Rheological measurements of fibrin gels during clotting

THROMBOSIS RESEARCH Printed in the United

Suppl. II, VOI.. 8, 1976 Pergamon Press, Inc.

States

SECTION

RHEOLOGICAL

MEASUREMENTS Eiichi Fukada

I

OF FIBRIN GELS DURING CLOTTING and Makoto Kaibara

Biopolymer Physics Laboratory, The Institute of Physical and Chemical Research Wako-shi, Saitama 351, Japan

ABSTRACT The temporal change of the dynamic rigidity and loss Four moduli of clotting fibrin was investigated. different kinds of apparatus: Thrombelastograph(TEG), Multiple viscoelastorecorder Viscoelastorecorder(VER), (MVER) and Low Shear Viscoelastometer(LSVE.) were used at The different ranges of frequency and shear rate. rigidity of the fibrin gel at the saturation of clotting decreased with the increase of shear rate of Non-linearity measurement above about 0.5 set-l. between stress and strain was observed at the shear With the increase of the strain above about 1 percent. amplitude of oscillation, the rigidity increased due to the stretching of network chains of fibrin. The comparisons of the clotting curve and the rigidity at saturation were made among different kinds of apparatus.

INTRODUCTION Rheological studies for the coagulation of blood have been carried out by a number of apparatus(l-7). In order to study the mechanism of formation of fibrin clots, the dynamic rigidity modulus and loss modulus are determined as functions of time. The clotting time, the rate constant, and saturated value of rigidity are the important quantities to be determined. It has been found that these quantities vary with the shear strain and the shear rate imparted to the fibrin clot during measurement(8). In the present paper, we shall report some of the effects of the shear strain and shear rate on the dynamic properties of fibrin clot obtained by different apparatus. 49

50

MATERIALS Commercially available purified bovine fibrinogen was dissolved at the concentration of 1 or 2 weight percent into a buffer solution of 0.05 M sodium citrate and 0.5 M sodium chloride. Thrombin (26.8 unit/mg) was also dissolved at the concentration of 0.1 or 0.2 mg/ml into the same buffer solution. At the start of measurement, the fibrinogen solution and the thrombin solution were mixed together at the volume ratio of 3 to 1 and immediately poured into the sample container of the apparatus. A drop of paraffin oil was put on the surface of the sample solution in order to avoid the effect of surface coagulation. The solution was adjusted to pH 7.5 and the ionic strength (u) was 0.8.

APPARATUS We have set up three different kinds of apparatus for determining the dynamic rigidity and loss moduli of liquids during gelation. The viscoelastorecorder(VER) employs horizontally oscillating double cylinders. The sampel liquid is filled between the gap of 1 mm between cylinders. The shear strain is varied between 0.01 and 0.1. The measuring frequency is fixed at 3, 10, and 30 Hz. The details of this apparatus have been described in the previous paper(l). The multiple viscoelastorecorder(MVER) employs the six The schematic diagram is sample holders of parallel plate type. shown in Fig. 1. The outer vessel is oscillated mechanically and the forces acting on the inner plates are detected by the strain The outputs of the strain gauges are amplified and led gauges. to the phase sensitive detectors from which the real and imaginary components of the rigidity, G' and G", are derived and recorded The shear strain of the liquid is between as functions of time. 0.004 and 0.1 and the frequency is varied continuously from 0.5 to 5 Hz. The amount of liquid required for each holder is about 1.7 ml. The low shear viscoelastometer(LSVE) employs double The schematic diagram is shown cylinders horizontally rotatable. in Fig. 2. The outer cylinder is sinusoidally rotated and the torque of the inner cylinder is detected by a mechanism similar The rotation of the cylinder causes the to the electric balance. The d.c. output change of the reflected light from the mirror. from the phototube is amplified and led to a coil placed between magnetic poles in order to give a torque which nullifies the At the null condition, the electric deflection of the mirror. current in the coil gives the amount of the torque, which is The amplitude of introduced to the Y axis of the x-y recorder. rotational oscillation of the outer cylinder, which is proportional to the shear strain of the sample liquid, is introduced to the x axis of the x-y recorder. The shear strain is varied between 0.05 and 0.2 and the frequency is varied between 0.002 and 0.3 Hz. Thus the shear The amount of rate covers a range from 5~10~~ to 5x10-1 see-1. the sample liquid is about 7 ml. An example of the Lissajous' figure obtained in the x-y recorder is illustrated in Fig. 3.

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Strain wwe x6 -4

PSD ’ x6

--7-T--

Strain gauge

I

1

G’

1

Tacho generator

The schematic

diagram

G"

1

_

Synchro resolver

FIG. 1 of multiple viscoelastorecorder(MVER).

