Blood low shear rate rheometry: influence of fibrinogen level and hematocrit on slip and migrational effects

Biorheology35:4,5(1998) 335-353

Blood low shear rate rheometry: influence of fibrinogen level and hematocrit on slip and migrational effects C. Picart, *t J.M. Piau, * H. Galliard, * and P. Carpentier f * Laboratoire i Laboratoire

de Rhkologie, Universite’ Joseph Fourier - Grenoble 1, Institut National Polytechnique de Grenoble, et CNRS UMR 5520, BP 53, 38041 Grenoble cedex 9, France de Midecine Vasculaire, Universiti Joseph Fourier - Grenoble 1, Centre Hospitalier Universitaire, BP 217 X, 38043 Grenoble cede.r 9, France

Received18December1997;acceptedin revisedform 09 October1998

Abstract

Red blood cell (RBC) aggregation is of prime importance in viva and in vitro for low flow rates. It may be estimatedby rheometrical measurementsat low shearrates, but theseare perturbed by slip and migrational effects which have already been highlighted in the past. Theseeffects lead to a torque decay with time so that the true value of the stressat low shearrates may be greatly underestimated. Elevated aggregationbeing associatedwith different diseases,pathological blood samplesshow more pronouncedperturbing effects and a strong time dependencyin low shearrate rheometry. To test the dependence of slip and migrational effects on RBC aggregation, and particularly to determine the way in which they depend upon fibrinogen concentration ([Fb]), a home-made measuring system with roughened internal and external walls (170 pm roughness) was used to study low shear rate rheometry for RBC suspensionsin PBS buffer containing albumin (at 50 g/l) and fibrinogen at various concentrations. The influences of hematocrit, shear rate, and fibrinogen concentration were investigated. Particular attention was paid to data acquisition at low shear rates (lo-” s-I to 3 x 1O-* s-l). The combined influence of hematocrit and fibrinogen was investigated by adjusting hematocrit to 44 or 57% and fibrinogen concentration ([Fb]) to 3.OA.5-6.5 g/l. Microscopic observationsof the blood samplesat rest were performed. They showedthat different structures were formed according to fibrinogen concentration. The rheometrical measurementsindicated that torque decay with shearingduration was strongly dependenton fibrinogen concentration and on shearrate at fixed hematocrit. Migrational and slip effects were more pronouncedasshearrate decreased,fibrinogen concentration was raised, and hematocrit was lowered. The resultshave beenexplained on the basisof the expected microstructure of flowing blood in relation to the microscopic observationsat rest. Keywords:

Hemorheology; rheometry; RBC aggregation; fibrinogen; microstructure

Reprint requeststo: C. Picart, current address,INSERM U 424, Facultt de Medecine,Bat 3, 11 rue Haumann,67 085 Strasbourgcedex,France;Tel.: +33 3 88 24 3394;Fax: +33 3 88 24 3399;e-mail:Catherine. [email protected] 0006-355X/98$8.000 199810s Press.All rightsreserved

