Microphotometric
determination
hematocrit in small vessels
AXEL
R. PRIES,
GEORG
KANZOW,
of
AND PETER
Institut fiir Normale und Pathologische Physiologie,
D-5000 K&z-41, Federal Republic of Germany
PRIES,AXEL R., GEORGKANZOW,ANDPETERGAEHTGENS.
Microphotometric determination of hematocrit in small vessels.
Am. J. Physiol. 245 (Heart Circ. Physiol. 14): H167-H177,
1983.-Evaluation and calibration of a microphotometric
method for hematocrit determination in microvessels of
transilluminated tissuesis described.This method is basedon
the relation of the optical density (OD) of a microvesselto its
hematocrit (Hct). The following requirementsof the microphotometric systemappear essential:narrow-band monochromatic
light sourcewith efficient false light suppression,high numerical aperture of the objective and low numerical aperture of the
condenser.We useda video system to measurethe intensities
of incident (lo) and transmitted (I) light. For converting of lo
and I into OD values, correcting procedureswere evaluated to
eliminate the influence of glare, shading, and fading. The
calibration procedure was performed with glasstubes of inner
diameter (ID) between 13 and 68 pm perfused with red cell
suspensions.A function was fitted to the data, correlating OD
to ID and Hct. The standard deviation of the original data from
this function is to.02 units of fractional hematocrit. The presented method allows the continuous determination of the
hematocrit in a microvesselaswell as the off-line evaluation of
the hematocrit distribution within a microvesselnetwork.
GAEHTGENS
Universitdt
zu K&a,
method is time-consuming
and limited to the very smallest vessels and low hematocrits because of cell overlapping. The photometric
approach of Jendrucko and Lee
(12) represented significant progress but the methods
based on it (12, 20) were hampered by their limited
resolution and the fact that they are sensitive to hemaa
tocrit changes only in the low hematocrit range.
The present study represents an attempt to improve
this approach by optimizing the pertinent parameters of
the method after an analysis of the phenomena contributing to the loss of light energy in a transilluminated
vessel. In vitro experiments were carried out to evaluate
the measuring technique that was designed for an application to transilluminated
microvascular systems in vivo.
It is shown that the photometric
technique can yield
reliable hematocrit data in vessels ranging between -10
and 70 pm and will therefore be useful to analyze microvessel hematocrits
and their distribution
in vascular
networks.
THEORY
Although it is widely accepted that the Lambert-Beer
video microdensitometry; optical density of red cell suspensions;light scattering; sieve effect; glare
law holds for hemoglobin
in solution (3, ll), it is also
IN THE CONTEXT of microcirculatory
studies aimed at
the understanding
of blood flow in the terminal vasculature, it has become increasingly evident that the distribution of red blood cells and plasma to the component
vessels of a network is not homogeneous. A wide distribution of capillary hematocrits has been experimentally
observed (14,16,19,33) and explained by flow-dependent
uneven apportionment
of red cells to the daughter vessels
at microvascular bifurcations (6,13,29,36,41).
Although
qualitative
descriptions
of this phenomenon
can be
traced back to early studies (7, 17), a quantitative
analysis of these phenomena was hitherto limited by the lack
of a method to determine microvascular hematocrit simultaneously in the vessels constituting a microvascular
network. Previous attempts have made use of red cell
counting on photographic
or video images, but this
0363-6135/83
$1.50 Copyright
0 1983 the American
Physiological
Society
known that it does not hold in the case of blood, a
particulate
suspension (1, 2, 26, 40). Thus the optical
density (OD) of blood is not simply given as the product
of the millimolar
extinction coefficient, the hemoglobin
concentration,
and the sample depth, because it is not
proportional
to each of these parameters. In contrast,
the OD depends in a complex nonlinear way on these
variables along with a number of parameters such as the
index of refraction, the shape, concentration,
and orientation of red blood cells, and the characteristics of the
illumination
and imaging system.
Only some of these parameters can be measured during
experiments
with transilluminated
living tissues, and
even fewer can be controlled. Therefore it is difficult to
establish exact theoretical descriptions for the transfer
of electromagnetic
energy through a vessel in such a
system. However, in a semiempirical
approach, in which
the relation between OD and hematocrit is experimenH167
PRIES, KANZOW,
H168
tally determined, theory could be used to optimize the
controllable
parameters and help to understand and
process the data.