D. C.

Potentiometer I

The schematic

diagram

FIG. 2 of low shear viscoelastometer

(LSVE).

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FUKADA AND KAIBARA

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When the figure is elliptical we can easily determine the real and imaginary components of the stress, 0' and o", as represented in Fig. 3. Since the strain is given by yo, we obtain G' = a'/~, and G" = o"/y,. The phase angle 6 between the stress and the strain is given by tan6 = all/a'. When the coagulation proceeds, the Lissajous' figure usually presents non-linear behavior as in Fig. 3. If we use the Fourier analysis, we may be able to obtain the higher terms of rigidity modulus. For the present case, in order to avoid the mathematical complexity, we simply take the maximum value of stress an and define a non-linear rigidity modulus Gn = an/y,. We observed the appearance of the non-linear rigidity for almost all the fibrin gels we investigated. This is because the shear strain of our measurements is higher than 1~10'~(4). Figure 4 shows the comparison of the frequency and the shear rate of measurement used in our apparatus and the thrombelastograph(TEG) which is widely used for clinical investigation TEG employs the frequency approximately l/9 Hz and the of blood. shear rate in the test sample changes from 0.1 set-1 to nearly zero during the course of coagulation.

f

FIG. 3

u” 0:

Lissajous' figure of stress and strain. Gn: apparent non-linear rigidity, G': dynamic rigidity, loss modulus G"Z

G” = On/ )6 G'

??

0’/ Zo

6’=cf/lo

tan6 = UT/d

Strain

SHEAR RATE DEPENDENCE We have reported in the previous paper(8) that the shear rate given to the liquid during the measurement gives an influence on the magnitude of the rigidity modulus of the fibrin gels. The higher shear rate results in the lower rigidity modulus of the fibrin gel.

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Figure 5 shows our recent results for the shear rate dependence of the saturated values of rigidity, G' and G"S, It has been foun 3 that if the which have been obtained by VER. measuring shear rate is lower than about 0.5 set-1 G', and G"s Such small are almost constant independent of the shear rate. shear rate does not disturb the gelation process of fibrin.

VER 0

_MVER

00

FIG. 4

_

Comparison of frequency and shear rate of four apparatus: Thrombelastograph(TEG), ViscoelastorecorderWER), Multiple viscoelastorecorder (MVER) r and Low shear viscoelastometer(LSVE).

LSVE

/

I

Kj4

m3

1

I

ICY

Frequency

IO

I ) *

LSVE

Kj4

1 lo-* Shear

VER

MVER

1

I Id3

I

IO’

(t&

I TEG

I

1

16’

) )

* I lo-’ Rate

I

I

I IO (sac’)

IO2

L---+--tsi

0

Shear

IO

2 Rate

2

20

(soi”)

FIG. 5 Shear rate dependence G"s for fibrin gels.

of saturated

values

of rigidity,

G', and

5’1

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When we use TEG and LSVE, which work at the shear rate less than 0.5 set-1, there will be no mechanical disturbance which decreases the value of rigidity modulus. Figure 6 shows the shear rate dependence of the coagulation curves obtained by different apparatus. With TEG, the rigidity E was calculated from the formula c = lOOa/(lOO-a), where a is the amplitude of the TEG curve. With the shear rate lower than 0.5 sec'l, the time dependence of normalized rigidity, that is, the rigidity G' over the saturated rigidity G's, is nearly the same for TEG and MVER. However, with the shear rate 2.5-see-1 by VER, the shape of the coagulation curve becomes different, which gives the longer retardation time. We may summarize, therefore, that the high shear rate results in the lower rigidity modulus at saturation and in the longer reaction time for network formation. The shear rate lower than 0.5 set-1 will not have such influence. 1.0 -”

0

-2 0.8 L -0 : 0.6

freq.(Hzl o---o

MVER

g 0.4

----

TEG

;2 5 0.2 ._0, [L

M

MVER (G’)

-

VER

T

0

IO

20

30

40

60

50 Time

63’) (&I (G’)

70

shear rate (seE’)

0.5

0.14

l/S

0.12Cmaxi

I

0.7

10

2.5

80

SO

100

(min.)

FIG. 6 Shear rate dependence time.

of clotting

curves,

normalized

rigidity

vs.

