Laser Doppler measurements of blood flow
in capillary tubes and retinal arteries
Charles Riva, Benjamin Ross, and George B. Benedek
We have used the technique of Laser Doppler Velocimetry (LDV) to measure the velocity of
blood floioing in retinal arteries of the rabbit. This technique does not require mechanical
perturbation of the blood flow or alteration of chemical environment. It is more precise and.
clinically less demanding than previous methocb, and gives information on the velocity distribution as well as the average velocity. We have also used LDV to measure the velocity distribution of whole blood, flotoing in <-^200 /.i diameter capillary tubes; our measurements agree
with previous experimental results for the flow of erythrocyte ghost suspensions in larger tubes.
Similar measurements on dilute suspensions of polystyrene spheres agree well with the hydrodynamic predictions.
Key words: laser Doppler velocimeter, blood flow, retinal artery, flow velocity,
velocity measurement.
velocity of blood is determined by measuring the distance traveled by the dye
profile between successive frames of the
film. This method is limited by substantial
blurring of the front of the fluorescein bolus
and the noise associated with the granularity of the film. This limitation is severe
when the dye is injected into the antecubital vein. Manipulating a catheter into
the carotid artery improves the dye profile and allows a better estimation of the
flow rate.3 However, this procedure is clinically quite demanding and is useless for
routine clinical studies of retinal blood
flow rate.
The Laser Doppler Velocimeter may
make it possible to perform such velocity
measurements routinely. The Laser Doppler Velocimeter is an instrument that
measures the velocity of particles suspended in a fluid.4~s The instrument is
based on the Doppler effect: The laser
light scattered from a moving particle
lood velocity in the human retina is
currently estimated by means of fluorescein
fundus cinematography.1-'- Fluorescein dye
is injected intravenously and the passage
of the dye bolus through the retinal vessels
is recorded with a movie camera. The
From the Retina Foundation, Boston, Mass., and
the Department of Physics and Center for
Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge,
Mass.
This research was supported in part by Public
Health Service Grant No. EY-00227 and Public
Health Service Fellowship Grant No. EY-54465
of the National Eye Institute, and Public Health
Service Grant No. 1 PO1 HL14322-01 from the
National Heart and Lung Institute to the
Harvard-Massachusetts Institute of Technology
Program in Health Sciences and Technology,
and by Advanced Research Projects Agency
Contract No. DAHC1567 CO222.
Manuscript submitted June 5, 1972; revised manuscript accepted Aug. 21, 1972.
936
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Volume 11
Xumber 11
Laser Doppler measurements 937
Fig. 1. Optical and electronic setup for measurement on capillary tube.
is shifted in frequency in proportion to
the velocity of the particle. The magnitude of the frequency shift is measured by optical heterodyning. With this
technique, the light from particles moving
with velocity V is combined at the surface
of a photodetector with a local oscillator
or reference beam consisting of light from
the same laser. The photodetector mixes
the two signals to give in the output photocurrent a signal at the difference frequency.
The particle velocity is directly proportional
to this difference frequency and can be
measured absolutely from the scattering
geometiy and the laser wavelength.
We carried out an in vitro experimental
study of the feasibility of this technique
by measuring the velocity of whole blood
flowing through a glass capillary tube
~200 /J. in diameter. This is about twice
the diameter of the largest retinal vessels.
We followed this by a successful detection
of the blood velocity in the retinal arterioles
of a living rabbit.
Optical and electronic system
The optical setup used in the in vitro experiments described in this paper is shown in Fig. 1.
Light from a Helium-Neon laser, after being
focused by Li on the pinhole Pi is collimated by
lens L- and falls perpendicularly on the glass
capillary tube CC. The size of the beam at its
intersection with the tube is about twice the tube
diameter. Light scattered at an angle 9 with respect to the incident beam from each moving
particle is mixed at the photocathode of the photomultiplier with light scattered by the glass surface
of the tube. This latter light has the same frequency as the incident light and acts as local
oscillator. In front of the photomultiplier, an
aperture P2 (1 mm. in diameter) limits the angular
spread of the light accepted from the scattering
region to less than 0.02 rad.
