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(Echocell) to the Determination of Red Blood Cell Sedimentation Rate at Low Hematocrit
S. Razavian, D. Quemada, M. Guillemin, Y. Beuzard, M. Boynard
To cite this version:
S. Razavian, D. Quemada, M. Guillemin, Y. Beuzard, M. Boynard. Contribution of an Ultrasonic Interferometry Method (Echocell) to the Determination of Red Blood Cell Sedimentation Rate at Low Hematocrit. Journal de Physique III, EDP Sciences, 1995, 5 (6), pp.903-912. �10.1051/jp3:1995167�.
�jpa-00249353�
J. Phys. III IFance 5 (1995) 903-912 JUNE 1995, PAGE 903
Classification Physics Abstracts
87.45 87.70
Contribution of an Ultrasonic Interferometry Method (Echocell)
to the Determination of Red Blood Cell Sedimentation Rate at Low Hematocrit
S-M- Razavian(~), D. Quemada(~), M.Th. Guillemin(~), Y. Beuzard(~) and M. Boynard(~
(~) Laboratoire de Biophysique Appliqude et Groupe de Recherche
en Physique et Biophysique, UFR Biom4dicale des Saints-Pkres, Universit4 Paris V, France
(~) Laboratoire de Biorhdologie et d'Hydrodynamique Physicochimique, Universit4 Paris VII, France
(~) INSERM U 91, H6pital H. Mondor, Cr4teil, France
(Received 26 October 1994, revised 13 March 1995, accepted 16 March 1995)
Rdsum4. La vitesse de sddimentation (VS) des globules rouges (GR) du sang, individuels, en suspension, a dt4 d4termin4e par une mdthode originale d'interf4rom4trie ultrasonore (Echocell).
La m4thode, dont le principe repose sur l'4chographie mode-A, permet de mesurer la vitesse d'accumulation des GR sur un plan solide lors de leur s4dimentation. La vitesse d'accumulation, qui est relide I leur vitesse de s4dimentation, est obtenue I partir de l'interf4rence des ondes
r4fl4chies par les deux interfaces ~'plan solide / particules sddimentdes" et "particules sddimen- t4es / suspension". La m4thode permet de distinguer les vitesses de s4dimentation de globules
rouges I VS moyenne et 41evde. Les r4sultats pr4sent4s sont comparables (I) aux mesures ex- pdrimentales utilisant un tube cylindrique de mime g40m4trie que l'Echocell et (it) aux valeurs thdoriques propos4es par certains modkles et en particulier celui de Kermack et al.. La relation lin4aire retrouvde entre la VS et l'hdmatocrite avec la mdthode ultrasonore est concordante avec celle retrouvde en utilisant la m4thode du tube cylindrique.
Abstract. The sedimentation rate (SR) of red blood cells (RBCS) in suspensioi1was deter- mined at low volume fractions (1%-5%) by a new ultrasonic interferometry method (Echocell).
This method is based
on A-mode echography and measures the accumulation rate of RBCS on
a solid plate during RBC settling. The RBC accumulation rate, which is related to the SR, is obtained from interference of waves reflected by the two interfaces "plate / sedimented parti- cles" and "sedimented particles / suspension". The method allows to distinguish SR of RBCS with high and mean settling velocity. Present results are compared (I) to the experimental SR measured by using a cylindrical tube of same geometry as the Echocell cavity and (it) to the theoretical SR predicted by some models, especially the Kermack et al. one: the linearly rela-
tionship found between the volume fraction of RBCS (or hematocrit) and SR, obtained at low hematocrit using the ultrasonic interferometry method, agrees with the cylindrical tube method.
Q Les Editions de Physique 1995
Introduction
Sedimentation of particles suspended in liquid is a subject of great interest in chemistry [I], oceanography [2] and medicine [3] as well as in other fields. In some extent, measurement of the sedimentation rate (SR) of particles as a function of their volume fraction (#) is a
way to improve our knowledge on particle interactions. Different experimental methods have
already been used to study interactions between red blood cells (RBC) cylindrical tube method [4], microscopic observation [5], spectrophotometry [6], photography [7], conductimetry [8],
ultrasonic backscattering [9]. The cylindrical tube method (c.t.m.), the most commonly method used in clinical investigation to assess RBC aggregation, is based on the detection of the
suspension-supernatant interface versus time. The time dependent position of the interface is usually not very well defined and measurements are not accurate and reproducible. This
method, which determines the SR of the slowest settling particles, is then questionable.
Therefore, an ultrasonic interferometry method has been developed to determine precisely
the sedimentation rate of particles in suspension, especially aggregated red cells in blood. It
was found [10] that the experimental cell volume fraction providing, in aggregating conditions, the best sensitivity of the method was about 5%. In non-aggregating conditions, I-e-, for RBCS suspended in a saline buffer solution at such a low hematocrit, the method was shown to be sensitive enough to measure mechanical properties (volume, density, shape) and packing of in-
dividual cells [11]. The method also provides evidence of electrical and mechanical interactions between cells.