The most prominent phenomenon occurring in particulate suspensions in contrast to solutions is the scattering of light. In the case of blood, light scattering can be
attributed to 1) reflection and deflection of light at the
blood cell surface or inner structures, 2) diffraction of
light by the red blood cells (Huygens principle), and 3)
interference effects due to a phase shift of light passing
the red blood cells. Inasmuch as blood cells are large
compared with the wavelength of light and their refractive index differs little from that of the embedding medium, they can be considered as large, tenuous scatterers
(39). For a suspension of such particles Twersky (37-39)
has developed a formalism that describes the OD of a
transilluminated
sample (OD,,,) as the sum of the ODs
caused by absorption (OD& and by scattering (OD,,,)
of the incident light
OD sus=
ODabs
+
(1)
ODsca
This is explicitly given by Twersky as
OD sus= red - log,, [ lo-“d’H”t - HCt’)
+ q (l-lo-Sd’Hct -
Hct2’]]
10 (1 - Hct) + I0 Hct TP
that is transmitted
through it. The OD of such a layer
(OD,&
can then be calculated as
OD abs += - loglo [ 1 - Hct (1 - TJ]
(4
The difference between the absorption of a solution
(OD,,l) and that of a particulate
suspension (ODabs)
containing the same amount of absorbing substance is
called “sieve” effect (30) and must be accounted for if
the optical density of a suspension such as blood is
investigated (18, 22). Therefore the substitution of ODabs
by the term Ecd (equal to OD&, which is implicitly done
in Eq. 2, is insufficient. Duysens (8) derived ODabs for m
layers of randomly distributed, cubical particles
OD abs
-n-z loglo [l - Hct (1 - TP)]
(5)
This is identical to the ODabs+ of a single layer (as given
in Eq. 4) multiplied
by the number of layers.
Figure 1 serves to illustrate these theoretical considerations. Figure 1A shows the absorption spectrum (OD,,l
vs. X) of an oxygenated hemoglobin solution as measured
in a recording spectrophotometer
(Beckman ratio-recording spectrophotometer).
In addition, the optical density of a red cell suspension (OD,,,) of identical hemoglo=
(2)
where c is extinction coefficient (quarter millimolar)
of
hemoglobin; c is hemoglobin concentration;
d is sample
depth; red = OD,,l is the OD of a hemoglobin solution
according to the Lambert-Beer
law; s is scattering coefficient, depending on the relative refraction index of the
red blood cells (v’ ), their dimensions, and the wave length
(X) of the incident light in the suspending medium; Hct
is hematocrit, particle volume fraction in the suspension;
and 4 is fraction of the scattered light flux that is detected
by the photosensing system, depending on q’, X, the
particle dimensions, and the aperture half angle (y) of
the photosensor.
All reflected and scattered flux into the back half space
of the sample is neglected (38, 39), and it is thereby
assumed that 4 = 1 for an aperture half angle of 90”.
From Eqs. 1 and 2 it can be deduced that I) OD,b, equals
the OD of a hemoglobin solution with identical hemoglobin concentration (OD,,l). 2) OD,,, equals 0 if q = 1 or s
= 0 or Hct = 1. 3) In the formalism of Eq. 2 independent
changes of OD,b, and OD,,, are not impossible,
e.g.,
changes in 6 without concomitant
changes in r’ and X
will not influence OD,,,. 4) OD,,, is governed by the
parabolic function (Hct - Hct2) and shows a maximum
at Hct = 0.5. 5) OD,,, > OD,,l.
A simple thought experiment, described by Duysens
(8), shows that deduction 1 cannot be true. Consider the
case of a light beam incident on a monolayer of dispersed,
homogeneous, cubical particles that absorb but do not
scatter light. If the particles are each oriented with one
of their walls perpendicular
to the incident light beam,
the transmitted flux (I) through the layer is given by
I=
AND GAEHTGENS
co
where lo is the light intensity incident on the layer and
Tp is the fraction of the light incident on a single particle
0
300
500
h,nm
A,nm
FIG. 1. A: optical density of an oxygenated hemoglobin solution
(solid line, OD,,J and that of a red cell suspension (broken lines) vs.
light wave length X. Suspension spectra were recorded with an aperture
half angle (y) of approximately 1” (OD,,“) and approximately 40”
(OD,,,). Hemoglobin concentration was 0.017 g/d1 in all samples. B:
absorption component (solid line, OD,,,,) and scattering component
(broken line, OD,,) of suspension spectrum OD,,, from A. C: magnitude
of sieving effect (solid line, Asie) and difference between optical densities
of suspension and solution (broken line, A,,) as function of X.
MICROPHOTOMETRIC
DETERMINATION
OF
HEMATOCRIT
H169
bin concentration as function of the light wavelength (X)
is given for a photodetector aperture (y) of approximately
1 O (ODsus*) and approximately
40” (OD,,,), respectively.
The latter aperture angle was achieved by placing diffusing plates directly behind the measuring and reference
cuvettes (35). Thereby an important part of the scattered
light flux was collected and could be detected by the
photosensor.