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1. Introduction Clinical interest in low shear rate rheometry has greatly increased since the work of Chien et al. (1970), who attributed the increase in blood viscosity at low shear rates to RBC aggregation in the presence of plasma macromolecules. RBC aggregation induced by plasma macromolecules is a reversible phenomenon (Bronkhorst et al., 1997). The linear (rouleaux) or three dimensional structures (aggregates) formed at low shear rates (or stress) can be easily disrupted when shear rate increases. Fibrinogen has often been considered as the most important protein inducing RBC aggregation (Maeda et al., 1987; Shiga et al., 1983; Game et al., 1996) since it has the biggest size (48 nm). Evaluation of RBC aggregation has been performed by many different experimental techniques such as light transmission (Schmid-Schtinbein et al., 1972) or retrodiffusion (Donner et al., 1989). These techniques provided useful aggregation indices and disaggregation thresholds, but these were always derived for shear rates greater than 5 s-l and are representative of the fast-phase aggregation process. Better understanding of shear dependent rouleaux formation and of shear stress dependent aggregate size has been obtained with a rheoscope (Shiga et al., 1983; Chen et al., 1996) but only at low hematocrit. At still lower shear rates (down to lo-* s-l) and at physiological hematocrit, the formation of large aggregates and also of a continuous network can be observed by microscopy under shear flow (Copley et al., 1975). As blood exhibits a yield stress, directly related to its microstructure and to aggregate formation, these measurements are of great patho-physiological importance. Unfortunately, however, rheometrical measurements with conventional surfaces (smooth walls) are associated with torque decay during shearing (Cokelet et al., 1963; Cokelet, 1972; Merrill, 1969b), which has been explained by the formation of a plasma layer at the rheometer walls (Cokelet et al., 1963). These experimental problems are a common feature of all types of suspensions (Barnes, 1995) and are representative of the slip of the sample along the rheometer walls (phase separation leading to a cell depleted layer along the walls) and of the shear migration of particles. Recently, migrational and slip effects have been be mitigated for normal blood in the hematocrit range 55 to 95% by roughening the rheometer walls (Picart et al., 1998a). Cokelet (1972) indicated qualitatively that the torque decay was dependent on fibrinogen concentration and on hematocrit. Perturbing effects are expected to be more pronounced for pathological blood samples in which fibrinogen concentration can increase up to 7 g/l compared to 2.5 to 3.0 g/l for normal blood samples. Further work on pathological blood samples with high fibrinogen concentrations (up to 7 g/l) demonstrated that the stress-net shear deformation curves were different according to the surface roughness of the rheometer walls (Picart et al., 1998b), suggesting that the interactions of the sample with the walls are of prime importance. A higher surface roughness (170 pm) was needed to mitigate time-dependent effects for pathological blood samples. The aim of the present study was to test the dependence of the torque decay during shearing on RBC aggregation and to evaluate how it depends on several factors influencing RBC aggregation such as (i) fibrinogen concentration (normal to pathological range 3 to 7 g/l), (ii) hematocrit, and (iii) shear rate. Rheometrical measurements at low shear rates were therefore performed at different fibrinogen concentrations (3.0, 4.5 and 6.5 g/l) for two

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337

cell concentrations (44 and 57%) with a roughened walls rheometrical device (Picart et al., 1998a). Microscopic observations of three blood samples at rest were performed to give a better understanding of the structural organization.

2. Experimental Methods 2.1. Red blood cell suspensions

Fresh blood from fourteen healthy donors (Grenoble Blood Transfusion Center) was drawn by venipuncture and anticoagulated with Ethylene-Diamine-Tetraacetic-Acid (EDTA). Plasma and buffy coat were removed after centrifugation at 3000 rpm for 10 min. Red blood cells were then washed twice in phosphate buffered saline (PBS, pH 7.4, osmolarity 300 mOsm/l, 0.15 M). Suspensions of RBCs in phosphate buffered saline (PBS) were prepared at two cell concentrations (45 and 60%, seven donors for each) and for each donor, at three fibrinogen concentrations (4, 7, 10 g/l). These hematocrits were chosen by taking into account the sensitivity limits of the rheometer and to represent (i) physiological hematocrit and (ii) a more concentrated suspension (where individual RBC interactions are increased; Murata and Secomb, 1989). The three fibrinogen concentrations were chosen to reproduce normal and pathological ranges. 2.2. Suspending medium

Human freeze-dried fibrinogen (fraction I, type 1, from human plasma, 92% clottable, Sigma) and bovine albumin (fraction IV, Sigma) were dissolved in isotonic phosphate buffered saline (PBS) at high concentrations (40 g/l for fibrinogen and 400 g/l for albumin). Aliquots of 1 ml were prepared and stored at -22°C. Dilution’s of the aliquots in PBS were performed just before the sample preparation in order to have final concentrations of 50 g/l for albumin and between 3 and 10 g/l for fibrinogen in the suspending medium. Fibrinogen and albumin solutions were added to the packed red blood cells (1.8 ml for hematocrit 45% and 2.4 ml for hematocrit 60%). Final fibrinogen concentration was controlled at the end of the sample preparation (after mixing and new centrifugation) by the thermocoagulation method (Foster et al., 1951). They were 3.0, 4.5 and 6.5 g/l within a 10% uncertainty associated with the experimental method. Experimental values were around 25 to 30% lower than expected, which may be due to absorption of fibrinogen on the RBC or on tube walls. Final hematocrits were controlled automatically with a Coulter device (Coultronics) and were respectively 44 f 1% and 57 f 1%. The difference between expected and final hematocrit values may be explained on the basis of the entrapped extracellular buffer in the packed RBCs. Final measured hematocrit and fibrinogen values at the end of sample preparation were taken for the analysis of results. The shape of the erythrocytes was observed with an optical microscope to ensure that no noticeable changes occurred. Samples were stored at 6°C and measurements were made within the day following blood sampling. 2.3. Rheometry

The stress measurements were made using the Contraves Low Shear 40 rotatiqg coaxial rheometer (Mettler Toledo Inc., Switzerland) working under controlled velocity conditions.

