Download Blood velocity and volumetric flow rate in human retinal

Blood Velocity ond Volumetric Flow Rote
in Humon Retinal Vessels
Charles E. Riva, Juan E. Grunwald, Stephen H. Sinclair, and Benno L. Perrig
The distributions of blood velocity and volumetric flow rate in individual vessels of the normal human
retina were determined as a function of vessel diameter. The mean velocity of blood, Vmean, was
calculated from the centerline velocity measured by bidirectional laser Doppler velocimetry (LDV).
Volumetric flow rate was determined from Vmean and the vessel diameter, D, measured from
monochromatic fundus photographs. Diameter of the arteries and veins at the site of the LDV
measurements ranged from 39 to 134 /tin and 64 to 177 nm, respectively. Flow velocity correlated
with D (P < 0.001 for both arteries and veins). Volumetric flow rate varied with D at a power of
2.76 ±0.16 for arteries and 2.84 ±0.12 for veins, in close agreement with Murray's law. Calculated
from 12 eyes, the average total arterial and venous volumetric flow rates were 33 ±9.6 and 34 ±6.3
/xl/min, respectively. The good agreement between both flow rates suggests that the technique and
the assumptions for calculating flow yield results that satisfy mass conservation. Total arterial and
venous volumetric flow rates correlated with total arterial and venous vessel cross-section. Volumetric
flow rate in the temporal retina was significantly greater than in the nasal retina, but the difference
is likely to be due to the larger area of the temporal retina. No difference in flow rate was observed
between the superior and inferior retinal hemispheres. Finally, blood velocity in the major retinal
vessels measured under normal experimental conditions appears remarkably constant over short
(hours) and long (months) periods of time. Invest Ophthalmol Vis Sci 26:1124-1132, 1985
ments of the centerline velocity of red blood cells
(RBCs) in individual retinal vessels.1 LDV combined
with vessel diameter measurements enables the determination of volumetric flow rate in the major retinal
vessels. In this article, we present quantitative measurements of blood velocity and volumetric flow rate
in individual arteries and veins of the normal human
retina and establish their relation to vessel diameter.
Total arterial volumetric flow rate is compared with
total venous volumetric flow rate to verify the conservation of mass, and the flow rates are correlated
with total vessel cross-section. Finally, we demonstrate
the stability over time of retinal blood flow velocity
when measured under normal physiologic conditions.
The retina is one of the few human tissues where
the blood circulation can be observed directly and
noninvasively. This has, on the one hand, facilitated
a detailed description of retinal vascular morphologic
changes for a variety of ocular and systemic diseases.
On the other hand, in spite of the accessibility of the
retinal vasculature and the importance of blood flow
measurements, quantitative data on retinal hemodynamics in both health and disease is still lacking. The
available information consists primarily of subjective
and qualitative assessments of "normal" or "low"
flow conditions obtained by fluorescein angiography.
Attempts to obtain quantitative information using
the fluorescein dye dilution technique have had limited
value.
Bidirectional laser Doppler velocimetry (LDV) allows direct quantitative and noninvasive measure-
Materials and Methods
Doppler shift power spectra of laser light scattered
from RBCs in retinal vessels were recorded simultaneously for two directions of the scattered light using
a fundus camera-based LDV system. The centerline
or maximum velocity, V max , was determined according to the relation:
From the Scheie Eye Institute, Department of Ophthalmology,
School of Medicine, University of Pennsylvania, Philadelphia, PA
19104.
Supported by NIH Grant EY-03242 from the National Eye
Institute, the Pennsylvania Lions Sight Conservation and Eye
Research Foundation, Inc., and by the F. Roland and Marianne
E. Sargent Teaching and Research Fund.
Submitted for publication: August 13, 1984.
Reprint requests: Dr. Charles E. Riva, Scheie Eye Institute, 51
North 39th Street, Philadelphia, PA 19104.
