AMERICAN JOURNAL OF CLINICAL PATHOLOGY
Vol. 33, No. 2, February, 1960, pp. 138-143
Printed in U.S.A.
MEASUREMENT OF RED BLOOD CELL VOLUME WITH THE ELECTRONIC
CELL COUNTER
JOSEPH L. GRANT, M.D., MELVIN C. BRITTON, JR., A.B.,
AND THOMAS E. KURTZ, P H . D .
Medical Service and Department of Research, Veterans Administration Hospital,
White River Junction, Vermont
The introduction of an electronic blood
cell counter permits more frequent use of red
blood cell counts. Total red blood cell counts
can be performed rapidly and accurately,
and one may also study variations in red cell
size. Mattern and associates4 have described
the apparatus* in detail, and Brecher and
coworkers1 have reported that its accuracy is
approximately 2 per cent. The instrument
has a glass tube with a pore 100 yu in diameter
through which is aspirated a suspension of
cells in saline solution. Each cell passing
through the pore displaces its own volume of
saline, and causes a voltage drop across the
pore. This is measured by electrodes whose
circuit also passes through the pore. The
larger the cell, the greater the voltage drop,
and the greater the signal offered to the
signal amplifier, f Decreasing the signal amplification progressively eliminates the
smaller cells from the count and gives
counts at increasing "thresholds" (Fig. 1A).
From the differences between these threshold counts one can plot cell volume frequency distribution curves (Fig. IB).
can be obtained. No photographic equipment is needed.
Control knobs are provided for the aperture current and for the threshold circuit.
Increasing the aperture current causes a
greater strength and density of current
through the pore, and smaller particles will
be counted, inasmuch as they will cause a
greater voltage change at any threshold. In
counting red blood cells, the aperture current
setting is kept constant. The signal amplification, or threshold control, is set at a fixed
low position for total red blood cell counts,
and turned to successively higher settings
to plot threshold curves. The count is constant at low thresholds and drops as the
threshold rises (Fig. \A). The threshold
scale supplied with the instrument has
arbitrary units that range from 0 to 100.
This paper describes a method of calibrating
the instrument so that these threshold units
can be used to measure cell volume directly
in cubic microns.
These frequency distribution curves differ
from the original red cell distribution curves
of Price-Jones,8 in that they describe cell volume instead of cell diameter. The blood
sample is much larger and can be studied
quickly. In 40 min., data for triplicate curves
Multiple hematocrits, total red blood cell
counts, threshold curves, and frequency
distribution curves were made on 27 specimens of oxalated blood from 4 apparently
normal persons, 12 patients with emphysema, 2 patients with macrocytic anemia, 5
chickens, 2 rabbits, a cat, and a goose. All
counts were performed on the Coulter
counter, the mean of 3 counts at each threshold being taken as the final count. Total
counts were taken at a threshold of 4 units,
or at the middle of the plateau in the threshold curve (Fig. \A). Two 0.002-ml. micro
pipets used for blood delivery were calibrated by weighing the mercury they
delivered and observed to be accurate within
1.5 per cent of each other. The same volumetric 100-ml. pipet was used throughout
for saline measurement; it was found to
Received, May 27, 1959; revision received,
August 13; accepted for publication October 2.
Dr. Grant is Chief, Medical Service; Mr. Britton is Science Aide, Department of Research;
and Dr. Kurtz is Consultant in Biostatistics,
Department of Research, Veterans Administration Hospital.
* Available as the Coulter Counter, Coulter Electronics, Inc., 5227 North Kenmore Ave., Chicago
40, Illinois.
t For present purposes, the volume measured
is regarded as the physical volume of saline solution each cell displaces.
METHOD
138
Feb. 1960
MEASUREMENT OF EED BLOOD CELL VOLUME
139
CELL
COUNT
5,ooqpoo
4,000000
3,000,000
2P00.00C
1,000,000,
\
—I
4
I
I
I
I '
12
I
I
I
I I
• I
• I
20
28
THRESHOLD
'
I
36
'
I
S 7 9
II
»»I7I92ISS»Z7»3I3S3S37
THRESHOLD
F I G . \A (left). Sample threshold curve, normal human blood. As the threshold is increased, the smaller
•cells are eliminated and the cell count decreases.