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Table 1 Experimental conditions of data acquisition at low shear rates. Acquisition time and corresponding net shear deformation (y = ,’ x to) were chosen according to shear rate so that the time required for the whole procedure did not exceed 50 min

i, (s-9

Duration (to in min)

Deformation (p x to)

1 x 10-j

20

1.2

3 x 10-s

15

2.7

1 x 10-2

5

3.0

3 x 10-2

3

5.9

All measurements were carried out with a home-made measuring system (R, = 7.16 mm, Ri = 6.34 mm, and L = 18 mm, where R, and Ri represent the radii of the measuring cup and measuring bob, and L the length of the bob). The internal and external walls were roughened by sticking silicon carbide particles (average size 200 pm) on double-sided waterproof adhesive (3M Laboratories) which was firmly stuck to the stainless steel surfaces. Further description of the device including geometrical factor calculations and surface roughness evaluation is described in (Picart et al., 1997, 1998a). Surface roughness was measured with a profilometer (Palmer) and estimated at 170 pm for the given measuring system. For this geometry, the theoretical minimal shear stress measured was 0.56 mPa. The temperature of the outer cylinder was regulated with a controlled water bath (T = 25°C). The rheometer was linked to a computer (IBM 386) for automatic operation and shear stress acquisition during shearing duration. Scanning electron microscopic observations were performed to ensure that the shape of the erythrocytes after one hour’s shearing in this system was not altered. 2.4. Methodology

Measurements were made at 25°C with a sample volume of 4 ml. The internal static cylinder was centered with distilled water in the most sensitive range. As a control, the viscosity of water was measured at 1 s-r (0.9 mPa s f 5%) to ensure the reproducibility of the calibration. Blood was set in the outer cup and the inner cylinder was lowered into the outer cup and raised one or two times to overcome surface tension effects and to ensure an even distribution of blood in the annulus without air bubbles. The torque exerted on the internal bob is measured via a deflection system in the measuring head. Measurements at shear rate higher than 3 x 10e2 s-‘were made by decreasing the shear rate from 100 to 3 x 1O-2 s-i in eight steps and reading the stationary value for each step. Particular attention was paid to data acquisition at lower shear rates using the following procedure in order to have the same initial conditions (Fig. 1A): (i) pre-shearing at 30 SK’, (ii) short resting period, (iii) application of the given shear rate for a given period (summarized in Table 1). Results were analyzed in term of total net shear deformation instead of time (net shear deformation = shear rate times duration: y = p x to, which is a dimensionless parameter). Acquisition time for each shear rate was chosen to have at least a deformation of 2.5 (Picart et al., 1998a), except for the lowest shear rate of 10V3 s-‘. A 20 min acquisition time was deliberately chosen to ensure that the whole procedure time did not exceed 50 min. Indeed, values obtained at 3 x 10e2 s-t by decreasing

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ii

t----)-m 15 s

-1

0

Time to

10s

1

2

3

4

5

6

DEFORMATION

Fig. 1. (A) Procedure of data acquisition with pre-shearing fi = 30 s-’ (values of 9 are given in Table 1). (B) Experimental curves were plotted in terms of shear stress against total net shear deformation, instead of duration (y = ,’ x to, dimensionless parameter) in order to compare the different plots. Three parameters were derived from the stress deformation curve: maximum stress (o,), slope of stress growth which represents the modulus (G) and elastic modulus when 2’ = 10e3 s-r, and in case of stress decay, slope of this decay (SD).

shear rate or using the protocol described in Fig. lA, agreed within 15%. Three parameters were derived from the stress deformation curves (Fig. 1B): maximum stress (q& slope of stress growth (modulus G), which represents the elastic modulus at low shear rate, and in case of stress decay, the slope of this decay (SD). There was an initial stress at zero time a(O), corresponding to the relaxation from the high pre-shearing and associated with the beginning of restructuring at rest, since blood exhibits a yield stress. As a consequence, the first part of the curves may be slightly moved on the deformation scale but this had no influence on the

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representative parameters chosen. For the 44% cell concentration, measurements could not be made below lo-* s-l because of the sensitivity limit of the stress measurement (0.56 mPa). 2.5. Microscopic observations