= K-XeAf/(ncos|3)
(0
where Af = f2 — fj. fi and f2 are the cutoff frequencies
of the power spectra recorded for two directions of
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No. 8
HUMAN RETINAL BLOOD FLOW / Rivo er ol.
the scattered light.2 X is the wavelength of the incident
helium-neon laser beam (0.6328 nm); e, the axial
length of the eye as measured by A-scan ultrasonography; h, the index of refraction of the flowing
medium (assumed to be equal to that of the vitreous,
1.336); and /3, the angle between the direction of
Vmax and its projection on the plane defined by the
two scattering directions. Since publication of the
LDV system,2 an instrumental modification has been
made which enables the continuous rotation of this
scattering plane so that (3 can be set equal to zero
(cos /9 = 1) for each measured vessel. K is an
instrumental constant related to the geometry of the
optical pathways used in the detection system. For
our instrument, K is equal to 4.58.2 Refraction of
the incident and scattered beams at the vessel wall
was disregarded.
For each vessel measured, the two photocurrent
signals were recorded on a Honeywell 5600C magnetic
tape system for 5 sec at 5-sec intervals for a total
period of 3-5 min. Between each 5-sec recording, the
fundus camera was recentered; the position of the
incident laser beam and light-collecting optical fibers
remained unchanged. The level of laser light illumination was approximately 0.08 Watt/cm 2 , a value
below the maximum permissible level of retinal irradiance for an illumination of 5-sec duration. 3
Throughout the recording session, the fundus was
diffusely illuminated with monochromatic light
(wavelength of 0.57 /im) at a constant intensity. This
wavelength was chosen because it enhances the contrast between vessels and background4 while it can
be filtered out by the laser light transmitting optical
filter placed in front of each photomultiplier.2 The
LDV recordings were made at sites which provided
the most distinct cutoff frequencies when the laser
beam was moved along the vessel. Sites close to
arterial branchings, venous junctions or arteriovenous
crossings were avoided. All locations of measurement
were within one to two disc diameters from the center
of the disc and were marked on Polaroid color fundus
photographs for referencing diameter measurements.
Processing the Doppler Signal
The taped photocurrent signals were analyzed by
a two-channel spectrum analyzer (Unigon, model
4520). One of the signals was also supplied to a
loudspeaker. Only those portions of tape were analyzed from which a clearly pulsatile pitch (for arteries)
or a monotonous, high frequency pitch (for veins)
could be heard. The power spectra were displayed in
pairs on the screen of a two-channel oscilloscope.
Each spectrum was inspected for the presence of a
1125
distinct drop of both the spectral power and the
magnitude of the spectral power fluctuations. If such
a drop could be identified on both spectra, the
frequencies at which it occurred were documented as
cutoff frequencies fi and fj. The examiner was masked
with regard to the location and diameter of the
vessels.
In arteries, Vmax has been found to be pulsatile, in
synchrony with the heartbeat. Previously, we have
recorded the power spectra for 0.1 sec at various
phases of the cardiac cycle5 and calculated a mean
value of V max , (V m a x ) by integrating over the cardiac
cycle. This procedure was abandoned because it was
time consuming. Instead, we have calculated (V m a x )
using an empirical formula
/v
\
T
J + - rv
—v
.. 1
* max.dia ' o I max.sys
* max.diaj
\ = v
max/
IT\
\^J
which is derived from the relationship for the mean
blood pressure6
MBP = BPdia + - (BPsys - BPdia).
This formula was found to provide values of (V m a x )
in good agreement with those obtained by integrating
Vmax over the cardiac cycle. Equation (2) can be
rewritten as
max.dia
(3)
where p, the pulsatility of the RBC velocity is defined
as:
_
* max.sys _ * 1 ,sys
V
v
~ f
max.dia
M,dia
Vmax.dia was determined using equation (1) by averaging values of Af obtained from nine pairs of power
spectra (Fig. 1), each taken during diastole at different
cardiac cycles, p was calculated by averaging five
values of the ratio fi,sys/fi,dia- Recording time of each
pair of spectra was 0.1 sec.
Pulsatile velocity was rarely observed in the veins
measured. Therefore, for these vessels, the power
spectra were recorded without regard to the phase of
the heart cycle. (V m a x ) was calculated by averaging
nine values of Af obtained from pairs of power
spectra recorded during different cardiac cycles in
0.32 or 0.64 sec. Figure 2 displays a pair of power
spectra obtained from a retinal vein.
