was measured with a caliper.
rack-and-pinion drive was removed. Capron No. 4 was                   To assess the state of the microvascular bed around the
used in control group, and sterilized and factory-packed          wound during tissue tension, a study of the skin
suture material in experimental group No. 2.                      temperature was carried out in dynamics (Struchkov V.I.,
     Microbiological studies were carried out on the basis        1975). The skin temperature was measured with a TEN-5
of the Research Institute of Epidemiology and                     electronic thermometer, manufactured in 2001 (Moscow),
Microbiology of the Ministry of Health of the Russian             intended for use in medicine and veterinary with 0.1°C
Federation. I.N. Blokhina. The consultant was the leading         resolution.
researcher at the Laboratory of Microbiology and                      All animal operations were carried out in compliance
Diagnosis of Dysbiosis, candidate of biological sciences          with the order of the USSR Ministry of Health No. 755 of
E.V. Belyaevа in compliance with the order of the USSR            08.22.77.
Ministry of Health No. 535 of 04/23/85. The range of
studies included quantitative and qualitative determination       2. Results and discussion
of microflora. To quantify microorganisms, colony                     The entire devices is subdivided according to the
forming units (CFU) were counted with limiting dilutions          bringing together mechanism working part into the
per 1 ml of wound, 1 cm2 of skin and 1 cm of suture. The          following main subgroups: 1 - spoke, 2 - lamellar, 3 -
skin and the animal’s hair were studied in the area of            filament, 4 - spoke and 5 - rod.
purulent wound modeling, separated from the wound at the              Depending on the wound location and shape, the RС
stage of purulent inflammation and regeneration, as well          are divided into: general (for all wounds) and special (for
as suture material inside the tissues.                            operations on the limbs, etc.). By appointment, the RС are
     The “surface biopsy” method according to M.F.                divided into the following types: fixation (for gripping and
Kamaev (1970) was applied to cytological studies.                 holding tissues); hemostatic (for temporary, preventive or
Material for histological examination was taken                   final stop of bleeding); immobilization; for the
immediately after suturing and on the 3rd day after               implementation of programmed rehabilitation of the
suturing the wound. Cytological and histological studies          pathological hotbed.
were carried out in consultation with an assistant professor          The most universal devices are SPARC with parallel
of the Department of Forensic Medicine and Pathological           holding of spokes relative to the axis of the wound. The
Anatomy of the Novosibirsk State Medical Academy A.A.             goal of the work is to substantiate the use of curved
Artifeksova.                                                      knitting spokes in parallel by the methods of mathematical
     The strength properties of the scar were studied by          modeling. The feasibility of using bent knitting spokes is
ranotensiometry method on the 3rd day after suturing of           justified by the following circumstances.
the granulating wound by a special device (Grechko V.N.,              We assume that the place of entry A (A0) and the place
1993).                                                            of exit B (B0) of these spokes coincide. Denote by l the
     Experimental and clinical measurements of the elastic        length of the straight spoke in the soft tissue, l0 the length
forces separating the edges of the soft tissue wound along        of the curved spoke in the soft tissue (l0 > l) (Fig. 2).
its entire length were carried out by the dynamometric




                                                  Fig. 2. Two types of spokes

    Consider two cases of spoke: straight and curved                                       𝑞𝑞0
                                                                                                 =
                                                                                                     𝑙𝑙
                                                                                                           < 1,             (3)
spokes (Fig. 2). Since most of the spoke is located in the                                  𝑞𝑞       𝑙𝑙0

soft tissue at the curved spoke, and not at the straight          where q0, q are the pressures of the curved and straight
spoke, and given the formula                                      spokes on the soft tissue respectively.
                            𝑃𝑃      𝑃𝑃
                       𝑞𝑞0 = , 𝑞𝑞 = ,               (1, 2)            We carry out a numerical estimate of inequality (3). It
                             𝑙𝑙0     𝑙𝑙
                                                                  is known that
we obtain the following inequality                                                𝑙𝑙0 = 𝑟𝑟 ∙ 𝛼𝛼, 𝑙𝑙 = 2𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟�∝�2�     (4)
   Here r is the radius of the curved spoke, α is the central                                   𝑞𝑞0       𝑙𝑙        𝑆𝑆𝑆𝑆𝑆𝑆�∝�2�
                                                                                                      =         =        ∝�            (5)
angle in radians.                                                                                𝑞𝑞       𝑙𝑙0              2
   Find the q0 / q ratio for different types of knitting                    Let us plot the relationship between the pressure ratio
spokes                                                                  of the curved spoke and the straight spoke as a function of
                                                                        the central angle α of the curved spoke (Fig. 3).