Three samples of erythrocytes suspended in their medium at 3.0, 4.5 and 6.5 g/l fibrinogen concentration and at 57% hematocrit were observed with an optical microscope (Axioskop, Zeiss) with PlanApo 10x, 0.25 NA and PlanApo 40x oil, 1 .O NA immersion lenses. The images were magnified with a 1.6x lens and photographed with a Nikon camera. One drop of the suspension was set with a capillary tube on a microscope slide. A cover slip was carefully laid on the top, and held down with a finger. In these conditions, the thickness of the blood sample could not be precisely controlled but it was estimated at 40 pm with a micrometer (Palmer). Thus, a layer of cells could be observed. MicroPhotographs were taken at 160x and 640x magnifications after 3 min of stasis. Image processing and binarization were performed on the 160 x magnification photographs with home made software in order to deduce quantitative parameters of RBC network structure. As RBC diameter represented 12 pixels (leading to an equivalent length of 0.5 pm per pixel), the following procedure was performed by the software in order to separate single cells from cells in clusters: (i) low pass filter (64 x 64 pixels): each pixel is removed according to the value in the 64 x 64 neighbors, (ii) median filter (3 x 3 pixels): each pixel is replaced with the median value of 3 x 3 neighborhood in order to reduce noise, and (iii) opening: this operation performs an erosion (a pixel is removed if four or more of its eight neighbors are white) followed by a dilation (a pixel is added if four or more of its eight neighbors are black). As a result, objects are smoothed and isolated objects smaller than 2 x 12 pixels (two RBCs) were removed. After image processing, a network structure index was derived and given as a number of red blood cells. The higher this index is, the more clustered the sample is. 3. Results Results are given for forty-two blood samples from fourteen donors: seven donors for each hematocrit 44 and 57%, and three fibrinogen concentrations for each donor. The mean parameters and standard errors derived from the stress-net shear deformation curve results are given in Table 2. 3.1. Stress versus shear rate curves

Maximum stress is plotted as a function of shear rate for the different fibrinogen concentrations ([Fb]) and hematocrits (Fig. 2). The stress increased as shear rate increased and, at fixed hematocrit, as the Fb concentration rose. At 57% and [Pb] = 3.0 g/l, the curve had a gentle slope and tended to a constant value, indicating the presence of a yield stress. For the highest concentrations, a break in slope was observed for shear rates lower than lo-* s-i. If we consider the experimental plots for shear rates greater than lo-* s-’ the curves were expected to tend to a yield value. But for lower shear rates, a reverse trend was observed. Mean stress at 10m3 s-’ was lower for [Fb] = 6.5 g/l than for 4.5 g/l. At 44%, stress did not to tend to a plateau at [Fb] = 3.0 g/l, whereas it did at the highest [Fb].

57%

44%

H

2.8 f 0.2

4.1 f 0.2

5.4 f 0.3

7.7 f 0.4

3 x 10-3

10-2

3 x 10-2

2.4 f 0.2

1.3f0.1

%I

10-J

3 x 10-2

10-2

P

4.4f0.5

3.7f0.3

3.0fO.l

2.6fO.l

1.3f0.3

1.3f0.2

G

3.0 g/l

-

-

-

-

-

-

SD

13.1 f0.5

9.2 f 0.2

6.8 f 0.2

4.4 f 0.2

5.1 f0.3

3.5 f 0.3

am

10.1 f0.8

7.7 f 0.6

6.3 f 0.6

5.9 f 0.3

2.9 f 0.5

2.8 f 0.3

G

4.5 g/l

-

0.1 fO.O

0.3 f 0.0

1.3fO.l

0.1 f 0.0

0.4fO.l

SD

10.4 f 0.9* p < 10-4

12.2 f 0.3* p < 10-4

p < 10-4

p < 10-4

p < 10-4

p < 10-4

9.0 f 0.9*

7.1 f 0.3*

12.7 f 0.6*

p < 10-4 p = 0.008

17.5 f 0.9*

7.1 f 1.5*

p = 0.003

p < 10-4 3.8 f 0.5*

4.3 f 0.4*

p < 10-4

p < 10-4 5.2 f 0.3*

4 f 0.2*

G

3.6 f 0.3*

urn

6.5 g/l

-

NS

0.8fO.l

p=10-4

1.1*0.1*

p=o.O03

3.9f0.6*

NS

0.5fO.l

p=O.o08

1.2*0.2*

SD

Mean f SE values of the parametersfor the forty-two blood samples(sevenfor each given hematocrit and fibrinogen concentration): maximum stressurn (in mPa), modulus G (in mPa) which representselastic modulus at low shearrate (10m3s-l), slope of stressdecay SD(in mPa/unit of deformation), as a function of hematocrit (H) (44 or 57%), fibrinogen concentration (3.0, 4.5 and 6.5 g/l) for shear rates of 10m3s-t; 3 x 10-3 s-t; lo-* s-1; 3 x 10-2 s-1

