Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

54, 2, pp. 411-421, Warsaw 2016
DOI: 10.15632/jtam-pl.54.2.411

A PRELIMINARY STUDY ON THE OPTIMAL CHOICE OF AN IMPLANT

AND ITS ORIENTATION IN VENTRAL HERNIA REPAIR

Izabela Lubowiecka, Katarzyna Szepietowska
Gdansk University of Technology, Faculty of Civil and Environmental Engineering, Gdańsk, Poland

e-mail: lubow@pg.gda.pl; katszepi@pg.gda.pl

Czesław Szymczak
Gdansk University of Technology, Faculty of Ocean Engineering and Ship Technology, Gdańsk, Poland

e-mail: szymcze@pg.dga.pl

Agnieszka Tomaszewska
Gdansk University of Technology, Faculty of Civil and Environmental Engineering, Gdańsk, Poland

e-mail: atomas@pg.gda.pl

This paper addresses the problem of ventral hernia repair. The main goals are to find an
optimal surgical mesh for hernia repair and to define its optimal orientation in the abdomi-
nalwall tominimise themaximum force at the tissue-implant juncture. The optimalmesh is
chosen from a set of orthotropicmeshes with different stiffness ratios for typical hernia pla-
cement in the abdominal area.The implant is subjected to an anisotropicdisplacement field,
different for the selected hernia placements. The assumed displacement fields correspond to
regularhumanactivity.Proper implantationof themeshmaydetermine the success of hernia
repair and/or the postoperative comfort of patients.The proposed solution is based onFEM
simulations of different surgicalmeshes behaviour. In typical hernia placements, the optimal
orientation of the stiffer direction of the implant is perpendicular to the spine. However, the
presented results show some cases that an oblique directionmay be the optimum one.

Keywords: biomechanics, surgical mesh, finite element modelling, optimisation

1. Introduction

Ventral hernia is a common medical problem researched by surgeons and engineers for many
years, but question about themain factors influencing hernia repair efficiency still remains open
(Muysoms et al., 2013). This problem refers to primary hernias as well as to incisional ones. It
is estimated that there is a 12% chance of incisional ventral hernia occurrence after abdominal
surgery and a 3.2% chance after laparoscopic operation (Bensley et al., 2013). Laparoscopic
ventral hernia repair is believed to be superior to an open operation (Qadri et al., 2010), however
the best treating scheme is not specified for the time being, and such problems as recurrences
or chronic pain happen (Sommer and Friis-Andersen, 2013). It is believed that the success of
ventral hernia repair depends mainly on selection of an appropriate implant and its fixation
(Muysoms et al., 2013). In the authors’ opinion, mathematical modelling and simulations can
provide information about the best course of the treatment, and then, a combination ofmedical
andmechanical knowledge may lead to an increase in hernia treatment efficiency.
This paper refers to laparoscopic repairs.Theprinciple that the properties of surgicalmeshes

shouldmatch the properties of the abdominal wall and that implants should be oriented in the
human body in accordance with the mechanics of the abdominal wall has been reported in the
literature since 2001 (Junge et al., 2001). This issue was discussed e.g., byKirilova et al. (2012),
Hernández-Gascón et al. (2013), Anurov et al. (2012). All these studies are limited to just one



412 I. Lubowiecka et al.

position of hernia orifice and two perpendicular orientations of implants. As the abdominal wall
is subjected to various strains during human activity, both in magnitudes and in orientations
in different locations (Szymczak et al., 2012), it is reasonable to find the best orientation of the
implant for different hernia locations in the abdominalwall. This problemwas already addressed
in (Lubowiecka et al., 2014).

The main goal of this study is to investigate the influence of implants orientation on forces
in fasteners. The value of this force determines the success of hernia repair since its increase can
lead to the junction failure which is a common cause of the illness recurrence.The maximum
force on a fastener affixing an implant should be smaller than the allowable tearing force for
a selected tack (Tomaszewska et al., 2013). The proposed solutions are derived from structural
mechanics and optimisation methodology. In order to analyse the behaviour of the surgical
mesh, amathematical model of the tissue-implant system, which is created during laparoscopic
hernia operation, is applied. The modelling of implant-tissue systems began with the cable
model (Szymczak et al., 2010). Next, two-dimensional finite element (FE) membrane models
with various boundary conditions were defined (Lubowiecka et al., 2010; Lubowiecka, 2015;
Tomaszewska et al., 2013). An FE model of the implant-hernia system was also proposed by
Guérin and Turquier (2013) and Hernández-Gascón et al. (2013). Some mechanical properties
of surgical meshes were recognized for their application in different material models including
an orthotropic linear or bilinear elastic material model (Lubowiecka et al., 2014) or a dense
net material model (Lubowiecka, 2015), a hyperelastic constitutive model (Hernández-Gascón
et al., 2013) and a beammodel reflecting the implant material structure (Hernández-Gascón et
al., 2012).