From a theoretical point of view, the sedimentation velocity of a single spherical particle
in an infinite viscous medium was proposed by Stokes. Application of Stokes's equation to the sedimentation rate of red blood cells in a liquid medium raised some experimental interest
[5,12-15]. However, to take into account mechanical interactiolis between individual particles
in suspension, some authors modified this theory [15-17]. Particularly, the role of the RBC volume fraction (which can be considered as the hematocrit H, in first approximation) on
the sedimentation rate was studied theoretically and experimentally by Kermack et al. with the cylindrical tube method [12]. Independently, Groom and Anderson [6] measured with the
same method the sedimentation rate of small, mean and large RBCS. They demonstrated an
important difference between the results given by these three types of cells.
The aim of the present paper is to apply to RBC sedimentation a very sensitive ultrasonic
interferometry method [18] in order to show precisely the effect of the hematocrit H (I$lo < H
< 5%) on the sedimentation rate of individual RBCS of large and mean size and then to assess interactions between red cells in these conditions. The method measures the accumulation rate of particles on a horizontal solid plate, this accumulation rate being related to their
sedimentation rate (SR). Comparison of SR of RBCS given by the ultrasonic method with results given by other experimental methods and theoretical results are presented.
1. Theoretical Background
The sedimentation velocity of a single spherical particle in an infinite viscous medium, Vo, has been proposed by Stokes:
Vo = 2(p a)gr~ /9~ (1)
where p and r are respectively the density and the radius of the sedimenting particle; a and ~ are respectively the density and the viscosity of the suspending medium; and g is the gravitational
acceleration.
To take into account mechanical interactions between isolated particles in suspension (in
non-aggregating conditions) and to calculate the theoretical qi-dependent sedimentation rate,
N°6 ULTRASONIC INTERFEROMETRY AND INDIVIDUAL RBC SEDIMENTATION 905
supernatant ~
suspension sediment
intedace 12 E2
intedace I, Ei
Eo
acoustical coupling medium
transducer
A-echogram
a b
Fig. I. Vertical section of the measurement cell and A-mode echogram. El and E2 are the echos
generated respectively by the solid plate/sediment interface fi and the sediment/suspension interface 12. r is the ultrasonic propagation time.
two theoretical models can be used. The first one is Kermack et al. model given by the
following expression [12]:
SR = SRO(I K#) (2)
In this relation, SRO is the sedimentation rate of a single spherical particle given by equation (I) (putting SRO + Vo)I K is a calculated constant equal to I-I for normal RBCS suspended
at low hematocrit [12]; and # is the volume fraction of particles in the suspension which is measured by centrifugation.
The second one is Oka's model [15] which takes into account the effect of the particle volume fraction by introducing a correction factor (depending on #) to calculate the theoretical SR.
That is the reason for which when using this model, interpretation of experimental results is
difficult. In the following, the Oka's model has not been used.
2. Materials and Methods
2.I. ECHOCELL METHOD. The principle of the ultrasonic interferometry method (Echo-
Cell), previously described [11,18], is based on A-mode echography. The device measures the
amplitude of ultrasonic wave bursts reflected (echo) by a horizontal solid plate when particles
are sedimenting on it in a tube.
The measurement cell (Fig. I) is an altuglas (polymethacrylate) cylinder which is divided
into two cavities by an altuglas plate (solide plate), perpendicular to the axis of the cylinder.
The choice of the material of the plate is such as its acoustical impedance (2.36x106 Rayleigh) is
near that of the sedimented RBCS (about 1.8 x10~ RayJeigh) in order to increase the sensitivity of the method. The upper cavity, 7 mm in diameter, contains the suspension of particles and
the lower one, the transmit-receive ultrasonic transducer. The transducer (8 MHz), placed
at a distance from the plate, just at the calculated boundary between the Fresnel and the Fraunhofer zones, and excited by an electrical pulse generator at a repetition rate of 2 kHz, emits wave bursts which propagate along the axis of the cell and are then reflected by each
acoustical impedance discontinuity.
,za t~o t=to, t~'u '??~"
.~" .o" .o° f°$
suspensions .°J ..f °°I
slates
~ ~ ~ ~ ~
thickness at
~ ~ ~ ~i, e .h/, e.=q e,»%
~~dj~ent '~ '
A, wave burst reflected by I,
Ai wave burst reflecled
At + A~
A-mode echogram
signal ~, ~.
Fig. 2. Interpretation of the interference phenomenon and formation of the signal for different sedimentation times. Al and A2 are the amplitudes of the waves reflected respectively by the interfaces fi and I21 A is the amplitude of the high frequency wave after reflection. The A-mode echogram and the signal are shown on the two last lines of the figure.
