Influence of fibrinogen concentration on the Young’s ... · Influence of fibrinogen concentration on the Young’s modulus in fibrin gels BMTE02.44 Julienne Brouwers Supervisors:

Influence of fibrinogenconcentration on the Young’s

modulus in fibrin gels

BMTE02.44

Julienne Brouwers

Supervisors: Drs. M. van Lieshout, Dr. Ir. G. Peters

Eindhoven, November 2002

Influence of fibrinogen concentration in fibrin gels on Young’s modulus

Department of Biomedical Engineering 2

Abstract

For tissue engineering a heart valve, the idea has risen to combine the advantages ofpolycaprolactone and fibrin by using the first as a mechanical backbone and the latter as acell-delivery substance surrounding the backbone. The mechanical properties of fibrin shouldstill be high enough to be used as part of a scaffold for a heart valve. Therefore, areproducible protocol has been developed to determine the Young’s modulus using a tensiletesting machine. Also, the influence of fibrinogen concentration in fibrin gels on the Young’smodulus has been determined, by using the developed protocol. The protocol consisted ofmaking gels, which originated from mixing a fibrinogen solution with a thrombin solution.This was done for fibrinogen solutions with a concentration of 4, 8, 10, 14, 18 and 30 mg/mland a thrombin solution of 5 IU/ml. Then the fibrin gels were placed in the tensile testingmachine with dimensions 5 mm in width and 30 mm in length. The results showed a linearincreasing Young’s modulus with increasing strain for all samples. The correlation betweenthe Young’s modulus and the concentration was linearly increasing until a concentration ofabout 14 mg/ml showing a maximum initial Young’s modulus of 9995 Pa (+-185.5) and amaximum Young’s modulus at +-20 % strain of 29600 Pa (+-932.8). The reproducibility washigher at high fibrinogen concentrations than at lower ones. The developed protocol isespecially suited for the testing of fibrin gels with a high fibrinogen concentration.



Table of contents

Abstract ---------------------------------------------------------------------------------------- 2

1. Introduction -------------------------------------------------------------------------------- 4

1.1 Fibrinogen ------------------------------------------------------------------------------ 51.1.1 Structure---------------------------------------------------------------------------- 51.1.2 Formation of fibrin network ----------------------------------------------------- 6

1.2 Mechanics------------------------------------------------------------------------------- 61.2.1 Neo-Hookean ---------------------------------------------------------------------- 7

1.2.1.1 Uniaxial extension-------------------------------------------------------------- 71.2.1.2 Planar extension ---------------------------------------------------------------- 9

2. Materials and Methods------------------------------------------------------------------10

2.1 Fibrin gel preparation ----------------------------------------------------------------11

2.2 Tensile testing -------------------------------------------------------------------------11

2.3 Data processing -----------------------------------------------------------------------12

2.4 SEM preparation ----------------------------------------------------------------------12

2.5 Rheology testing -----------------------------------------------------------------------12

3. Results --------------------------------------------------------------------------------------14

3.1 Uniaxial extension --------------------------------------------------------------------14

3.2 Planar extension----------------------------------------------------------------------17

3.3 SEM-------------------------------------------------------------------------------------18

3.4 Rheometer------------------------------------------------------------------------------18

Conclusions-----------------------------------------------------------------------------------19

Discussion-------------------------------------------------------------------------------------20

Acknowledgements--------------------------------------------------------------------------22

References: -----------------------------------------------------------------------------------22

Appendix A-----------------------------------------------------------------------------------23

Appendix B -----------------------------------------------------------------------------------24

Appendix C-----------------------------------------------------------------------------------26



1. Introduction

Tissue engineering has emerged as a rapidly expanding approach to address the organshortage problem. It is an interdisciplinary field that applies the principles and methods ofengineering and the life sciences toward the development of biological substitutes that canrestore, maintain, or improve tissue function. Much progress has been made in the tissueengineering of structures relevant to cardiothoracic surgery, including heart valves, bloodvessels and myocardium [1]. Usually, isolated cells are used to engineer new tissues. Thecells are seeded on a three dimensional scaffold followed by in vitro culturing. The scaffoldsserve as physical supports and templates for cell attachment and tissue development [2].

The requirements for an ideal scaffold are the easy handling and moulding of complex 3-Dstructures like valve conduits or vessels with complex side branches. The material should notbe toxic or have any immunologic side effects. The diffusion barrier of the scaffold has to beas low as possible to guarantee an optimal nutrition in thicker tissues. The mechanical as wellas the chemical properties (e.g. the integration of growth factors) should be modifiable. Thecontrol of the degradation is important to adapt the structural support of the scaffold to thetissue development. Many substances are used in the production of scaffolds, e.g. syntheticpolymers, natural polymers or biological scaffolds [2].

Fibrin is a biodegradable polymer and the major component of blood clots. It is formed bypolymerisation of fibrinogen monomers catalysed by thrombin. In comparison to othermaterials used for tissue engineering purposes, fibrin gel combines some importantadvantages. At first, the degradation rate is controllable and can be adapted to the tissuedevelopment. Beyond it, fibrin gel can be produced from patient’s blood and thereforeimmunogenic reactions are improbable [2]. Inhomogeneous distribution of cells in a scaffoldis often a problem. In contrast, when cells are incorporated before gelling, the distribution inthe fibrin gel is homogeneous from the beginning, caused by the fast immobilization of thecells during the polymerisation of the gel/cell suspension within a few minutes. Structureswith a layer thickness up to 3 mm can be produced without the problem of local cell necrosiscaused by diminished diffusion [2].

