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Measuring Velocity of Flow in Aqueous Veins*
MEASURING VELOCITY O F F L O W IN AQUEOUS VEINS* JOSEF STEPANIK, +
M.D.
Vienna, Austria
Charged with investigation of the amount of aqueous humor visibly eliminated by aqueous veins compared with the amount of aqueous humor eliminated as found by tonography, we (Stepanik and Kemper, to be published) were faced with the problem of measuring the speed of flow in the aqueous veins. The first attempt to estimate the amount of fluid visibly eliminated by the aqueous veins was made by Ascher.1 Instead of diameters of aqueous veins, Ascher used Leber's measurements of conjunctival veins and Theobald's2 figures for the diameters of the deep outlets of Schlemm's canal, and tentatively assumed that Zeller's3 estimations of velocity of flow in conjunctival veins (be tween 0.7 to 1.8 mm./sec.) might roughly correspond to that in aqueous veins. Using these figures and the formula:
section with the time between two pulse beats. Due to the fact that the red blood-cell waves are not found in every aqueous vein, De Vries ascertained the velocities in but four of his numerous subjects and found them to be 1.5, 3.3, 3.5, and 7.5 mm./sec. Using these figures and the measured widths of the aqueous veins, he calculated the amount of fluid leaving the anterior chamber, and arrived at values similar to those published by Ascher and by previous investigators. We could have tried to measure the ve locity of the red blood cells in aqueous veins by the procedure of Basler,6 who determined the speed of flow in the capillaries of the nail bed, a method dating back more than 30 years and also used by Zeller3 for the blood vessels of the human conjunctiva. However, the following method seemed to be suitable.
Minute volume = x (major semiaxis) (minor semiaxis) (velocity)
METHOD
Ascher reached an approximate accord be tween the amount of fluid eliminated by aqueous veins and estimations based on dif ferent methods, published by other authors. 4 De Vries 5 attempted measurement of the actual velocity in aqueous veins by following the course of tiny waves of red blood cells, shooting through the aqueous veins. These red-cell waves, rhythmically entering an aqueous vein, were first described by Ascher ;* he found that they generally arrive in the intervals between two radial pulse beats. De Vries, calling these blood-cell waves "projectiles," compared the time needed for them to pass a previously measured vessel
On considering the mechanism of the pul sating blood waves which enter aqueous veins, I devised a relatively simple method of producing such projectiles artificially. Clear aqueous veins often show minute tribu taries supplying small amounts of blood at low speed (fig. 1-a). If gentle compression is exerted proximally from the entrance of such a minute vein, using a bent Bowman probe (fig. 1-b), the intravascular pressure inside the aqueous veins will suddenly drop for a moment and will permit the entrance of more blood into the aqueous veins during this period of decreased intravascular pres sure.
* From the Department of Ophthalmology, Col lege of Medicine, University of Cincinnati, Cincin nati, Ohio. t Research Fellow, U.S.P.H. Grant B-1S8. 918
As soon as compression is released, the previous pressure gradients become re-estab lished, further entrance of blood from the tributary is restricted to its original trickle, while the "projectile" formed during the period of reduced aqueous humor pressure is
VELOCITY OF FLOW IN AQUEOUS VEINS
Original Appearance
The Projectile Generated
919
Projectile On If» Count
Fig. 1 (Stepanik). Production of "projectiles" in a clear aqueous vein by touching it upstream from its junction with a small venous tributary.
being carried on with the aqueous stream (fig. 1-c). A short touch suffices to produce the projectile; prolonged compression would allow entrance of a longer cylinder of blood. With the help of Mr. F. H. Eastabrooks, we succeeded in photographing one of these projectiles on its way through the aqueous vein, corresponding to the sketch drawn in Figure 1-c. Figure 2A shows the aqueous vein clear, prior to compression. Figure 2B
shows the same vein with the projectile pass ing. It is interesting that, even in aqueous veins without visible tributaries, short gentle com pression produced projectiles of red blood cells. Although less clearly outlined, these cell clusters could be used for estimation of the velocity as easily as those coming from superficially visible tributaries. These swarms of red blood cells, emerg-
Fig. 2A (Stepanik). Clear aqueous vein, prior to compression.