Accumulation of particles on the solid plate induces the formation of a fixed "solid plate /
sediment" interface Ii and of a second interface (sediment / suspension) 12 which moves up with time (Fig. I). The ultrasonic waves which are reflected by Ii and 12 interfere at the beginning
of the sedimentation when the second interface is very close to the first one. The amplitude
of echo El given by Ii, which is measured by the Echocell, oscillates first before reaching a
constant value since it depends, in addition to mechanical properties of the three media (solid plate, sediment and suspension), on the thickness of the sediment [11]. Figure 2 details for
different times this interpretation and the formation of the signal, based on the interference phenomenon. The measurement of the amplitude of Echo El is performed, after demodulation of the electrical signal, via an acquisition module which contains a sample and hold circuit and
a 12-bit-analog-to digital converter. A special made software displays the amplitude variation of El (called in the following the signal, after normalization with respect to the amplitude
detected from water) as a function of time. For more details, see reference [18].
Figure 3 exhibits typical variation of the signal versus time obtained with a suspension of
non-aggregated polystyrene particles of diameter 7.0 pm at I% volume fraction. The signal is maximum (Ao) at the initial time (t
= 0). It decreases until a minimum value Am at t
= tm
and then increases until a maximum value AM, for t = tM. The signal then oscillates with
damping to reach a final plateau Af. Two other parameters ~A
= AM Am and ~t
= tM tm
are also defined. The two times tm and ~t which are shown on Figure 3 are related to the accumulation rate of particles, I-e-, to their sedimentation rate [11].
The ultrasonic interferometry method consists in measuring the time tm required for the formation of a sediment of thickness 1/4, where I is the mean ultrasonic wavelength of the ultrasonic wave burst, e-I-, calculated from the nominal frequency of the transducer. In a
previous paper [18], we already showed that in the present conditions the sedimentation rate
N°6 ULTRASONIC INTERFEROMETRY AND INDIVIDUAL RBC SEDIMENTATION 907
signal
AM
~~~'~f~1
' '
,
At
05 ' ~AA
'
' ,
' ,
' ' i
---~---___Am~ I,
'At
->-- '---w
/~
o j
~~ ~" ~~S~~'fllentati0'n time~t (mn)
Fig. 3. Signal variation versus sedimentation time for
a suspension of polystyrene particles of diameter 7.0 ~m and density 1.312 at a volume fraction of1%.
SR is given by:
sR = ((i~~~Ii) i)c~/4Ft~ (3)
# and #~~d are respectively the initial volume fraction of particles in the suspension and the volume fraction of particles in the sediment; c+ is the speed of ultrasound in the sediment; F is the mean frequency of the ultrasonic wave burst.
However, to calculate SR from relation (3), we need to know #~~d. The volume fraction of
particles in the sediment #~~d has been calculated (Appendix A) by determining the volume of the suspension giving a sediment of thickness 1/4, from a set of suspensions of various but
known volumes at a constant volume fraction ofI%. The volume concentration of the sediment is then given by the relationship [18]:
4sed " 4F#Usus/scs (4)
where S is the cross-section of the tube and v~u~ is the volume of the suspension of concentration
#, for which all the particles sediment to form a sediment of thickness 1/4.
As we obtained the same volume fraction of sediment #~~d for the two sets of suspensions of initial volume fractions I% and 2% (Appendix A), we assumed that in the 1-5$lo volume concentration range, the concentration in the sediment is constant. In these conditions, it is
possible to calculate from equation (3) and equation (4) the sedimentation rate SR of particles by the relationship:
SR = (v~u~/Stm) (c~/4Ftm) (5)
This equation will be used thereafter to express the experimental results given by the ultra- sonic interferometry method. The speed of ultrasound, c~, was experimentally determined by
measurement of the ultrasound time of flight through suspensions of various particle concen-
trations.
2.2. CYLINDRICAL TUBE METHOD (c.T.M.). Measurements of SR were also performed
by the c.t.m. in a cylindrical tube of the same geometry as the ultrasonic cell, called after
"our cylindrical tube method". This method measures the relative height of the suspending
medium with respect to the height of the initial suspension of particles as a function of time.
SIGNAL
OH
= I%
.H = 2%
OH = 3%
OH = 4%
OH =5%
~
~ .° ~:., °
.°
/
o
*
~ «
~ /
o~~o"
~ TIME (min)
° 2d 4o' W' 80' '
Fig. 4. Signal variation versus sedimentation time for suspensions of normal non-aggregated red blood cells at various volume concentrations between 1% and 5%.