 Fig.3. The ratio of pressure on the soft tissue of a curved spoke to a straight line, depending on the central angle of the curved spoke

    It can be seen from the graph that, as α increases, q0 /               Fig. 4 shows a top view of a schematic diagram of the
q decreases. In limiting cases, when α = π (h = l = r), q0 is           proposed device
less than q by 36.34% (2.8 times).




                                                     Fig. 4. Top view of the device

    As an example, Fig. 3 shows two pairs of spokes (N =                    Second, deformation of the skin tissue and adjacent
2, N is the number of pairs of spokes). Here A1, A2, C1, C2             soft tissues at the points of entry / exit of the spoke occurs.
are the entry points of the spokes; B1, B2, D1, D2 - exit                   In places of entry / exit to the spoke, skin and adjacent
points of the spokes; F [H] - the total force acting from the           soft tissues, P / 2 forces act (Fig. 5).
side of the device on the tissue.
    Let us evaluate the spokes pressure q [H / m] to the
tissue. We will consider two factors. First, an increase in
the number of N pairs of spokes. Assuming that the length
of the spoke in different pairs varies slightly, we can
assume that the force P acting on one spoke is
approximately equal to P = F / N.
    An increase the number N of pairs of spokes decreases
their pressure q on the tissue (q = P / l). For uniform                  Fig. 5. The forces acting on the soft tissue during the knitting
pressure on the fabric, it is necessary to arrange the spokes
at different depths and distances. It is necessary that the                 Therefore, in the places of entry / exit of the spokes soft
distance between the spokes is greater than their diameter              tissue is crushed. The creasing of the fabric will occur due
d [m], since they do not affect on the tissue at the distance           to the tangential forces τ, which are determined by the
greater than d.                                                         following expression
                          𝜏𝜏 =
                                     𝐹𝐹
                                          2   .              (6)           The data obtained in an animal experiment confirmed
                                 𝑁𝑁�𝜋𝜋𝑑𝑑 �2�                           mathematical calculations. Thus, the experimental studies
    It follows from (6) that an increase in the number of              showed that the closure of the granulating wound in the
spokes reduces the trauma of the skin at the points of entry           experiment (using hardware) occurred in more favorable
and exit of the spokes.                                                conditions with the possibility of using precision
    Thus, the implementation of spokes in the form of                  technology and thin suture threads (Capron No. 2, thread
curved surgical spokes in the form of 1/2 - 5/8 of the                 diameter 0.25 mm). In the control group of animals joining
diameter of the circle provides a deep and wide capture of             the wound edges was possible only when using Nylon
tissues of the edges of the wound in a limited area. This              thread No. 4 (thread diameter 0.45 mm). With this
reduces the morbidity of the wound edges and improve the               diameter, the suture material retained its initial strength,
adaptation of wound surfaces with deep soft tissue defects             and during visual inspection there were no signs of
healing by secondary intention. Fixing SPARC-III to the                excessive threading of the tissue with the thread at the time
skin with spokes in the form of surgical needles in 5/8 of             of wound closure. The breaking load of the used suture
the circle diameter allows the device to be used to reduce             material with a diameter of 0.25 mm and 0.45 mm was on
the edges of small wounds when the use of more bulky                   average (M ± m) 9.9 ± 1.2 N and 33.4 ± 2.3 N, respectively
spoke devices is traumatic. An increase in the number of               (p <0.05). The use of RC completely excluded the
curved spokes, parallel to the branches and with the                   “sawing” action of the thread observed with the traditional
possibility of moving in horizontal and vertical directions,           method of suturing. The experiments showed (table 1) that
allows tissue traction at different levels determined by the           when using the RC, a stress distribution in the weld area
depth of the spokes simultaneously or alternately turning              that is safe in terms of healing is achieved.
on or off a pair of spokes, reduces tissue trauma to all
layers of the wound edge.