Table 2

n

‘;I 2

2

g 3 8 F 2 2 8zs

T

f 2

b Fij-

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lo4

ld

ld

IO’

lO0

10-l 10”

1W3

lo-*

I@’ SHEAR

IO” RATE

(i’

IO’

lo2

lo3

)

Fig. 2. Maximum shearstress(a,) as a function of shearrate for the three fibrinogen concentrations 3,0,4.5 and 6.5 g/l at 44 and 57% hematocrit. Experimental points are meansof the measurementson sevendonors for each curve. Standard errors are not representedsince they were low and could not be seenon the plot. Experimental points at shearrates lower than 3 x 10M2SC’ are the maximum stresses derived from the stress-deformationcurves (given in Table 2).

3.2. Influence ofjbrinogen

concentration

(constant shear rate and hematocrit)

At 57% hematocrit, the stress-deformation

curves associated with the experimental plots below 10e2 s-t, for which a break was observed, showed great differences depending on fibrinogen concentration (Fig. 3). No stress decay was observed for the lowest concentration, but it was present for [Fb] = 4.5 g/l. The curves obtained for [Fb] = 6.5 g/l showed the strongest instabilities. At 10-s s-l, the curve decayed but also oscillated. This may be related to the migration of the structure near the walls and to slip effect. As a consequence, the mean maximum value was less than for [Fb] = 4.5 g/l (Fig. 2). Thus, for a given shear rate, stress decay was strongly dependent on, and increased with, increasing Fb concentration. At 44% hematocrit, the same trend was observed. Stress decay increased with increased fibrinogen concentration (Fig. 4). 3.3. Injuence

of shear rate (constant hematocrit

and$brinogen

concentration)

At both hematocrits, no stress decay was observed for [Fb] = 3.0 g/l, over the whole range of shear rate (Fig. 5). For the [Fb] = 4.5 g/l, stress decay was significant for shear rates lower than 10m2 s-t, but not for greater shear rates. For [Fb] = 6.5 g/l, a shear rate of 3 x 10m2 s-t was needed to mitigate the slip and migrational effects. At 44% hematocrit, no decay occurred for [Fb] = 3 g/l (Fig. 6). For [Fb] = 4.5 g/l, significant decay occurred at 10e2 s-‘, but not at 3 x 10m2 s-t, whereas the decay was always statistically significant at the highest Fb concentration. ,

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(1998) 335-353

’

4

*...-

’

’

. . ..-. :****..**.*

. ...***

.-*

I-

0

0.2

0.4

0.6

I”,’

- 3x10

SHEAR

0.5

A

0.8

1.2

1

1.4

DEFORMATION

‘.“,”

-3 s -’

II,, 0

’ ’ r *.-.. *....

-7

NET

H=S7%

343

1 NET

I

1.5 SHEAR

2

I,,,

I I,,,

1

2.5

3

DEFORMATION

Fig. 3. Stress-net shear deformation curves for one donor at 57% hematocrit and at 3.0 g/l (o), 4.5 g/l (+) and 6.5 g/l (A) fibrinogen concentrations for (A) lo-” s-‘, (B) 3x lo-” s-l shearrates. Experimental data were analyzed by means of Student’s t-test. Significant differences were observed between the decay slopefor shearrates lower than lo-’ s-l.

3.4. Infruence of hematocrit

(constant shear rate andfibrinogen

Stress decay, when present, was more pronounced 0.008 at 44% and NS at 57%, Fig. 7).

concentration)

at 44% hematocrit

than at 57% (p =

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344

0

1

0.5

NET SHEAR

1.5

2

2.5

3

DEFORMATION

Fig. 4. Stress deformation curve at lo-’ SC’ for one sample at 44% hematocrit and at three fibrinogen concentrations 3.0, 4.5 and 6.5 g/l. Significant stress decays were present at this shear rate at [Fb] = 4.5 and 6.5 g/l. Table 3 Domains of validity of accurate stress measurement with the 170 pm surface roughness measuring system as a function of shear rate, hematocrit and fibrinogen concentration H (%>

44

Shear rate, s-’

F-b19g/l lo-”

3 x lo-’

3

NM

NM

4.5

NM

NM

6.5

NM

NM

lo-*

3 x 10-2

--.__ ‘>,I ij, : ‘:r. : I;, I’. I ..‘.;,.I ,: ~i .;.j,;~:~,:;.’ ,*i,!i.;,;I .I.,.,A;rj;, , ‘,, ‘G’fj’;;:<%, :.<:.‘d’. ~