A major disadvantage of fibrin is the mechanical stiffness, which seems to be low (table 1.1).

Table 1.1 Details of experiments with fibrin gels.Reference Quantity Fibrinogen

concentration(mg/ml)

Valuerange(kPa)

Correlation Experiment

[3] Young’smodulus

0.5-3 0.93-6.49 Unclear Uniaxial extension

[4] Storage shearmodulus

0-6 0-0.15 Unclear Rheometer

[5] Young’smodulus at10% strain

30-70 6.7-23.9 Unclear Uniaxial extensionRate=25 mm/min

[6] TensileStrength

25-75 2-foldincrease

Directlyproportional toconcentrationof fibrinogen

Tensile testing

[7] Young’smodulus

16-28 12 Not influencedby fibrinogenconcentration

Tensile testingRate= 30 mm/min

[8] TensileStrength

20-60 5-foldincrease

Unclear Unclear



The influence of the fibrinogen concentration in fibrin on the mechanical properties has beeninvestigated but researchers have produced varying values for this influence and also for theYoung’s modulus; unfortunately, often the testing protocol is unclear. Moreover, the testingprotocols, if known, are very different.

Other materials have been considered, like polycaprolactone. This material is well suited to beknitted as a scaffold, which seems to be more mechanically compatible than fibrin. The ideahas risen to combine the advantages of polycaprolactone and fibrin by using the first as amechanical backbone and the latter as a cell-delivery substance surrounding the backbone.The mechanical properties of fibrin should still be high enough to be used as part of a scaffoldfor a heart valve. Different combinations of factors leading to the optimal mechanicalproperties have to be determined. Therefore, a reproducible mechanical test should bedeveloped. The preceding has led to the following two questions:

What is the optimal protocol for a reproducible mechanical test on fibrin gel?What is the influence of the concentration of fibrinogen in the fibrin gel on the Young’smodulus?

1.1 Fibrinogen

1.1.1 StructureFollowing vascular injury, fibrin comprises the major protein component of the hemostaticplug and fibrinogen is the target protein of the coagulation cascade. It can also be used as‘fibrin glue’ during surgery. Fibrinogen is a 340-kDa soluble plasma protein consisting ofthree pairs of disulfide-bonded α-, β- and γ-chains arranged as depicted in figure 1.1. The Eand D regions in each half-molecule are delineated by a pair of disulfide rings, which linkchains α to β, β to γ and γ to α [9].

Figure 1.1 Schematic structure of fibrinogen. Fibrinopeptides A and B are shown as black boxes on theα- and β-chains, respectively. The disulfide bonds joining the chains are shown as lines [9].



1.1.2 Formation of fibrin networkSeveral thrombin-sensitive bonds have been identified and are shown as small arrows infigure 1.1. Thrombin converts fibrinogen to fibrin by catalysing the proteolytic removal ofboth fibrinopeptide A and fibrinopeptide B. These cleavages unmask two polymerisation sitesin the E region, forming soluble fibrin, to which one D region from each of two fibrin(ogen)molecules can bind. The fibrin spontaneously polymerises to form double-strandedprotofibrils, with the fibrin monomers within each strand end-to-end and the fibrin acrossstrands arranged in a half-staggered overlap, as depicted by the combination of strands a and bin figure 1.2 [9].

Figure 1.2 The formation of fibrin network [9].

The protofibrils may further associate laterally to produce fibres, which themselves mayassociate to form fibre bundles. As also indicated in figure 1.2, the γ-chains of adjacent Dregions within a strand of a protofibril are covalently cross-linked by isopeptide bonds, theformation of which is catalysed by factor XIIIa. Thus, in cross-linked fibrin, the individualstrands consist of polymers of covalently linked fibrin molecules [9].Covalent cross-linking within fibrin networks produces dramatic effects on rheologicalproperties. Ligated clots exhibit mechanical stiffnesses up to five times greater than theirunligated counterparts [4].

1.2 Mechanics

Fibrin gel is a visco-elastic material, which means that it exhibits both viscous and elasticproperties. A common approach to modelling visco-elastic behaviour is by means ofcombining elements representing ideal elastic behaviour and ideal viscous behaviour. Theusual method of doing this is using a spring and dashpot analogy. The spring represents idealelastic properties and the dashpot, ideal viscous properties. The simplest combinations are toput the two elements in series and in parallel. This leads to the so-called Maxwell element andthe Kelvin or Voigt element. These are illustrated in figure 1.3 [10]. Different combinationsof several Maxwell and Kelvin-Voigt elements can be used to model visco-elastic materials.

Maxwell Element Kelvin-Voigt ElementFig 1.3 Spring and Dashpot models for visco-elasticity [10].



If a strain is applied to a visco-elastic material there is an instantaneous response (elastic) anda delayed response (viscous). A purely elastic response is in phase with the strain and a purelyviscous response is out of phase with the strain. The relationship between the applied strainand the stress response is expressed for a visco-elastic material by defining two shear moduli,G' and G". These are known as the storage modulus and the loss modulus respectively. Thestorage modulus describes the component of the stress that is in phase with the strain andindicates the stored energy and the loss modulus describes the component that is out of phasewith the strain and indicates the dissipated energy [10].The shear modulus is defined as

''' iGGG += and )'''( 22 GGG += (1)

1.2.1 Neo-HookeanAnother way to describe the dynamic behaviour of fibrin is by using the neo-Hookean model[11]. The Neo-Hookean constitutive equation is given by:

EI GpT +−= (2)

where T is the stress, p is the hydrostatic pressure, G is the elastic modulus in shear and E thestrain tensor.