For a particle moving with velocity V, the wellknown Doppler effect leads to a frequency shift f
between the frequency of the light scattered' fuom
the moving particle, and the incident light frequency. Appendix 1 shows that for our scattering
geometry the frequency shift f is related to the
velocity V, the light wavelength X (in vacuo) and
the scattering angle 0 by the formula
V
f = - Sin 0
X
(1)
This frequency shift appears explicit)' in the
photocurrent output as a result of the optical mixing process on the photocathode.
The optical arrangement differs from the usual
setups described in the literature in that no particular optical elements such as beamsplitters or
masks are used to produce the local oscillator.0"12
Light scattered from the tube itself is mixed
with the light scattered from the particles to
provide the heterodyne detection of the Doppler
shift. This considerably simplifies the problem of
accurate alignment of the wavefronts between
the local oscillator and the signal.
The electronic system at the output of the
photomultiplier consists of a cathode follower amplifier, a Hewlett Packard 310 A Spectrum Analyser, a squarer, and an integrator. The spectrum
analyzer was scanned at a rate of 100 Hz. per
second. Integration time was 2 seconds.
Results
Flow of polystyrene spheres in water.
To test the apparatus, measurements were
performed with distilled water containing
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Investigative Ophthalmology
November 1972
938 Riva, Ross, and Benedek
r
Frequency |khz)
Fig. 2. The power spectrum N ( t ) of light scattered by a dilute suspension of polystyrene
spheres in water flowing through a capillary tube.
a suspension of polystyrene spheres 0.56
[i in diameter. Fig. 2 shows a typical power
spectrum N(f) of the light scattered
from the moving particles. N(f) is proportional to the number of particles scattering light at the Doppler frequency f,
which is related to the velocity V by
Equation 1. Bandwidth of the spectrum
analyzer was 1,000 Hz. and frequency was
varied from 2 to 40 KHz. The angle G
was ~60°.
This spectrum contains not just a single
frequency corresponding to the movement
of particles with a single velocity, but a
range of frequencies corresponding to a
range of velocities. In fact the form of
N(f) contains information on the velocity
profile of the flowing fluid. Appendix 2
demonstrates that if the velocity profile
across the tube is parabolic, as is the case
for Poiseuille flow," the spectrum of the
scattered light is flat up to a maximum
frequency im«x. This frequency is related
to the maximum velocity V,, at the tube
center by formula 1:
v
— sin 6
(2)
The flat spectrum is a direct consequence
of the fact that, for a parabolic velocity
profile, there are equal numbers of particles flowing at each velocity up to the
maximum velocity V,,. As is discussed
further in Appendix 2, the flatness of the
spectrum for parabolic flow depends on
the assumption that the heterodyne mixing
of the scattered light and local oscillator
is the same for all velocities.
The experimentally observed spectral
distribution illustrated in Fig. 2 clearly
shows this flat spectrum, which cuts off
at ~32 KHz. This cutoff frequency corresponds to a maximum flow velocity of ~2.3
cm. per second which is in agreement with
the measured pump flow rate of 0.0206
c.c. per minute and the tube diameter
~200 /*. In Appendix 2, we also show that
the quantitative relationship between flow
rate Q and V,, is given by
where A is the cross-sectional area of
the tube.
Measurements similar to those shown in
Fig. 2 were made with rate of flow ranging from 0.00206 c.c. per minute to 0.05
c.c. per minute. In each case the cutoff
frequency was in good agreement (within
± 10 per cent) with the maximum velocity
as determined from measurement of the
flow rate.
We have also studied the form of the
power spectrum N(f) as a function of
the scattering angle e. We found that
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Volume 11
Number 11
Laser Doppler measurements 939
?(khzj
Fig. 3. The power spectrum N (f) of light scattered by whole blood flowing through a capillary
tube.
N(f) was always independent of frequency
up to the cutoff, and that the maximum
frequency at each angle was consistent with
the value expected for the particles of highest velocity in accordance with Equation
2.