While the spectrum of the oxyhemoglobin
solution
shows the well-known shape (3, 11) with pronounced
absorption bands, the suspension spectrum obtained
with the usual small photometric
aperture angle is flattened and the extinction maxima are shifted to longer
wavelengths. This is consistent with both theoretical and
experimental reports in the literature (18, 31, 39). With
an increased photometric
aperture angle the predominance of scattering is reduced, and therefore the resulting
spectrum is less distorted (15, 18). This spectrum will be
used for the following analysis as it is similar to the
spectrum that would be obtained with a microscope
where the “photometric
aperture angle” in mainly determined by the numerical aperture of the objective.
According to Eq. 1 this spectrum can be decomposed
into an absorption and a scattering component (Fig. 1B).
ODabs, which is independent of the aperture angle, was
calculated from Eq. 5. Thereto, Tp was derived from the
red cell volume, the hemoglobin concentration within the
red cells, and c, assuming-a cubical cell shape. Values of
e were taken from the data of ODSOl in Fig. lA, whereas
w1was calculated by dividing the sample depth d by the
edge length of the particles. OD,,, is then obtained as the
difference between OD,b, and OD,,,. Other investigators
have reported spectra of red cell suspensions obtained
after experimental
correction for scattering (5, 18) and
sieve effect (18). These spectra and the correction spectra
are qualitatively
comparable to the curves shown in Fig.
1.
OD,b, deviates appreciably from ODsolonly at absorpshown in Fig. 1C by
tion maxima, as is quantitatively
the Asie curve, where
A sie
=
OD abs
-
OD
sol
(6)
The scattering spectrum, in contrast, exhibits an inverse
behavior with ODsca minima corresponding to maxima of
ODsol
or
ODabs-
It is noteworthy that the difference between the optical
density of a red cell suspension and that of its hemolysate
(A,,,) is not always positive, as is shown in Fig. 1C. Atot
becomes negative if c assumes very high values (23, 31).
This finding, which is in contrast to Twersky’s theoretical treatment (see Eq. 2 and deduction 5), can only be
explained if it is understood that the spectrum of the
suspension is not only influenced by light scattering,
which leads to an increase in optical density, but also by
the sieve effect, which reduces optical density. In the
present analysis, any possible interaction between these
two effects is neglected and thus Eq. 1
OD sus= ODabs + ODsca
(1)
is used but now accounts for the sieve effect in evaluating
using
OD abs,which was calculated from Eq. 5 implicitly
the cubical cell model.
Whereas the assumption
of independence between
ODabs and ODs,a (see Eq. 2, deduction 3) simplifies the
qualitative interpretation
of OD,,, spectra, it is certainly
not adequate for obtaining exact solutions of the problem. For example, the increase of effective optical path
length caused by the scattering properties of a suspension
will alter the light attenuation by absorption.
It was not possible to calculate ODsca from Eq. 2 since
not all necessary parameters of the suspension and the
measuring system are known. Therefore theory and experiment could not be quantitatively
compared.
MATERIALS
AND
METHODS
For the calibration of the hematocrit measuring technique, small-bore glass tubes of 3-cm length with inner
diameters (ID) ranging from 13 to 68 pm were used.
Diameters were measured end on with the capillary tube
mounted vertically. Each capillary was then mounted on
a glass slide; one end reached approximately
1 cm over
the edge of the slide and the other was glued into a
microhematocrit
tube. This assembly was then placed
horizontally
on the stage of a microscope (Leitz). The
capillary was immersed in oil of appropriate refractive
index and transilluminated
using Kohler illumination
conditions. The free. end of the capillary was inserted
into one of a series of syringes that were used as feed
reservoir. The syringes were filled with hemoglobin solutions or suspensions of red blood cells (RBC) in KrebsRinger solution that were stirred immediately
prior to
measurement.
A negative pressure was applied to the downstream
end of the microhematocrit
tube to generate flow through
the capillary. The center-line velocity generally exceeded
2 mm/s.
Blood was obtained by exsanguination
of heparinized
Wistar rats through a carotid catheter. After centrifugation and removal of the buffy coat, RBC suspensions
were prepared by adding various amounts of KrebsRinger solution to the packed cells. Hematocrits
in the
feed reservoir were determined by the microhematocrit
method without correction for trapped plasma. Hemoglobin solutions were prepared by adding 300 ~1 of saponin
solution (16 g/l00 ml) to 10 ml of packed cells. Following
filtration
(Millipore
filter, 1.2~pm pore diam) the hemoglobin concentration
of the solution was adjusted by
adding various amounts of distilled water and determined
using the cyanmethemoglobin
method. Full oxygen saturation of all samples was achieved by equilibration
with
room air. Percent saturation as well as the absence of
methemoglobin
and CO-hemoglobin
was checked with
an IL 282 oximeter (Instrumentation
Laboratory).