 Table 1. Comparative assessment of the thread tension force (FН), normal (σ) and tangential (τ) stresses, pressure (P) of the edges of
                       the wound against each other with different methods of suturing granulating wounds
                     FН matching the wound edges, N        FН tightening the
  Suturing Method                                                                   σ·106 Pa           τ·106 Pa          Р·106 Pa
                      central part        edge part        seam assembly, N
    Traditional        18,1±0,6           13,7±0,6             34,1±0,7             8,2±0,4            1,5±0,2          0,20±0,05
     Hardware              0                  0                 2,0±0,1             1,6±0,1           0,10±0,02         0,01±0,003
          р              <0,01              <0,01                <0,01               <0,01              <0,01              <0,01


    According to electro thermometry, the average skin                 significant increase in the number of microorganisms to
temperature of healthy tissues in the wound area in the                (3.5 ± 0.6) 105 CFU / cm. Moreover, an increase in
control group was (M ± m) 29.7 ± 0.3 ° C, and in the main              bacterial contamination of suture material was
group 29.8 ± 0.2 ° C (p> 0.05 ) In the stage of purulent               accompanied by an increase in the frequency of detection
inflammation, the temperature of the perivular zone in the             of pathogen associations on suture material in this group
area of the purulent wound decreased (p <0.05) to 26.2 ±               of animals. The studied state of the wound edges tissue in
0.2 ° C and 26.1 ± 0.1 ° C, respectively, and in the                   the subsequent healing periods showed that wound
regeneration phase before suturing it reached the initial              complications occurred more often in the control group
values (29.7±0.4 and 29.4±0.3, respectively). In the                   than in the experimental group. So, on the 3rd day after
control group, when wounds were sutured in the traditional             suturing in 4 of 6 animals of the control group, purulent-
way, when the sutures were tightened and the edges of the              inflammatory complications (infiltrates, suppuration of the
wound were tensioned, the skin temperature in the area of              wound, teething) from the side of the wound were
the suture line decreased by an average of 1.8 ± 0.4 ° C (p            clinically observed. All animals in the control group
<0.05), and in the experimental group compared to the                  revealed partial eruption of sutures. In 2 series of the
initial ones figures on average 0.6 ± 0.1 ° C (p <0.05). The           experimental group, only in 1 case out of 12 there was
differences between the gradients of temperature reduction             suppuration of the postoperative wound in a limited area,
in the control and experiment are statistically significant            requiring removal of 1 suture (rTMP <0.05). In the
(p <0.05).                                                             remaining 11 observations, wound healing was of the type
    It was found that when suture material was passed                  of primary tension.
through the tissue of a granulating wound, in 100% of                      The wound tensiometry showed that at the 3rd day
cases of both experimental and control groups of animals,              after suturing the experimental group the average rupture
suture material was contaminated. Most often,                          of the scar was (M ± m) 21.7 ± 0.6 kPa in 1 series and 22.6
S.epidermidis was found in the studied material in a                   ± 0.5 kPa in 2- th and was respectively 1.6 and 1.7 times
monoculture or in associations with S.aureus and                       higher (p <0.05) than in the control group (13.6 ± 1.0 kPa).
E.faecium, and the average microbial number averaged in                The differences between the first and second series in the
the experimental group (3.4 ± 0.8) · 101 CFU / cm suture               experimental group are statistically insignificant (p> 0.05).
and ( 3.3 ± 0.8) 101 CFU / cm - in the control. Three days                 The histology confirmed the results obtained by
after suturing, the number of microorganisms on the suture             tensiometry at the microscopic level. Zones of primary
in the experiment did not significantly increase from the              alteration were found in the entire control group of animals
statistic and averaged (4.1 ± 0.7) 101 CFU / cm. At the                immediately after suturing of the granulating wound in a
same time, in the animals of the control group there was a             cross section of the suture area, the tissue was teething
while reducing the wound edges and tightening the knot.         Based on the analysis of numerous studies in various
With a hardware method for wound suturing, the alteration       industries, the authors of [2, 8] propose a generalized
zone was limited only by the diameter of the thread             formulation of the Stretched Grid Method (SGM), which
without additional eruption of tissue. Compared with the        is a kind of grid methods that allows very efficient
control group of animals, large hotbeds of necrotic             modeling of the behavior of equilibrium continuum by
changes were not detected. At the same time, the structure      representing it as an energy-equivalent grid structure. The
of surrounding tissues was preserved.                           generalized formulation assumes the presence of external
    Three days after suturing by the traditional suturing       influences on the system in the form of superimposed
method vertical and horizontal sections around the suture       elastic nodal bonds and nodal pseudo-loads, which allows
threads showed signs of massive tissue destruction in the       us to simulate external constrains and continuum loads,
form of large necrosis fields saturated with purulent           namely
exudate. In this case, not only tissues bordering the                                            𝑘𝑘=1 𝐶𝐶𝑖𝑖𝑖𝑖 (Δ𝑋𝑋𝑖𝑖𝑖𝑖 ) − ∑𝑘𝑘=1 𝑃𝑃𝑖𝑖𝑖𝑖 Δ𝑋𝑋𝑖𝑖𝑖𝑖 ), (7)
                                                                Π = ∑𝑛𝑛𝑗𝑗=1 𝐷𝐷𝑗𝑗 𝑅𝑅𝑗𝑗2 + ∑3𝑖𝑖=1(∑𝑚𝑚                    2   𝑚𝑚