The width of the high frequency cutoff
is determined by: (1) the range of collection angles e, (2) the time the scattered
particles remain in the illuminated region,
and (3) the instrumental width of the
spectrum analyzer and the integration time
of the integrator following the squarer.
In our experiments the width of the cutoff was found experimentally to be 1 KHz.
This width corresponds to the instrumental
width of the spectrum analyzer.
Flow of red celh (RBC) in whole blood.
Similar measurements were made with
whole rabbit blood. This blood was heparinized with 5 units heparin per milliliter
of blood. To prevent the blood from coagulating on the glass wall, the inner surfaces
of the tubes were previously siliconed. The
scattered light was collected from a small
range of angles, around 9 = 160°. This
backscattering configuration was chosen because the intensity of the heterodyne beat
was stronger than at smaller scattering
angles. Furthermore, the 160° scattering
angle simulates more closely the geometry
employed in the in vivo experiments. Fig.
3 shows a power spectrum N(f) of light
scattered by the RBC in whole blood
flowing at a rate of 0.033 c.c. per minute.
Since the tube area A of our 200 ju. capillary
is 3.1 x 10 4 cm.2 we calculate that the
mean speed VUTl. for the flow is 2.0 cm.
per second.
There are two major differences between
the spectra obtained with RBC and with
the polystyrene spheres in water. First, with
RBC, N(f) rises as the frequency increases.
Second, the falloff near the maximum frequency is much slower than that for the
polystyrene spheres in water. The rise in
in N(f) may be associated with a flattening
of the velocity profile, as is known to occur in erythrocyte flow." However, this
effect cannot explain the slow frequency
falloff of the tail of the spectral distribution. This broad tail may be associated
with the presence of multiple scattering
of light by RBC18: Light can be scattered
by two or more red cells before entering
the phototube entrance aperture, thereby
broadening the spectral profile since two
or more velocity combinations are possible
in the multiply scattered light.
Nevertheless, we observed that this
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Unistitiativc Ophthalmology
November 1972
940 Riva, Ross, and Benedek
F i g . 4 . P o w e r s p e c t r a i \ ( f ) of light s c a t t e r e d b y b l o o d w h i c h is flowing t h r o u g h a c a p i l l a r y
t u b e a l t e r r e s t i n g in a s y r i n g e tor s e v e r a l h o u r s . T h e s p e c t r a ( a ) - ( d ) c o r r e s p o n d t o different
rates of flow: ( a ) 0.0097 c.c. p e r m i n u t e , ( b ) 0 . 0 1 9 4 c.c. p e r m i n u t e , ( c ) 0 . 0 3 8 8 c.c. p e r
m i n u t e , a n d ( d ) 0.097 c.c. p e r m i n u t e .
"knee" is shifted to higher frequencies
in proportion to the flow rate, and that
the mean velocity of 2 cm. per second
corresponds to a frequency of approximately 11 KHz., which occurs near the peak
of the spectrum.
Unlike the measurement with polystyrene
spheres in water, the spectra obtained with
blood changed over time. After 1 or 2
hours of measurement with the same blood,
which was not stirred so that sedimentation was not prevented, spectra like those
shown in Figs. 4A to 4D could be recorded.
These spectra are characterized by the
appearance of two peaks, a broad one at
the low frequency range of the spectra
and a narrow one at the higher frequencies,
followed immediately by a sharp cutoff
(within two or three bandwidths of the
spectrum analyzer). Within the range of
accuracy of the apparatus, the frequency
of the narrow peak varies proportionally
to the rate of flow as is demonstrated in
Fig. 5. The peak at the high frequencies
corresponds to the flattening of the velocity profile. The sharpness of the cutoff
in this case suggests that multiple scattering has been reduced. This may be attributed to the decrease in density of the
RBC flowing through the tube due to
blood cell sedimentation in the reservoir
syringe. Because of the sharpness of the
cutoff we believe that the velocity corresponding to the peak of N (f) is the same
as the maximum velocity of the flow.