F I G . IJB (right). Sample frequency distribution curve, normal human blood. The differences between
instrument counts a t even-numbered thresholds (8, 10, 12, 14, and so on) are plotted a t t h e midpoints
(9,11, 13, 15, and so on), in order to indicate the distribution of cells in terms of threshold units. Distribution curves may be constructed as above, using absolute values, or as per cent of total counts.
deliver 99.95 ml. of water by weight at 20 C.
No correction for this error was made. Into
100 ml. of 0.9 per cent NaCl solution (Abbott) was delivered 0.002 ml. of whole blood.
This gives a dilution of 1:50,000. The number of cells counted in 0.5 ml. was multiplied
by 100 to give the number of cells per cubic
millimeter of whole blood. The aperture
current setting was kept at 4 throughout the
study. To avoid the effects of prolonged
exposure of the cells to the electric current,
and to minimize the settling of red blood cells
in the saline, counts were made promptly
after preparation of the suspension. Five
minutes after the beginning of counting, the
cells were resuspended by decanting back
and forth to another beaker, and the determinations for each curve were completed
within at least 10 min. Counts were discontinued when remaining counts were less than
1 per cent of the total; the decrement was
then less than 0.2 per cent.
Microhematocrits were performed by the
method of Strumia and associates6 on blood
collected in balanced oxalate tubes.
The mean cell volumes derived from the
total red blood cell count and hematocrit
were plotted against the mean thresholds
determined from the frequency distribution
curve. (The frequencies with which values
for threshold were found were multiplied by
the values themselves, and the sum of their
products divided by the sum of the frequencies to give the mean threshold.3)
When 2 or more cells of threshold size pass
through the aperture together, they may
erroneously be recorded as 1, and the count
will be too low. On the other hand, if 2 or
more cells smaller than threshold size pass
through the aperture together, a signal will
be recorded when none should be, and the
count will be too high. These 2 sources of
bias are referred to, respectively, as primary
and secondary coincidence. The method used
to correct them follows the approach suggested in Mattern and associates,4 and is
based on the Poisson probability distribution. Without going into the details of the
derivation of the formulas, Nt, the estimated
true count obtained at a particular threshold,
140
GRANT ET
Vol. 33
AL.
is computed by
TABLE 1
N,=
R E D BLOOD C E L L VOLUME AND THRESHOLD
VALUES
- - loge (1 - dNa) - Nsc
a
(1)
where
Nt is the estimated true count,
N0 is the observed count,
d is a constant of the system, and
Nsc is the estimated number of secondary
coincidences.
The quantity d is the ratio of the so-called
critical volume of the pore to the total volume of the liquid passing through the pore;
hence, 1/d represents the number of discrete
volumes of liquid being measured for the
presence of zero or one-or-more cells. In this
work, d is taken to be 0.354 by 10~7, and
was computed on the assumption4 that the
critical volume is 8 times the pore volume.
The correction formula uses "natural" logarithms; if they are not available in table
form, "common" logarithms can be approximately converted to natural logarithms by
multiplying them by 2.302. Thus,
loge x = 2.302 Zo<7io x.
Omitting the last term of formula (1) will
yield a correction for primary coincidence
only. Nsc, the estimated number of secondary coincidences, is given approximately by:
Nsc = -[1d
e~dHl + dA)}
(2)
A is the estimated number of cells ranging in
size from the current threshold level to the
threshold level 80 per cent below, and may
be given as
A = N't ~ Nt
(3)
where N't is the estimated true count at a
threshold 80 per cent of the current level, f
Unfortunately, Nsc depends on Nt, which in
turn depends on N,c. One way out of this
circular dilemma is to iterate the 2 formulas
* For less t h a n 1 million, the error in Nsc using
formula (2a) is less t h a n 2.5 per cent.
t Interpolation will usually be necessary, and
graphic interpolation using normal probability
paper is suggested.