The vessel diameter, D, at the site of the LDV
recordings was estimated from photographic negatives
taken with an interference filter centered at 0.57 /im.
The photographic negatives were projected onto a
screen and the diameter of the vessels were measured
with a caliper. Total magnification of the fundus'
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INVESTIGATIVE OPHTHALMOLOGY 6 VISUAL SCIENCE / August 1985
Vol. 26
Equation (4) assumes a circular cross-section of the
vessels and equation (5) uses a constant of proportionality of 1.6 between centerline red cell velocity
and mean blood velocity. This relation has been
demonstrated for blood flowing in glass tubes with a
diameter in the range of those measured in our study
(Baker and Wayland,7 Lipowsky and Zweifach,8 Damon and Duling9).
(V m a x ), Q, and D were obtained from retinal
arteries and veins in 12 eyes of seven healthy volunteers, all males, ranging in age from 20 to 45 yr
(mean, 34 yr). These subjects had normal intraocular
pressure, no fundus pathology, and steady target
fixation. Axial length ranged from 22.6 to 24.4 mm
(mean, 23.5 mm). Informed consent was obtained
from all subjects prior to undertaking the study.
oc
UJ
o
Q.
OC
UJ
o
oc
Q.
UJ
O
0.
5
10
15
FREQUENCY I KHZJ
20
Fig. 1. A pair of Doppler shift power spectra of laser light
scattered in two directions from red blood cells in a retinal artery
(78 ixm in diameter). Both spectra were recorded simultaneously
during diastole. Time window: 0.1 sec. Frequency range: 0-20
kHz. The cutoff frequencies f, and f2 were determined by visual
inspection of the spectra (arrows).
oc
projected image was XI67. This includes the magnification of the eye-fundus camera system, for which
we assumed a value of X2.5 for all subjects. All vessel
diameters were measured by the same individual and
were obtained from an average of three measurements.
The average coefficient of variation of D was 3%.
Volumetric blood flow rate, Q, was estimated as
UJ
o
Q.
20
Vc
A
* mean
(4)
FREQUENCY CKHZ3
with the mean blood velocity, V mean , calculated as
Vr
(5)
Fig. 2. A pair of Doppler shift power spectra obtained from a
retinal vein (92 /xm in diameter). Time window: 0.32 sec. Frequency
range: 0-20 kHz. Arrows indicate fi and f2, the cutoff frequencies
determined by visual inspection of the spectra.
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HUMAN RETINAL BLOOD FLOW / Rivo er ol.
No.
1127
Venous
Arterial
3.5
3
Fig. 3. (V max ) vs vessel
diameter based on measurements in 64 retinal arteries
and 71 retinal veins. Correlation coefficient, r, for the
linear fit between (V max ) and
D is 0.52 (P< 0.001) for the
arteries and 0.66 (P < 0.001)
for the veins.
2.5
2
1.5
-1.0
.5
140 120 100
80
60
40
20
20
40
60
80
100 120 140 160 180 200
Vessel Diameter (pm)
for arteries (linear correlation coefficient r = 0.52, P
< 0.001) and for veins (r = 0.66, P< 0.001), demonstrating that flow velocities increased with increasing
diameter. Such a correlation was evident for seven
arteries measured in one eye (r = 0.91, P < 0.01).
The correlation coefficient between Q and D based
on a power curve fit was 0.89 (P < 0.001) for the
arteries and 0.92 (P < 0.001) for the veins. Volumetric
flow rate was found to vary with the diameter at a
power of 2.76 ± 0 . 1 6 for the arteries and at a power
of 2.84 ±0.12 for the veins. A significant correlation
Results
Velocity azjd Volumetric Flow Rate
Figures 3 ahd 4 demonstrate the dependence of
( V ^ x ) and Q upon the diameter of the arteries and
veins which, at the site of the LDV measurements,
ranged from 39 to 134 nm and from 64 to 177 /jm,
respectively.
For any given vessel diameter, (V m a x ) and Q were
generally greater for arteries than for veins. A significant correlation was found between (V m a x ) and D
<Q >
(pl/min)
Arterial "*— — • Venous
Fig. 4. Volumetric flow
rate vs vessel diameter, D,
for 64 arteries and 66 veins.
