Current Directions in Biomedical Engineering 2018; 4(1): 181 – 184

Andreas J. Horbach and Manfred Staat*

Optical strain measurement for the modelingof surgical meshes and their porosity
https://doi.org/10.1515/cdbme-2018-0045

Abstract: The porosity of surgical meshes makes them flexible for large elastic deformation and establishes the healing
conditions of good tissue ingrowth. The biomechanic modeling of orthotropic and compressible materials requires new
materials models and simulstaneoaus fit of deformation in theload direction as well as trannsversely to to load. This nonlinear modeling can be achieved by an optical deformation measurement. At the same time the full field deformation measurement allows the dermination of the change of porosity with deformation. Also the socalled effective porosity, which has been
defined to asses the tisssue interatcion with the mesh implants,
can be determined from the global deformation of the surgicalmeshes.
Keywords: Porosity, Orthotropy, Surgical mesh, Digital image correlation

1 Introduction
The main motivation for this work was to develop a method
to determine material parameters for compressible surgicalmeshes for a specific material model. Normally, such meshes
are characterized for their biocompatibility [1],[2],[3] andtheir interactions with the surrounding tissue. One outcomeof in vivo experiments is that the effective porosity is an important geometric criterion for the biocompatibilty of mesh
implants [5] .
Additionally the deformation behavior of surgical meshes under load was observed in the present study and evaluated with
optical full field strain measurement by digital image correlation. From this the nonlinear stress-stretch behavior and thechange in porosity were derived. It could be shown that it ispossible to derive the porosity change via image correlation
without recourse to the hyperelastic constitutive law.

Fig. 1: Left side: PVDF-mesh; Right side: TPU - mesh

2 Material and Methods
2.1 Implants
Two different mesh types (FEG Textiltechnik mbH, Aachen,Germany) have been tested. The meshes have been producedwith iron oxides to make them visible in MRI for test purposes and are not for clinical usage (but they have been used
for research for hernia repair , see [3]). They are made outof PVDF (polyvinylidene difluoride) but one of them has asmall amount of TPU (thermoplastic polyurethane) added
to achieve softer properties. TPU and PVDF are no trading
names but they are used to identify the meshes in presentationof results. The figure 1 shows the examined meshes with theprinciple stretching directions (L = longitudinal and T = transverse).

2.2 Optical Strain Measurement*Corresponding author: Manfred Staat, Biomechanics
Laboratory, Institute for Bioengineering, Heinrich-Mußmann-Str.1,
Jülich, Germany, e-mail: staat@fh-aachen.deAndreas J. Horbach, Biomechanics Laboratory, Institute for Bioengineering, Heinrich-Mußmann-Str.1, Jülich, Germany, e-mail:horbach@fh-aachen.deWith the aid of optical strain measurement, the deformation ofmaterials can be measured during a tensile test. In this way,
the anisotropic material behavior can be observed in a simple way. In the present case, a mesh sample was clamped intoa tensile testing machine with a clamping distance of 50mm.
The test started with a preconditioning of 2N for 3 cycles. Af-Open Access. © 2018 Andreas J. Horbach and Manfred Staat, published by De Gruyter.
NonCommercial-NoDerivatives 4.0 License.

This work is licensed under the Creative Commons Attribution-

182 — A. J. Horbach and M. Staat: Optical strain measurement of surgical meshes

Fig. 2: Field of interest.

terwards the samples were extended individually at a speedof 30mm/min until failure. This test was performed for eachmesh in transverse and longitudinal direction.
The mesh deformation is then measured with the digital image correlation software ISTRA 4D (Limess Messtechnik undSoftware GmbH, Krefeld or Dantec Dynamics GmbH, Ulm,
Germany). A homogeneous measuring field is selected (compare to Fig2) to obtain the right Cauchy-Green deformation
tensor C. Least squares fitting is performed with Matlab (TheMathWorks, Natick, MA, USA) simultaneously for both meshorientations with respect to uniaxial stress and biaxial stretch.