For each of these spectra we have calculated the maximum velocity V,, from f,,mx
and the average velocity V11V,. from the
flow rate. In each case, Vo is about twice
as large as V.,,,,, indicating that the velocity
profile has become flat in only a small
part of the tube cross-section. However,
there is a considerable uncertainty in this
figure due to an uncertainty of about 5°
in the measurement of the angle O.
Flow of blood in the retinal artery of
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Volume 11
Number 11
Laser Doppler measurements 941
1
1
1
1
60 -
/
50 -
/
40 -
/
30 -
/
/
20 _
10 -
/
/
/
/
/
/
/
/
•
//
V
/
/
~
/
~
/
~
/
/
/
/
/
_
/
—
/
/
n / 1 1
1
0.0097:
0.0388
0.0194
1
0.097
Flow rate (cc/min)
Fig. 5. Peak frequency of the spectra
Fig. 4 plotted against flow rate. Because
is so sharp, the peak frequency can be
with the maximum frequency shift
shown in
the cutoff
identified
f,,,,IX-.
an albino rabbit. Fig. 6 illustrates a recording of the power spectrum N(f) of
the backscattered light obtained with the
laser beam aimed at the retinal artery near
the optic disc of an albino rabbit. The
setup for this experiment is shown in Fig.
7. The Goldmann17 lens was used to illuminate the vessel with a collimated beam
and to facilitate the positioning of the laser
beam on. the vessel. The incident laser
beam power was about 10 mw. and the
exposure time for one measurement was
about 2 minutes.
The rabbit was anesthetized and its
pupil dilated. It was placed on a platform,
the upper incisive teeth were inserted into
a metallic ring, and the maxillary bones
were supported by two screws to restrain
head movements. A 0.5 c.c. retrobulbar
injection of 2 per cent xylocaine hydrochloride was given in the orbit to eliminate
the saccadic eye movements. The angle 0
between the incident laser beam and the
scattered beam was approximately 170°.
The direction of blood flow in the optic
disc is normal to the incident laser beam
as is assumed in Equation 1. The spectrum
of N(f) suggests that the maximum velocity of flow corresponds to frequencies
between 3 and 5 KHz. The former figure
corresponds to the peak of N(f), and the
latter to the approximate half width. The
corresponding flow velocities according to
Equation 1, are between 1.1 and 1.8 cm.
per second.
At the present time, there are to our
knowledge no published data which can
be made compatible with our measurements. However, Greenls has found that
for a dog, the flow velocity of blood in
vessels of 0.02 mm. in diameter is 0.32
mm. per second and in an artery of 0.6
mm. in diameter, 6 cm. per second. Our
values refer to an artery of approximately
0.0S mm., and are not inconsistent with
these results. Ophthalmoscopic observation
of the rabbit fundus immediately after the
experiment and two days later showed
no damage to the vessel or surrounding
tissues.
Conclusion
The experiments described here demonstrate the utility of LDV for studying the
flow of fluids in small tubes. It can very
sensitively indicate departures from the
parabolic velocity profile. The present
method provides a much more quantitative,
safe, and rapid means of measuring retinal
blood velocity than has previously been
available.
The measurement with whole blood is
complicated by multiple scattering, at
least in the case of tubes of a diameter
of 200 /x or larger. However, in small blood
vessels like those in the ocular fundus
or in the conjunctiva, multiple scattering
should be less troublesome. Already in
this first experiment the spectral distribution of the light scattered from the retinal
arteries of the rabbit permits reasonable
estimates of the flow velocity. The sensitivity of the method indicates that interesting information on the velocity and
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hit estimative Opltthnlntology
November 1972
942 Riva, Ross, and Bcncdck
Fij». (i. The power spectrum M f ) of light scattered from a retinal arteriole or a rabbit.
Goldmann Lens
Fig. 7. Optics of experimental setup for measurements on rabbit. Electronics were identical to
those of Fig. 1.
velocity distribution in pathologic cases
can be obtained even in the absence of
a detailed explanation for the spectral
features.