To be able to derive the tube hematocrit (HctT) from
the known hematocrit
in the feed reservoir (HctF), a
preliminary
set of experiments
was performed. Glass
tubes of appropriate diameters were perfused at various
HctF values, ranging from 0.1 to 0.88 and sealed with
epoxy resin after the flow was suddenly stopped (9). No
significant differences were seen between the discharge
hematocrit and HctF. Hctr values were then determined
H170
PRIES,
after centrifugation
of the tubes at 12,000 g for 10 min.
The ratio HctT/HctF as a function of the feed hematocrit
was fitted for each tube diameter separately by linear
regression lines, the parameters of which are given in
Table 1.
The light intensities 10 and I were determined on a
video image of the glass tubes perfused with KrebsRinger solution or the sample under investigation.
The OD
signals were integrated over a period of at least 1 s. The
1.0
rectangular measuring window was positioned over the
tube center line, its edge length being adjusted to approximately one-third of the tube diameter.
DISCUSSION
AND
GAEHTGENS
nm
ODsus
OF METHODS
The applicability
of the method for hematocrit determination using OD measurements of transilluminated
microvessels requires the optimization
of some methodical parameters, which are discussed in the following
sections.
WaveLength. The first parameter to choose is X and
implicitly
E. For spectrophotometry
it can be calculated
that the measurement will be most accurate if OD is
approximately
0.4, and an acceptable small error is
achieved in the OD range between 0.15 and 1.0 (3). If
this rule is adopted for measurements of hemoglobin in
concentrations from 0 to 20 g/d1 in vessels with diameters
between 10 and 50 pm, X should be chosen as to provide
an 6 of about 20. This guideline is not directly applicable
to a suspension of RBCs as the absorption in the suspension is lower than that in the corresponding solution due
to the sieve effect, especially near the Soret band, while
there is an additional loss of light intensity caused by
scattering. For the precision of hematocrit measurement,
the relative magnitudes of OD,,, and OD,b, are more
important
than the absolute OD range because their
individual relationships to the hematocrit are quite different.
Figure 2 shows OD,,, and the two calculated components constituting OD as functions of hematocrit. These
measurements were performed with a 35pm cuvette in
a spectrophotometer
(Zeiss PMQ II) at a wavelength of
448 nm. While ODabs, calculated from Eq. 5, increases
almost proportionally
with hematocrit, which is favorable for the hematocrit
determination,
OD,,, shows a
parabolic shape with a steep increase at low HctT and
almost constant values between hematocrits of 0.25 and
0.75. This finding is consistent with other experiments
reported in the literature (1, 22) and also with Twersky’s
TABLE 1. Regressionparameters for
functions correlating HctT/HctF to HctF with
HctT/HctF = m HctF + b
IQ pm
13
26
34
47
68
m
0.36
0.40
0.44
0.26
0.16
b
0.50
0.52
0.73
0.85
Hctr, tube
inner diameter.
A =448
KANZOW,
hematocrit;
HctF,
0.54
hematocrit
from
feed reservoir;
ID,
0
0
1
0.2
1
1
1
0.4
I
0.6
1
‘\
0.8
Hctr
FIG.
OD,b,
depth
2. Hematocrit
dependence
of OD,,
and its two
and OD,,
as determined
in a spectrophotometer
of 35 pm. Abbreviations
in Fig. 1.
theoretical
treatment
components
at a sample
of the scattering process (Eq. 2,
as the shape of the curve relating
OD,,, to Hctr impairs hematocrit measurements except
at very low cell concentrations,
the relative magnitude
of the absorption component must be rendered as high
as methodically
feasible even if the spectrophotometric
rule cited above is violated in doing this. Figure 1B has
already shown that the absorption share of OD,,, increases with increasing c (33). Thus four isosbestic wavelengths can be considered; i.e., 398 nm (c = 56), 422 (t’ =
113),448 (c = 19), and 548 (E = 12.5). The application of
the 398nm and especially the 422-nm wavelength is
restricted to low hematocrits and small vessels if a reasonable upper OD limit of 2.3 (light attenuation 2OO:l)
is fixed. Therefore we chose to establish the relation
between OD,,, and HctT at a X of 448 nm.
It is necessary, as in all photometry, to use sufficiently
monochromatic
light for the measurements.