Threshold
Observation Situation
39.5
61.4
63.1
75.3
77.8
80.9
81.7
82.4
84.7
85.4
85.5
86.7
87.2
89.3
90.2
91.4
91.8
92.0
9.0
13.0
11.4
13.5
15.1
16.2
15.4
15.3
15.3
16.2
15.5
15.9
16.2
16.1
16.2
16.2
16.0
17.2
94.6
97.2
108.5
113.2
16.4
17.4
21.2
22.1
114.9
22.3
122.0
122.3
126.6
154.7
22.0
19.6
22.0
28.6
Cat
Rabbit
Rabbit
Emphysema
Emphysema
Normal man
Emphysema
Emphysema
Normal man
Emphysema
Emphysema
Normal man
Normal man
Emphysema
Emphysema
Emphysema
Emphysema
Chronic pancreatitis
Emphysema
Emphysema
Chicken
Cirrhosis and macroc ytosis
Cirrhosis and macrocytosis
Chicken
Chicken
Chicken
Goose
MCV 0i»)
(1) and (2) alternately, first compute Nt
without Nsc, then compute Nsc using that
value of Nt, then recompute Nt with N,c, and
so on, until the value of Nt does not change
with further iteration. For most purposes,
however, a reasonably accurate estimate of
Nsc may be obtained by using the observed
counts rather than the true counts, thus
A = N'0 ~ N0
(4)
Nsc rarely exceeds 3 to 5 per cent of the
estimated true count, and that only where JV(
is changing most rapidly.
After final corrections, the changes in
counts were plotted against mean thresholds
to obtain frequency distribution curves (Fig.
IB).
Feb. 1960
MEASUREMENT OF RED BLOOD CELL VOLUME
i
5
1
•—i
1
8
1
1—i—i
II
1—i
14
1
1
1—l—l
r7
THRESHOLD
1
20
1
141
1—l
23
1—l
26
1
1—r~
29
FIG. 2. Calibration line for electronic counter
RESULTS
Values of mean cell volume in the specimens studied varied from 39.5 to 154.7 /i3.
Table 1 lists these values with their corresponding thresholds. Figure 2 illustrates the
relation between the mean cell volume and
the threshold units. The line represents the
regression equation MCV = 5.724T - 5.34
where MCV is the mean cell volume in cubic
microns corresponding to a reading of T on
the threshold scale; the standard deviation
of MCV is 4.67 ixi. The coefficient of correla-
tion for the data was +0.978, and the
standard error of the coefficient 0.196.
DISCUSSION
Any measuring instrument should, if possible, be calibrated in terms of a wide range
of the populations to be studied. Lacking
specimens of human blood with extremely
high or low mean cell volumes, we used
blood from other species. Frequency distribution curves (Fig. 15) could be prepared
according to changing thresholds, and the
142
GRANT BT
mean threshold from the curve related to the
mean cell volumes derived independently
from the hematocrit. The mean threshold is
a more valid figure for this purpose than the
threshold at the peak of the curve, inasmuch
as the curves are not symmetrical. (Asymmetry of the curves based on volume is expected
from populations whose curves based on
diameter are symmetrical, 2,5 if increases in
size occur equally in all dimensions.) In
practice, the threshold counts at readings of
4, 6, and 8 represented total red blood cell
counts, and readings dropped off increasingly
rapidly as thresholds increased up to approximately 14, and then less rapidly from 14
to 34. When mean frequency distribution
curves from threshold values are plotted
against the mean cell volumes calculated
from the hematocrit and total red blood cell
count, the result is an empirical line of
calibration for use of the instrument in
determining red cell volume (Fig. 2). Inasmuch as a straight line fits the data adequately, major distortion in volume measurements by the instrument is ruled out.
The dotted lines in Figure 2 are 95 per
cent confidence limits for a future value of
MCV as determined from the threshold
level. For example, if a mean threshold is
observed to be 20 units, then one may be 95
per cent sure that the MCV computed by
the hematocrit method will be between 99
and 119 M3All values were equally affected by a
background count of minute particles that
occurred in the saline solution. This count
proved negligible with use of saline supplied
as 0.9 per cent NaCl by Abbott. These
"dust" counts were consistently observed to
be approximately 0.2 per cent of the cell
count for threshold counts greater than 5000.
With lower counts, larger dust particles became a progressively more important per
cent of the total count, but it was observed
that the values for dust tended to become
constant above thresholds of 24, so they no
longer contributed to the decrements in cell
counts, and were, therefore, not reflected in
that portion of the frequency distribution
curves.
All values for threshold red blood cell
counts are likewise increased uniformly by
Vol. 33
AL.
the white blood cell counts. White blood cells
can be observed in hanging drop preparations to be roughly spherical. The lower
limit of their diameter is usually given as 9
ix. A sphere with such a diameter has a
volume of approximately 190 n3. The smaller
leukocytes thus far exceed red blood cells in
volume, all of them are counted at each
threshold, and they do not contribute to the
decrements observed. They, therefore, presumably do not affect red blood cell frequency distribution curves.