The novel approach presented in this paper is formulating and solving the optimisation
problem,which results in the selection of theoptimal orthotropic implant and its best orientation
in the anisotropic abdominal wall. We consider five possible hernia placements, where implants
are imposed to different fields of displacements caused by deformation of abdominal wall during
daily activities. The optimisation criterion is minimising the maximum forces on tissue-implant
junctures resulting from the patient’s bodymovements.

2. Materials and methods

2.1. Formulation of the optimisation problem

The force acting on a single fastener of a given type ofmesh implant depends on the implant
mechanical properties, its orientation relative to the direction of the spine, and the layout of
the fasteners. In this model, a circular layout of point fasteners is assumed. To find the optimal
orientation for an implant, the minimisation of the force F(i,α,s) is defined as an objective
function

min
i∈I, 0¬α¬2π, s⊂S

max F(i,α,s) (2.1)

where i denotes the number of fasteners indicating their position, I stands for the fastener set,
α is the angle between the implant primary axis and the spine, and s indicates the implant
number from the set of implants S considered.

A three-stage process of minimising objective function (2.1) is proposed herein. During the
first stage, themaximum forceFmax(i,α,s) in the fastener is sought for a chosen implant s and
the implant angle of orientation as a solution of the sub-problem (according to Eq. (2.2). The
outcome of this step is the number i0 that indicates the fastener at which Fmax occurs

max
i∈I
F(i,α,s) (2.2)



A preliminary study on the optimal choice of an implant... 413

In the second stage, the angle specifying the implant orientation in relation to the spine is
sought. The problem is formulated as aminimisation of themaximum force obtained in the first
stage with respect to the angle α

min
0¬α¬2π

Fmax(i0,α,s) (2.3)

Theminimisation procedure is conducted in a discretemanner; the implant orientation angle α
changes by the assumed increment∆α. Thus the orientation angle of the implant α0 for which
the minimal force in tack i0 (selected in the first step), is identified.

In the last stage, steps one and two are repeated for each implant s from the considered set
of implants S

min
s⊂S
Fmax(i0,α0,s) (2.4)

Finally, the implant s0, its orientation α0 and the corresponding fastener number i0 are deter-
mined to solve the objective function. This finalises the optimisation procedure.

2.2. Modelling and simulation of the implanted surogical mesh

Four popular synthetic implants used in ventral hernia repair are considered in this study,
ProceedTM Surgical Mesh (Ethicon Endo-Surgery, Inc., USA), ParietexTM Composite (Covi-
dien, USA), DynaMesh

R
O

-IPOM (FEG Textiltechnik mbH, Germany) and Gore
R
O

Dualmesh
R
O

Biomaterial (W.L.Gore&Associates, Inc., USA). They are knitted structuresmade of polypro-
pylene and cellulose, polyester, polypropylene and polyvinylidene fluoride treads, respectively.
The lattermaterial is in formof a smoothmembranemade of expandedpolytetrafluoroethylene.
A suggestion concerning proper orientation of the implant in the abdominal wall can be found
only in specification of DynaMesh

R
O

. Themanufacturer recommends a craniocaudal orientation
of the mesh, but does not distinguish different hernia locations. The analysis refers to practi-
cal cases concerning the first few weeks following the operation, when the implant is not yet
encapsulated by a fibrous capsule and when most hernia recurrences occur. The correct mesh
orientation decreases the risk of possible postoperative fixation failure evenwhen themechanical
properties of the implant are changed due to tissue overgrowth (Oettinger et al., 2013).
Herniawith an orifice diameter of 5cm is considered in this study.A standard clinical case is

taken into account, in which the implant is affixed to the tissuewith point fasteners in a circular
order. The least favourable situation is applied with 4cm spacing between fasteners. The circle
of joints has a diameter of 13cm, and then a radial distance of 4cm between the hernia orifice
edge and joints is preserved according to medical standards. There are 10 fasteners in such a
layout.
Themesh ismodelledwith apolygonalmembrane structure (Fig. 1a), supported in 10points.