IBü −= (3)

TFFB *= (4)

where F is the deformation gradient tensor.

1.2.1.1 Uniaxial extensionFor uniaxial extension with length of the sample>>width of the sample, B becomes:

=

==

−

−

−

−

−

−

11

11

21

2/11

2/11

1

2/11

2/11

1

00

00

00

00

00

00

.

00

00

00

αα

α

αα

α

αα

αTF*FB (5)

where α is the ratio of deformed to undeformed length.The stress components are calculated by substituting the components of B into eq. 2

2111 αGpT +−= (6)

13322 α

GpTT +−== (7)

The deformation is achieved by applying a force f in x1 direction, at the ends of the sample.The true stress acting on the ends is divided by the area of the deformed sample ∆x2∆x3=a1,so that

2111

1

1 αGpTa

f +−== (8)



Because no tractions act on the sides of the block, T22= T33 = 0 and p=G/α1. Substituting thisexpression in eq. 8 gives

)1

(1

2111

1 αα −== GT

a

f(9)

For an incompressible material

*1

*111 xaxavolume ∆=∆= or

1

*1

1 αa

a =

where *1a and *

1x∆ are the original area and length.

Eq. 9 can also be expressed in terms of the strain ε. Recalling that α=1+ε and substituting,yields

)1

33(

32

11 εεεε

+++= GT (10)

In the limit of small strain

εGT 311 = for 1<<ε (11)

which is in the linear region of figure 1.4.

Figure 1.4. Tensile and compressive stress versus extension ratio for a rubber sample [11].

The Young’s modulus can be defined as

εε

2211

0lim

TTE

−=

→(12)

which gives

GE 3= (13)

Thus, the Young’s modulus is three times the modulus in shear, a well known result forincompressible, isotropic materials.



1.2.1.2 Planar extensionFor planar extension with width of sample >> length of sample >> thickness of sample, thewidth will change little compared to the length and thickness. B becomes:

=

==

21

21

1

1

1

1

100

010

00

100

010

00

.1

00

010

00

α

α

α

α

α

αTF*FB (14)

The stress components are calculated by substituting the components of B into eq. 2

2111 αGpT +−=

GpT +−=22 (15)

21

33 αG

pT +−=

Since there are no forces acting on the x3-surface, T33=0, p=G/α21. Thus

)1

(2

1

2111 α

α −= GT (16)

For small strains it can be deducted that the “planar” tensile modulus is four times that inshear

GE 4= (17)



2. Materials and Methods

Fibrinogen type 1-S from bovine plasma (Sigma) and thrombin from bovine plasma (Sigma)were both dissolved in medium, which consisted of 90% Ham’s F-12 with L-Glutamin(Biowhittaker), 9% fetal bovine serum (Biochrom ag) and 0.9% penicillin/streptomycin10.000 u/10.000 µg/ml (Biochrom ag). A fresh fibrinogen solution was made for everyexperiment, but the thrombin solution was used for about 7 days. In order to fill the mouldwith fibrinogen and thrombin a double-seringe (two-component fibrin sealant) was usedcalled Geratzesatz/Kit-5.0 ml (Baxter) (figure 2.1).

Figure 2.1 The two-component fibrin sealant.

It mixes the two components completely right before they enter the mould, so the fibrinogenstarts polymerising once in the mould. All moulds were 4 cm in length, 1 cm in width and 0.5cm in depth (figure 2.2).

Figure 2.2 The moulds used for the production of fibrin gels.

A Zwick Z010 tensile testing machine with a 20 N-sensor in series with a 10 kN-sensor wasused to do the tensile testing. The clamps used were 1 cm in width. As mentioned in thesection mechanics, pieces of fibrin with length >> width (uniaxial extension) could be used orpieces of fibrin with width >> length (planar extension). At first, fibrin gels with width >>length were used to do tensile testing. Then it was decided to apply uniaxial extension withpieces of fibrin of 5 mm in width and with length >> width.It was hypothesized that during the experiments the concentration of thrombin in the fibringels was high enough to establish complete polymerisation of the fibrinogen. However, theamount of thrombin was doubled twice to make sure the concentration was high enough forcomplete polymerisation. SEM pictures were taken to get a view of the structure of differentfibrin gels. A few rheology tests were performed to compare the tensile testing results withrheology results.



2.1 Fibrin gel preparation

The fibrinogen and thrombin needed were weighed. Fibrinogen was dissolved in medium,often using a stirring bar. Thrombin was dissolved in medium. The double-seringe was filledwith fibrinogen and thrombin solutions. Then the needle was placed on the seringes and themoulds were filled while the solutions mixed. Then the moulds were placed in the incubatorfor 1 hour at 370, which is the optimum temperature for thrombin. Carefully, the fibrin gelswere taken out of the moulds. The pieces for the planar extension were sectioned tranverselyand the pieces for the uniaxial extension were sectioned longitudinally using a scalpel. Eachpart of the fibrin gels was weighed to determine its dimensions and put in a petri dish withmedium to prevent from dehydration.