Threshold counts used for frequency distribution curves must be corrected, both for
coincident passages of 2 or more cells
through the aperture, which are counted as
1, giving too low a count, and also for recorded counts which are, in fact, owing to
passage of 2 or more smaller cells that give
too high a count. Total counts need only be
corrected for the first of these errors. Correction of the second error was based on a
statement in the technical bulletin supplied
with the instrument that on the average,
cells must each have a volume 80 per cent of
those being counted before they can register
when they pass together through the aperture. Both errors were corrected by formulas
based on the statement by Mattern that the
critical volume in which cells can not be
resolved into individual impedance pulses is
3 times the actual physical volume of the
pore. These corrections based on the Poisson
distribution series differ slightly from the
table of coincidence corrections supplied by
the manufacturer that are for primary coincidence only.
After calibration, the instrument seems to
be admirably suited to the study of red blood
cell frequency distribution curves provided
appropriate corrections for coincidence are
applied. Because potentiometer settings will
vary from one machine to another, each
instrument used for volume studies should
be calibrated individually.
SUMMARY
1. The electronic cell counter is an instrument with which total red blood cell counts
can be rapidly and accurately performed.
2. By increasing the threshold systematically,-one can record the differences in counts
Feb. 1960
at various cell sizes, and if the relation of the
threshold scale to cell volume is known, one
can record red blood cell frequency distribution curves.
3. The relation of the threshold scale to
cell volume has been determined by plotting
cell-size distribution curves for blood samples with various cell volumes and deriving
the relation between the mean threshold
points and the mean cell volume calculated
from hematocrits and total red blood cell
counts.
4. The results reveal a linear relation between threshold scale and cell volume, and
indicate that the instrument is satisfactory
for red blood cell frequency distribution
studies.
SUMMABIO I N
143
MEASUREMENT OP RED BLOOD CELL VOLUME
INTEELINGUA
1. Le contator electronic de cellulas es un
instrumento per medio del qual total numerationes erythrocytic pote esser effectuate
rapide- e accuratemente.
2. Per augmentar systematicamente le
limine de sensibilitate del contator, on pote
registrar le differentias inter le numerationes
pro varie dimensiones cellular, e si le relation del scala de limines al volumine cellular
es cognoscite on pote construer curvas de
distribution frequential pro le volumine del
erythrocytes.
3. Le relation inter le scala de limines e le
volumine cellular esseva determinate per
construer curvas del distribution de volumines cellular pro specimens de sanguine con
varie volumines cellular e per derivar le
relation inter le punctos de limine medie e
le volumine cellular medie calculate ab lecturas de hematocrite e ab total numerationes
erythrocytic.
4. Le resultatos revela un relation linear
inter le scala de limines e le volumine cellular
e indica que le instrumento es satisfactori pro
studios del distribution frequential del volumines erythrocytic.
REFERENCES
1. B E E C H E R ,
G.,
SCHNEIDERMAN,
M.
A.,
AND
WILLIAMS, G. Z . : Evaluation of electronic
red blood cell counter. Am. J. Clin. Path.,
26: 1439-1448, 1956.
2. G R A N T , J . L., M A C D O N A L D , A., E D W A R D S ,
J . R., STACEY, R. R., AND STUECK, G. H., J R . :
Red cell changes in chronic pulmonary insufficiency. J . Clin. Invest., 37: 1166-1175,
1958.
3. H I L L , A. B . : Principles of Medical Statistics,
Ed. 3. London: The Lancet, L t d . , 1942.
4. M A T T E R N ,
C.
F.
T.,
BRACKETT, F .
S., AND
OLSON, B . J . : Determination of number and
size of particles by electronic gating: blood
cells. J . Appl. Physiol., 10: 56-70, 1957.
5. P R I C E - J O N E S , C.: Red Blood Cell Diameters.
London: Oxford Medical Publications, 1933.
6. STRUMIA, M . M . ,
S A M P L E , A. B . , AND H A R T ,
E . D . : An improved micro-hematocrit
method. Am. J. Clin. P a t h . , 24: 1016-1024,
1954.