Fig. 3: Concept of determining the initial state of the two circles for
effective porosity calculation.

open, which are large enough for the ingrowth of the surrounding tissue. Mühl and Klinge use their concept of the effective
porosity in different studies and compare the results with thephysical definition of porosity [4],[3]. Effective porosity excludes all pores, which are smaller in diameter than a critical
diameter which depends on the mesh material, but is typically
1 mm. They move a circle of critical diameter in each open
2.3 The Itskov Modelpore and measure the effective pore area as the area which canbe covered by the motion [5]. The effective porosity changes
Soft tissues are incompressible like most other materials,
with deformation of pores during a deformation of the surgicalwhich show large elastic deformations. Itskov and Aksel [6]mesh.
have developed a material model which can also represent theTo determine the effective porosity over the entire deforlarge changes of area of knitted fabrics. The model has beenmation, the pore size was measured using two representative
modified and allied to sports wear in [7]. The strain energy(︀)︀
pores under a digital microscope VHX-600 (Keyence, Japan).
function 𝑊𝑊 𝐼𝐼˜𝑟𝑟 , 𝐽𝐽˜𝑟𝑟 , 𝐼𝐼3 is written with the generalized pseudo
An inner circle with 𝑅𝑅0 and an outer circle with 𝑅𝑅0 + 𝑑𝑑𝐹𝐹𝐹0
invariants 𝐼𝐼˜𝑟𝑟 , 𝐽𝐽˜𝑟𝑟 of C; 𝐼𝐼3 is its determinant:are measured in the undeformed mesh. The inner circle cor(︀)︀
𝑊𝑊 𝐼𝐼˜𝑟𝑟 , 𝐽𝐽˜𝑟𝑟 , 𝐼𝐼3 = responds to the individual pore and the second circle corre[︂𝑁𝑁(︁)︁(︁)︁]︂ sponds to the pore with the surrounding mesh area (compare)︀
1 ˜𝛽𝛽𝑟𝑟11 ∑︁
1 (︀ ˜𝛼𝛼𝑟𝑟−𝛾𝛾𝑟𝑟
to figure 3). The ratio of the two surfaces can be used to de𝜇𝜇𝑟𝑟
𝐼𝐼−1𝐼𝐼𝑟𝑟 − 1 +𝐽𝐽𝑟𝑟 − 1 +
4𝛼𝛼𝑟𝑟
𝛽𝛽𝑟𝑟
𝛾𝛾𝑟𝑟 3𝑟𝑟
termine the corresponding effective porosity for the respective
The material constants can be found by fitting with the prop- area. We assume that the deformation is homogeneous overerty: 𝜇𝜇𝑟𝑟 > 0, 𝛼𝛼𝑟𝑟 ≥ 0, 𝛽𝛽𝑟𝑟 ≥ 0. A detailed calculation of the the entire evaluation range and calculate the deformation of
the individual pore from a circle to an ellipse from the global(true) Cauchy stress as derivative of 𝑊𝑊 can be found in [8]optical strain measurement. Furthermore, the area of the mesh
was assumed to be constant during the measurement. Fromthese assumptions we were then able to calculate the porosity
for each load step. This included the case that below a certain
2.4 Effective Porosity
size of the minor axis of the ellipse, the pore is no longer conMühl et al. (2008) [5] introduced the definition of the effective sidered effective and is therefore not counted in the effective
porosity for surgical meshes. They count only those pores as area of porosity. The detailed calculation can be found in [8].

A. J. Horbach and M. Staat: Optical strain measurement of surgical meshes — 183

Tab. 1: Parameters for PVDF mesh(𝑟𝑟)𝜇𝜇𝑟𝑟 [MPa]

𝛼𝛼𝑟𝑟

𝛽𝛽𝑟𝑟

𝛾𝛾𝑟𝑟

𝑤𝑤1

𝑤𝑤2

120.19250
0.3

1.03.89972

3.08488
3.063190.00.01.00.70368

0.00.29632

Tab. 2: Parameters for TPU mesh(𝑟𝑟)10501(𝑟𝑟)r𝜇𝜇𝑟𝑟 [MPa]

𝛼𝛼𝑟𝑟

𝛽𝛽𝑟𝑟

𝛾𝛾𝑟𝑟

𝑤𝑤1

𝑤𝑤2

1
20.22343
0.05773

2.93787
3.29183

1.04.86367

0.0
0.0

0.0
0.35339

1.00.64661

3 Results and Fittings
For the TPU and PVDF meshes a total number of 8 meshes
each were tested. The following parameters were calculated:biaxial stretch in two directions, uniaxial Cauchy stress in load
direction, and actual effective porosity during load steps.