The numerical model of the implant is defined within the Finite Element Method using the
MSC.Marc

R
O

commercial system.Eight-nodemembrane elementsQUAD(8)with 3 translational
degrees of freedom at each node are used. The model is discretised by 960 finite elements with
mesh refinement around the tissue-implant joints (Fig. 1b).

The model is subjected to kinematic extortions related to displacements of the abdominal
wall when the patient moves. The range of extortions can be derived from a map of possible
strains of the external layer of the abdominal wall, which was discussed by Szymczak et al.
(2012). A summary of those results is presented in Fig. 2a. However, the strains on the internal
surface of the abdominal wall are 2.6-fold smaller than on the external surface (Podwojewski et
al., 2013). Thus the reduction factor of 2.6 is applied to the results described by Szymczak et al.
(2012). The values and directions of maximal strains of the abdominal wall are different in its
various regions, so the implant is subjected to various extortions when placed in different parts



414 I. Lubowiecka et al.

Fig. 1. (a) Schememodel of the implanted surgical mesh; b) Finite Elementmesh

Fig. 2. (a) Directions and values (in %) of strains on the external abdominal surface in different
sections, according to Szymczak et al. (2012); (b) considered hernia cases

Table 1.Reduced abdominal strains in the radial direction at the fastener imposed in themodel
supports [%]

[%] p1 p2 p3 p4 p5 p6 p7 p8 p9 p10

Case 1 9 3 3 6 7 7 6 3 3 9

Case 2 9 3 2 6 7 7 6 2 3 9

Case 3 12 4 3 7 9 9 7 3 4 12

Case 4 9 6 3 5 13 13 5 3 0 0

Case 5 9 5 3 7 13 13 7 3 5 9

of the abdomen. Thus, five hernia locations are considered as marked in Fig. 2b. For each case,
the extortions are estimated basing on the abdominal strains presented in Fig. 2a, scaled by a
factor of 2.6 and they are applied to the supporting points of themodel (p1 to p10, see Fig. 1a).
The final values of the extortions applied to each supporting point are included in Table 1.

Mechanical properties of themeshes selected for the analysis differ significantly. Orthotropic
or isotropic, linear or bilinear elastic constitutive models have been identified for them, basing
on Biot stress and Biot strain experimentally measured in one-dimensional tensile tests. The
experiments are presented in (Tomaszewska et al., 2013). As one can notice, basing on the
data summarised in Table 1, in each hernia case the meshes are subjected to strains smaller
than 0.3. Thus, constitutive models of themeshes have been specified for the strain range 0-0.3.
The least squaresmethod applied in theMarquardt-Levenberg algorithm is used for parameters



A preliminary study on the optimal choice of an implant... 415

identification.Finally, theobtainedparameters of the constitutivemodels applied for eachkindof
the implant are presented inTable 2. It has been observed thatDualmesh

R
O

is a nearly isotropic
material. The rest of the meshes considered here is distinctly orthotropic, but with different
orthotropy ratios calculated asE1/E2.E1 andE2 are the elastic moduli of the implants derived
for two perpendicular directions wherein E1 > E2. The directions of orthotropy, indicated by
E1 andE2, for the considered meshes are marked in Fig. 3.

Table 2.Parameters of linear or bilinear elastic orthotropicmaterial models of the implants for
the strain range 0-0.3

Limit E [N/mm] E1/E2 Poisson’s
Mesh A stress for for for for εl [–] ratio

[N/mm] ε< εl ε> εl ε<εl ε> εl ν21 [–]

Dualmesh
(2.1) 8.4 28

1.1 N/A 0.3
(2.2) 6.1 26

DynaMesh
(2.1) 4.5 6.4 14

18 39
0.15

0.3
(2.2) 1.7 0.36 N/A

Parietex
(2.1) 3.7 1.6 21

1.8 10 0.15 0.3
(2.2) 2.0 0.87 2.1

Proceed
(2.1) 4.2 40

5.3 N/A 0.3
(2.2) 4.1 7.6

A – Direction of bigger (2.1) or smaller (2.2) stiffness of the mesh

Fig. 3. Directions of the higher and lower stiffness of the consideredmeshes

The accuracy of the implant model with a proposed polygonal shape has been successful-
ly verified against experiments on a physical model of the system subjected to impact loads
resulting from postoperative cough (Lubowiecka, 2015). The h-convergence analysis has been
performed within simulations.
According to the optimisation procedure described in Section 2.1, for each implant placed in

each hernia case, the reaction forces in the supporting points are calculated (stage 1). Nonlinear
static analysis in the range of large strains is performed. Twelve orientations of each implant in
each simulated hernia location are considered (α=0-180 degrees with 15 degree intervals). The
angleα=0 stands for the craniocaudal orientation ofE1 direction of the considered implant as
marked in Fig. 1a.
The influence of the implant orientation on reaction forces is expressed by the value of the

coefficient D = (Fmax −Fmin)/Fm · 100%, where Fmax is the maximum reaction obtained for
the orientation αmax,Fmin is the maximum reaction obtained for the orientation α0 (stage 2 of
the optimisation). The smallest maximum reaction occurs for the optimal orientation α0 of the