Continuous lines are the
power curve fit to the data
points from arteries and
veins. QA varies as 2.0- 10"5
D 276 and Q v as 8.25-10" 6
D 284 where D is in pm. Correlation coefficient, r, is 0.89
(P < 0.0001) for arteries and
0.92 (P < 0.0001) for veins.
-15
\
V;
•io
A-
140
'
/
.
120 100
.
V-
-5
80
60
40
20
/:•..
/
20
40
60
80
100
120 140 160 180
Vessel Diameter (pm)
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INVESTIGATIVE OPHTHALMOLOGY 6 VISUAL SCIENCE / Augusr 1985
1128
2.0
8 1-5
~
1.0
> E 0.5
10
20
30
40
50
Time (minutes)
Vol. 26
was calculated for three ranges of diameters, and was
26%, 17% and 16% for veins with diameters between
62 and 99 /im, 100 and 139 ixm, and 140 and 176
nm, respectively. For arteries, this coefficient was
constant (34%) for the three ranges of diameters (4069 tim, 70-99 /im, and 100-130 /mi)- The average
coefficient of Q was only a few percent greater than
that of <(Vmax) since the coefficient of variation of D
was only 3%.
2.0
Flow Measurements Along a Vessel
I 10
.
0.5
20
40
60
80
Time (days)
Fig. 5. A, top, Retinal blood velocity in a 119-Mm vein of a
normal subject measured during approximately 50 min. Error bars
represent ±1 SD. B, bottom, Retinal blood flow velocity in the
same vein measured over a period of 2 mo.
between Q and D was also apparent for the arteries
and the veins measured from the same eye.
In all arteries, pulsatile flow velocity was observed
to be in phase with the cardiac cycle. The pulsatility,
p, ranged from 2.26 to 3.45. For one eye in which
the diameter of seven arteries ranged from 39 to 105
ixm, p was found to correlate significantly with D
(linear correlation coefficient r = 0.77, P < 0.05). p
decreased by 0.1 as D decreased by 10 fim. Venous
pulsatility was seldom perceptible in the Doppler
signal; it could be measured in only two of the 71
veins and was 1.68 and 1.69.
Reproducibility of LDV Measurements
Intraobserver: LDV recordings from 19 vessels of
six eyes were analyzed twice by the same observer in
a masked manner. Nine pairs of spectra were recorded
to determine Af, identifying f, and f2 by visual inspection of the power spectra. The average absolute difference between both determinations, |Afi - Af2|, was
10.7% of the average Af calculated as (Af, + Af2)/2.
Interobserver: Recordings from 52 veins were analyzed independently by two observers. Average value
of |Afobs! — Afobs2| was 13.8% of the average Af.
Variability of (V max ) and Q
The average coefficient of variation of (V m a x ),
i0(M<v ma x))
<v max >
In two subjects, volumetric flow rate was measured
in four veins at various sites between two junctions.
Separation between the first and last sites was one
and one-quarter disc diameter. The coefficient of
variation of the mean flow rate ranged between 2
and 12%. The difference between flow rates obtained
from any two sites along the same vessel ranged from
1 to 22% (mean 8.2%) of the average flow rate.
Stability of Retinal Blood Flow Velocity
The stability of Vmax was determined from repetitive
BLDV measurements in veins of two subjects. The
power spectra were analyzed by the same observer.
Figure 5 shows Vmax values obtained from a 119-^m
vein in one subject over a period of 50 min and on
different days over a period of 2 mo. Each Vmax was
calculated from 1 to 1.5 min of recording (approximately 20 pairs of power spectra). The coefficient of
variation of Vmax was less than 10% in both cases.
Similar results were obtained from a 127-fim vein of
the other subject. Blood flow velocity, when determined with a time constant of 1 to 1.5 minutes,
appears, therefore, to be remarkably constant in
normal subjects since the variations in Vmax are
within the range of errors of the technique. Furthermore, measurements performed twice, on different
days and under the same experimental conditions,
showed average coefficient of variation for Vmax of
10.6 ± 8.5% in 11 veins with a diameter between 64
and 172 ^m.