2.2 Tensile testing

The clamps were placed exactly parallel. The fibrin gel was measured in length and then hungin the upper clamp of the tensile testing machine. When it was hanging freely, straight down,the force was nulled to rule out the stress created by its own weight. Then the fibrin gel waslet down and tightened in the bottom clamp leaving a distance of approximately 10 mmbetween the clamps for the planar extension and 30 mm for the uniaxial extension. Becauseoften, when tightened, the samples enforced a negative force about -0.003 N, a pre-load of0.005 N was first applied at a speed of 30 mm/min. In this way, the samples were all stretchedat the same initial load. Then the sample was stretched to a strain of 25% at a speed of 30mm/min (earlier tests had shown that the strain at break was over 100 % (appendix A)). Theclamps returned back to their original position. The fibrin gel was taken out and placed backagain in the same position as the first time. The sample was tested again to collect moreresults (earlier tests had shown that at 25 % strain no plastic deformation had taken place(Appendix A)). For the planar extension the distance between the clamps was now 5 mm, forthe uniaxial extension it was again 30 mm. Again the force was nulled while the sample washanging freely. This was often necessary, because water was pressed out making the weightless and thus the force smaller. The protocol was the same for all the different concentrationsof fibrinogen (table 2.1). The experiments with short samples were only performed once withseveral fibrin gels. Of all experiments with long samples the concentration 30 mg/ml wastested once, the concentrations 4, 8 and 14 mg/ml were tested twice and the concentration 18mg/ml was tested three times. Moreover, the concentrations 14 and 18 mg/ml were also testedonce with a doubled amount of thrombin. During every experiment several fibrin gels weretested.

Table 2.1 Several concentrations of fibrinogen and thrombin, which have been tested.Concentration

fibrinogen (mg/ml)Concentration

thrombin (IU/ml)Length of clamp sample

(mm)10 5 10/ 514 5 10/ 54 5 308 5 30

14 5 3014 10 3018 5 3018 10 3030 5 30

Because most concentrations were tested on more than one date, not only the reproducibilitybetween the fibrin gels of the different moulds could be determined, but also thereproducibility between different testing dates.



2.3 Data processing

The computer program which switched on the tensile testing machine was programmed toproduce *.Tra files which contained a ‘length of the sample’ column and a ‘force’ column.The area of the sample was calculated by dividing the volume by the length. Because thefibrin gels almost entirely consist of medium, the density was assumed to be 1g/ml.The strain was determined using the length of the sample at the time of the pre-load as initiallength. This means that all the samples started at the same force. The advantage is that theinitial length doesn’t differ because of different initial forces caused by tightening of theclamps. Of course, the initial stress wasn’t exactly the same for all fibrin gels, because ofdifferent areas, but this was considered negligible.The tensile testing machine was not developed for materials with a low Young’s modulus likefibrin. Probably because the 20-N sensor was measuring forces of not even 1 % of itsmaximum, the force-strain curves showed irregularities instead of being smooth. Therefore,the strains and forces were averaged. For data-files containing about 2500 numbers 9 pointsbefore and after each number were summed, all weighed equally, and divided by 19 tosmooth the curve. For data-files containing less numbers, the averaging was done usingapproximately the same ratio of 2500/9 (appendix B).The stress was determined by using eq. 9. The Young’s modulus was determined by takingthe derivative of the stress against α2-1/α for uniaxial extension times three (eq. 11) and bytaking the derivative of stress against α2-1/α2 times four for planar extension (eq. 17). For aNeo-Hookean material the curve should be at least initially flat, but this wasn’t the case. Itwas assumed that the first part of the curves was linear. Data of the four curves of one fibringel (recall that every sample was sectioned longitudinally and both pieces were tested twice)were taken together and a linear line was fitted through all data up to α2-1/α =0.25 usingMatlab-tools-datafitting. The first 25 data were left out, because often in the beginning therewere strong irregularities. For data-files containing less numbers, the amount of data left outusing approximately the same ratio of 2500/25. The initial Young’s modulus was defined asthe value of the curve at the x-axis intercept (appendix C).Then all data of one sample were plotted up to α2-1/α =0.7 and another curve was fitted. A4th degree polynomial was experimentally determined to be the best fit. Although therelationship between G and E is only valid for small strains, the Young’s modulus at a strainof 20 % was nevertheless determined, because this level of strain corresponds with the strainsoccurring in a human aortic valve.

2.4 SEM preparation

Fixated or freeze-dried samples were used to make SEM pictures (SEM Philips XL30Scanning Electron Microscopes). The samples with the highest and the lowest concentrationin this study were used to see if there was any difference in structure. All samples were usedafter tensile testing was done.Two pieces of fibrin of 30 mg/ml were placed in water for an hour and then placed in thefreezer of 800 C together with two pieces of fibrin of 30 mg/ml that came directly out of themedium. Two pieces of fibrin of 4 mg/ml and two pieces of fibrin of 8 mg/ml that camedirectly out of the medium were also placed in the freezer of 800 C. All fibrin pieces werefreeze-dried and gold-sputtered (Labconco FreeZone freeze dry system). Then SEM pictureswere taken. Both samples kept in water and medium were used to rule out the possibility thatsalts would reduce the view when SEM pictures were taken.

2.5 Rheology testing

A cylindrical sample of fibrin with concentration 18 mg/ml was prepared according to theprotocol described above. It was placed in the rheometer (Rheometric Scientific). It wascompressed to about 10% and a frequency sweep test was performed. Earlier research found a



strain of 0.5 % to be the optimum strain to measure at. Other strains were applied as well. Toobtain more results the experiment was done with another sample. The rheometer producedvalues for the dynamic modulus, which were multiplied by three. These tests were performedto check whether they would give the same value for the Young’s modulus as the tensiletesting did.



3. Results

3.1 Uniaxial extension

Figure 3.1 shows the non-averaged force against strain for one sample with a fibrinogenconcentration of 18 mg/ml. The two sectioned pieces of a fibrin gel were always slightlydifferent in area which can be seen in the figure by the two different levels of forces. Also, theirregularities of the curve are depicted. There was no decline in strength between the first andthe second measurement on one piece of fibrin. Differences in value occurred simply becauseof a new measurement. Forces could be slightly higher as well as lower during the secondmeasurement.