416 I. Lubowiecka et al.

implant andαmax is the orientation corresponding to the largest maximum reaction that occurs
in the supporting points of the mesh. αmax is the least appropriate orientation. The larger the
value of theD coefficient, the greater is the effect of the implant orientation on the reaction force.
In the final step of the optimisation problem, the optimal solution described by the implant type
along with its optimal orientation is found (implant type along with its optimal orientation).

3. Results

The calculated values of the angles α0 and αmax along with D coefficients are presented in
Table 3. For almost isotropic Dualmesh

R
O

, D value does not exceed 5% in any area, but
for other meshes it is visibly higher. The largest values of D are obtained for DynaMesh

R
O

(36%-55%) and for ProceedTM (35%-53%). D value of ParietexTM is in the range of 26%-34%.

Table 3.The best and the worst orientations of implants

DynaMesh Parietex Proceed Dualmesh
Case αmax α0 D αmax α0 D αmax α0 D αmax α0 D

[deg] [deg] [%] [deg] [deg] [%] [deg] [deg] [%] [deg] [deg] [%]

1 15 75 36 15 90 28 30 90 36 15 75 4

2 15 75 42 15 90 26 30 90 35 15 75 5

3 15 75 47 30 90 29 15 90 47 15 90 4

4 165 75 55 90 60 34 0 75 53 165 75 3

5 15 90 48 15 90 33 15 90 50 15 90 4

Fig. 4. Maximum reactionsF
max
in meshes depending on the orientation angle α for the following

implants: DynaMesh (DM), Parietex (Px), Proceed (P) and Dualmesh (DMG)

Thevalues of allmaximumreaction forces obtained in this studyare presented inFig. 4. The
distribution of all reactions in theworst and best orientation case is shown inFig. 5. Finally, the
identified optimal orientations of three considered anisotropic implants for each hernia location
considered here are shown inFig. 6. Dualmesh

R
O

is the onlymesh investigated in this study that



A preliminary study on the optimal choice of an implant... 417

Fig. 5. Reactions F obtained in each support for all investigated orientations of the implant, the solid
line is for the best orientation, the dashed line is for the worst orientation of the mesh



418 I. Lubowiecka et al.

Fig. 6. Optimal orientation anglesα0 (orientation of the direction ofE1)

does not have distinct anisotropic properties. A single optimal orientation does not exist in such
a case, any orientation is acceptable.

4. Discussion

Figures 4-6 describe the effects of the implant material orientation on the reaction forces that
occur at the supporting points in the tissue-implant interface. These forces cannot exceed the
capacity of the tissue-implant juncture, otherwise the junction damage and recurrence of the
sickness occurs. The larger the range of junction forces between themost and least appropriate
orientations of the implant, the greater is the influence of the implant orientation on the forces
in the supporting tacks. This range is measured byD coefficient presented in Table 3.D values
of Dualmesh

R
O

are relatively small (3%-5%), so any orientation of this mesh can be applied
in practice. The largest D values are obtained for DynaMesh

R
O

(33%-55%) and for ProceedTM

(36%-53%), which means that surgeons should pay special attention to the proper orientations
of those implants. Values ofD for ParietexTM are in the range of 28%-34%. Those results relate
to the orthotropy ratio of eachmesh (Table 2). The largest forces for each implant can be found
in zone 4 (see Fig. 4). Also the influence of orientation (represented byD value) is the highest in
that zone. The results presented in Fig. 4 prove that the lowest maximal reactions are observed
for ParietexTM in each hernia case.

Variability of reaction forces in all fixation points for certain mesh orientations is shown in
Fig. 5. These results prove that in the optimal orientation, the reactions are relatively low and
they are the most evenly distributed on the supporting points comparing to other orientations.
It is visible that in the case of Parietex, which initially has a small orthotropy ratio, the change
of orientation from the worst to the optimal one causes reduction of the reaction forces but
does not change significantly the shape of the reaction distribution graph.Whereas for strongly
orthotropic meshes, like DynaMesh

R
O

and ProceedTM in their optimal orientations, the distri-
bution of forces ismore even. Such even force distribution justifies regularly spaced fixing joints.
For an orientation different than the optimal, more joints (or stronger ones) should be used in
places where larger reaction forces occur than in places with smaller reaction forces.