Total Retinal Blood Flow
In order to estimate total retinal arterial and venous
volumetric flow rate, the flows for the individual
arteries or veins were summed. In many eyes, however,
not all vessels were measurable by LDV as shown by
the value of %SA and %SV in Table 1. %SA or %SV
represents the sum of the cross-sections of the arteries
or veins which could be measured by LDV, expressed
as a percent of the sum of the cross-sections of all
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HUMAN RETINAL DLOOD FLOW / Rivo er ol.
No. 8
Table 1. Total arterial and venous retinal blood flow
QA
QACOIT
(nl/min)
(lil/min)
Qv
(til/min)
(nl/min)
Qvcorr/QAcorr
17.6 ± 2.8*
35.1 ± 6 . 4
18.1
35.1
23.7 ± 1.7*
34.1 ± 3.2
23.8
34.1
1.31
.97
91
96
43.6 ± 8.3
43.1 ± 7.2
45.7
45.2
40.6 ± 4.4
39.6 ± 3.7
40.8
40.9
.89
.90
78
73
98
94
34.6 ± 4.7
29.0 ± 4.3
43.1
36.6
39.6 ± 2.7
39.0 ± 3.8
39.7
40.0
.92
1.09
OD
OS
71
64
81
-100
21.4 ± 3.9
17.3 ± 3.8
27.1
24.4
29.1 ± 3.2
28.2 ± 2.9
33.4
28.2
1.23
1.16
5
OD
OS
96
79
91
83
26.2 ± 3.3
28.5 ± 3.7
27.1
32.7
27.6 ± 1.9
34.8 ± 2.3
30.7
41.2
1.13
1.26
6
OS
89
81
41.0 ± 4 . 5
44.6
31.2 ± 1.5
36.9
.83
7
OD
-100
88
24.1 ± 3.2
24.1
23.2 ± 1.4
25.5
1.06
34 ± 6.3
1.1 ± 0.16
%sA
%SV
Subject
Eye
1
OD
OS
95
-100
98
-100
2
OD
OS
94
93
3
OD
OS
4
30
Mean
± 9.4
33 ± 9.6
32
± 6.3
Qvcorr
* ±1 SD (calculated from the standard deviations of V max , D and p).
%SA (%SV): Sum of cross section of all arteries (veins) from which LDV
measurements could be obtained, expressed as percentage of the cross section
of all visible arteries (veins), SA (S v ).
QA (QV): Sum of the arterial (venous) volumetric flow rates measured.
QAcorr (Qvcorr): Corrected value of QA (Qv) based on an estimation of volumetric flow rates in the vessels not measured by LDV.
arteries or veins measurable on fundus photography.
For example, a %SA of 98 means that only a very
small artery could not be measured by LDV. Therefore, to include all the vessels in the calculation of
total flow, we have estimated the volumetric flow
rates of the vessels which were not measured based
on the regression lines in Figures 4 and 5 and have
added these values to the sum of the measured flows,
QA and Q v , to obtain the total corrected volumetric
flow rates QACOIT and Qvcorr (Table 1). A highly
significant correlation was found between QACorr and
Qvcorr (P < 0.001). The average ratio Qvcorr/QAcorr was
equal to 1.06 ± .16 (SD). Figure 6 is a plot of QAcorr
and Qvcorr vs SA and S v respectively, demonstrating
a significant correlation (P < 0.02) between total
volumetric flow rate and total vessel cross-section.
-£ 50-
2> 4 0 -
Fig. 6. Total arterial (•)
and venous (O) retinal volumetric flow rate vs the corresponding total cross-section. Correlation coefficients
for the linear regression are
0.86 (P < 0.01) for arteries
and 0.76 (P < 0.01) for veins.
o
^
30 H
0)
J
20
10-
10
20
Total Vessel
30
40
50
Cross-section (cm 2 . io 5 )
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60
70
80
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INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / August 1985
Vol.