channel of the thread were exposed to necrosis, but also        where n is the total number of mesh segments, m is the
distant areas located on the line of tension of the thread.     total number of mesh nodes, Rj is the length of segment
The cause of these necrosis could be both the mechanical        number j, D is the stiffness of the segments (assumed to be
effect of the thread on the surrounding tissue during           the same for all), ΔXik is the increment of the coordinate of
contraction of the wound edges (direct necrosis), and           the kth node along the i axis, Cik is stiffness of the elastic
vascular disorders in distant areas in the form of sweets,      bond in the node number k along the i-axis, Pik - external
blood clots (indirect vascular necrosis). The                   load in the node number k along the i-axis.
intracanalicular pathway of infection spread is obvious,            It is assumed that soft tissue is a continuum modeled
since leukocytes were found not only at the edges of the        by an equivalent grid structure, which is a set of point
thread channel, but also in the channel itself, as well as      masses connected by springs. In [4-6], the following law
between the elements of the thread.                             of motion was obtained for node number i of the nodal-
    In the granulating wound, which was sutured by              spring model
hardware, the cellular infiltration of stitched tissues was          𝑑𝑑 2 𝑟𝑟𝑖𝑖           𝑑𝑑𝑟𝑟𝑖𝑖
                                                                                                                            0
                                                                                                                         �𝑙𝑙𝑖𝑖,𝑗𝑗 −�𝑟𝑟𝑖𝑖 𝑟𝑟𝑗𝑗��𝑟𝑟𝑖𝑖 𝑟𝑟𝑗𝑗
significantly less compared to the control, which indicated     𝜇𝜇               = −𝛾𝛾            + ∑𝑗𝑗∈𝑁𝑁(𝑖𝑖) 𝐾𝐾𝑖𝑖,𝑗𝑗                                     ,   (8)
                                                                     𝑑𝑑𝑑𝑑 2              𝑑𝑑𝑑𝑑                                     �𝑟𝑟𝑖𝑖 𝑟𝑟𝑗𝑗 �
a weak severity of the inflammatory reaction.                   where μ is the mass of the point, γ is the damping
    Thus, the conducted experimental studies have               coefficient, Ki,j is the stiffness coefficient of the spring
established that the convergence of the rigid edges of the      connecting the i and j points, N (i) is the set of points
granulating wound using the suture in the traditional way       connected to this, l0i,j is the distance between the i and j
under the conditions of tensile forces, the tightening of the   points in an unstressed state.
sutures leads to the formation of primary hotbed of                 Minimization of functional (7) with respect to
necrosis in the sutures and edges of the wound,                 unknown nodal changes in the coordinates of the points
intraoperative eruption of the suture, hemorrhages and          allows obtaining a relationship that differs from equation
reduced vascularization of stitched tissues. This is the        (8) only in the inertial term on the left equation side and
reason for the decrease in local resistance of tissues to       the first term on the right, which reflects the damping
infection, their regenerative ability, which creates            properties of the tissue model. Thus, SGM allows the
unfavorable conditions for the course of the wound              formation of a nodel-spring model that is in good
process and thereby significantly increases the risk of         agreement with those developed earlier. The advantage of
purulent-inflammatory wound complications even in               SGM is in solving the problem in a quasi-static setting,