In themajorityof cases considered in this study, theoptimalorientation of the stifferdirection
of an implant is the transverse direction (90deg) of the abdominal wall (Table 3 and Fig. 6).
This observation corresponds to the results obtained experimentally by Anurov et al. (2012)
and numerically byHernández-Gascón et al. (2013), who investigated only two orientations of a
surgical mesh in the central area of the abdominal wall. However, also a frequent solution of our
optimisation scheme is 75deg especially for hernia located in zone 4. In this case when operating
with ParietexTM, the optimal orientation of its stiffer direction is 60deg.

The study emphasises the importance of the proper orientation of surgical mesh when im-
posed to kinematic extortions related to abdominal wall movements. Thus we do not include
constrains on the implant deflection related to bulging in the optimisation procedure. Bulging



A preliminary study on the optimal choice of an implant... 419

is related to intraabdominal pressure load and does not take place when the implant undergoes
only kinematic extortions. However, in amore general procedure of finding an optimal implant,
additional constraints upon the maximum displacements could be included to avoid excessive
bulging of the implant.

5. Conclusions

This paper presents an investigation on the influence of orthotropic implant orientation on forces
on tissue-implant junctures caused by deformation of the anisotropic abdominal wall.Moreover,
it gives a study on the optimal choice of surgical orthotropic meshes and their orientation
in ventral hernia repair. Surgeons may consider these results when choosing an implant and
when determining its position in different areas of the abdominal wall, particularly when no
manufacturer’s recommendation exists. Themost important findings are presented below.

• The implant ParietexTM bestminimises reaction forces. Hence, according to our optimisa-
tion procedure, application of this mesh gives the optimal solution. However DynaMesh

R
O

has a better orthotropy ratio giving more even distribution of forces on all supporting
points.

• For optimal orientations of implants in the abdominal wall, forces acting on different
supporting points have themost similar values. Then, a regular distribution of supporting
points is themost justified.When the implant orientation is far from the optimal one, then
the reaction forces are very different in various fixation points, and there is nomechanical
justification for the regular joint distribution around the hernia orifice, and some fixation
regions should be strengthened.

• In zone 4, in the upper lateral part of the abdominal wall, the supporting points face the
largest forces (see Fig. 4) and the implant orientation has the greatest influence on those
forces.

• The orientation of orthotropic implants (DynaMesh
R
O

, ParietexTM andProceedTM) stron-
gly influences the forces on the supporting points (up to 55%, 34% and 53%, respectively).

• Placing the implant in the optimal orientation, as shown in Fig. 6, greatly reduces the
forces on the supporting points, which may determine the success of hernia repair or
postoperative comfort of patients. Although significant influence of the orientation of an
orthotropic implant in the anisotropic abdominalwall onhernia repair persistence seems to
be expected from themechanical point of view, this fact is still underestimated in surgical
practice as confirmed by the newest medical conference reports and scientific papers, see
e.g., Oettinger et al. (2013), Li et al. (2014).

• Our results shownotonly anoptimalmeshplacement butalso results for other orientations
(Fig. 4). On the basis of that, safer and less safe range of orientations can be established.
Information about this range can be useful in clinical practice. Surgeons should pay atten-
tion to the orientation of the implant, which currently is not a common practice, and try
to avoid orientations whichmay highly increase reactions in fasteners and, in consequence,
increase the risk of exceeding the capacity of tack and cause hernia relapse.

• Displacement of the fasteners during regular activity influences the level of junction for-
ces. As a result, the displacement of fasteners should be considered when analysing and
designing the fixation of implants. These results may serve as a basis for the formulation
of a relationship between the optimisation ofmesh implantation and the recurrence rate of
hernias as well as they can be applied in the process of individualisation of the treatment
of abdominal hernias.



420 I. Lubowiecka et al.

Acknowledgments

This study has been partially supported by the EU as a part of the Innovative EconomyOperational

Programme (contract No. UDAPOIG.01.03.01-22-086/08-00) and by the subsidy for the development

of young scientists given by the Faculty of Civil and Environmental Engineering, Gdansk University of

Technology. The computations have been done in TASK Computer Science Centre, Gdańsk, Poland.

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Manuscript received May 27, 2014; accepted for print August 10, 2015