26
Table 2. Vessel cross-section and blood flow in temporal and nasal retina
Subject
Eye
Si
S»A
SI
SV
Ql
QN A
Ql
nN
\lv
1
OD
OS
17.4
18.1
8.2
12.5
31.3
40.7
12.6
21.0
12.5
22.0
5.6
13.1
18.3
20.9
5.4
13.2
2
OD
OS
29.4
28.5
27.3
21.6
42.0
31.2
22.5
34.1
24.5
28.2
21.2
17.0
29.4
22.4
11.4
18.5
3
OD
OS
19.1
19.9
23.2
14.9
40.7
45.0
20.0
24.0
16.4
18.2
26.7
18.4
25.4
25.7
14.3
14.0
4
OD
OS
16.5
23.9
14.9
12.3
47.0
27.7
15.4
21.2
15.5
16.7
11.6
7.7
25.5
14.3
7.9
13.9
5
OD
OS
31.0
21.0
16.8
17.0
33.6
44.1
38.0
39.7
19.6
16.7
7.5
16.0
15.7
21.2
15.0
20.0
6
OS
24.2
23.9
44.7
30.1
25.5
19.1
23.4
13.5
7
OD
17.3
10.5
36.8
18.3
15.6
8.5
18.4
7.1
22 ± 5.1
17 ± 5.9
39 ± 6.4
25 ± 8.8
19 ± 4.8
14 ± 6.5
22 ± 4.5
13 ± 4 . 3
Mean ± SD
2
5
Sl(S£), Sv(Sv): Total arterial (A) or venous (V) cross-section (cm • 10~ ) of
the temporal (T) or nasal (N) vessels.
QA(QA), QV(QV): Corrected total arterial or venous flow rates (/xl/min) in
the temporal or nasal retina.
Correlation coefficients for linear regression of Q j vs S j : r = 0.67, P < 0.02;
Q j vs SJ r = 0.74, P < 0.01; Q£ VS Si? r = 0.82 P < 0.01; Q v vs S v r = 0.85
P < 0.001.
Regional Blood Velocity and Volumetric Flow Rate
rate as a function of vessel diameter. It also provides
the first measurement of total retinal volumetric flow
rate in normal subjects and demonstrates that this
parameter correlates with the total cross-section of
the retinal vessels.
The measured flow rates represent, obviously, an
estimation of the true flow rates. Inaccuracy in the
measurements can be expected from errors in the
determination of the diameter and the velocity. An
uncertainty is associated with the cross-sectional area
estimates which assume a unique optical magnification
of the eye-fundus camera system and which do not
take into account the marginal plasma zone (2-4 /zm
for the vessels measured in this study10) nor the
actual shape of the vessels. The use of a model eye
and neglect of the refraction of the laser light at the
vessel wall may also be a source of error when
defining the actual scattering geometry. Furthermore,
the assumption of a unique and invariant relationship
between Vmax and Vmean is based on in vitro measurements and may not apply in vivo." Our velocity
and flow values from main superior retinal arteries
are, however, in close agreement with the values of
2-4 cm/sec and 7 /il/min obtained from such arteries
by high speed cinematography after carotid artery
injection of fluorescein.12
No difference was observed in the average velocities
within arteries and veins of equal diameters when
nasal and temporal regions of the fundus were compared. V maxj for nasal and temporal arteries between
80 and 100 /tm in diameter, for example, was 2.49
± 0.22 (SE) cm/sec and 2.47 ± 0.25 (SE) respectively.
For those between 100 and 140 /im in diameter, the
nasal and temporal (V m a x ) were 2.51 ±0.13 (SE) and
2.47 ± 0 . 1 6 (SE). The average velocity in superior
and inferior vessels of similar diameter were also not
statistically different. Table 2 shows the total crosssections of the temporal and nasal vessels with the
corresponding corrected flow rates. The linear correlations between the arterial (venous) flows and arterial
(venous) cross-sections are all significant.
A significant difference was found (Table 2) between
the average volumetric flow rates of the nasal and
temporal retina (P < 0.02 for arteries and P < 0.001
for veins) as well as between the nasal and temporal
cross-sections (P < 0.05 for arteries and P < 0.001
for veins). Average temporal flow rate and crosssection (arterial and venous) were 52% and 45%
greater than average nasal flow rate and cross-section,
respectively. There was however no significant difference in volumetric flow rates and cross-sections between the superior and inferior retinal hemispheres.