920
JOSEF STEPANIK
Fig. 2B (Stepanik). The same vein with the projectile passing. (P) Projectile. (PB) Metal probe. ing out of the scleral tissues, most probably originate from intrascleral blood vessels and the relatively long way they have to pass be fore reaching the surface explains why their borders are less sharply outlined as com pared to those deriving from tiny superficial venous tributaries. All projectiles disintegrate after having passed a certain length of the vessel; the higher the velocity in the observed aqueous vein, the shorter is the distance between the points of appearance and of disintegration of a projectile. While the compression produces a short stoppage of flow, no change in dis tribution of blood and aqueous was observed after cessation of the compression and dis appearance of the projectile. Our measurements were performed with out the use of anesthetics. Main sources of error in estimating the velocity by this method include the inexact ness of measuring the time and the distance travelled by the projectile. Aqueous veins shorter than one mm. were not used at all. The error in measuring length was estimated as ±0.02 mm. In most cases, the time was
less than one second. The times reported in the table are the averages of three separate measurements. Using a stop-watch with scale marked in tenths of seconds, we might have made errors of ±0.1 second. Therefore, the errors in timing are the more serious. Another error, difficult to be evaluated, is the disturbance of the natural conditions of current and pressure produced by compres sion of the aqueous vein. In three prelimi nary experiments, I compared the velocities of spontaneous blood cell waves with those of artificially produced projectiles in the same vessel, and the values were identical in both cases. RESULTS
I attempted to measure the velocity of cur rent in 67 aqueous veins of 30 normal eyes. In 60 of these vessels, projectiles could be produced by the method described above; five aqueous veins were too short and two were situated so deeply that observation was difficult. The velocities found for the 60 aqueous veins of 30 normal eyes were be tween 1.3 and 7.6 mm./sec, with an average
TABLE 1 VELOCITY OF FLOW IN AQUEOUS VEINS OF NORMAL EYES
Eye No.
Aqueous Vein No.
d mm.
I mm.
t sec.
mm./sec.
1
1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO 51 52 S3 54 55 56 57 58 59 60 61 62 63 64 65 66 67
O.OSO 0.050 0.050 0.035 0.035 0.035 0.070 0.035 0.050 0.035 0.035 O.OSO 0.03S 0.050 0.035 0.050 0.035 0.050 O.OSO 0.050 0.050 0.03S 0.035 0.035 0.035 0.070 0.035 0.035 0.050 0.050 0.070 0.035 0.070 0.050 0.050 0.036 0.050 0.070 0.050 0.035 0.050 0.035 0.035 0.050 0.035 0.035 0.050 0.050 0.035 0.035 0.035 0.035 0.050 0.035 0.035 0.035 0.035 0.050 0.025 0.070 0.035 0.050 0.035 0.070 0.025 0.050 0.035
2.70 1.52 3.80 2.28 2.66 1.71 4.18 2.28 deep 2.66 3.80 3.42 1.14 3.80 short 1.52 2.28 3.80 1.33 2.66 3.04 1.71 1.90 1.71 1.90 4.56 2.09 1.14 3.23 3.80 3.61 short 1.52 2.09 3.04 2.66 3.80 3.80 1.52 deep 3.04 2.85 2.28 2.66 2.28 short 3.42 3.04 1.52 1.71 1.52 1.33 1.90 short 2.40 2.28 2.66 short 3.42 3.04 3.80 3.80 2.65 3.42 2.28 4.00 4.56
0.6 0.3 1.5 0.3 0.5 0.3 0.7 0.4
4.5 5.1 2.5 7.6 5.3 5.7 5.9 5.7
0.7 0.7 0.5 0.4 l.S
3.8 5.4 6.8 2.8 2.5
2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20
21 22 23 24 2S 26 27 28 29 30
d=Width of aqueous vein in mm. 1 = Length of measured section of aqueous vein.