0 0.05 0.1 0.15 0.2 0.25-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

strain

forc

e (

N)

force-strain curves

sample A test 1sample A test 2sample B test 1sample B test 2

Figure 3.1 Force-strain curves for all four pieces of one sample with a fibrinogen concentration of 18mg/ml.

Figure 3.2 shows the stress against α2-1/α for the same sample. The irregularities havebecome less by the averaging of the forces and strains, but are still apparent.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1000

0

1000

2000

3000

4000

5000

6000

7000

alfa2 - 1/alfa

stress -strain curves

stre

ss (

N/m

2)


Figure 3.2 Stress-strain curves for all four pieces of one sample with a fibrinogen concentration of 18mg/ml.



Therefore, the derivatives of these curves, which have been taken to determine the Young’smodulus, show an enormous spreading (figure 3.3).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1x 10

5

alfa2 - 1/alfa

Yo

un

gs'

mo

du

lus

(Pa

)Young's modulus


Figure 3.3 The Young’s modulus curves for all four pieces of one sample with a fibrinogenconcentration of 18 mg/ml.

Figure 3.4 shows the linearly fitted line through all data of this sample up to α2-1/α =0.25.

0 0.05 0.1 0.15 0.2 0.25-2

-1

0

1

2

3

4

5x 10

4

y = 4.134e+004*x + 9574

Young's modulus

alfa 2 - 1/alfa

Y o u n g ' s m o d u l u s ( P a )

data 1 linear

Figure 3.4 Linear fit through all data up to α2-1/α =0.25.

The initial Young’s modulus here is 9.574 kPa.Figure 3.5 shows all data of this sample up to α2-1/α =0.7 and the fitted 4Th degreepolynomial. The Young’s modulus at α2-1/α =0.6 (~20 % strain) is 29.76 kPa.



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-8

-6

-4

-2

0

2

4

6

8x 10

4 Young's modulus

alfa2 - 1/alfa

Yo

un

g's

mo

du

lus

(Pa

)

Figure 3.5 Fitted polynomial through all data of this sample up to α2-1/α =0.7.

For all uniaxial extension tests these four above shown figures were similar.Table 3.1 shows the calculated averaged Young’s moduli. During every experiment severalfibrin gels were tested. First the average value within one experiment was taken for everyexperiment of the same concentration. Then the average of these values was taken. Thestandard deviation was determined by averaging the standard deviation of all experimentswith the same concentration. The experiments with doubled thrombin concentration did notshow higher Young’s moduli. Therefore, the results have also been used to calculate theaverage modulus and the standard deviation.

Table 3.1 Calculated Young’s moduli for uniaxial extension. Upper standard deviation is the averagedstandard deviation of all experiments with the same concentration. The lower is the standard deviationof the averaged values of all experiments with the same concentration and thus a measure for thereproducibility between experiments.Fibrinogenconcentration(mg/ml)

Number ofexperiments

Initial Young’s modulus(Pa) (mean +-SD)

Young’s modulus at α2-1/α=0.6 (Pa) (mean +-SD)

4 2 4722 +- 881.6 (18.7%) +- 690.8 (14.6 %)

10480 +- 2320 (22.1%) +- 1472 (14.0 %

8 2 5898 +- 889.8 (15.1%) +- 276.5 (4.7 %)

15060 +- 1041 (6.9%) +- 438.4 (2.9 %)

14 3 9584 +- 417.4 (4.4 %) +- 2026 (21.1 %)

26720 +- 1399 (5.2 %) n.d.

18 4 9809 +- 501.8 (5.1%) +- 495.8 (5.1 %)

29600 +- 932.8 (3.2%) +- 63.64 (0.2 %)

30 1 9995 +- 185.5 (1.9%) n.d.

28550 +- 1184 (4.2%) n.d.

Figure 3.6 and figure 3.7 depict the upper standard deviation of table 3.1.



Initial Young's modulus

0

2000

4000

6000

8000

10000

12000

0 5 10 15 20 25 30 35

concentration fibrinogen (mg/ml)

Yo

un

g's

mo

du

lus

(Pa)

Young's modulus and standard deviation

Figure 3.6 Initial averaged Young’s modulus and standard deviation

Young's modulus at alfa^2 - 1/alfa =0.6

0

5000

10000

15000

20000

25000

30000

35000

0 5 10 15 20 25 30 35

Concentration fibrinogen (mg/ml)

Yo

un

g's

mo

du

lus

(Pa)

Young's modulus and standard deviation

Figure 3.7 Averaged Young’s moduli and standard deviation at at α2-1/ α =0.6.

3.2 Planar extension

The planar extension experiments using fibrin samples with width >> length resulted in anenormous spreading and a much lower Young’s modulus than obtained using the other tensiletesting results as can be seen in table 3.2.

Table 3.2 Calculated Young’s moduli for planar extension.Concentration Initial Young’s modulus (Pa)

(mean +-SD)Young’s modulus at α2-1/α=0.6 (Pa) (mean +-SD)

10 3101 +- 600.2 (19.4 %) 6421 +- 1188 (18.5%)14 4604 +- 706.9 (15.4 %) 14710 +- 433.1 ( 3.0%)



3.3 SEM

The pictures of all samples taken by the SEM showed areas with a different kind of structure,which would suggest that the fibrin gels were inhomogeneous (figure 3.8). There was nodifference in structure seen between the samples of different concentrations. Also, someabnormalities were found on the surface as depicted in figure 3.9. In a lot of regions thestructure shown in figure 3.10 was seen.