L1L2L3L - fitted
T1T - fitted

151.2

1.4

1.6

1.8

2stretch / λFig. 4: Tensile tests in longitudinal (L) and transverse (T) direction
and fits, PVDF - mesh
Cauchy stress / N/mm 2(𝑟𝑟)rCauchy stress / N/mm 220L2L3
L - fitted
T1T2T - fitted

86

4

2

0
1

1.2

1.4

1.6

1.8

2

stretch / λThe tables 1 and 2 below show the results of the curve fit
for the two meshes for N=2. For N>2 the computing time increased enormously, without any significant improvements ofthe results.

0.4
L1
L2
L3
T2

effective Porosity/ Φ

3.1 Cauchy stress and Material
Parameters

Fig. 5: Tensile tests in longitudinal (L) and transverse (T) direction
and fits, TPU - mesh

0.3

0.2

The figures Fig. 6 and 7 show the change of the effectiveporosity 𝜑𝜑𝑒𝑒𝑒𝑒 𝑒𝑒 in the evaluated region (according to the calculated porosity in Table 3) during deformation. Each figure
shows two jump like drops of the porosity. These jumps represent the situation when one family of pores has a calculateddiameter of 𝑑𝑑 𝑑 0.6𝑚𝑚𝑚𝑚, which means that these pores can beconsidered as fully closed. The critical loss of effective porosity occurs for the PVDF mesh at much lower stretch 𝜆𝜆 than for
the TPU mesh.

0.1

01

1.2

1.4

1.6

1.8

2

2.2stretch/ λFig. 6: Effective porosity under uniaxial loading as function ofmajor principal stretch in loading direction, PVDF - mesh
0.4
L2
L3
T1
T2

Effective Porosity/ Φ

3.2 Effective Porosity

0.3

0.2

0.1

3.3 Optical strain measurement with ahigher resolution
Figure 8 shows results of the digital image correlation measurement of the TPU-mesh in a higher resolution of the strain
field. It is visible that the strain is not as perfectly homoge-

01

1.2

1.4

1.6

1.8

2stretch/ λFig. 7: Effective porosity under uniaxial loading as function ofmajor principal stretch in loading direction, TPU - mesh2.2

184 — A. J. Horbach and M. Staat: Optical strain measurement of surgical meshes

[2]

[3]

[4]

[5]
Fig. 8: Strain field with a higher resolution[6]

neous as expected. Therefore, we plan to text an image based
analysis of the local pore deformation.
[7]

4 Conclusion
The experiments have shown that optical strain measurement
can be used to model compressible surgical meshes. Furthermore, the Itskov model could be successfully used simulatemechanical behavior of the tested surgical meshes. The effective porosity can be calculated from the observed global deformation of the implant.
However, due to its construction as a sum function, the Itskov
model can quickly lead to very long computing times for curve
fitting. This similarly effects the implementation of the Itskov
model in programs for finite e lement a nalysis a nd numericalsimulations. Therefore, a decision should be made after curve
fit as to how large the respective 𝑁𝑁 should be selected for thesum function in order to use the respective material parameters
within an acceptable time.
Nevertheless, it has been shown that the change in effective
porosity can be determined directly from global mesh deformation. For a preliminary assessment of the tolerability of thesurgical meshes after implantation, the procedure describedhere can also be used completely without modeling.
Author Statement
Research funding: The authors state no funding involved.
Conflict of interest: Authors state no conflict of interest.
Informed consent: Informed consent is not applicable.
Ethical approval: The conducted research is not related toeither human or animals use.

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