—
•—•
0.2 1.0 0.5 0.2 0.4 0.6. 0.3 0.3 0.3 0.5 0.7 0.4 0.8 0.7 0.8 0.8
V
—
—
7.6 2.3 7.6 6.6 6.7 5.0 S.7 6.4 5.7 3.8 6.5 5.0 1.4 4.6 4.7 4.5
0.4 0.4 0.8 2.0 1.5 0.7 0.3
— 3.8 S.O 3.8 1.3 2.5 5.4 5.0
0.6 0.6 0.6 0.5 1.1
5.0 4.7 3.8 5.3 2.0
0.8 0.5 0.5 0.5 0.3 0.3 0.5
4.3 6.0 3.0 3.4 5.0 4.4 3.8
0.8 0.4 0.6
3.0 5.7 4.4
1.0 1.0 1.0 0.6 0.5 1.7 0.7 0.8 0.7
3.4 3.0 3.8 6.3 5.3 2.0 3.2 5.0 6.5
—
—
—
—
—
—
—
—
—
t =Time required by projectile to pass through. v = Velocity of the projectile in mm./sec.
JOSEF STEPANIK
922
velocity of 4.6 mm./sec. (table 1). The average error was 19.2 percent, the lowest being estimated at five percent and the highest at SO percent. There seems to be no correlation between vessel diameter and speed of current in the aqueous veins. In the same eye, the velocities vary con siderably from aqueous vein to aqueous vein. DISCUSSION
In streamline flow through very small ves sels the movement of fluid takes place in lamellae paralleling the vessel walls. It is well known that in this case the velocity is greatest along the axis of the capillary and decreases parabolically to zero at the vessel wall. It is also known that the axial velocity equals twice the average velocity; that is, Vmax
^Vav.
If the projectile diameter were very small as compared with the vessel diameter, the speed of the projectile would be only slightly less than the axial velocity. At the other ex treme, if the projectile diameter equals the vessel diameter, then the velocity of the pro jectile would equal the average velocity in this vessel. According to my observations and the drawings published by De Vries 5 the pro jectile diameters are, if not equal to the vessel diameters, at least not very much smaller. It is therefore probable that the ob served projectile velocities are closer to the average velocity than to the axial velocity.
Two additional factors, not already con sidered, may influence the results, namely, the change in pressure in the vessel due to compression when the projectile is being pro duced, and the plugging effect of the projec tile. These factors probably act in opposite ways and may or may not balance each other. The relative effects are difficult to evaluate. It would seem, therefore, that at the present time the closest approximation is to use the velocity of the projectile as the average ve locity of the flow in the vessel observed. SUMMARY
In a great percentage of aqueous veins it is possible to estimate the velocity of the current by observation of artificially pro duced projectiles of blood cells. In aqueous veins of 30 normal eyes, the values were be tween 1.3 and 7.6 mm./sec. with an average of 4.6 mm./sec. These values are well in accord with those obtained by De Vries. The average error of my measurements was esti-' mated at 19.2 percent. The results are dis cussed in connection with the laws of stream line flow in small vessels. Cincinnati General Hospital, Cincinnati 29, Ohio. I gratefully acknowledge Dr. W. M. Spurgeon's advice in mathematical and physical problems. The drawings from my original sketches were made in the Department of Medical Art, College of Medi cine, University of Cincinnati. These investigations were aided by United States Public Health Grant B-1S8.
REFERENCES
1. Ascher, K. W.: Aqueous veins: Physiologic importance of the visible elimination of intraocular fluid. Am. J. Ophth. 25:1192, 1202 (Oct.) 1942. 2a. Leber, T.: Die Zirkulations und Ernährungsverhältnisse des Auges, Graefe-Saemisch's Handbuch der gesamten Augenh. Leipzig, W. Engelmann, 2 :63 ff, 1903. 2b. Theobald, G.: Schlemm's canal: Its anastomoses and anatomic relations. Tr. Am. Ophth. Soc, 32: 589, 1934. 3. Zeller, K.: Studien an Bindehautgefässen. Klin. Monatsbl. f. Augenh., 66:613, 1921. 4a. Duke-Elder, W. S.: Textbook of Ophthalmology, London, Kimpton, 1:45S, 1932. 4b. Friedenwald, J., and Pierce, H.: The circulation of the aqueous. Bull. Johns Hopkins Hosp., 49:257, 1931. 5. De Vries, S.: De zichtbare afvoer van het Kamerwater. Drukkerij Kinsbergen, Amsterdam, 1947, p. 75, plate VIII, fig. 12c. 6. Basier, A.: Ueber die Bestimmung der Stroemungsgeschwindigkeit in Blutkapillaren der menschlichen Haut. München. Med. Wchnschr., 66:1, 13, 347, 1919.