Figure 3.8 SEM picture (60x) of a fibrin sample with a fibrinogen concentration of 4 mg/ml.



3.4 Rheometer

Both samples had a Young’s modulus of about 3 kPa, with a range from 2.1 to 3.6 kPa.



Conclusions

An optimal protocol for reproducing mechanical testing on fibrin gel has been set up and isdescribed above. The reproducibility within an experiment and between several experimentsis good. The correlation between the fibrinogen concentration in fibrin gels and the Young’smodulus is linear for concentrations between 4 and about 14 mg/ml showing a maximuminitial Young’s modulus of 9995 Pa and a maximum Young’s modulus at +-20 % strain of29600 Pa. Above that, changing the fibrinogen concentration has no influence on the Young’smodulus. The reproducibility within an experiment is higher at high fibrinogen concentrationsthan at all of the lower ones. This applies for the initial Young’s modulus and the modulus atα2-1/α =0.6.



Discussion

Initially, fibrin gels with width >> length were used to do tensile testing. Unfortunately, itappeared that gels of 1 cm width (recall that the clamps were also 1 cm in width) showed tobulge out of the clamps once tightened and this affects the measurement by causing a lowerYoung’s modulus and a higher standard deviation. Because either fibrin gels with length >>width or with width >> length had to be used to comply with respectively uniaxial extensionor planar extension it was decided to use pieces of fibrin of 5 mm in width and with length >>width.Because it would have taken too long to wait for new moulds with a width of 5 mm it wasdecided to section the fibrins longitudinally.There are several causes for the deviations that are seen. When the fibrins were taken out ofthe moulds sometimes they stuck to the mould, especially the fibrins with low concentrationof fibrinogen. Consequently, there were tears or variations in width. Because by dividing theweight by the length, the averaged area was determined. The samples which had beendamaged had in fact a lower true area, because the smallest area determines the amount ofstrain a certain force causes. Also, sometimes the fibrin gels had a slanting side, which alsocauses a deviated area.When sectioning the fibrin gels it was difficult to section them exactly straight. Moredifficulties occurred with fibrin gels with a low fibrinogen concentration than with the oneswith a high concentration, because of their weakness. This variance in width influenced theYoung’s modulus slightly.Sometimes it was not possible to place the fibrin pieces exactly straight in the clamps,because for example they were a bit twisted. This probably caused shear stresses, whichlowered the calculated Young’s modulus. When tightening the clamps, the fibrin present inbetween the clamps was pushed out and caused a negative force. A pre-load was applied totry to compensate for this but the negative force is not completely caused by compression sothis pre-load is not completely correct.The length of the sample was hard to determine. While measuring the fibrin sample it washard to say whether it might be compressed, extended or in its original length, especially withthe fibrin gels of low concentration fibrinogen.Once sectioned, the samples were kept in medium till they were used for the measurement.Two samples were once placed in medium for an hour and weighed before and afterwards todetermine any swelling or shrinking. The two samples had shrunk for about 2 % after an hour.Therefore it was decided to regard this negligible. This was only done for a sample of 30mg/ml, the influence on fibrin gels with other concentrations was assumed to be the same buthas not been determined.

The initial Young’s modulus, which has been calculated, is in fact not the real initial modulusbecause a pre-load was applied. For the samples with a fibrinogen concentration of 14 mg/mland higher a strain of about 3 % was apparent at the pre-load which is quite low. For thelower concentrations this strain was higher and it is thus less correct to call the calculatedYoung’s modulus initial. The applied pre-load was the same for all samples. Better wouldhave been to apply the same stress for all samples thus to immediately adapt the force to thearea. But it would have been best to apply the same strain for all samples thus adapting theforce to the area and the Young’s modulus for all samples. At first, a few experiments shouldbe performed to estimate the Young’s modulus and then this estimate could be used in thesetting of the pre-load.

There was no difference in structure seen between the three concentrations. This may becaused by the freeze-drying, which caused artefacts. The abnormalities seen on the surface ofsome samples may have been caused by pollution.



Both samples used for the rheometer were in moderate condition. The first one had a varyingthickness. A constant thickness is a requirement for a rheometer to measure a correct dynamicmodulus. The second one had a tear, which probably influenced the measurement. Varyingthe input for the area largely caused the great differences in the found values for the dynamicmodulus. This was done, because the effective area was hard to determine. A possibleexplanation for the differences between the found values for the Young’s modulus with thetensile testing machine and the rheometer is the fact that the way of loading between the twomethods is different. Fibrin gels align when stretched; when compressed there is no alignmentand if shear is then applied, the loading is different than with tensile testing.

It can be said that the protocol that has been set up is very suitable for the testing of fibrin gelswith a high fibrinogen concentration. It would be recommended to use moulds of 5 mm inwidth to avoid the influence of sectioning. When testing fibrin gels with a fibrinogenconcentration of 30 mg/ml the thrombin concentration used was 5 IU/ml. It would beinteresting to see what the influence on the Young’s modulus would be when using a higherconcentration of thrombin. Also, the influence of the formation of cross-links by factor XIIIaon the Young’s modulus would be interesting to investigate.



Acknowledgements

I would like to thank Drs. M. van Lieshout for her very pleasant coaching. She was alwayswilling to help me with any kind of problem. I also would like to thank Dr. Ir. G. Peters forhis very helpful insights.