SHEAR STRAIN DEPENDENCE We have already shown that the Lissajous' curve of stressThis strain is not elliptic but substantially deformed. indicates that the non-linear terms are present for the rigidity modulus and also that the apparently observed rigidity G' is a function of the measuring amplitude or the shear strain. Figure 7 illustrates an experimental result showing the dependence of G' and G" of fibrin gel on the amplitude of oscillation. The gelation was performed at measuring amplitude At about 180 minutes after starting the of 90 urn with VER. measurement with the amplitude of 90 urn, the amplitude was decreased to about 13 urn. The rigidity G' decreased with the decrease of measuring ampitude as shown in Fig. 8. Then if the

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amplitudewas increased to 35 urnand the measurementtias continued at that amplitude, G' was observed to increase again as shown in Fig. 7. At 280 minutes when G' became saturated again, the amplitude of measurement was decreased. The value of G' decreased with the decrease of amplitude and approached to the same limiting value of G' as the previous experiment of decreasing the amplitude as shown in Fig. 8. This limiting value of G, which is about 630 dyne/cm2, appears to present the rigidity modulus for the unstretched fibrin network. The increase of G' with the larger amplitude would represent the stretching effect of molecular chains between crosslinkages.

~\~slIz]

FIG. 7

200

300

SOP1 / I I

Thixotropic behavior observed in clotting curves of fibrin. At 180 min. after starting measurement, the amplitude of vibration was decreased from 90 urnto 10 pm, and then increased to 35 pm.

j/-Y

1 0

lo0

-a0

Tim*

300

(min.)

F1G. 8 Measuring amplitude dependence of G' and G" for fibrin gel.

xd

0

IO

1 20

1

30

40

so

funPlilua()I)

60

m

I

80

so

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When we use VER and MVER we measure G' as the component of the stress which has the same frequency as the exciting oscillation. This can be a function of amplitude of strain, if the rigidity contains nonlinear terms. If we use Lissajous' figure with LSVE as shown in Fig. 3, we can separate visually the nonlinear component of the stress as Gn - G'. Figure 9 illustrates the clotting curve with LSVE at the shear strain-of 0.2 and the frequency of l/20 Hz.

FIG. 9 c

G”

Clotting curves of nonlinear rigidity, Gn, dynamic rigidity G', and loss modulus G", observed by Low shear viscoelastometer(LSVE).

-

G'

??

i

COMPARISON

WITH TEG

TEG is a simple apparatus compared with VER, MVER and LSVE. However, the present work has demonstrated several advantage of TEG from the standpoint of fundamental research besides its First, since the shear rate convenience in clinical application. employed is lower than 0.1 set-1 no mechanical disturbance will be effective to destroy the fibrin network during its formation. Second, since the wave form of exciting strain is made flat near the maximum amplitude, the contribution of nonlinear component of stress is effectively reduced and the measured rigidity is near to the rigidity G' without stretching effect. From the amplitude a of TEG curve, the rigidity is The relation between E and the calculated as E = lOOa/(lOO-a). absolute value of G', was obtained using our experimental results for the fibrin gels at the same conditions. Figure 10 shows such Using the data by MVER we obtained G'~/E = 32 dyne/cm2 relation. The values of G', measured by VER is and G*s/~ = 34 dyne/cm2. smaller because of the larger shear rate employed in this apparatus.

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FIBRIN GEL RHEOLOGY

FIG. 10 Comparison of saturated rigidity values obtained by Thrombelastograph(TEG) , Multiple viscoelastorecorder (MVER), and viscoelastorecorder(VER).

VER - TEG

REFERENCES 1.

SCOTT BLAIR, G.W. Rheology of blood coagula. In: Flow Proterties of Blood and other Biological Systems. A.L. Copley and G. Stainsby (Eds.) Oxford: Pergamon Press, 1960, p,172.

2.

HARTERT, H. and SCHAEDER, J.A. The physical and biological Biorheology, I, 31, 1962. constants of thrombelastography.

3.

Rigidity COPLEY, A.L., KING, R.G. and SCHEINTHAL, B.M. moduli of bovine fibrin gels initiated by thrombin. Biorheology, 1, 81, 1970.

4.

ROBERTS, W.! KRAMER, O., ROSSER, R.W., HENRY, F., NESTLER, M. and FERRY, J.D. Rheology of fibrin clots I, Dynamic viscoelastic properties and fluid permeation. Biophys. Chem., I, 152, 1974.

5.

THURSTON, G.B. Viscoelasticity 12, 1205, 1972. -

6.

DINTENFASS, 1971.

L.

of Human Blood. Biophys.

Blood Microrheology,

London:

Butterworths,

J.,

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AND KAIBARA

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7.

KAIBARA, M. and FUKADA, E. Non-newtonian viscosity dynamic viscoelasticity of blood during clotting. Biorheoloqy, 2, 73, 1969.

8.

FUKADA, E. and KAIBARA, M. The dynamic gels. Biorheoloqy, 10, 129, 1973.

rigidity

and

of fibrin