conditions of low microbial contamination of the wound          which greatly simplifies the solution of the problem. This
surface, when the number of microbial bodies does not           formulation can be used in both static and dynamic
exceed the critical level 105 CFU.                              settings. Minor modifications of relation (7), related to the
    In contrast to the traditional suturing method the          inertial and damping components allows obtaining the
closure of the granulating wound using the RС is carried        corresponding equations of motion of an elastic grid with
out without suture thread. The latter is used only to keep      point masses, which can be solved using step-by-step
the edges of the wound defect at a reduced state. This          algorithms. Modeling of cuts and seams is done by
achieves anatomically accurate reconstruction of tissues in     removing or creating bonds between the corresponding
the wound area, minimal damaging effect on stitched             point masses.
tissues, complete elimination of the “sawing” effect of the         When using a grid structure with point masses for
thread and its eruption at the moment of matching the           modeling soft tissue the following problems need to be
wound edges. In addition, optimal conditions are provided       solved
for adequate blood supply in the area of a wound defect.        1. The bonds topology. The number and arrangement of
This increases the resistance of local tissues to infection          bonds between the masses greatly affects the behavior
and reduces the risk of wound suppurative inflammatory               of the entire system. If the number of bonds is
complications.                                                       insufficient or there are too many of them, the model
    When modeling the process of suturing a wound, an                will not reflect the actual behavior of the soft tissues.
important step is the selection of a soft tissue model. Some         Because of these they are usually limited to a regular
existing models created for different purposes were                  lattice structure.
analyzed: finite element model [1], various point models        2. Physic-mechanical properties of grid segments. The
[4-6]. In [7], the advantages and disadvantages of these             problem lies in determining the bond properties
representations of soft tissue for modeling were described.
     between the masses for the correct modeling of soft          2.   The grid topology. The hexagonal regular grid
     tissues.                                                          structure is not enough. Therefore, additional diagonal
    The model for studying the process of suturing a                   bonds were added (see Fig. 6).
wound using RC is a regular 3D grid with point masses in          3.   Grid bond properties. Different elastic parameters for
nodes, which represents soft tissues of various properties.            bonds between point masses can be applied to
Bonds between nodes between nodes have only tensile-                   simulate different layers of different tissue elasticity.
compression rigidity and act as springs. Three main                    In [1] data of the tissue elasticity obtained by
aspects can be distinguished that affect the consistency of            vibroelastometry. These data were used to set the
the real tissue model                                                  quantitative characteristics of model grid correctly.
1. Nodes of regular grid. Different masses of nodes
     model different layers of tissue that have different
     density.