2.3. SUSPENSIONS. Red blood cell suspensions were prepared from normal human blood samples (N
= 5) collected on heparin. The cells were washed three times in Phosphate Buffer Solution (P.B.S.: sodium phosphate 10 mM, Nacl
= 0.15 M, pH
= 7A, 300 mosm) and
resuspended in PBS at various hematocrit values H (I% < H < 5%). Before any measurement, all the suspensions were kept at room temperature (25°C + 1°C). Absence of aggregation was
verified by optical microscopy.
In order to calculate the theoretical SR of RBCS, the mean density of blood cells was mea- sured by the phtalate method [19], their mean volume was measured by Coulter counter [20]
and the viscosity ~ of the suspending medium was measured by a capillary viscometer (Ubbe-
lohde Micro-Viscosimeters). The viscosity ~(#) of the dilute RBC suspensions was determined by the Einstein equation (21):
~J(4) = ~Jli + 2.5j) (6)
3. Results and Discussion
Figure 4 exhibits the signal variations versus time obtained from RBC suspensions at hema- tocrits I% < H < 5%. For any concentration, the curves are similar with, as H grows, an
increasing time scale and a lowering of Ao, ~A = AM Am, tm, tM and ~t
= tM tm, whereas Af remains constant. We can notice that ~t is slightly smaller than t~.
Figure 5 compares the experimental sedimentation rates determined by the ultrasonic method
(using equation (3) and t~ data) with results given by our c-t.m.. The coefficient of variation of SR, calculated for each experimental condition over 5 measurements, is respectively better
than I% when measuring with the ultrasonic method and better than 7% when measuring with
the c-t-m-- We have also presented in that figure (I) experimental data obtained by Kermack
et al. [12] in the same conditions and (it) experimental results obtained by Groom and Ander-
son [6] with RBCS of small and mean sizes from suspensions of normal RBCS at hematocrit 0.15$lo. In the I$lo-5$lo hematocrit range, we observed, as expected, a very good agreement first
between SR data obtained from the Echocell and those obtained by Groom and Anderson
coming from RBCS of mean size and, secondly, between results from our c-t.m. and those com-
N°6 ULTRASONIC INTERFEROMETRY AND INDIVIDUAL RBC SEDIMENTATION 909
6 Kermack et al. jR.fJ.C, of amalf size) s~ j~m/s) A Cyllndrlcal tube jR.fJ.C. of small size)
X Ultrasonlc method (R.fJ.C. of mean size)
lj Groom and Anderson (R.fJ.C. of small size)
. Groom and Anderson (R.fJ.C. of mean sJze)
-irj_
'"~Z~,
".A
~f HfJm8t0crit (%)
o i , , »
Fig. 5. Comparison for normal non-aggregated red blood cells between the variations of the sedi- mentation rate (SR) given by the ultrasonic method and experimental data given by the cylindrical
tube method. Theoretical data given by the Kermack et al. model are also shown. For each experi- mental condition, measurements were repeated 5 times. The variation coefficient of SR is respectively
better than 1% when measuring with the ultrasonic method and better than 7% when measuring with the c-t-m-.
ing both from Kermack et al. and from Groom and Anderson measurements, both previous results corresponding to SR of RBCS of small size.
Two comments can be given from a precise examination of Echocell results.
a) It is well known that non-aggregated particles sediment with a constant rate. The sedi- mentation rate measured with the ultrasonic interferometry method used here is related to the two times t~ and tM which respectively correspond to the formation of a sediment of thickness 1/4 and 1/2 [18]. As the hematocrit of the suspension increases (Fig. 4), the
number of particles which accumulate on the sediment per unit time increases. So, t~
and ~t decrease when H increases. Theoretically, in the case of monodisperse particles such as RBCS, which sediment with a constant rate, t~ is equal to ~t (~t
= tM t~)
since tM " 2t~ (Fig. 2). The slight difference found between ~t and t~ can be explained by a small RBC polydispersity in size and density. The decrease of Ao, as H increases,
can be explained by an enhancement of the mean acoustical impedance of the suspension
that approaches the acoustical impedance of the solid plate. This enhancement can also
explain (at least in part, I-e-, close to the sediment) the observed decrease of ~A, which also may result from an increase (close to the suspension) of the packing of the sediment.
The amplitude Af which is constant for any hematocrit only depends on the density of the RBCS and on the packing of the sediment and does not vary with the initial hematocrit value.
b) RBC dispersion in size and density is likely the cause of the important difference found between the Kermack et al. results and those given by the ultrasonic method. The ultrasonic method determines the SR by measuring the time required to form a sediment of a given known thickness. During this time, RBCS which contribute to the formation of
the sediment are the fastest cells which arrive close to the plate, I-e-, especially the largest and the more dense cells. The ultrasonic method determines the sedimentation rate of
these cells whereas, at the opposite, the cylindrical tube method determines the SR of