For the
wavelength chosen, the use of a xenon arc lamp is favorable since it supplies a fairly constant, intensive radiation
over the whole visible spectrum. Compared with a halogen tungsten lamp this reduces markedly the necessity
to suppress long-wavelength false light. Our combination
of a XBO 150 W/l lamp (Osram) driven by a VX 150
power supply (Leitz) yielded a sufficient stability.
The requirements of the monochromatizing
device for
application in microscope photometry are 1) high maximal transmission to provide a sufficient signal-to-noise
ratio at the photodetector; 2) narrow transmission band
and efficient false (or stray) light supression, because
broad transmission bands as well as false light cause the
absorbing system to show irregular multicomponent
properties that lead to nonlinear concentration-OD
relationships even for solutions; and 3) compatibility
with
the microscope optics. To meet these demands we chose
a narrow-band interference filter (hmax 447.7 nm, 7ME1x
0.45, HW 3.7 nm; type MA 3-0.3; Schott, Mainz, West
Germany). With an additional
long-wavelength
block
filter (BG 12, 3mm; Schott) we achieved a total false
light attenuation
greater than 2 x 106. For this filter
deduction 4). Inasmuch
MICROPHOTOMETRIC
DETERMINATION
OF
HEMATOCRIT
combination
we proved independence of the measured
OD values from oxygen saturation in the range from 5
to 95% HbO, both for hemolysates and RBC suspensions.
Aperture angles. As stated above, it is advantageous
for the purpose of hematocrit determination
to reduce
the scattering component of OD,,, as much as possible.
This can be done not only by adjusting the measuring
wavelength but also by optimizing the aperture angles of
the incident and accepted light beams.-With
increasing
acceptance angle (y) the amount of scattered light flux
detected by the photosensor is increased. It is obvious
from Fig. 1A as well as from Eq. 2 that OD,,, is thereby
reduced. This phenomenon is demonstrated for the whole
hematocrit range in Fig. 3, which combines the macroscale photometer
data of Fig. 2 with the microscope
measurements made in a 35pm diameter glass tube. The
acceptance angle for the microscopic measurements was
varied by using objectives of different numerical apertures (na) while the aperture angle of the incident light
cone (CU)was adjusted with the aperture diaphragm of
the substage condenser. The difference between the individual OD,,, curves and the calculated OD,b, line indicates the loss of light due to scattering and decreases
drastically with increasing y. As a similar effect is obtained on reduction of cy,it is necessary to minimize the
condenser aperture (25, 27) and combine it with a highna objective, in contrast to the procedures of Jendrucko
and Lee (12) and Lipowsky et al. (20), who matched the
apertures of condenser and objective. In the succeeding
A=448
nm
experiments we therefore used a water-immersion
objective (25 W, na 0.6; Leitz) yielding a y of 23” and a longworking-distance
condenser (L 20, na 0.45; Leitz) adjusted to an aperture angle cyof 4" (na 0.1).
GZare. A special feature of microscope photometry
is
that, in contrast to large-scale, parallel-beam
photometry, only a part of the incident light cone is attenuated
by the specimen and supposed to be transmitted
to the
photometric
field. However, due to reflections at the
multiple surfaces and lens mounts in the illuminating
and imaging system, the measuring field will be illuminated with light that has not been attenuated by the
specimen under investigation (Schwarzschild-Villiger
effect; 24, 25, 34). The intensity of this unwanted light is
called “glare” (G), and its influence on OD measurement
is mathematically
given as
(7)
or
(8)
where lo and I are the incident and transmitted
light
intensities. The asterisks indicate values that are erroneous due to glare. Since G is a constant for a given set
of operating conditions the difference between OD and
OD* increases with OD.
Because some of the measures usually taken to reduce
the rise of glare (25) are not applicable here (e.g., the
reduction of the illuminated
area), it is especially necessary to use an empirical
correction procedure. Glare
values can be measured directly for a given set of conditions as the light intensity of the image of a totally
opaque specimen that resembles the object to be studied.
In our in vitro experiments we perfused the glass tubes
with a highly concentrated dye solution (congo red) to
render them nontransparent
within the limits of intensity resolution. Because it was not possible to fill living
vessels with this dye, we placed thin metal wires (diam
ranging from 14 to 75 pm) on the rat mesentery for the
in vivo determination
of G. A correcting factor independent of the absolute intensity of the incident light (lo) was
then defined as
Hctr
3. Influence
of photometric
and OD,,l. Also shown is calculated
data are given in table.
aperture
on relation
OD,b, curve (broken
FIG.