3 57

4.5 6.5

Gray areas represent measurements with stress decay greater than 0.2 mPa per unit of deformation; NM (no measurement) areas represent the range where measurements were not allowed because of the sensitivity limit of the rheometer. 3.5. Reliability

of rheometrical

measurements

The stress-net shear deformation curves acquired for different sets of parameters (shear rate, hematocrit, [Fb]) allowed the range of reliability of the rheometrical measurements to be determined according to these different parameters. Stress measurement was considered

C. Picart et al. / Biorheology 20 - H&7%

I - 3.0 g/L

I

I ”

345

(1998) 335-353 ”

I ”

”

I ”

” A

-

ok...,,....,..,,,,,,,,,,,,,,,,, 0

1

2

1

3

NET SHEAR

4

5

6

5

6

DEFORMATION

“,,,..,,rr,,,,,,,..,,,,r,i,,,,,

0

3

2

I

NET SHEAR

20

I ” H&7%

01 , , ,, 0

”

4

DEFORMAnON

I ”

”

I ”

”

I

- 6.5 @.

, I

,

,I,, 2 NET SHEAR

1, 3

, ,.I

., 4

I., 5

‘. C

.] 6

DEFORMATION

5. Stress deformation curves for one sample at 57% hematocrit, at different shear rates (0) 10m3s-l, (A) 3 x 10e3 s-l, (+) IO-’ s-l, and (0) 3 x 1O-2 s-‘, for three fibrinogen concentrations (A) 3 g/l; (B) 4.5 g/l; (C) 6.5 g/l.

Fig.

346

d

-I

1

0

1

2 NET SHEAR

IO

&.“‘I”’

-

IO

__ H-

8

H=44%

t

H44%

3

4

1.

_‘I.‘.

6

I”“

B

- 4.5 #I.

I’.“I.-’ - 6.5 g!L

5

DEFORMATION

-

I~‘~~I--“I’~” C

1

Fig. 6. Stress deformation curves for one sample at 44% hemalocrit, at different shear rates (A) l.T2 s-* and (0) 3 x 1o-2 4, for three fibrinogen concentrations (A) 3,O g/l; (B) 4.5 g/l; (C) 6.5 g/I,

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347

16

ot,“‘l”““,‘,“““,‘,,““.1 0

0.5

1 NET SHEAR

1.5

2

2.5

3

DEFORMATION

Fig. 7. Stressdeformation curves at 10m2s-’ for two samples,one at 44% hematocrit and the other at 57%. Both have a fibrinogen concentration of 6.5 g/l. Decay was statistically significant at 44% hematocrit but not at 57%.

reliable if stress decay was less than 0.2 mPa per unit of deformation. Table 3 summarizes the conditions of reliability of the measurements as a function of the hematocrit, fibrinogen, and shear rate parameters, for the home-made measuring system (surface roughness 170 pm) used in this study. For example, with this roughened geometry, measurements at 57% hematocrit and at [Fh] = 6.5 g/l were reliable for shear rates greater than 10V2 s-r, whereas at 44% hematoctit (for the same [Fb]), a shear rate higher than 3 x 10m2 s-i was required. 3.6. Modulus

G and elastic modulus

The modulus G was dependent on the shear rate and was significantly different for the three [Fbs], as is shown on Fig. 8. It increased with the fibrinogen concentration at constant hematocrit and was higher at 57% hematocrit than at 44%. It also increased with increasing shear rate since the structure is broken by the shear rate and loses its elasticity. The modulus G can be considered of pure elasticity when shear rate is sufficiently low (i.e., when shear rate is equal to lop3 s-i) and may thus be taken as an elastic modulus. 3.7. Microscopic observations Observations of the suspensions at rest gave information on their microstructure. Figures 9 and 10 show the direct microscopic observations respectively at 640x magnification and 160x magnification after binarization. For blood at a fibrinogen concentration of 3.0 g/l, the microstructure was composed of small and scarce rouleaux with few connections between them. The length scale of this structure was of the order of 10 to 20 pm. At 4.5 g/l, rouleaux were longer and more interconnected. Branched structures were visible and the length scale may be 30 to 50 pm. At 6.5 g/l, the sample had percolated and a continuous network of large clusters had formed. Clusters may have a 50 to 100 pm size.

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6 -

4 MG

2

B

1

I

ot, ,*,I

1o.3

-I

1o-2 SHEAR

RATE

i

(a’ )

Fig. 8. Mean modulus G (in mPa) as a function of shearrate. Means and standarderrors are given for the fourteen samples(seven at 44% hematocrit and seven at 57%) at 3.0, 4.5 and 6.5 g/l fibrinogen concentration.

[Fb] = 3 g/l

[Fb] = 4.5 g/l

Fig. 9. Microscopic observations(x640 magnification) of three samplesat 57% hematocrit and at 3.0,4.5, and6.5 g/l fibrinogen concentrations. [Fb]

= 6.5

g/l

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[Fb] = 3 g/l - Networkstructureindex= 2.05

349

(1998) 335-353

[Fb] = 4.5 g/l - Network structureindex = 3.2

Fig. 10. Binary images (x 160 magnification) for the three samples at different fibrinogen concentrations(sameasin Fig. 9). [Fb] = 6.5g/l - Network structureindex = 4.2

y = 0.32 +0.61x R = 0.99 6 -

o-""""""""""""2

3

4 FIBRINOGEN

5 CONCENTRATION

6

7

&IL)

Fig. 11. Network structure index for three samplesat 3.0, 4.5 and 6.5 g/l fibrinogen concentration at 57% hematocrit. A linear regressionis also shown (R = 0.99).

350

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So, by increasing fibrinogen level from 3.0 to 6.5 g/l, the structure becomes stronger, more cohesive and organized. Preliminary results from image analysis allowed significantly different parameters to be determined between the three concentrations (Fig. 11). The network structure index, a measure of cell clustering determined by the software, increased linearly (R = 0.99) with increasing fibrinogen concentration.

4. Discussion 4. I. Precision

and reproducibility

of measurements

The data scatter was always less than 10% for each mean value of the seven blood donors (seven samples for a fixed hematocrit and Fb concentration). This can be partly related to the variability of the suspensions and especially to the heterogeneity of fibrinogen and albumin aliquots. Indeed, final hematocrits were 44 or 57 f l%, final fibrinogen concentration had a 10% uncertainty, and the precision of the stress measurements was estimated to be of the order of 30% at low shear stress (l-2 mPa). To check the reproducibility of the procedure for the same blood donor, two sets of samples were prepared independently by using the same aliquots of protein. The curves agreed within less than 10%. 4.2. Stress decay and time dependent effects Stress decay has been attributed in the past to sedimentation (Quemada et al., 1981) and shear migration, which lead to the development of a cell poor layer near the rheometer walls (Cokelet, 1972). This is the case for blood but also is a common feature for all types of twophase systems (Barnes, 1995). Thus, it is important to compare the time constant for the aggregate formation to the time constant for the different physical phenomena. Erythrocyte sedimentation rate (ESR) measurements were performed by the Westergreen method for normal blood at 40% hematocrit and above. As ESR markedly decreases with increasing hematocrit, and as there was neglibible sedimentation at 57% hematocrit over a period of 20 min of shear, other factors are expected to be responsible for the stress decay. Moreover, stress decay was found to be dependent upon wall surface roughness (Picart et al., 1998b) and could be mitigated by the use of a high surface roughness, suggesting that factors others than ESR play a more important role. It has been postulated that the decay was dependent on aggregate size which changes according to plasmatic content, shear rate, and shearing duration (Picart, 1997). It is expected that the structure formed at these extremely low shear rates is similar to that formed at rest, as was already shown by microscopic observations under shear flow at 10m2 s-’ (Copley et al., 1975). At these low shear rates, the stress against shear rate curves show a progressive restructuring over the time period (Fig. 5). The characteristic time of the phenomenon is of the order of tens of minutes at lop3 s-’ (Picart et al., 1998a). Although the present device does not allow for direct microscopic observation to be performed (since the surfaces are roughened), it may thus be expected that, for hematocrit 57% (Figs 9 and lo), a percolating network of branched rouleaux forms, depending upon fibrinogen concentration.

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4.3. Relation

to microstructure

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351

and aggregate size

Numerous studies have shown that elevated fibrinogen level increases RBC aggregation (Chien et al., 1966; Shiga et al., 1983; Maeda et al., 1987; Rampling, 1990; Game et al., 1996), but rheometry at low shear rate (down to low2 s-l) had only been performed in the normal range of concentration (Merrill, 1969b) or evaluated by extrapolation in the case of hyperfibrinogenemia blood (Merrill, 1969a). Rheometrical measurements at high fibrinogen level (up to 10 g/l) were always limited to moderate shear rates (>0.3 s-l) (Rampling, 1990). Thus the above results, obtained with an adapted rheometrical device allowing measurements at lower shear rates (Picart, 1997; Picart et al., 1998a) gave new insight of blood rheological properties at extremely low shear rate. They emphasize how crucial the role of RBC-RBC and RBC-walls interactions in these experimental conditions are and showed quantitatively how the measurements depend upon fibrinogen concentration, hematocrit, and shear rate. Our results suggest that physical exclusion of the structures near the walls, leading to torque decay, depends upon the length scale of the microstructure as compared to surface roughness. This length scale varies greatly depending on fibrinogen level, hematocrit, and shear rate. This means that studies on blood samples containing a high concentration of aggregating macromolecules need to be conducted very carefully and may explain why measurements on pathological blood samples needed time dependent corrections (Quemada et al., 1981), or why experimental results were limited to moderate shear rate (Rampling, 1990), for which smaller size structure are formed (Chen et al., 1996) and where time dependent effects are not strong (Figs 5 and 6). The photographs of the microstructure at rest support the hypothesis of a different aggregation organization according to fibrinogen concentration, with the progressive formation of a stronger percolating network as fibrinogen concentration increases. The rheometrical results and combined microscopic observations at rest may be associated and summarized as follows, with the goal to propose a physical explanation relating the migrational and slip effects to the expected microstructure. 1) The formation of small rouleaux (at 3.0 g/l) did not lead to stress decay. As the expected structure became stiffer with bigger clusters and network arm formation (4.5 g/l and 6.5 g/l) (Figs 9 and lo), perturbing effects were enhanced (Figs 3 and 4). 2) At given fibrinogen concentration, slip and migrational effects decreased as shear rate increased (Figs 5 and 6). This is consistent with a decreased aggregate size as shear rate (or shear stress) increases, as shown at low hematocrit by Chen et al. (1996), and of rouleaux size, as theoretically evidenced by Murata and Secomb (1988). 3) The combined influence of fibrinogen and shear rate showed that higher stress levels were needed to break bigger and stronger structures (high fibrinogen concentration) into small rouleaux and to mitigate perturbing effects. 4.4. Importance

offibrinogen

dependent RBC aggregation

in vivo

Although it is difficult to extrapolate the process seen in the rheometer to that occurring in small vessels, where shear rate and yield stress may be higher (Lipowsky et al., 1978), the data do provide additional information on the rheological properties of blood and aggregate formation. Even if the formation of a branching network may not occur because of the geometrical constraints (size) of the vessels, recent work evidenced that RBC aggregation

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is a main factor influencing vascular conductance and reducing it by 50% at normal flow rate (Cabel et al., 1997). Besides observations of microvessels in vivo showed the presence of a central core of RBC surrounded by a peripheral cell-depleted layer (Vicaut et al., 1994; Tateishi et al., 1994), which means that the effective shear rate in the core is much lower than the apparent wall shear rate. If aggregates formation is enhanced in the core, as is the case for high [Fb] blood samples (Fig. 9), problems may appear in areas where disaggregation is needed. 5. Conclusion Perturbing effects were evaluated with a home-made roughened cup and bob geometry (170 pm) at different cell concentrations (44 and 57%) and at fibrinogen levels of 3.0, 4.5 and 6.5 g/l. Time dependent effects (stress decay as a function of shearing duration) were found to increase with increasing [Fb] and to decrease with increasing shear rate and hematocrit. The results obtained allowed us to define the limits of the rheometrical measurements at low shear rate and high [F’b]. The conditions of reliability of the stress measurements have been given for the measuring system used (170 ,wm surface roughness) as a function of [Pb], hematocrit, and shear rate. Combined microscopic observations showed that bigger and stronger structures were formed as [Fb] increased. This supports the hypothesis of a direct relation between the length scale of the structure, surface roughness, and perturbing effects (stress decay as a function of time). Acknowledgments The authors wish to thank Raphael Marcelpoil and Jean-Marc Chassery (TIMC, Universite Joseph Fourier, Grenoble) for image analysis. They also wish to thank Dr Sotto, Denise Bose and Sandrine Brasseur for their technical assistance. References BarnesHA. A review of the slip (wall depletion) polymer solutions,emulsionsand particle suspensions in viscometers: its cause, character and cure. Journal of Non-Newtonian Fluid Mechanics, 1995;54:221-251. Bronkhorst PJH, Grimbergen J, Brakenhoff GJ, Heethaar RM, Sixma JJ. The mechanismof red cell

(dis)aggregation investigated by means of direct cell manipulation

using multiple optical trapping.

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