It is natural to speculate as to whether
or not these experiments can be conducted
safely on the human fundus. In this connection, we observe that the 10 mw., 2
minute exposure in the rabbit produced no
retinal damage detectable with the ophthal-
moscope. Furthermore, the signal-to-noise
ratio achieved in the present experiments
suggests that a reduction of incident power
by a factor of 10 or more would still permit the observation of the spectrum. Also,
the exposure time can be reduced by at
least a factor of 50 if more sophisticated
recording and analysis techniques for the
photoeurrent are used. Both intensity and
exposure time diminution are most en-
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Laser Doppler measurements 943
Volume 11
Number 11
couraging indicators for the applicability
of this method to the study of blood flow
in the living human eye. We also intend
to investigate the effect of the saccadic
movements of the eye on the detection
of the blood flow with this Doppler velocimeter.
The authors wish to thank Lon Hocker for
helpful discussions concerning this work and Dr.
F. Crignolo for assistance during the in vivo experiment and post experimental ophthalmoscopic
examination. We also thank Dr. C. L. Schepens
for making this collaborative effort between the
Massachusetts Institute of Technology Department
of Physics and the Retina Research Foundation
possible.
REFERENCES
1. Bulpitt, C. J., and Dollery, C. T.: Retinal
cineangiography,
British
Kinematography
Sound and Television, January, 1970, p. 14.
2. OberhofF, P., Evans, P. Y., and Delaney, J. F.:
Cinematographic documentation of retinal circulation times, Arch. Ophthalmol. 74: 77,
1965.
3. Delori, F. C, Airey, R. W., Dollery, C. T.,
et al.: Image intensifier cine-angiography,
Fifth Symposium on Photo-electronic Image
Devices, London, September, 1971, Academic
Press (In press.)
4. Yeh, Y., and Cummins, H. Z.: Localized fluid
flow measurements with an He-Ne laser spectrometer, Appl. Phys. Lett. 4: 176, 1964.
5. Foreman, J. W., Jr., George, E. W., and
Levis, R. D.: Measurement of localized flow
velocities in gases with a laser doppler flowmeter, Appl. Phys. Lett. 7: 77, 1965.
6. Rudd, M. J.: The laser dopplermeter—a
practical instrument, Opt. Technol. 1: 264,
1969.
7. Lading, L.: Differential doppler heterodyning
technique, Appl. Opt. 10: 1943, 1971.
8. Blackshear, P. L., Forstrom, R. J., Dorman,
F. D., et al.: Effect of flow on cells near
walls, Fed. Proc. 30: 1600, 1971.
9. Wilmshurst, T. H.: Resolution of the laser
fluid-flow velocimeter, J. Phys. Eng. Sci. Instrum. 4: 77, 1971.
10. Bedi, P. S.: A simplified optical arrangement
for the laser doppler velocimeter, J. Phys.
Eng. Sci. Instrum. 4: 27, 1971.
11. Mayo, W. T., Jr.: Simplified laser doppler
velocimeter optics, J. Phys. Eng. Sci. Instrum.
3: 235, 1970.
12. Adrian, R. J., and Goldstein, R. J.: Analysis
of a laser doppler anemometer, J. Phys. Eng.
Sci. Instrum. 4: 505, 1971.
13. Li, W. H., and Lam, S. H.: Principles of
14.
15.
16.
17.
18.
Fluid Mechanics, Reading, Mass., 1964, Addison Wesley.
Benedek, G. B.: Optical mixing spectroscopy,
with applications to problems in physics,
chemistry, biology, and engineering, in the
jubilee volume in honor of Alfred Kastler,
Polarization, Matter and Radiation, Paris,
1969, Presses Universitaires de France, p. 49.
Goldsmith, H. L.: Microscopic flow properties
of red cells, Fed. Proc. 26: 1813, 1967.
Anderson, N. M., and Sekelj, P.: Reflection
and transmission of light by thin films of nonhemolyzed blood, Phys. Med. Biol. 12: 185,
1967.
Coldmann, H., and Schmidt, T.: Ein Kontaktglas zur Biomikroskopie der Ora Serrata und
der Pars Plana, Ophthalmol. 149: 481, 1965.