Magnification
na
Microscope
0
cl
V
A
Large-scale
X
X0
(ho
23
23
13
9
8
21
11
8
1
1
photometer
0.60
0.60
0.35
0.25
x25
x25
x25
x10
I$
I; - G
(9)
F was determined
Objective
Symbol
F --
between HctT
Line). Original
photometer
in vitro and in vivo; the results are
given in Fig. 4. There is no systematic difference between
the in vivo and in vitro values if all optical parameters
including cleanliness of the surfaces are held constant so
that the additional
glare arising from the mesenteric
tissue seems to be negligible. This may not be true for
other tissues used in vital microscopy.
With the use of &. 9, Eq. 8 can be rewritten as
OD = logI
Gi
FU * - I$ + G/F)
(10)
H172
PRIES,
10 was employed for all calculations
of OD
values from microscope photometer measurements.
Photosensing
system. The ideal photosensing
system
for the present purpose should fulfill three major requirements, i.e., 1) sufficient absolute and relative sensitivity
in the employed spectral range; 2) high intensity resolution and signal-to-noise
ratio; and 3) suitability
for in
vivo application. As fairly monochromatic
light of high
intensity was used, the first demand is accomplished by
a variety of devices such as photomultipliers,
phototransistors, blue-enhanced
photoelements
(29)) or vidicon
tubes. Between the second and the third requirement
compromising
is necessary. The common photosensors
(photomultiplier,
photoelement,
phototransistor)
provide high resolution and signal-to-noise ratio for a single
measuring spot. The video system, on the other hand,
makes it possible to analyze off-line the simultaneous
values of OD in any number of vessels present in a field
of view.
We therefore decided to use a closed-circuit TV sysEquation
1107
I
F = 0.274
I D-o*657+
’
I
F 1.0s
%b . 0----h.I
loo!
20
0
I
1
60
I
80
FIG. 4. Glare correction factor (F), determined for the microscope
photometer equipment, as a function of tube diameter (ID). Shown are
in vivo values (I, determined with glass tubes filled with congo red dye)
and in vitro values (0, determined with metal wires placed on the
mesentery) with SD (bars). Also given is the least-square power regression function fitted to both in vivo and in vitro data.
q
A
AND
GAEHTGENS
tern, consisting of a RCA 1005 camera equipped with an
ultricon tube and an IPM 202 video analyzer (IPM, San
Diego, CA), which provides a signal-to-noise
ratio of
approximately
200:1, allowing measurements up to an
optical density of 2.2. This upper limit is acceptable
because the measurement of higher ODs is restricted due
to the increasing error caused by glare, false light, and
so on. In spite of the fact that the automatic gain control
was disabled, the camera showed some overall sensitivity
reactions upon changes in image contrast and light intensity. Therefore it was not possible to perform the zero
adjustment by simply shutting off the light beam. In
contrast, it was necessary to introduce a black area into
the image that could be used as a permanent zero reference. To eliminate simultaneously
the influence of other
illumination
and sensitivity
inhomogeneities
in time
(fading) and space (shading) a grid of 6 X 6 small black
dots painted on a cover glass was placed into the light
beam at the level of the primary image. With the use of
one of these totally opaque dots in the immediate neighborhood of the measuring field as zero reference, both
zero and sensitivity
(100% transmittance)
adjustment
could be renewed with every measurement and at any
spot within the field of view. In the in vitro experiments
the bright level reference for the sensitivity adjustment
was obtained by perfusing the glass tubes with KrebsRinger solution. For in vivo measurements a “homogenous” tissue area adjacent to the vessel under observation has to be employed for this purpose.
The overall performance of the microscope photometer
system consisting of light source, monochromatizing
filters, microscope optics, vidicon tube, video camera, and
analyzer is demonstrated in Fig. 5 in which the OD,,l is
given as function of hemoglobin concentration
(c) for
five glass tubes with inner diameters between 13 and 68
pm. The data show fair agreement with the theoretical
68pm
47pm
KANZOW,
cl
/
20.
OD sol
1.c
FIG. 5. Optical density of hemoglobin
solutions (OD,,J as a function of the
hemoglobin concentration (c) for 5 tube
diameters and X = 448 nm. Lines shown
beside original data are calculated from
ID, c, and c using Lambert-Beer equation. Average percent deviation of measurements from the theoretical curves is
-3.3
t 12.4%.
MICROPHOTOMETRIC
DETERMINATION
OF
H173
HEMATOCRIT
values calculated from ID, hemoglobin
concentration,
and the 6 value taken from the literature (3), using the
Lambert-Beer equation. The requirements as to linearity
and validity of the measuring system seem to be fulfilled,
keeping in mind that some systematic deviation of the
experimental data is introduced by errors in determination of tube diameter and hemoglobin concentration.
atocrit range. This is due to the above-mentioned
methodical measures that are aimed at reducing the relative
magnitude of OD,,, compared with OD,b,. For the experiment shown in Fig. 6A the OD,,, values are given in Fig.