Discussion
This investigation attempts, for the first time, to
determine retinal blood velocity and volumetric flow
As observed in other vascular beds, 1314 the velocity
in retinal vessels increases with the diameter. This
increase is steeper for the arteries than for the veins,
most likely due to the steeper blood pressure gradient
in arteries. The velocity also varies greatly between
vessels of approximately the same diameter. This
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HUMAN RETINAL DLOOD FLOW / Riva er ol.
variability results from instrumental uncertainties
(variance <T2DV) anc * ^ r o m statistical fluctuations of
the velocity (variance o-2tat) in different vessels of
similar size. Assuming these two types of fluctuations
to be uncorrelated (as we believe to be the case with
our measurements), it is possible to determine the
relative contribution of OLDV ar»d oftat t 0 ffm, the
variance of the measured velocities, using the formula:
ffm = OIIDV +ffstat-15Calculations for the three ranges
of arterial and venous diameters specified earlier
(Results, variability of (V m a x ) and Q) show that o-2tat
represents 60-70% of oi, in arteries and 57-72% of
a2m in veins, whereas (TLDV represents approximately
30-40% of the measured variability of (V m a x ).
Presently, LDV measurements from veins are more
reliable and less time consuming than measurements
from arteries. Variability of arterial velocities is increased by two factors. First, the random motion of
the laser beam across arteries produces larger variations of Af than for veins because the arteries are
generally smaller than the veins. Second, the variability
of the pulsatility measurements must be added to
that of V maxdia .
The average total volumetric flow rate of approximately 34 pil/min is comparable to previously reported
values obtained from eyes of the macaque monkey
by means of the microsphere technique: 25 ± 9 (SD)
^l/min 16 and 34 ± 8 (SD) /d/min. 17 Values published
for the eye of the rhesus monkey are somewhat larger
(50 ± 39 (SD) /il/min) 18 but the standard deviation
is to large to allow meaningful comparison.
The intersubject variability of the total arterial and
venous volumetric flow rates, which range from approximately 18-44 /Ltl/min and 24-41 jil/min, appears
to be large. It is, however, similar to the variability
observed in eyes of monkeys. It may be explained by
the large variability of the total arterial and venous
cross-section with which it correlates significantly (P
< 0.01) (Fig. 6).
The difference between temporal and nasal flow
rates (5-9 /til/min on the average) (Table 2) correlates
significantly with the difference between temporal
and nasal cross-sections. Some of these differences
are explainable by the 20-25% larger size of the
temporal retina. The rest could be due to a higher
metabolic activity in the temporal retina.
The exponent of 2.76 ± 0 . 1 6 and 2.84 ± 0 . 1 3 for
the variation of the volumetric flow rate with the
arterial and venous diameter respectively conforms
closely to Murray's law.19 This law predicts an exponent of 3 for a vascular system which either seeks an
optimum compromise between blood volume and
vascular resistance or which minimizes its resistance
for a given volume. This observation may lead to
interesting speculations on the properties of the retinal
vascular system which, however, are beyond the
scope of the present work.20
Bidirectional laser Doppler velocimetry combined
with monochromatic fundus photography provides a
reliable and reproducible technique for retinal blood
flow measurement. The measurements of Vmax and
D and the assumptions of a unique and invariant
relation between Vmean and Vmax and circular vessel
cross-section yield arterial and venous volumetric
flow rates which satisfy mass conservation. Increased
accuracy in the determination of the volumetric flow
rates could be gained from more accurate measurements of V max , by recording the LDV signals only
when the laser beam is perfectly centered on the
vessel, and possibly of D, as described recently.21
Clinical application of the technique will be facilitated
by shortening the time of recording of the power
spectra (presently acquisition of the data to obtain
total retinal blood flow requires about 1 hr) and
implementation of online computer determination of
the cutoff frequencies.22
Key words: retinal blood flow, red blood cell velocity, laser
Doppler velocimetry, retinal hemodynamics, Murray's law
Acknowledgments
The authors thank Joan Baine for her skillful technical
assistance and Virginia Mesibov for typing the manuscript.
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