Green, H.: Circulation: Principles, in Glasser,
O., editor: Medical Physics, Vol. 1, Chicago,
1944, The Year Book Medical Publishers, Inc.,
p. 210.
Appendix I
In general, if the wave vector Ki of the incident
light makes an angle ©i with the flow velocity V
and the wave vector Ks of the scattered light
—>
makes an angle ©8 with V, then the Doppler frequency shift f is given by
C
.
(Ks
- K,)-V
2TT
— (K. cos e s - K, cos 6 , )
2
K, = Ks =
Since
where n is the refractive index of the following
medium and X is the wavelength in vacuo, this
implies in general:
nV
f = — (cos ©s - cos ©i).
X
In our experiments, ©i was always 90°, and therefore cos ©i = 0. If we call the angle between
the incident and scattered beams, as measured
inside the tube, 0I,1SI.I.;, we have ©S = 90° ©I,,SUI<>.
Our formula then reduces to:
nV
e
f =
-
• A
Sill ©inside
X
But the measured angle ©, as shown in Fig. 1, is
the angle between the incident and scattered
beams as measured outside the tube. Snell's law
gives sin © = n sin ©inside. Thus we find, when
the incident beam is normal to the flow velocity,
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944 Riva, Ross, and Benedek
Investigative Ophthalmology
November 1972
that the magnitude of the Doppler shift is given
by:
f = — sin ©
Appendix II
The correspondence between the flat spectrum
shape shown in Fig. 2 and a parabolic velocity
profile may be seen from the following argument.
Since the number of particles scattering light
with a frequency shift between f and f + df is
equal to the number of particles with velocity between V and V + dV we have
N(f)df = N(V) dV
Furthermore, since V is a function of the distance r from the tube center to the particle, we can
also write
Thus, if the light illuminates all the elements of
the flowing fluid equally and if the velocity profile
is parabolic, the power spectral density in the
scattered light will be flat between 0 frequency
shift and the maximum fllinx = V,, sin ©A. This
results from the fact that the number of particles
with velocity between V and V + dV is constant
up to the maximum flow velocity for a parabolic
profile.
It is often convenient to define a mean velocity
of flow Vnvc which is related to the volumetric
flow rate Q by the formula
Q = VoveA
Here A is the cross-sectional area of the tube.
In the case that the flow has a parabolic velocity profile we have seen that N(V) is a constant up to V,,. It follows that the mean velocity
V,,ve is related to the maximum velocity V» by
N(V)dV = N(r)dr
V,,, = -
where N(r)dr is the number of particles between
r and r + dr. Thus
dr dV
N(f) = N(r)
dV df
.
For a circular tube of radius r and particles of
uniform density p,
for r < ro
N(r) =
0
for r > in
For a parabolic profile
V(r) =
- [r/r..]*)
where V,, is the velocity at the center of the tube.
Thus
— = iv/2V o r
dV
moreover, from Equation 1 we have
dV _ X
df ~~ sin e
Therefore, the velocity distribution has the form
mvpX
N(f) = • Vt
0
G
for f < f111BX
for f > f,,,,,v
where
f.n«, =
V.
Thus, also
Q = - V.,A
The interpretation given here for the spectral
distribution in the scattered light is based implicity
on the assumption that the heterodyne mixing of
the light is equally effective for all velocities. In
the present experiments, the spatial distribution
of particles with different velocities is such that
those particles with large velocities are located
in a small cylinder near the center of the tube,
while those with small velocities are located in
large cylinders close to the walls of the tube.
Thus, we can expect that at the photocathode the
coherence area corresponding to high velocity flowing particles will be larger than the coherence area
associated with low velocity flowing particles.14 If
the size of the coherence area of the local oscillator
field is small compared to the coherence area corresponding to each group of flowing particles,
particles of each velocity will contribute equally
to the spectrum. We believe that the latter situation applied in our experiments because the local
oscillator originated from the total illuminated
surface of the tube which provides a source
volume of larger crossection than any of the flow
cylinders mentioned above. This consideration
should be kept in mind when a beam splitter arrangement is considered for use to provide a local
oscillator.
Vo sin 0
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