M.D.
Vienna, Austria
Charged with investigation of the amount of aqueous humor visibly eliminated by aqueous veins compared with the amount of aqueous humor eliminated as found by tonography, we (Stepanik and Kemper, to be published) were faced with the problem of measuring the speed of flow in the aqueous veins. The first attempt to estimate the amount of fluid visibly eliminated by the aqueous veins was made by Ascher.1 Instead of diameters of aqueous veins, Ascher used Leber's measurements of conjunctival veins and Theobald's2 figures for the diameters of the deep outlets of Schlemm's canal, and tentatively assumed that Zeller's3 estimations of velocity of flow in conjunctival veins (be tween 0.7 to 1.8 mm./sec.) might roughly correspond to that in aqueous veins. Using these figures and the formula:
section with the time between two pulse beats. Due to the fact that the red blood-cell waves are not found in every aqueous vein, De Vries ascertained the velocities in but four of his numerous subjects and found them to be 1.5, 3.3, 3.5, and 7.5 mm./sec. Using these figures and the measured widths of the aqueous veins, he calculated the amount of fluid leaving the anterior chamber, and arrived at values similar to those published by Ascher and by previous investigators. We could have tried to measure the ve locity of the red blood cells in aqueous veins by the procedure of Basler,6 who determined the speed of flow in the capillaries of the nail bed, a method dating back more than 30 years and also used by Zeller3 for the blood vessels of the human conjunctiva. However, the following method seemed to be suitable.
Minute volume = x (major semiaxis) (minor semiaxis) (velocity)
METHOD
Ascher reached an approximate accord be tween the amount of fluid eliminated by aqueous veins and estimations based on dif ferent methods, published by other authors. 4 De Vries 5 attempted measurement of the actual velocity in aqueous veins by following the course of tiny waves of red blood cells, shooting through the aqueous veins. These red-cell waves, rhythmically entering an aqueous vein, were first described by Ascher ;* he found that they generally arrive in the intervals between two radial pulse beats. De Vries, calling these blood-cell waves "projectiles," compared the time needed for them to pass a previously measured vessel
On considering the mechanism of the pul sating blood waves which enter aqueous veins, I devised a relatively simple method of producing such projectiles artificially. Clear aqueous veins often show minute tribu taries supplying small amounts of blood at low speed (fig. 1-a). If gentle compression is exerted proximally from the entrance of such a minute vein, using a bent Bowman probe (fig. 1-b), the intravascular pressure inside the aqueous veins will suddenly drop for a moment and will permit the entrance of more blood into the aqueous veins during this period of decreased intravascular pres sure.
* From the Department of Ophthalmology, Col lege of Medicine, University of Cincinnati, Cincin nati, Ohio. t Research Fellow, U.S.P.H. Grant B-1S8. 918
As soon as compression is released, the previous pressure gradients become re-estab lished, further entrance of blood from the tributary is restricted to its original trickle, while the "projectile" formed during the period of reduced aqueous humor pressure is
VELOCITY OF FLOW IN AQUEOUS VEINS
Original Appearance
The Projectile Generated
919
Projectile On If» Count
Fig. 1 (Stepanik). Production of "projectiles" in a clear aqueous vein by touching it upstream from its junction with a small venous tributary.
being carried on with the aqueous stream (fig. 1-c). A short touch suffices to produce the projectile; prolonged compression would allow entrance of a longer cylinder of blood. With the help of Mr. F. H. Eastabrooks, we succeeded in photographing one of these projectiles on its way through the aqueous vein, corresponding to the sketch drawn in Figure 1-c. Figure 2A shows the aqueous vein clear, prior to compression. Figure 2B
shows the same vein with the projectile pass ing. It is interesting that, even in aqueous veins without visible tributaries, short gentle com pression produced projectiles of red blood cells. Although less clearly outlined, these cell clusters could be used for estimation of the velocity as easily as those coming from superficially visible tributaries. These swarms of red blood cells, emerg-
Fig. 2A (Stepanik). Clear aqueous vein, prior to compression.