References:

1. Julie R. Fuchs MD. et al, Tissue engineering, a 21st century solution to surgicalreconstruction, The annals of thoracic surgery, 72 (2), 577-591, 2001

2. Stefan Jockenhoevel. et al, Fibrin gel – advantages of a new scaffold incardiovascular tissue engineering, Eur. j. of Cardio-Thoracic surgery, 19 (4), 424-430, 2001

3. M. Benkherourou. et al, Quantification and Macroscopic Modeling of the NonlinearViscoelastic Behaviour of Strained gels with Varying Fibrin concentrations, IEEETransactions on Biomedical Engineering, 47 (11), 2000

4. Esther A. Ryan. et al, Structural origins of fibrin clot rheology, Biophysical Journal,77, 2813-2826, 1999

5. D. Sierra. et al, Failure characteristics of multiple-component fibrin-based adhesives,Department of Biomedical Engineering, University of Alabama at Brimingham, 2001.

6. S. Marshall, Commercial fibrinogen, Autogenous plasma, whole blood andcyopecipitate for coagulum pyelolithotomy: a comparative study, J. of Urology, 119 ,1978.

7. J. Velada. et al, Reproducibility of the mechanical properties of Vivostat systempatient-derived fibrin-sealant, Biomaterials, 25 , 2002.

8. Wan. et al, Is the amount of fibrinogen in cryoprecipitate adequate for fibrin glue?Introducing an improved recycled cryoprecipitate method, Transfusion, 29 , 1989.

9. John B. Walker. et al, The molecular weights, mass distribution, chain composition,and structure of soluble fibrin degradation products released from a fibrin clotperfused with plasmin, J. of biological Chemistry, 274 (8), 5201-5212, 1999

10. G. Walker, Teaching Notes, University of Teesside, UK, 2000.11. C. Macosko, Rheology, principles, measurements and applications, VCH Pubishers,

1994.



Appendix A

-0.5 0 0.5 1 1.5 2-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

strain

forc

e (

N)

deformation of fibrin till break

Figure A.1 A sample of fibrin with fibrinogen concentration of 10 mg/ml and an area of 7 *10^-6 m2.

0 100 200 300 400 500 600 700 800 900-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04cyclic loading

timestep

forc

e (

N)

Figure A.2 Cyclic loading to 20 % strain of a sample of fibrin with fibrinogen concentration of 10mg/ml and an area of 50 *10^-6 m2



Appendix B%name: 'force'%This m-file is to display the four curves of force against%the strain of one sample

clear allclose all

load A.TRA;length1=A(:,1);strain11=(length1-length1(5,1)) /length1(5,1);%length1 (5,1) contains the length of the sample at the pre-load

%this loop is made to keep out the irregularities seen in the very%beginning of the testingr=0;l1=length(A);for i=1:l1 strain11(i); if strain11(i)>0.001 r=r+1; strain1(r)=strain11(i); force1(r)=A(i,2); endend

%all forces and strain data of test A are being averagedfor i=10:length(strain1)-9 strainaver1(i)=(strain1(i-9)+strain1(i-8)+strain1(i-7) +strain1(i-6)+strain1(i-5)+strain1(i-4)+strain1(i-3)+strain1(i-2) +strain1(i-1)+strain1(i)+strain1(i+1)+strain1(i+2)+strain1(i+3) +strain1(i+4)+strain1(i+5)+strain1(i+6)+strain1(i+7)+strain1(i+8) +strain1(i+9))/19; forceaver1(i)=(force1(i-9)+force1(i-8)+force1(i-7)+force1(i-6) +force1(i-5)+force1(i-4)+force1(i-3)+force1(i-2)+force1(i-1) +force1(i)+force1(i+1)+force1(i+2)+force1(i+3)+force1(i+4) +force1(i+5)+force1(i+6)+force1(i+7)+force1(i+8)+force1(i+9))/19;end

%the same procedure is now done for the three other curves

load B.TRA;length2=B(:,1);strain22=(length2-length2(5,1)) /length2(5,1);

r=0;l2=length(B);for i=1:l2 strain22(i); if strain22(i)>0.001 r=r+1; strain2(r)=strain22(i); force2(r)=B(i,2); endend

%all forces and strain data of test B are being averagedfor i=10:length(strain2)-9 strainaver2(i)=(strain2(i-9)+strain21(i-8)+strain2(i-7) +strain2(i-6)+strain2(i-5)+strain2(i-4)+strain2(i-3)+strain2(i-2) +strain2(i-1)+strain2(i)+strain2(i+1)+strain2(i+2)+strain2(i+3) +strain2(i+4)+strain2(i+5)+strain2(i+6)+strain2(i+7)+strain2(i+8) +strain2(i+9))/19; forceaver2(i)=(force2(i-9)+force2(i-8)+force2(i-7)+force2(i-6) +force2(i-5)+force2(i-4)+force2(i-3)+force2(i-2)+force2(i-1) +force2(i)+force2(i+1)+force2(i+2)+force2(i+3)+force2(i+4)



+force2(i+5)+force2(i+6)+force2(i+7)+force2(i+8)+force2(i+9))/19;end

load C.TRA;length3=C(:,1);strain33=(length3-length3(5,1)) /length3(5,1);

r=0;l3=length(C);for i=1:l3 strain33(i); if strain33(i)>0.001 r=r+1; strain3(r)=strain33(i); force3(r)=C(i,2); endend