7. They were obtained as the difference between the
measured optical density of the suspension and the OD,b,
values calculated from Eq. 5. According to Twersky’s
formalism (Eq. Z), the scattering function should have a
parabolic shape with a maximum
at Hctr = 0.5 and
should exhibit zero values at Hctr = 0 and HctT = 1.
The data shown in Fig. 7 show reasonable agreement
with these requirements although the maximum of OD,,,
appears to be shifted to Hctr values below 0.5.
Since changes in RBC conformation
and orientation
will mainly influence the scattering properties of the
suspension, the reduction of the scattering component of
OD achieved in the present method may explain the fact
RESULTS
The results of two separate calibration
experiments
with red cell suspensions are shown in Fig. 6. RBC
suspensions and capillary assemblies were independently
prepared for both experiments. In contrast to the results
of Jendrucko and Lee (12) and Lipowsky et al. (20), there
is a significant, single-valued correlation between Hctr
and OD for all capillary diameters over the entire hem1
1
1
1
L
I
L
1
1
4
o
A
0
o
v
68 pm
47 pm
34 w
26 pm
13pm
OD sus
1.0
Hct T
OD sus
Hct T
FIG. 6. Results
of 2 separate
calibration
experiments at X = 448 nm. OD,,, values vs. HctT are shown
for 5 tubes of different
diameters.
H174
PRIES,
KANZOW,
AND
GAEHTGENS
04. -
03.
0
68 pm
A
47pm
0
o
34 pm
26 pm
v
13um
02.
FIG. 7. OD,
values for the data of
Fig. 6A as a function
of HctT. OD,, was
calculated
as difference
between
OD,,,
OD,b, was obtained
and ODabs, where
from Eq. 5.
OD sea
01.
0
I
I
0’2.
014
.
Hct T
1
I
I
06
l
that we found no detectable variations of OD,, values
with changes in flow velocity. Only at extremely low
perfusion rates (center-line velocity below 0.1 mm/s) or
for stopped flow did the measurements become erratic.
For a convenient application of these data to in vivo
measurements it is desirable to express OD as a singlevalued function,of HctT and ID for the entire calibrated
range. This was achieved by using a “unifying term” (E)
of the general form
E = (ID + A) (D(HctT
+ K) + [(Hct*
(11)
-I- K) - (HctT + K)2])
where the parameters A, D, and K were optimized separately to analyze both data sets of Fig. 6, and ID is given
in pm. The constant D is of interest insofar as it determines the linear component of the relation between
hematocrit and optical density, whereas the term (HctT
+ K) - (Hctr + K)2 delineates the parabolic dependence
of OD,,, on HctT according to Twersky’s theory (Eq. 2).
OD,,, values are plotted as function of the unifying term
E in Fig. 8, A and B, for the data of Fig. 6 together with
their linear regression fits.
A common regression line fitted to all data of both
experiments after optimizing the parameters A, D, and
K of the unifying term is described by the function
OD = (ID + 9) [2 (Hctr
- 0.03) - (Hctr
- o.03)2] 0.02719 + 0.00134
(12)
(r = 0.9956)
Solving Eq. 12 for HctT yields
Hctr = 1.03 -
OD - 0.00134
(ID + 9) 0.02719
(13)
.
08.
.
*
I
I
I
to
The tube hematocrit
HctT can be obtained from this
equation for each pair of ID and OD values, provided the
calibrated range is not exceeded. While ID is measured
directly, OD is calculated from measured light intensities
using Eqs. 9 and 10.
To evaluate the precision of the method the difference
between the actual HctT in the capillary tube (derived
from HctF) and the HctT value calculated using the above
procedure was determined; for this purpose the data set
in Fig. 6B and the corresponding parameters of the
unifying term given in Fig. 8B were used. A standard
deviation of -1-0.02 units of fractional hematocrit was
found for this experiment. To test the reproducibility
of
the method the two calibration experiments underlying
Fig. 6, A and B, were compared. If the OD-ID data of the
experiment shown in Fig. 6B were fed into the regression
function of Fig. 8, A and B, a set of paired HctT values
is obtained. The differences between the HctT values in
each pair averaged 0.025 t 0.01 units of fractional hematocrit. Relative to the absolute level of HctT, this corresponds to an error of 7.5 t 3% within the calibrated
HctT range.
It is concluded that this represents a significant improvement in comparison to an rms error of t26.2%
reported by others (20). This improvement
appears essential in view of additional errors that might occur if
the method is applied in vivo. If, for instance, a measurement is performed in a 40 pm-vessel with a hematocrit
of 0.26, an error in the measurement of ID of 5% (2 pm)
and an error in the determination
of OD of 10% will in
the worst case lead to a hematocrit deviation of 14.5% of
the correct value.