920
JOSEF STEPANIK
Fig. 2B (Stepanik). The same vein with the projectile passing. (P) Projectile. (PB) Metal probe. ing out of the scleral tissues, most probably originate from intrascleral blood vessels and the relatively long way they have to pass be fore reaching the surface explains why their borders are less sharply outlined as com pared to those deriving from tiny superficial venous tributaries. All projectiles disintegrate after having passed a certain length of the vessel; the higher the velocity in the observed aqueous vein, the shorter is the distance between the points of appearance and of disintegration of a projectile. While the compression produces a short stoppage of flow, no change in dis tribution of blood and aqueous was observed after cessation of the compression and dis appearance of the projectile. Our measurements were performed with out the use of anesthetics. Main sources of error in estimating the velocity by this method include the inexact ness of measuring the time and the distance travelled by the projectile. Aqueous veins shorter than one mm. were not used at all. The error in measuring length was estimated as ±0.02 mm. In most cases, the time was
less than one second. The times reported in the table are the averages of three separate measurements. Using a stop-watch with scale marked in tenths of seconds, we might have made errors of ±0.1 second. Therefore, the errors in timing are the more serious. Another error, difficult to be evaluated, is the disturbance of the natural conditions of current and pressure produced by compres sion of the aqueous vein. In three prelimi nary experiments, I compared the velocities of spontaneous blood cell waves with those of artificially produced projectiles in the same vessel, and the values were identical in both cases. RESULTS
I attempted to measure the velocity of cur rent in 67 aqueous veins of 30 normal eyes. In 60 of these vessels, projectiles could be produced by the method described above; five aqueous veins were too short and two were situated so deeply that observation was difficult. The velocities found for the 60 aqueous veins of 30 normal eyes were be tween 1.3 and 7.6 mm./sec, with an average
TABLE 1 VELOCITY OF FLOW IN AQUEOUS VEINS OF NORMAL EYES
Eye No.
Aqueous Vein No.
d mm.
I mm.
t sec.
mm./sec.
1
1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO 51 52 S3 54 55 56 57 58 59 60 61 62 63 64 65 66 67
O.OSO 0.050 0.050 0.035 0.035 0.035 0.070 0.035 0.050 0.035 0.035 O.OSO 0.03S 0.050 0.035 0.050 0.035 0.050 O.OSO 0.050 0.050 0.03S 0.035 0.035 0.035 0.070 0.035 0.035 0.050 0.050 0.070 0.035 0.070 0.050 0.050 0.036 0.050 0.070 0.050 0.035 0.050 0.035 0.035 0.050 0.035 0.035 0.050 0.050 0.035 0.035 0.035 0.035 0.050 0.035 0.035 0.035 0.035 0.050 0.025 0.070 0.035 0.050 0.035 0.070 0.025 0.050 0.035
2.70 1.52 3.80 2.28 2.66 1.71 4.18 2.28 deep 2.66 3.80 3.42 1.14 3.80 short 1.52 2.28 3.80 1.33 2.66 3.04 1.71 1.90 1.71 1.90 4.56 2.09 1.14 3.23 3.80 3.61 short 1.52 2.09 3.04 2.66 3.80 3.80 1.52 deep 3.04 2.85 2.28 2.66 2.28 short 3.42 3.04 1.52 1.71 1.52 1.33 1.90 short 2.40 2.28 2.66 short 3.42 3.04 3.80 3.80 2.65 3.42 2.28 4.00 4.56
0.6 0.3 1.5 0.3 0.5 0.3 0.7 0.4
4.5 5.1 2.5 7.6 5.3 5.7 5.9 5.7
0.7 0.7 0.5 0.4 l.S
3.8 5.4 6.8 2.8 2.5
2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20
21 22 23 24 2S 26 27 28 29 30
d=Width of aqueous vein in mm. 1 = Length of measured section of aqueous vein.