                                             Fig. 6. 3D grid model of soft tissue

    To simulate the process of wound suturing it is                   The approach of the wound edges by RC is
necessary to simulate an incision of the desired size and         schematically shown in Fig. 7. and consists of the
shape. In our grid tissue model this can be done by               following steps:
eliminating the bonds between the corresponding nodal             1. The intrusion of special curved spokes into the tissue.
masses. The cut is formed automatically due to the tension        2. Straightening spokes.
in the tissue itself.                                             3. Converging of the edges of the wound with the help
                                                                       of branches on the spokes.




                                          Fig. 7. Converging the wound edges by RC
    In order to simulate the converging of the wound edges            The knowledge obtained on the basis of this
the corresponding nodes in the regular grid are declared to       mathematical model of wound closure by various RC
belong to spokes or branches. In this case, all connections       options allows optimizing the constructive part of devices
with these nodes are saved. Next, you need to set the             for their more effective practical application.
trajectory and speed of these nodes. Thus, the deformation            An analysis of patient’s treatment with granulating
of tissues during the straightening of spokes can be              wounds showed that the use of RС with perpendicular
determined by comparing the geometry of the undeformed            holding of spokes and needles can lead to cosmetic defects
and deformed grid, taking into account the physical and           due to the frequency of purulent-inflammatory
mechanical properties of the grid segments.                       complications with overall good and satisfactory healing.
                                                                  This was confirmed by our research in the mathematical
modeling of the process of suturing soft tissue wounds.        [7] Popov, E.V. Metod natyanutyh setok v zadachah
Significantly fewer complications were observed when               geometricheskogo modelirovaniya: diss. d-ra tekhn.
using the RC with parallel edges of the wound using                nauk. - Nizhnij Novgorod: NNGASU, 2001. -350s.
curved knitting needles (22.6% and 11.8%, respectively).       [8] Svetuhin, A.M. Etiopatogeneticheskie principy
Purulent-inflammatory complications developed in 17.1%             hirurgicheskogo lecheniya gnojnyh ran / A.M.
with hardware and in 59% of cases with the traditional             Svetuhin, V.M. Matasov, V.G. Istratov i dr.//
method of suturing (p <0.05).                                      Hirurgiya, - 1999.-№ 1.- S. 9-11.
    The hardware application to the treatment of
abdominal hernias reduced the number of postoperative          About the authors
wound complications from 29.1 to 10.3% (p <0.001), the             Izmailov Sergey G., MD, professor, State Clinical Hospital
number of complications from the bronchopulmonary and          No. 35, Nizhny Novgorod. E-mail: izi28082009@yandex.ru
cardiovascular systems from 11.4 to 4% (p <0.005), the             Rotkov Andrey I., candidate of medical sciences, associate
number of relapses from 15.8 to 1.9% (p <0.001), which         professor, State Clinical Hospital No. 35, Nizhny Novgorod. E-
can primarily be explained by a decrease in the trauma of      mail: 3959400@mail.ru
stitched tissues and the reliability of closing a wound            Beschastnov Vladimir V., MD, Associate Professor, State
defect.                                                        Clinical Hospital No. 35, Nizhny Novgorod. E-mail:
                                                               vvb748@mail.ru
3. Conclusion                                                      Rotkov Sergey I., Doctor of Technical Sciences, Professor,
                                                               Nizhny Novgorod State University of Architecture and Civil
    The wound edges convergence is a preparatory               Engineering, Nizhny Novgorod. E-mail: rotkov@nngasu.ru
operation for suturing. However, in such a formulation it          Popov Evgeny V., Doctor of Technical Sciences, Professor,
is already possible to give not only a qualitative, but also   Nizhny Novgorod State University of Architecture and Civil
a quantitative assessment of the clinical efficacy of          Engineering,      Nizhny     Novgorod.       E-mail:   popov-
                                                               4487@yandex.ru
different RC constructs. To do this, it is necessary to            Lukoyanychev Egor E., candidate of medical sciences,
develop an algorithm for assessing the damage that tissue      associate professor, State Clinical Hospital No. 35, Nizhny
receives when various wound devices are applied to it.         Novgorod. E-mail: egor-lukoyanychev@yandex.ru
    The next step in modeling should be the wound
suturing in the state after applying the RC. The developed
mathematical model can be used for subsequent
optimization of wound suturing technology in a clinical
setting.
    The developed mathematical model is applicable for
studying the process of suturing a wound using RC from
beginning to end.

Acknowledgment
   The work was performed according to the RFBR grant
No. 19-07-01024.

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