Recently two methods have been described that yield
comparably precise hematocrit
measurements. For the
differential
wavelength method . (21) an rms error of
11.6% is reported for hematocrit determina .tions in tubes
MICROPHOTOMETRIC
DETERMINATION
l
4
_
IAl
A‘
L
OF
I
H175
HEMATOCRIT
1
L
I
r opm
1
2.0
2.0-
ocl 68Crm
68um
A
A47pm
47pm
00 34 pm
o 26 pm
pm
v 13pm
/
0
2’cl
I
U0
00 sus
00
1
/
A
/
/
IO-
A
/@
PO A
86
&
9 ,dG
,&-A
A
OD = E x O.O34l+
II
20
II
I
40
0.0165
II
44
11
60
E
L
I
‘
.
1
I
o 68pm
2.0I-
0'
A4?pm
0 34
FIG. 8. OD,,, data of Fig. 6, A and B,
vs. “unifying
term”
E. A: E = (ID + 7)
to.75 (HctT - 0.03) + [ (Hcb
- 0.03) (Hcb - 0.03)2]) (r = 0.9976). B: E = (ID
+ 10) il.3 (HctT - 0.03) + [(Hctr
- 0.03)
- (HctT - 0.03)2] 1 (r = 0.9984).
Also
shown
are the least-square
regression
fits for both experiments.
pm
o 26pm
v 13pm
OD sus
1.0 I-
1 OD-
O- F
0
,
I
30
I
I
60
E x0.021650.00234
I
I
90
E
from 40 to 70 pm ID. While the two-wavelength method
requires a simpler calibration
procedure, the in vivo
applicability
of the present technique to a larger range
of vessel diameters and the possibility of simultaneous
measurements in several vessels (from the video tape
recordings) should be emphasized.
The applicability
of the original red cell counting technique has been significantly increased by using fluorescently labeled erythrocytes (32, 42) as tracers. For this
method the standard deviation of the calculated hematocrit was determined
to be 17% (32). The counting
procedure needs no in vitro calibration
and is mostly
independent of the optical properties of the tissue under
investigation.
On the other hand, it depends absolutely
on normal rheological behavior of the labeled cells and a
precise estimate of the systemic tracer cell concentration.
Also the sampling period required for counting a sufficient number of labeled cells makes it impossible to
detect fast changes of microvessel hematocrit.
DISCUSSION
The purpose of the present study was to search for a
method capable of determining
hematocrit
values in
single microvessels as well as the hematocrit distribution
within a microvessel network.
Direct counting of RBC by means of a photoelectric
device or by analysis of microphotographs
is trustworthy
H176
PRIES, KANZOW,
only under single-file flow conditions (10) and is thereby
restricted to very small vessels or low hematocrits. It was
recently suggested that systematically
administered fluorescent red blood cells could be used as tracers (32, 42)
to extend the range of vessel diameters and hematocrits
that can be analyzed.
The approach of this study is based on the microphotometric determination
of the optical density over a
certain vessel that then is related to the HctT (12).
Because the necessary calibration procedure presented
here was performed in artificial tubes a systematic error
might occur when the results are applied to in vivo
measurements. Since it was shown that the absorption
part of OD was measured correctly in the calibrating
experiments, this uncertainty is restricted to the scattering component of OD,,,, whose relative magnitude was
reduced by the methodical measures described. The red
cell labeling technique (32, 42) might provide the possibility of an in vivo recalibration of the microphotometric
hematocrit measuring method. As the precision and reliability of the microphotometric
approach has been favorably increased, it is now possible to profit by its
advantages, which include no interference with the flow
AND GAEHTGENS
within the microvessels, no systemic administration
of
tracer material, continuous HctT determination
at a sampling rate limited by the video system used, and off-line
analysis of simultaneous
and sequential HctT values in
any number of vessels present in a field of view.
In designing a system based on the photometric
approach described here but with different components,
the following guidelines should be followed. 1) The incident light should have a narrow wavelength band and
very efficient long wavelength suppression. 2) A low-na
condenser should be combined with a high-na objective.
3) The response of the TV camera to changes in overall
light intensity must be recognized and corrected for.
Most TV cameras will show such reaction even if they
have no automatic gain control or such control has been
disabled. 4) Appropriate
correction must be made for
glare.
The authors thank Dr. Giles Cokelet for his efforts in discussing
and improving the manuscript.
This work was supported by a grant from the Deutsche Forschungsgemeinschaft. Preliminary material has been published (B&Z. Anut. 20:
24-27,
1981).
Received 1 June 1982; accepted in final form 7 February 1983.
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