—
•—•
0.2 1.0 0.5 0.2 0.4 0.6. 0.3 0.3 0.3 0.5 0.7 0.4 0.8 0.7 0.8 0.8
V
—
—
7.6 2.3 7.6 6.6 6.7 5.0 S.7 6.4 5.7 3.8 6.5 5.0 1.4 4.6 4.7 4.5
0.4 0.4 0.8 2.0 1.5 0.7 0.3
— 3.8 S.O 3.8 1.3 2.5 5.4 5.0
0.6 0.6 0.6 0.5 1.1
5.0 4.7 3.8 5.3 2.0
0.8 0.5 0.5 0.5 0.3 0.3 0.5
4.3 6.0 3.0 3.4 5.0 4.4 3.8
0.8 0.4 0.6
3.0 5.7 4.4
1.0 1.0 1.0 0.6 0.5 1.7 0.7 0.8 0.7
3.4 3.0 3.8 6.3 5.3 2.0 3.2 5.0 6.5
—
—
—
—
—
—
—
—
—
t =Time required by projectile to pass through. v = Velocity of the projectile in mm./sec.
JOSEF STEPANIK
922
velocity of 4.6 mm./sec. (table 1). The average error was 19.2 percent, the lowest being estimated at five percent and the highest at SO percent. There seems to be no correlation between vessel diameter and speed of current in the aqueous veins. In the same eye, the velocities vary con siderably from aqueous vein to aqueous vein. DISCUSSION
In streamline flow through very small ves sels the movement of fluid takes place in lamellae paralleling the vessel walls. It is well known that in this case the velocity is greatest along the axis of the capillary and decreases parabolically to zero at the vessel wall. It is also known that the axial velocity equals twice the average velocity; that is, Vmax
^Vav.
If the projectile diameter were very small as compared with the vessel diameter, the speed of the projectile would be only slightly less than the axial velocity. At the other ex treme, if the projectile diameter equals the vessel diameter, then the velocity of the pro jectile would equal the average velocity in this vessel. According to my observations and the drawings published by De Vries 5 the pro jectile diameters are, if not equal to the vessel diameters, at least not very much smaller. It is therefore probable that the ob served projectile velocities are closer to the average velocity than to the axial velocity.
Two additional factors, not already con sidered, may influence the results, namely, the change in pressure in the vessel due to compression when the projectile is being pro duced, and the plugging effect of the projec tile. These factors probably act in opposite ways and may or may not balance each other. The relative effects are difficult to evaluate. It would seem, therefore, that at the present time the closest approximation is to use the velocity of the projectile as the average ve locity of the flow in the vessel observed. SUMMARY
In a great percentage of aqueous veins it is possible to estimate the velocity of the current by observation of artificially pro duced projectiles of blood cells. In aqueous veins of 30 normal eyes, the values were be tween 1.3 and 7.6 mm./sec. with an average of 4.6 mm./sec. These values are well in accord with those obtained by De Vries. The average error of my measurements was esti-' mated at 19.2 percent. The results are dis cussed in connection with the laws of stream line flow in small vessels. Cincinnati General Hospital, Cincinnati 29, Ohio. I gratefully acknowledge Dr. W. M. Spurgeon's advice in mathematical and physical problems. The drawings from my original sketches were made in the Department of Medical Art, College of Medi cine, University of Cincinnati. These investigations were aided by United States Public Health Grant B-1S8.
REFERENCES
1. Ascher, K. W.: Aqueous veins: Physiologic importance of the visible elimination of intraocular fluid. Am. J. Ophth. 25:1192, 1202 (Oct.) 1942. 2a. Leber, T.: Die Zirkulations und Ernährungsverhältnisse des Auges, Graefe-Saemisch's Handbuch der gesamten Augenh. Leipzig, W. Engelmann, 2 :63 ff, 1903. 2b. Theobald, G.: Schlemm's canal: Its anastomoses and anatomic relations. Tr. Am. Ophth. Soc, 32: 589, 1934. 3. Zeller, K.: Studien an Bindehautgefässen. Klin. Monatsbl. f. Augenh., 66:613, 1921. 4a. Duke-Elder, W. S.: Textbook of Ophthalmology, London, Kimpton, 1:45S, 1932. 4b. Friedenwald, J., and Pierce, H.: The circulation of the aqueous. Bull. Johns Hopkins Hosp., 49:257, 1931. 5. De Vries, S.: De zichtbare afvoer van het Kamerwater. Drukkerij Kinsbergen, Amsterdam, 1947, p. 75, plate VIII, fig. 12c. 6. Basier, A.: Ueber die Bestimmung der Stroemungsgeschwindigkeit in Blutkapillaren der menschlichen Haut. München. Med. Wchnschr., 66:1, 13, 347, 1919.