%all forces and strain data of test C are being averagedfor i=10:length(strain3)-9 strainaver3(i)=(strain3(i-9)+strain3(i-8)+strain3(i-7) +strain3(i-6)+strain3(i-5)+strain3(i-4)+strain3(i-3)+strain3(i-2) +strain3(i-1)+strain3(i)+strain3(i+1)+strain3(i+2)+strain3(i+3) +strain3(i+4)+strain3(i+5)+strain3(i+6)+strain3(i+7)+strain3(i+8) +strain3(i+9))/19; forceaver3(i)=(force3(i-9)+force3(i-8)+force3(i-7)+force3(i-6) +force3(i-5)+force3(i-4)+force3(i-3)+force3(i-2)+force3(i-1) +force3(i)+force3(i+1)+force3(i+2)+force3(i+3)+force3(i+4) +force3(i+5)+force3(i+6)+force3(i+7)+force3(i+8)+force3(i+9))/19;end

load D.TRA;length4=D(:,1);strain44=(length4-length4(5,1)) /length4(5,1);

r=0;l4=length(D);for i=1:l4 strain44(i); if strain44(i)>0.001 r=r+1; strain4(r)=strain44(i); force4(r)=D(i,2); endend

%all forces and strain data of test D are being averagedfor i=10:length(strain4)-9 strainaver4(i)=(strain4(i-9)+strain4(i-8)+strain4(i-7) +strain4(i-6)+strain4(i-5)+strain4(i-4)+strain4(i-3)+strain4(i-2) +strain4(i-1)+strain4(i)+strain4(i+1)+strain4(i+2)+strain4(i+3) +strain4(i+4)+strain4(i+5)+strain4(i+6)+strain4(i+7)+strain4(i+8) +strain4(i+9))/19; forceaver4(i)=(force4(i-9)+force4(i-8)+force4(i-7)+force4(i-6) +force4(i-5)+force4(i-4)+force4(i-3)+force4(i-2)+force4(i-1) +force4(i)+force4(i+1)+force4(i+2)+force4(i+3)+force4(i+4) +force4(i+5)+force4(i+6)+force4(i+7)+force4(i+8)+force4(i+9))/19;end

plot(strainaver1,forceaver1,'y',strainaver2,forceaver2,'m',strainaver3,forceaver3,'b',strainaver4,forceaver4,'r')



Appendix C%name: 'E-modulus'%This m-file calculates the stress and E-moduli for uniaxial%extension using the columns generated in the m-file 'force'.%if planar extension is applied all 'xast'-columns have to be%changed in 'xasv'-columns. The constant a has to be changed in the value 4

%extensionalfa1(r)=1+strain1(r);alfa2(r)=1+strain2(r);alfa3(r)=1+strain3(r);alfa4(r)=1+strain4(r);

%For uniaxial extension alfa^2 - 1/alfa ('xast') has to be determined and%for planar extension alfa^2 - 1/alfa^2 ('xasv') has to be determined

for r=1:length(strainaver1) xast1(r)=(alfa1(r))^2-(1/alfa1(r)); xasv1(r)=(alfa1(r))^2-(1/((alfa1(r))^2));end




%the constants for the area of the two samples in m^2areaA=1.897*10^-5;areaB=2.97*10^-5;

a=3; % constant that calculates E by multiplying G with a

%determining the stress and Eclear tl1=length(strainaver1);for t=1:l1 stress1(t)=forceaver1(t)*((1+strainaver1(t)))/areaA;end

clear tfor t=1:(l1-1) E1(t)=a*(stress1(t+1)-stress1(t))/(xast1(t+1)-xast1(t));end

clear tl1=length(strainaver1);for t=1:l1 stress1(t)=forceaver1(t)*((1+strainaver1(t)))/areaA;end


clear t



l2=length(strainaver2);for t=1:l2 stress2(t)=forceaver2(t)*((1+strainaver2(t)))/areaA;end


clear tl3=length(strainaver3);for t=1:l3 stress3(t)=forceaver3(t)*((1+strainaver3(t)))/areaB;end


clear tl4=length(strainaver4);for t=1:l4 stress4(t)=forceaver4(t)*((1+strainaver4(t)))/areaB;end


%plotting of stressplot(xast1,stress1,'y',xast2,stress2,'m',xast3,stress3,'b',xast4,stress4,'r')xlabel('alfa^2 - 1/alfa')title('stress (N/m^2)')

pause

%plotting of Young's-moduliplot(xast1,E1(1:l1-1),'y',xast2,E2(1:l2-1),'m',xast3,E3(1:l3-1),'b',xast4,E4(1:l4),'r')xlabel('alfa^2 - 1/alfa')ylabel('Youngs-modulus')

pause

%taking all data togetherclear rclear tb=25; %constants are less when less data are present in file than 2500c=25;d=25;e=25;

f=0;for i= b:l1 if xast1(i)<0.25 %when determining the strain at alfa^2 - 1/alfa = 0.6 %then 0.25 turns into 0.7 f=f+1; endend

g=0;for i= c:l3 if xast2(i)<0.25 g=g+1;



endend

h=0;for i= d:l3 if xast3(i)<0.25 h=h+1; endend

j=0;for i= b:l4 if xast4(i)<0.25 j=j+1; endend

Ex=[xast1(b:f) xast2(c:g) xast3(d:h) xast4(e:j)];Ey=[E1(b:f) E2(c:g) E3(d:h) E4(e:j)];[x i]=sort(Exx);y=Eyy(i);plot(x,y)xlabel('alfa^2 - 1/alfa')ylabel('Youngs-modulus fitted')

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Influence of fibrinogen concentration on the Young’s ... · Influence of fibrinogen concentration on the Young’s modulus in fibrin gels BMTE02.44 Julienne Brouwers Supervisors: