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Cell-elastometry: a new method to measure erythrocyte membrane elasticity
Biorheology, Vol. $4, No. $, pp. ~2$--2$4, lgg7 Copyright © 1997 Elsevier Science Ltd Printed in the USA. All rights reserved 0006-$55X/97 $17.00 + .00
Pergamon
PII S0006-355X(97) 00026-7
CELL-ELASTOMETRY: A NEW METHOD E R Y T H R O C Y T E M E M B R A N E ELASTICITY
TO
MEASURE
R. FLIEGERt AND tL GREBES tInstitute of Physiology, Rheinisch-West~lische-Technische Hochschule Aachen, GERMANY; ++D~pt. G6nie Biologique, Universit6 de Technologie de Compi~gne, F 60205 Compi~gne cedex, FRANCE Reprint requests to: R. Flieger, Institute of Physiology, Klinikum RWTHAachen, PauwelsstraBe 30, D-52057 Aachen, GERMANY; Fax:+49/241 88 88 434; e-mail: [email protected]
ABSTRACT A new method for measuring erythrocyte membrane elasticity in physiological media is presented. Cells are loaded with well-def'med centrifugal forces and the restdting change in shape is observed indirectly by laser diffractometry. Only a small amount of data has to be acquired and evaluated to follow up all the shape information contained in the diffraction pattern. This method has been proven using native and chemically altered cells (glutaraldehyde and diamide treatment). Advantages of the proposed method are the ease of handling, the small blood volume (10~1) needed per measurement, a high sensitivity and the rational experimental setup. © 1997 Elsevier Science Ltd Introduction For basic research as well as for clinical diagnostics it is important to measure the elasticity of the erythrocyte membrane since it is of great influence on whole blood rheological properties. To determine the elasticity of a body one has to apply a defined mechanical force and to evaluate the resulting change in shape. In the past, a number of different methods have been introduced that apply this principle to measure red blood cell properties, e.g., rheoscopy (Schmid-Sch6nbein and Wells, 1969), filtrometry (Teitel, 1970), ektacytometry (Bessis and Mohandas, 1975), micropipet aspiration (Evans and LaCelle, 1975), flow chamber techniques (Artmann, 1995). Due to the size and fragility of the object under investigation all these methods have to deal with a problem of measurement, that is to apply a welldefined force without changing the ceils and especially their membrane properties by the measuring procedure or even select cells due to special properties. Furthermore, in some of these methods (e.g., ektacytometry, filtrometry) it is not possible to differentiate between membrane elasticity and viscosity of the cytoplasm. KEYWORDS:
Erythrocyte; membrane; centrifugation; diffraction; elasticity; deformability 223
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H e r e we present a m e t h o d by which it becomes possible to measure b l o o d cells in an appropriate physiological e n v i r o n m e n t as well as u n d e r the influence o f arbitrary drugs to d e t e r m i n e , in particular, the elastic properties o f the erythrocyte m e m b r a n e .
Materials and Methods
Principle Well-defined centrifugal forces were applied to a suspension o f erythrocytes in a transparent rotating chamber. T h e acting forces could be varied over a wide range by changing the spinning rate. At the beginning, when the c h a m b e r started to rotate, a m o v e m e n t of the erythrocytes, best described as sedimentation towards the o u t e r wall, was induced. After they had r e a c h e d the wall they settled down f o r m i n g a monolayer. In parallel to a f u r t h e r increase o f the centrifugal force, the cells changed their shape continuously and in a predictable m a n n e r from the n o r m a l discocytic shape to a flat-oblate like shape. This d e f o r m a t i o n was visualized and evaluated by diffractometry as d o n e and well established in o t h e r m e t h o d s ( G r o n e r et al., 1980; Murakawa et al., 1992). Since the whole sequence of shapes d u r i n g the d e f o r m a t i o n process was o f rotational symmetry, the diffraction pattern exhibited rotational symmetry also. T h e r e f o r e , all available information is c o n t a i n e d in every cross-section through the diffraction pattern. For this reason a o n e dimensional p r o b l e m only has to be treated, which means a remarkable r e d u c t i o n of data. This facilitates data acquisition as well as its interpretation.
Experimental setup T h e center piece of the experimental setup (Fig. 1) was an a n n u l a r Plexiglas chamber, which c o n t a i n e d the erythrocyte suspension. T h e present centrifugal c h a m b e r consisted of two concentric parts. T h e outer body included the channel, which c o n t a i n e d the blood sample and which was closed by the i n n e r part, the inset. T h e radius of the exterior channel wall was 25 mm. To prevent
cell suspension centrifuge
mirror !iiim0~0ri~iii
pol.-filter
computer 1 dim CCD-array
Fig. 1.
Experimental setup.
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u n d e s i r e d m o v e m e n t of the suspension inside the c h a m b e r d u r i n g acceleration the channel was completely closed at o n e p o i n t by a barrier. T o the right a n d the left of this barrier there was o n e o p e n i n g for filling and releasing the b l o o d suspension. A d i o d e laser b e a m ( 6 7 0 n m ) was lead t h r o u g h the centrifugation chamber. Its intensity was adjustable by a polarization filter. T h e b e a m ran t h r o u g h the rotating m o n o l a y e r of erythrocytes and p r o d u c e d the diffraction pattern described above which was r e c o r d e d by a linear CCD-array. T h e linear array consisted o f 1024 elements o f an overall length of 25.4 m m and was r e a d out by an interface five times per second. T h e o u t p u t o f the interface was an electrical 'boxcar' signal. After standard S / H - and A / D - c o n v e r s i o n the signal was stored and evaluated online by a system integrated c o m p u t e r . T h e centrifuge c h a m b e r was driven by a DC m o t o r . T h e system allowed rotation rates o f up to 250 Hz. T h e rotational velocity was m e a s u r e d by an integrated t a c h o m e t e r with a precision o f +- 0.25 Hz. Procedure
Hematocrit T o achieve the best results with this m e t h o d , diffraction patterns o f sufficient contrast were required given the availability of an a p p r o p r i a t e m o n o l a y e r o f erythrocytes. T h e a m o u n t of cells n e e d e d to reach a closed layer could easily be c o m p u t e d since the o u t e r surface area of the channel as well as the m e a n projection of a horizontally oriented cell were known. Although calculations for the chamber, described here, predicted that a h e m a t o c r i t o f 0.09% s h o u l d give such a monolayer, the best results were achieved using a h e m a t o c r i t o f 0.035% up to 0.065%. This discrepancy was due to the fact that sedimentation is a statistical process and therefore will not p r o d u c e a perfect layer of equally distributed cells but r a t h e r an overlapping of cells will occur. Cell p r e p a r a t i o n A d r o p l e t of 10/al native whole b l o o d was harvested by lancet-prick from the earlobe of healthy h u m a n volunteers with a heparinized glass capillary. It was diluted in 10 ml p h o s p h a t e buffer (PBS) containing 1 g / l glucose and 0.25 g/1 albumin to achieve a suspension h e m a t o c r i t of ca. 0.045%. No further treatment, e.g., cell separation, was n e e d e d since the n u m b e r o f erythrocytes by far e x c e e d e d that o f all o t h e r cells. T h a t is why the diffraction pattern was governed by erythrocytes, the influence of the o t h e r cells could be neglected. T o check this m e t h o d and to get an idea of its sensitivity, experiments with altered erythrocytes were carried out. Cells were fixed by i n c u b a t i o n (20 min at 21°C) in a 1.5% glutaraldehyde PBS solution. F u r t h e r m o r e , the m e m b r a n e properties were r e n d e r e d m o r e distinct by treatment with i o d o a c e t a t e / d i a m i d e as described by Fischer et al., (1978). Diamide concentrations used for incubation were: 0.1, 0.2, 0.4, 0.8, 1.0 mMol/1. Measurement
T h e centrifuge c h a m b e r was filled with the erythrocyte suspension through o n e of the two openings while the displaced air left the c h a m b e r through the o t h e r one. It was very i m p o r t a n t to avoid any air bubbles in the c h a m b e r because they would disturb the laser b e a m and thereby seriously affect the quality of the diffraction pattern. At the first step of the m e a s u r e m e n t the filled and closed c h a m b e r rotated for at least 60 s with a constant f r e q u e n c y of 20 Hz. During this initial phase the centrifugal forces i n d u c e d sedimentation o f the cells to the o u t e r c h a m b e r wall
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where they f o r m e d the desired monolayer of erythrocytes (Fig. 2). This process can be followed up by the change of the intensity distribution o f the diffraction pattern. F r o m a gaussian-like intensity profile it c h a n g e d into a structured diffraction pattern. This was due to the fact that from the optical point o f view the suspension exhibited, in the beginning, a three-dimensional o b j e c t distribution, i.e., multiple scattering, while afterwards the m o n o l a y e r gave the diffraction pattern of a layer of u n a r r a n g e d particles. This process was normally c o m p l e t e d after 3 9 + 1 s. After 60s the rotational speed was increased rampwise, i.e., linearly within 100s from 20 Hz to 210 Hz. This m e a n t an increase o f the applied centrifugal acceleration from 40 g to 4400 g (see paragraph Applied Forces). During the whole process the diffraction pattern was continuously sampled and stored.
Theoretical considerations Diffraction T h e relationship between the shape of small bodies and their diffraction pattern was used in a great n u m b e r of applications. T h e advantage o f this m e t h o d was that shape and shape changes of diffracting objects could be detected without further optical c o m p o n e n t s . T h e intensity of the diffraction pattern was directly related to the n u m b e r of diffracting objects because the pattern o f each of, for example, n objects a d d e d up to a resulting diffraction pattern which showed the same intensity distribution but an n-fold total intensity. This idealization held strictly only for objects that were identical and situated in the same place. In the following a simplification o f the change o f the diffraction pattern of o n e object is discussed.
Fig. 2. RBC-monolayer as formed at the outer wall of the rotation chamber after sedimentation induced by constant rotation of 20 Hz for 60s (hct=0.035%). The photograph has been taken from the dismounted chamber by an inverse microscope.
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Here we used a very simple model to explain only the essential changes to be found in the diffraction patterns of erythrocytes when exposed to an increasing h o m o g e n e o u s field of force (Fig. 3). Using the imaging theory approach, to a certain extent the erythrocyte could be described as a phase object only. From this point of view, normal discocytes could be m o d e l e d as flat hollow cylindrical bodies (rings) which mainly disturbed the transmitted light at the inside and outside ring while the flattened erythrocyte disturbed the light only at the outside rim. The diffraction pattern of a ring, with a finite thickness (phase object), and that of an annular aperture (intensity object) was nearly the same if normalized to the same total energy. By analogy, this holds also for a disk and an aperture. The intensity distribution for each of these geometries can be calculated analytically (see Appendix). The rotational symmetry was used to simplify the problem in one dimension only. The result of the simulation given as intersection through the radial intensity distribution is shown in Fig. 3. It can be seen clearly that the intensity of the m a x i m u m of first order for a ring-like structure was increased when compared to that of the disk. These analytical results were easily explained based on the concept given above. Only the outer rim of the disk diffracted light and superimposed it d u e to the principles of interference into the first maximum. The ring, in addition, had a surplus of diffracting edges due to the inner rim and therefore a higher intensity in the first maximum, while the total intensity stayed constant. The intensity distribution, acquired by simulations based on this simple heuristic explanation, could be used for the principal interpretation of the experimental results. A more sophisticated theory will be presented in a subsequent publication. Anolied forces A
The resultant force ~'R v acting on the erythrocyte during rotation of the chamber is given by the following equation:
.> where FG is the gravitational force, FC the centrifugal force, VERy= 9 0 - 1 0 - 1 8 m 3 is the m e a n erythrocyte volume, ~ =9.81 m / s 2 the acceleration of gravity, v the frequency of revolution and ~ = 0.025 m the effective radius of the centrifuge. Ap is the difference in density between suspending m e d i u m and erythrocyte. This value can be estimated in the centrifuge as described in the next paragraph. Since the amplitude of FG even during the first phase of low rotation is less than it can be neglected in the following. Thus the scalar one. Even so, the surface of projection of deformed erythrocyte are taken to be equal, with T h e n the applied pressure PR is given by
(2)
2.5% of the amplitude of FC problem can be treated as a both the undisturbed and the an error of < 2%.
p R = V ERyAp (4/1:202r) . ff rIR Y
With the present setup pressures up to 12 Pa (120 d y n / c m 2) can be reached.
Erythrocyte m e m b r a ~ elasticity
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0,5 (:~ cell" shape ~ ' ~ : ~ discocyte "pizza"
**"
,~,
'-7' 0,4 "u~ 0,3
A,II,,
_
,,sc
I/ I
0,2 O 0,1 .....
_...~:~J
-1.o
° ,
-0,5
o,o
.
'-.¢-,-,.;~
0,5
. . . .
1,o
,
1,5
Diameter [cm], (Distance 5cm) Fig. 3. Models used for the simulations: The ring for the discocyte and the disk for the shape under maximal stress. Results: Diffraction pattern of a ring (solid line) and of a disk (dashed line). Ervthrocvte density In addition, o u r e x p e r i m e n t a l setup could be used to process the density o f the cytoplasm of cells. This was d o n e by m e a s u r i n g the time n e e d e d by the cells to s e d i m e n t down to the o u t e r c h a m b e r wall. T h e r e f o r e Stokes law c o u l d be u s e d to c o m p u t e the m e a n difference in density between cells a n d s u s p e n s i o n if the cells were taken to exhibit a sphere-like s h a p e a n d an estimate o f the effective erythrocyte d i a m e t e r was n e e d e d . L a m b (1945) showed that a circular disk s e d i m e n t i n g towards its small cross-section could be treated as a s p h e r e exhibiting a radius of k = 0.56 times that of the disk, while o r i e n t e d with its flat side down it exhibited the same flow resistance as a s p h e r e of k = 0.85 times this radius. G r o o m a n d A n d e r s o n (1971) have found, by :microscopical investigation, that d u r i n g s e d i m e n t a t i o n cells were o r i e n t e d r a n d o m l y a n d that this o r i e n t a t i o n c h a n g e d continuously with time. T h a t is why k could be taken as the m e a n of the two extremes. T h e n the s e d i m e n t i n g erythrocyte c o u l d be treated as a s p h e r e o f the effective erythrocyte radius (Oka, 1985): (3)
r e f f = 0.71. rER Y .
D e f o r m a t i o n of the erythrocytes which may o c c u r d u e to the small a c c e l e r a t i o n (40 g) could be neglected (Corry and Meiselman, 1978a). T h u s the m e a n difference in density Ap between m e d i u m a n d erythrocyte is given by 9 .s.r/ (4)
AP= 2 .a.t.r
2
'
elf where in o u r e x p e r i m e n t a l setup r/= 1.11 • 10 -3 k g / m s is the viscosity o f the s u s p e n d i n g m e d i u m , s = 2 m m the height o f the c h a m b e r , and a = 394 m / s 2 ( v = 20 Hz) the effective acceleration. Measures d o n e so far have given a
V o l . 34, N o . 3
Erythrocyte membrane elasticity
229
sedimentation time o f t = 39 _+ 1 s, which is due to a difference in density of Ap = 92.0 + 2.5 k g / m a. T h e r e f o r e , initially in each e x p e r i m e n t Ap could be estimated for the m e a n erythrocyte o f the population. T h e r e b y it was possible to calibrate the applied forces FR. This might be necessary because the density of cells o f different d o n o r s might vary due to physiological variation or pathological changes. T h e density of o u r suspending medium was chosen to b e P/'Bs = 1004.4 k g / m 3, so the absolute value of erythrocyte density could b e c o m p u t e d . For the cells o f the g r o u p of healthy d o n o r s investigated so far we f o u n d a value o f PERY=1096.4 k g / m 3 which is in g o o d a g r e e m e n t with the literature. Results and Discussion
T h e time course of a diffraction pattern of a standard e x p e r i m e n t with n o r m a l u n t r e a t e d erythrocytes is given in Fig. 4. Clearly the decrease in intensity of the m a x i m u m o f first o r d e r due to the increasing centrifugal acceleration is to be seen. Since the intensity o f the central b e a m is very high the CCD-array in this region is in saturation. Above a centrifugal acceleration o f a b o u t 1500 g the pattern stabilizes. T h e r e is no f u r t h e r change of erythrocyte shape because the cell volumes have r e a c h e d a stable distribution. Due to the restriction of surface to volume ratio f u r t h e r acceleration does not induce further change o f cell shape. T h e cells starting with the n o r m a l discocytic shape have continuously flattened with "quasi-static" increasing forces and r e a c h e d the final oblate-like flat shape ("pizza"). Figure 5 shows the intensity distribution to be f o u n d in contrast if cells are used that have b e e n fixed by glutaraldehyde. H e r e the diffraction pattern is completely i n d e p e n d e n t o f the acting forces after sedimentation. Due to the stiff m e m b r a n e no shape change can occur.
3 -2.5 -2
N"
-1.5 ~ C
o
- .lO~]
Fig. 4. Change in intensity of the first order maximum due to the centrifugal acceleration of untreated normal erythrocytes expressed in acceleration of gravity (g).
230
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2 -2.5
• 1.5~ 1
e.w
-0
~lrcgL,ffy] Fig. 5. No change in intensity of the first order maximum due to the centrifugal acceleration of erythrocytes fixed with glutaraldehyde (1.5%). Since until now we have only evaluated changes in the first m a x i m u m , we can r e d u c e the three-dimensional plot to a simple graph representing the maximal values of the m a x i m u m o f first order. T h e r e f o r e both the right and left course o f the m a x i m u m are c o m p u t e d , averaged, and plotted (Fig. 6). T h e intensities are normalized to the last values, i.e., the erythrocytes u n d e r highest gravitational field. For these values all normal cells have achieved a defined, reproducible, final "pizza" shape. It is well known that in contrast, the initial unstressed shapes can exhibit a whole sequence o f different configurations (Grebe and Schmid-Sch6nbein, 1985). In the final stage the same shape a n d thereby intensity profile is r e a c h e d for different cells in different experiments where the surface-volume-relationship is taken to be constant. T h e r e f o r e cells b e c o m e comparable, which is used for the described normalization. In addition, the results thereby b e c o m e i n d e p e n d e n t of changes in b e a m intensity and h e m a t o c r i t of the suspension in a wide range. For a first quantification of m e m b r a n e elasticity the following p r o c e d u r e has b e e n introduced: Since here we deal with a grid of simple shapes o f rotational symmetry, every value of the normalized intensity first m a x i m u m represents in the m e a n only o n e of the possible cell shapes (Fig. 6). This means every decrease of intensity of the m a x i m u m o f first o r d e r from, for example, I--- 1.5 to I = 1.25 u n d e r gravitational load is d u e to the same change o f cell shape. (These values due to slight shape changes have been proven to be the most effective for evaluation of the experiments.) T h e acceleration difference, Ag, n e e d e d to change the cell shape described by an intensity o f ( I = 1.5) to the shape giving (I = 1.25) can be used as a measure for the m e m b r a n e elasticity. Figure 7 (left panel) gives the normalized graphs for experiments d o n e to investigate the sensitivity of the m e t h o d . Cells have b e e n treated as d e s c r i b e d with increasing concentrations o f diamide. T h e i n d u c e d dose d e p e n d e n t
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~4
231
Erythrocyte membrane elasticity
1 2
2.25
E 2 N--,
Elasticity 1 < 2
o 1.75
.~O
m
1.5
~ 1,25 E o r-
Ag2
acceleration
Fig. 6. The graphs give the dependency of cell shape (right) measured as normalized intensity on the acting force/acceleration. The experimental results for two different typical erythrocyte populations with different membrane elasticities are shown: Agl < Ag2 ¢=~to induce the same change of shape in population 1, a smaller resistance has to be overcome than in 2. decrease of deformability is expressed as a n e e d for an increased acceleration for an equivalent degree of cell deformation, r e p r e s e n t e d by an increase o f the qualitative p a r a m e t e r Ag (Fig. 7, right panel). If the m e m b r a n e elasticity is extremely decreased the normalization p r o c e d u r e b e c o m e s invalid due to the fact that the applied forces are no longer large e n o u g h to reach the final standard shape. O u r results are in g o o d a g r e e m e n t with the ones given by D r o c h o n et al., (1993) who showed the effect o f low dose diamide t r e a t m e n t on erythrocyte m e m b r a n e s using a filtering technique with a suspension m e d i u m o f high viscosity (dextran).
Conclusions Centrifugation has b e e n used before by, for example, Sirs (1966), Corry a n d Meiselman (1978b), Abidor et al. (1993), and Pribush et al. (1995), to apply defined forces on RBC suspensions of physiological hematocrit, for example m e a s u r e m e n t of volume or electrical resistivity. H e r e , for the first time, we use this possibility to apply forces on b l o o d cells using o u r cell-elastometry m e t h o d . Defined shape changes are i n d u c e d which are analyzed and quantified by laser diffractometry. This is d o n e by online observation o f diffraction patterns, as p r o d u c e d by a great n u m b e r of cells giving the shape i n f o r m a t i o n for the m e a n cell u n d e r varying centrifugal load. Evaluation and m o d e l i n g becomes relatively simple because the shape o f all cells is c h a n g e d in the same rotational-symmetric m a n n e r . With cell-elastometry it b e c o m e s possible to apply well-defined forces to erythrocytes, to follow up instantaneously the i n d u c e d shape change, and to c o m p u t e parameters quantifying the elasticity of the cell m e m b r a n e . Using a low dose diamide treatment distinct changes in the mechanical properties of m e m b r a n e s can be detected.
Erythrocyte membrane elasticity
232
I - - ~ fl'fl mmolae
E
I
fl•l
~lar
Vol. 34, No. 3
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<1 8O0
1.75-
~}~
0
[~.-e.4 mole¢
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].5.
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0¢-
200 1
0,0
o
acceleration [n * gravity]
0,2
0,4
0,6
0,8
1,0
Diamid concentration [mMol/L]
Fig. 7. Normalized intensities of the first maximum as related to acceleration for the same erythrocyte population treated with increasing concentrations of diamide (left panel). The according relationship between the measure for elasticity Ag and the concentration of diamide is given by the graph in the right panel. Due to the fundamental, straight forward physical principles used, efforts for the experimental setup are restricted, the m e t h o d can be standardized easily, and the n u m b e r o f potential e r r o r sources is relatively small. F u r t h e r m o r e , this m e t h o d needs no undesired additives in the suspension, for example dextran, to generate the high viscosity required by o t h e r methods. F u r t h e r advantages o f cell-elastometry are as follows: - Only a small volume of b l o o d is needed• - Cell p r e p a r a t i o n is r e d u c e d to simple whole blood dilution only. A whole e x p e r i m e n t including evaluadon takes not m o r e than 4 min. - A box 25 x 15 x 10 cm contains the whole e x p e r i m e n t a l setup. - T h e centrifugal c h a m b e r is easy to fill, use and clean. - All evaluations are d o n e online automatically by c o m p u t e r . H e r e we have p r e s e n t e d the principals o f the cell-elastometry m e t h o d a n d given details of the advantages o f this m e t h o d in measuring distinctly the elasticity of the red blood cell m e m b r a n e . Details o f the theoretical basis o f this m e t h o d will be provided in a subsequent publication which will include m o d e l i n g and c o m p u t e r simulations o f cell shapes and according diffraction patterns u n d e r varying force fields. This gives the basis for a m o r e sophisticated way to extract information from the time course of the obseJ~,ed patterns regarding erythrocyte density distribution, elasticity m o d u l u s and :identification of subpopulations of cells. Basically this is d o n e using the spontaneous curvature model, i n t r o d u c e d by Helfrich (1973), e x p a n d e d by additional energy terms. Numerical simulations generate energy minimized cell shapes u n d e r gravitational acceleration. Subsequently these forms are used in numerical diffraction simulation. By c o m p a r i s o n o f the simulated experiments with real ones, m e m b r a n e parameters like b e n d i n g m o d u l u s and s p o n t a n e o u s curvature can be calculated.
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Appendix
Diffraction by disk and annular aperture The radial intensity distribution 1s(r)generated
by a disk with a small diameter as compared to the distance of the image is given by Hecht (1987): =
,
, with
(b) 2E
'
where J1 is the Bessel-function of first order, b= disk radius, Z= distance aperture to image, k = 27t/X wave number and Ea electrical field strength of the incoming wave of light. The function of the amplitude (a) is computed using the integral of diffraction (c) in the boundaries between 0 to b:
z
r=OL z )
'
Es(r) gives the
distribution of field strengths of the image and Jo the Besselfunction of order zero. To compute the intensity distribution IR(r) of the annular aperture the integral of diffraction (c) has to be calculated between a and b, where a is the inner radius of the ring. Thus the intensity distribution of an annular aperture is given by:
(d)
2E2 2 /R(r) = T r A [ b J
kbr kbr kar l~--~) - 2abJl(-[ ) Jl (-~ ) + a2J l~ k--~azr )l .
References ABIDOR, I.G., BRABUL, A.I., ZEHLEV, D.V., DOINOV, P., BANDRINA, I.N., OSIPOVA, E.M., and SUKHAREV, S.I. (1993). Electrical properties of cell pellets and cell electrofusion in a centrifuge. Biochim.Biophys.Acta 1152, 207-218. ARTMANN, G.M. (1995). Microscopic photometric quantification of stiffness and relaxation time of red blood cells in a flow chamber. Biorheology32, 553-570. BESSIS, M., and MOHANDAS, N. (1975). A diffractometric method for the measurement of cellular deformability. Blood Cells1, 307-313. CORRY, W.D., and MEISELMAN, H.J. human erythrocytes in a centrifugal field.
(1978a).
Deformation
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of
CORRY, W.D., and MEISELMAN, H.J. (1978b). Centrifugal method of determining red cell deformability. Blood51, 693-701. DROCHON, A., BARTHI~S-BIESEL, D., BUCHERER, C., LACOMBE, C., and LELIEVRE, J.C. (1993) Viscous filtration of red blood cell suspensions. Biorheology30, 1-8.
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EVANS, E.A., and LACELLE, P.L. (1975). Intrinsic material properties of the erythrocyte membrane indicated by mechanical analysis of deformation. Blood 45, 29-43. FISCHER, T.M., HAEST, C.W.M., STOHR, M., KAMP, D., and DEUTICKE, B. (1978). Selective alteration of erythrocyte deformability by SH-reagents. Evidence for an involvement of spectrin in membrane shear elasticity. Biochim. Biophys. Acta 510, 270-282. GREBE, R., and SCHMID-SCHONBEIN, H. (1985). counting for objective assessment of erythrocyte shape Biorheology 22, 455-469.
Tangent changes.
GRONER, W., MOHANDAS, N., and BESSIS, M. (1980). New optical technique for measuring erythrocyte deformability with the ektacytometer. Clin. Chem. 26, 1435-1442. GROOM, A.C., and ANDERSON, J.C. (1971). Measurement of the size distribution of human erythrocytes by a sedimentation method. J. Cell Physiol. 79, 127-138. HECHT, E. (1987). Diffraction. In: Optics. 2nd Edition, AddisonWesley Publishing Company, Inc,, pp. 416-421. HELFRICH, W. (1973). Elastic properties of liquid bilayers: theory and possible experiments. Z. Naturforsch. 28, 693-703. LAMB, H. (1945). Viscosity. In: Cambridge University Press, 604-605.
Hydrodynamics.
6th Edition,
MURAKAWA, K., KOHNO, M., KINOSHITA, Y., and TAKEDA, T. (1992). Application of diffractometry and a linear image sensor to measurement of erythrocyte deformability. Biorheology 29, 323-335. OKA, S. (1985). A physical theory of erythrocyte sedimentation. Biorheology 22, 315-321. PRIBUSH, A., MEYERSTEIN, D., and MEYERSTEIN, N. (1995). Conductometric study of erythrocytes during centrifugation. I+II. Biochim. Biophys. Acta 1256, 187-193 and 194-200. SCHMID-SCHONBEIN, H., and WELLS, R. (1969). Fluid drop-like transition of erythrocytes under shear. Science 165, 288-291. SIRS, J. (1966). The measurement of the hematocrit and flexibility of erythrocytes with a centrifuge. Biorheology 5, 1-14. TEITEL, P. (1970). Basic principles of the "filterability test" (FT) and analysis of erythrocyte flow behaviour. Blood Cells 3, 55-70. Acknowledgments The authors wish to thank Professor H. Schmid-Sch6nbein for his support. The helpful discussions with M. Baumann, K. Vietzke and the skillful technical assistance of Mrs. R. Degenhardt are gratefully acknowledged.
Received 8 April 1997; accepted in revised form 21 July 1997.
Pergamon
PII S0006-355X(97) 00026-7
CELL-ELASTOMETRY: A NEW METHOD E R Y T H R O C Y T E M E M B R A N E ELASTICITY
TO
MEASURE
R. FLIEGERt AND tL GREBES tInstitute of Physiology, Rheinisch-West~lische-Technische Hochschule Aachen, GERMANY; ++D~pt. G6nie Biologique, Universit6 de Technologie de Compi~gne, F 60205 Compi~gne cedex, FRANCE Reprint requests to: R. Flieger, Institute of Physiology, Klinikum RWTHAachen, PauwelsstraBe 30, D-52057 Aachen, GERMANY; Fax:+49/241 88 88 434; e-mail: [email protected]
ABSTRACT A new method for measuring erythrocyte membrane elasticity in physiological media is presented. Cells are loaded with well-def'med centrifugal forces and the restdting change in shape is observed indirectly by laser diffractometry. Only a small amount of data has to be acquired and evaluated to follow up all the shape information contained in the diffraction pattern. This method has been proven using native and chemically altered cells (glutaraldehyde and diamide treatment). Advantages of the proposed method are the ease of handling, the small blood volume (10~1) needed per measurement, a high sensitivity and the rational experimental setup. © 1997 Elsevier Science Ltd Introduction For basic research as well as for clinical diagnostics it is important to measure the elasticity of the erythrocyte membrane since it is of great influence on whole blood rheological properties. To determine the elasticity of a body one has to apply a defined mechanical force and to evaluate the resulting change in shape. In the past, a number of different methods have been introduced that apply this principle to measure red blood cell properties, e.g., rheoscopy (Schmid-Sch6nbein and Wells, 1969), filtrometry (Teitel, 1970), ektacytometry (Bessis and Mohandas, 1975), micropipet aspiration (Evans and LaCelle, 1975), flow chamber techniques (Artmann, 1995). Due to the size and fragility of the object under investigation all these methods have to deal with a problem of measurement, that is to apply a welldefined force without changing the ceils and especially their membrane properties by the measuring procedure or even select cells due to special properties. Furthermore, in some of these methods (e.g., ektacytometry, filtrometry) it is not possible to differentiate between membrane elasticity and viscosity of the cytoplasm. KEYWORDS:
Erythrocyte; membrane; centrifugation; diffraction; elasticity; deformability 223
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H e r e we present a m e t h o d by which it becomes possible to measure b l o o d cells in an appropriate physiological e n v i r o n m e n t as well as u n d e r the influence o f arbitrary drugs to d e t e r m i n e , in particular, the elastic properties o f the erythrocyte m e m b r a n e .
Materials and Methods
Principle Well-defined centrifugal forces were applied to a suspension o f erythrocytes in a transparent rotating chamber. T h e acting forces could be varied over a wide range by changing the spinning rate. At the beginning, when the c h a m b e r started to rotate, a m o v e m e n t of the erythrocytes, best described as sedimentation towards the o u t e r wall, was induced. After they had r e a c h e d the wall they settled down f o r m i n g a monolayer. In parallel to a f u r t h e r increase o f the centrifugal force, the cells changed their shape continuously and in a predictable m a n n e r from the n o r m a l discocytic shape to a flat-oblate like shape. This d e f o r m a t i o n was visualized and evaluated by diffractometry as d o n e and well established in o t h e r m e t h o d s ( G r o n e r et al., 1980; Murakawa et al., 1992). Since the whole sequence of shapes d u r i n g the d e f o r m a t i o n process was o f rotational symmetry, the diffraction pattern exhibited rotational symmetry also. T h e r e f o r e , all available information is c o n t a i n e d in every cross-section through the diffraction pattern. For this reason a o n e dimensional p r o b l e m only has to be treated, which means a remarkable r e d u c t i o n of data. This facilitates data acquisition as well as its interpretation.
Experimental setup T h e center piece of the experimental setup (Fig. 1) was an a n n u l a r Plexiglas chamber, which c o n t a i n e d the erythrocyte suspension. T h e present centrifugal c h a m b e r consisted of two concentric parts. T h e outer body included the channel, which c o n t a i n e d the blood sample and which was closed by the i n n e r part, the inset. T h e radius of the exterior channel wall was 25 mm. To prevent
cell suspension centrifuge
mirror !iiim0~0ri~iii
pol.-filter
computer 1 dim CCD-array
Fig. 1.
Experimental setup.
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u n d e s i r e d m o v e m e n t of the suspension inside the c h a m b e r d u r i n g acceleration the channel was completely closed at o n e p o i n t by a barrier. T o the right a n d the left of this barrier there was o n e o p e n i n g for filling and releasing the b l o o d suspension. A d i o d e laser b e a m ( 6 7 0 n m ) was lead t h r o u g h the centrifugation chamber. Its intensity was adjustable by a polarization filter. T h e b e a m ran t h r o u g h the rotating m o n o l a y e r of erythrocytes and p r o d u c e d the diffraction pattern described above which was r e c o r d e d by a linear CCD-array. T h e linear array consisted o f 1024 elements o f an overall length of 25.4 m m and was r e a d out by an interface five times per second. T h e o u t p u t o f the interface was an electrical 'boxcar' signal. After standard S / H - and A / D - c o n v e r s i o n the signal was stored and evaluated online by a system integrated c o m p u t e r . T h e centrifuge c h a m b e r was driven by a DC m o t o r . T h e system allowed rotation rates o f up to 250 Hz. T h e rotational velocity was m e a s u r e d by an integrated t a c h o m e t e r with a precision o f +- 0.25 Hz. Procedure
Hematocrit T o achieve the best results with this m e t h o d , diffraction patterns o f sufficient contrast were required given the availability of an a p p r o p r i a t e m o n o l a y e r o f erythrocytes. T h e a m o u n t of cells n e e d e d to reach a closed layer could easily be c o m p u t e d since the o u t e r surface area of the channel as well as the m e a n projection of a horizontally oriented cell were known. Although calculations for the chamber, described here, predicted that a h e m a t o c r i t o f 0.09% s h o u l d give such a monolayer, the best results were achieved using a h e m a t o c r i t o f 0.035% up to 0.065%. This discrepancy was due to the fact that sedimentation is a statistical process and therefore will not p r o d u c e a perfect layer of equally distributed cells but r a t h e r an overlapping of cells will occur. Cell p r e p a r a t i o n A d r o p l e t of 10/al native whole b l o o d was harvested by lancet-prick from the earlobe of healthy h u m a n volunteers with a heparinized glass capillary. It was diluted in 10 ml p h o s p h a t e buffer (PBS) containing 1 g / l glucose and 0.25 g/1 albumin to achieve a suspension h e m a t o c r i t of ca. 0.045%. No further treatment, e.g., cell separation, was n e e d e d since the n u m b e r o f erythrocytes by far e x c e e d e d that o f all o t h e r cells. T h a t is why the diffraction pattern was governed by erythrocytes, the influence of the o t h e r cells could be neglected. T o check this m e t h o d and to get an idea of its sensitivity, experiments with altered erythrocytes were carried out. Cells were fixed by i n c u b a t i o n (20 min at 21°C) in a 1.5% glutaraldehyde PBS solution. F u r t h e r m o r e , the m e m b r a n e properties were r e n d e r e d m o r e distinct by treatment with i o d o a c e t a t e / d i a m i d e as described by Fischer et al., (1978). Diamide concentrations used for incubation were: 0.1, 0.2, 0.4, 0.8, 1.0 mMol/1. Measurement
T h e centrifuge c h a m b e r was filled with the erythrocyte suspension through o n e of the two openings while the displaced air left the c h a m b e r through the o t h e r one. It was very i m p o r t a n t to avoid any air bubbles in the c h a m b e r because they would disturb the laser b e a m and thereby seriously affect the quality of the diffraction pattern. At the first step of the m e a s u r e m e n t the filled and closed c h a m b e r rotated for at least 60 s with a constant f r e q u e n c y of 20 Hz. During this initial phase the centrifugal forces i n d u c e d sedimentation o f the cells to the o u t e r c h a m b e r wall
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where they f o r m e d the desired monolayer of erythrocytes (Fig. 2). This process can be followed up by the change of the intensity distribution o f the diffraction pattern. F r o m a gaussian-like intensity profile it c h a n g e d into a structured diffraction pattern. This was due to the fact that from the optical point o f view the suspension exhibited, in the beginning, a three-dimensional o b j e c t distribution, i.e., multiple scattering, while afterwards the m o n o l a y e r gave the diffraction pattern of a layer of u n a r r a n g e d particles. This process was normally c o m p l e t e d after 3 9 + 1 s. After 60s the rotational speed was increased rampwise, i.e., linearly within 100s from 20 Hz to 210 Hz. This m e a n t an increase o f the applied centrifugal acceleration from 40 g to 4400 g (see paragraph Applied Forces). During the whole process the diffraction pattern was continuously sampled and stored.
Theoretical considerations Diffraction T h e relationship between the shape of small bodies and their diffraction pattern was used in a great n u m b e r of applications. T h e advantage o f this m e t h o d was that shape and shape changes of diffracting objects could be detected without further optical c o m p o n e n t s . T h e intensity of the diffraction pattern was directly related to the n u m b e r of diffracting objects because the pattern o f each of, for example, n objects a d d e d up to a resulting diffraction pattern which showed the same intensity distribution but an n-fold total intensity. This idealization held strictly only for objects that were identical and situated in the same place. In the following a simplification o f the change o f the diffraction pattern of o n e object is discussed.
Fig. 2. RBC-monolayer as formed at the outer wall of the rotation chamber after sedimentation induced by constant rotation of 20 Hz for 60s (hct=0.035%). The photograph has been taken from the dismounted chamber by an inverse microscope.
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Here we used a very simple model to explain only the essential changes to be found in the diffraction patterns of erythrocytes when exposed to an increasing h o m o g e n e o u s field of force (Fig. 3). Using the imaging theory approach, to a certain extent the erythrocyte could be described as a phase object only. From this point of view, normal discocytes could be m o d e l e d as flat hollow cylindrical bodies (rings) which mainly disturbed the transmitted light at the inside and outside ring while the flattened erythrocyte disturbed the light only at the outside rim. The diffraction pattern of a ring, with a finite thickness (phase object), and that of an annular aperture (intensity object) was nearly the same if normalized to the same total energy. By analogy, this holds also for a disk and an aperture. The intensity distribution for each of these geometries can be calculated analytically (see Appendix). The rotational symmetry was used to simplify the problem in one dimension only. The result of the simulation given as intersection through the radial intensity distribution is shown in Fig. 3. It can be seen clearly that the intensity of the m a x i m u m of first order for a ring-like structure was increased when compared to that of the disk. These analytical results were easily explained based on the concept given above. Only the outer rim of the disk diffracted light and superimposed it d u e to the principles of interference into the first maximum. The ring, in addition, had a surplus of diffracting edges due to the inner rim and therefore a higher intensity in the first maximum, while the total intensity stayed constant. The intensity distribution, acquired by simulations based on this simple heuristic explanation, could be used for the principal interpretation of the experimental results. A more sophisticated theory will be presented in a subsequent publication. Anolied forces A
The resultant force ~'R v acting on the erythrocyte during rotation of the chamber is given by the following equation:
.> where FG is the gravitational force, FC the centrifugal force, VERy= 9 0 - 1 0 - 1 8 m 3 is the m e a n erythrocyte volume, ~ =9.81 m / s 2 the acceleration of gravity, v the frequency of revolution and ~ = 0.025 m the effective radius of the centrifuge. Ap is the difference in density between suspending m e d i u m and erythrocyte. This value can be estimated in the centrifuge as described in the next paragraph. Since the amplitude of FG even during the first phase of low rotation is less than it can be neglected in the following. Thus the scalar one. Even so, the surface of projection of deformed erythrocyte are taken to be equal, with T h e n the applied pressure PR is given by
(2)
2.5% of the amplitude of FC problem can be treated as a both the undisturbed and the an error of < 2%.
p R = V ERyAp (4/1:202r) . ff rIR Y
With the present setup pressures up to 12 Pa (120 d y n / c m 2) can be reached.
Erythrocyte m e m b r a ~ elasticity
228
Vol. 34, No. 3
0,5 (:~ cell" shape ~ ' ~ : ~ discocyte "pizza"
**"
,~,
'-7' 0,4 "u~ 0,3
A,II,,
_
,,sc
I/ I
0,2 O 0,1 .....
_...~:~J
-1.o
° ,
-0,5
o,o
.
'-.¢-,-,.;~
0,5
. . . .
1,o
,
1,5
Diameter [cm], (Distance 5cm) Fig. 3. Models used for the simulations: The ring for the discocyte and the disk for the shape under maximal stress. Results: Diffraction pattern of a ring (solid line) and of a disk (dashed line). Ervthrocvte density In addition, o u r e x p e r i m e n t a l setup could be used to process the density o f the cytoplasm of cells. This was d o n e by m e a s u r i n g the time n e e d e d by the cells to s e d i m e n t down to the o u t e r c h a m b e r wall. T h e r e f o r e Stokes law c o u l d be u s e d to c o m p u t e the m e a n difference in density between cells a n d s u s p e n s i o n if the cells were taken to exhibit a sphere-like s h a p e a n d an estimate o f the effective erythrocyte d i a m e t e r was n e e d e d . L a m b (1945) showed that a circular disk s e d i m e n t i n g towards its small cross-section could be treated as a s p h e r e exhibiting a radius of k = 0.56 times that of the disk, while o r i e n t e d with its flat side down it exhibited the same flow resistance as a s p h e r e of k = 0.85 times this radius. G r o o m a n d A n d e r s o n (1971) have found, by :microscopical investigation, that d u r i n g s e d i m e n t a t i o n cells were o r i e n t e d r a n d o m l y a n d that this o r i e n t a t i o n c h a n g e d continuously with time. T h a t is why k could be taken as the m e a n of the two extremes. T h e n the s e d i m e n t i n g erythrocyte c o u l d be treated as a s p h e r e o f the effective erythrocyte radius (Oka, 1985): (3)
r e f f = 0.71. rER Y .
D e f o r m a t i o n of the erythrocytes which may o c c u r d u e to the small a c c e l e r a t i o n (40 g) could be neglected (Corry and Meiselman, 1978a). T h u s the m e a n difference in density Ap between m e d i u m a n d erythrocyte is given by 9 .s.r/ (4)
AP= 2 .a.t.r
2
'
elf where in o u r e x p e r i m e n t a l setup r/= 1.11 • 10 -3 k g / m s is the viscosity o f the s u s p e n d i n g m e d i u m , s = 2 m m the height o f the c h a m b e r , and a = 394 m / s 2 ( v = 20 Hz) the effective acceleration. Measures d o n e so far have given a
V o l . 34, N o . 3
Erythrocyte membrane elasticity
229
sedimentation time o f t = 39 _+ 1 s, which is due to a difference in density of Ap = 92.0 + 2.5 k g / m a. T h e r e f o r e , initially in each e x p e r i m e n t Ap could be estimated for the m e a n erythrocyte o f the population. T h e r e b y it was possible to calibrate the applied forces FR. This might be necessary because the density of cells o f different d o n o r s might vary due to physiological variation or pathological changes. T h e density of o u r suspending medium was chosen to b e P/'Bs = 1004.4 k g / m 3, so the absolute value of erythrocyte density could b e c o m p u t e d . For the cells o f the g r o u p of healthy d o n o r s investigated so far we f o u n d a value o f PERY=1096.4 k g / m 3 which is in g o o d a g r e e m e n t with the literature. Results and Discussion
T h e time course of a diffraction pattern of a standard e x p e r i m e n t with n o r m a l u n t r e a t e d erythrocytes is given in Fig. 4. Clearly the decrease in intensity of the m a x i m u m o f first o r d e r due to the increasing centrifugal acceleration is to be seen. Since the intensity o f the central b e a m is very high the CCD-array in this region is in saturation. Above a centrifugal acceleration o f a b o u t 1500 g the pattern stabilizes. T h e r e is no f u r t h e r change of erythrocyte shape because the cell volumes have r e a c h e d a stable distribution. Due to the restriction of surface to volume ratio f u r t h e r acceleration does not induce further change o f cell shape. T h e cells starting with the n o r m a l discocytic shape have continuously flattened with "quasi-static" increasing forces and r e a c h e d the final oblate-like flat shape ("pizza"). Figure 5 shows the intensity distribution to be f o u n d in contrast if cells are used that have b e e n fixed by glutaraldehyde. H e r e the diffraction pattern is completely i n d e p e n d e n t o f the acting forces after sedimentation. Due to the stiff m e m b r a n e no shape change can occur.
3 -2.5 -2
N"
-1.5 ~ C
o
- .lO~]
Fig. 4. Change in intensity of the first order maximum due to the centrifugal acceleration of untreated normal erythrocytes expressed in acceleration of gravity (g).
230
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2 -2.5
• 1.5~ 1
e.w
-0
~lrcgL,ffy] Fig. 5. No change in intensity of the first order maximum due to the centrifugal acceleration of erythrocytes fixed with glutaraldehyde (1.5%). Since until now we have only evaluated changes in the first m a x i m u m , we can r e d u c e the three-dimensional plot to a simple graph representing the maximal values of the m a x i m u m o f first order. T h e r e f o r e both the right and left course o f the m a x i m u m are c o m p u t e d , averaged, and plotted (Fig. 6). T h e intensities are normalized to the last values, i.e., the erythrocytes u n d e r highest gravitational field. For these values all normal cells have achieved a defined, reproducible, final "pizza" shape. It is well known that in contrast, the initial unstressed shapes can exhibit a whole sequence o f different configurations (Grebe and Schmid-Sch6nbein, 1985). In the final stage the same shape a n d thereby intensity profile is r e a c h e d for different cells in different experiments where the surface-volume-relationship is taken to be constant. T h e r e f o r e cells b e c o m e comparable, which is used for the described normalization. In addition, the results thereby b e c o m e i n d e p e n d e n t of changes in b e a m intensity and h e m a t o c r i t of the suspension in a wide range. For a first quantification of m e m b r a n e elasticity the following p r o c e d u r e has b e e n introduced: Since here we deal with a grid of simple shapes o f rotational symmetry, every value of the normalized intensity first m a x i m u m represents in the m e a n only o n e of the possible cell shapes (Fig. 6). This means every decrease of intensity of the m a x i m u m o f first o r d e r from, for example, I--- 1.5 to I = 1.25 u n d e r gravitational load is d u e to the same change o f cell shape. (These values due to slight shape changes have been proven to be the most effective for evaluation of the experiments.) T h e acceleration difference, Ag, n e e d e d to change the cell shape described by an intensity o f ( I = 1.5) to the shape giving (I = 1.25) can be used as a measure for the m e m b r a n e elasticity. Figure 7 (left panel) gives the normalized graphs for experiments d o n e to investigate the sensitivity of the m e t h o d . Cells have b e e n treated as d e s c r i b e d with increasing concentrations o f diamide. T h e i n d u c e d dose d e p e n d e n t
Vol. 34, No. 3
~4
231
Erythrocyte membrane elasticity
1 2
2.25
E 2 N--,
Elasticity 1 < 2
o 1.75
.~O
m
1.5
~ 1,25 E o r-
Ag2
acceleration
Fig. 6. The graphs give the dependency of cell shape (right) measured as normalized intensity on the acting force/acceleration. The experimental results for two different typical erythrocyte populations with different membrane elasticities are shown: Agl < Ag2 ¢=~to induce the same change of shape in population 1, a smaller resistance has to be overcome than in 2. decrease of deformability is expressed as a n e e d for an increased acceleration for an equivalent degree of cell deformation, r e p r e s e n t e d by an increase o f the qualitative p a r a m e t e r Ag (Fig. 7, right panel). If the m e m b r a n e elasticity is extremely decreased the normalization p r o c e d u r e b e c o m e s invalid due to the fact that the applied forces are no longer large e n o u g h to reach the final standard shape. O u r results are in g o o d a g r e e m e n t with the ones given by D r o c h o n et al., (1993) who showed the effect o f low dose diamide t r e a t m e n t on erythrocyte m e m b r a n e s using a filtering technique with a suspension m e d i u m o f high viscosity (dextran).
Conclusions Centrifugation has b e e n used before by, for example, Sirs (1966), Corry a n d Meiselman (1978b), Abidor et al. (1993), and Pribush et al. (1995), to apply defined forces on RBC suspensions of physiological hematocrit, for example m e a s u r e m e n t of volume or electrical resistivity. H e r e , for the first time, we use this possibility to apply forces on b l o o d cells using o u r cell-elastometry m e t h o d . Defined shape changes are i n d u c e d which are analyzed and quantified by laser diffractometry. This is d o n e by online observation o f diffraction patterns, as p r o d u c e d by a great n u m b e r of cells giving the shape i n f o r m a t i o n for the m e a n cell u n d e r varying centrifugal load. Evaluation and m o d e l i n g becomes relatively simple because the shape o f all cells is c h a n g e d in the same rotational-symmetric m a n n e r . With cell-elastometry it b e c o m e s possible to apply well-defined forces to erythrocytes, to follow up instantaneously the i n d u c e d shape change, and to c o m p u t e parameters quantifying the elasticity of the cell m e m b r a n e . Using a low dose diamide treatment distinct changes in the mechanical properties of m e m b r a n e s can be detected.
Erythrocyte membrane elasticity
232
I - - ~ fl'fl mmolae
E
I
fl•l
~lar
Vol. 34, No. 3
U) 900
<1 8O0
1.75-
~}~
0
[~.-e.4 mole¢
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].5.
c dl e~
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0¢-
200 1
0,0
o
acceleration [n * gravity]
0,2
0,4
0,6
0,8
1,0
Diamid concentration [mMol/L]
Fig. 7. Normalized intensities of the first maximum as related to acceleration for the same erythrocyte population treated with increasing concentrations of diamide (left panel). The according relationship between the measure for elasticity Ag and the concentration of diamide is given by the graph in the right panel. Due to the fundamental, straight forward physical principles used, efforts for the experimental setup are restricted, the m e t h o d can be standardized easily, and the n u m b e r o f potential e r r o r sources is relatively small. F u r t h e r m o r e , this m e t h o d needs no undesired additives in the suspension, for example dextran, to generate the high viscosity required by o t h e r methods. F u r t h e r advantages o f cell-elastometry are as follows: - Only a small volume of b l o o d is needed• - Cell p r e p a r a t i o n is r e d u c e d to simple whole blood dilution only. A whole e x p e r i m e n t including evaluadon takes not m o r e than 4 min. - A box 25 x 15 x 10 cm contains the whole e x p e r i m e n t a l setup. - T h e centrifugal c h a m b e r is easy to fill, use and clean. - All evaluations are d o n e online automatically by c o m p u t e r . H e r e we have p r e s e n t e d the principals o f the cell-elastometry m e t h o d a n d given details of the advantages o f this m e t h o d in measuring distinctly the elasticity of the red blood cell m e m b r a n e . Details o f the theoretical basis o f this m e t h o d will be provided in a subsequent publication which will include m o d e l i n g and c o m p u t e r simulations o f cell shapes and according diffraction patterns u n d e r varying force fields. This gives the basis for a m o r e sophisticated way to extract information from the time course of the obseJ~,ed patterns regarding erythrocyte density distribution, elasticity m o d u l u s and :identification of subpopulations of cells. Basically this is d o n e using the spontaneous curvature model, i n t r o d u c e d by Helfrich (1973), e x p a n d e d by additional energy terms. Numerical simulations generate energy minimized cell shapes u n d e r gravitational acceleration. Subsequently these forms are used in numerical diffraction simulation. By c o m p a r i s o n o f the simulated experiments with real ones, m e m b r a n e parameters like b e n d i n g m o d u l u s and s p o n t a n e o u s curvature can be calculated.
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Appendix
Diffraction by disk and annular aperture The radial intensity distribution 1s(r)generated
by a disk with a small diameter as compared to the distance of the image is given by Hecht (1987): =
,
, with
(b) 2E
'
where J1 is the Bessel-function of first order, b= disk radius, Z= distance aperture to image, k = 27t/X wave number and Ea electrical field strength of the incoming wave of light. The function of the amplitude (a) is computed using the integral of diffraction (c) in the boundaries between 0 to b:
z
r=OL z )
'
Es(r) gives the
distribution of field strengths of the image and Jo the Besselfunction of order zero. To compute the intensity distribution IR(r) of the annular aperture the integral of diffraction (c) has to be calculated between a and b, where a is the inner radius of the ring. Thus the intensity distribution of an annular aperture is given by:
(d)
2E2 2 /R(r) = T r A [ b J
kbr kbr kar l~--~) - 2abJl(-[ ) Jl (-~ ) + a2J l~ k--~azr )l .
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Received 8 April 1997; accepted in revised form 21 July 1997.