IOP remains practically constant during interval U, then increases during interval tr to reach saturation level Pi + SP. Ffytche et al.,(i showing that dilatation of the.
Invest. Ophthalmol. Visual Sci. June 1977
568 Reports
for other connective tissues verifies that the vitreous gel is of this class of tissue albeit very highly hydrated. The treatment of swelling tissue flow conductivity by Bert and Fatt 5 can be used to estimate the pore space in the vitreous gel through which water flows. Bert and Fattr> conclude that for very highly hydrated swelling materials the pore radius is given very approximately by i- = 8k
(5)
For the (k/?/)v values obtained for rabbit and bovine vitreous gel equation 5 gives the pore diameter as about 4,000 A. This large pore diameter explains why some investigators of the vitreous gel in vivo have been able to observe flow in this tissue when using tracer particles as large as 1,000 to 2,000 A. I wish to thank Dr. Richard F. Brubaker for making available unpublished data from his vitreous gel studies. From the School of Optometry and Department of Mechanical Engineering, University of California, Berkeley. Submitted for publication Oct. 25, 1976. Reprint requests: Dr. Irving Fatt, 7A, The Grove, Highgate Village, London N6 6JU, England. Key words: vitreous gel, flow conductivity. REFERENCES 1. Fatt, I., and Hedbys, B. O.: Flow of water in the sclera, Exp. Eye Res. 10:243, 1970. 2. Fatt, I.: Flow and diffusion in the vitreous body of the eye, Bull. Math. Biol. 37:85, 1975. 3. Brubaker, R. F., and Riley, F. C, Jr.: Vitreous body volume reduction in the rabbit, Arch. Ophthalmol. 87:438, 1972. 4. Pirie, A.: The vitreous body. In Davson, H., editor: The Eye, New York, 1969, Academic Press, Inc., vol. I, pp. 273-297. 5. Bert, J. L., and Fatt, I.: Relation of water transport to water content in swelling biological membranes. In Blank, M., editor: Surface Chemistry of Biological Systems, New York, 1970, Plenum Press, Inc., pp. 287-294. 6. Maurice, D. M.: The cornea and the sclera. In Davson, H., editor: The Eye, New York, 1969, Academic Press, Inc., vol. I, pp. 489600.
Autoregulation of blood flow in the capillaries of the human macula. CHARLES E. RIVA AND MICHAEL LOEBL.
The entoptic phenomenon by which one can observe leukocytes flowing in one's own parafoveal capillaries has been used to study the effect of changes in perfusion pressure on blood flow. Out
L.
measurements in humans with normal ocular fundi indicate that the retinal circulation of the parafovea is autoregulated in relation to perfusion pressure. The average time lag between a change in blood flow and the beginning of the autoregulatory response was about 46 sec, and the average duration of this response was about 48 sec. At the end of the autoregulatory response, the vascular resistance of the parafoveal segment was about 50% lower than that at normal intraocular pressure. The maintenance of constant blood flow despite changes in perfusion pressure (autoregulation) is an intrinsic property of nearly all body tissues.1 A small number of studies showing that the human retinal circulation responds actively to changes in perfusion pressure suggest that the retina also has an autoregulatory mechanism. For example, Dobree- found that constriction of arteries and veins occurs in patients with glaucoma after a decrease in the intraocular pressure (IOP) by either drugs or operation. Russel3 demonstrated that retinal arteries dilate when the IOP is increased by mechanical pressure on the globe in patients with Horner's syndrome. He attributed this effect to a homeostatic mechanism in the retinal circulation in these patients with oculosympathetic paralysis. Ernest'1 reported that the visual threshold in the Bjerrum area is elevated with an increase in IOP, but with time compensation takes place, reducing the visual threshold toward normal. None of these experiments, however, provides quantitative data on the fundamental parameters which generally characterize such physiological feedback control mechanisms as blood flow regulation. These parameters are the time lag between a change in the blood flow and the beginning of the regulatory response, the duration or time constant of the regulatory response, and the open-loop gain of the feedback control system. The last-named is a measure of the efficiency of the control mechanism in counteracting variations of blood flow from the normal state. Determination of these parameters requires measurements of blood flow as a function of the perfusion pressure. In an attempt to perform such measurements, Riehm, Podesta, and Bartsch5 have made use of the entoptic phenomenon by which one can observe leukocytes flowing in one's own parafoveal retinal capillaries. These authors used the number of leukocytes passing within 30 sec. in a capillary as a measure of blood flow. They found that blood flow in the parafoveal capillaries decreased linearly as the IOP was raised, up to about 40 mm. Hg. Thus no autoregulatory response was observed within the 30 sec. following a decrease in the perfusion pressure. The measurements of
Volume 16 Number 6
Reports 569
AA»RGTONOMfTER
RlCOROINtf 1O
Time (min) Fig. 1. Typical recording of IOP as subject maintains leukocytes at constant reduced speed. Pi = average IOP after initial sudden increase. IOP remains practically constant during interval U, then increases during interval tr to reach saturation level Pi + SP. Ffytche et al.,(i showing that dilatation of the retinal vessels of the pig occurs only after the IOP has been elevated for at least 1 min., suggest that the 30 sec. counting time chosen by Riehm, Podesta, and Bartschr> mtiy have been too short for autoregulation to take place. We repeated this experiment, trying to count the leukocytes for longer periods of time but found it very difficult to count them reliably for more than 30 sec. On the basis of the above phenomenon, we developed another method for studying the effect of changes in perfusion pressure on blood flow in the parafoveal capillaries over a period longer than 2 min. Our measurements indicate that retinal blood flow in this region of the fundus is autoregulated. They also provide quantitative data on the time delay with which the autoregulatory system responds following an abrupt change in perfusion pressure and on the time course of the autoregulatory response. Materials and methods. Seven healthy volunteers 22 to 39 years old, participated in this study. IOP was measured prior to the experiment by Goldmann applanation tonometry, and systemic blood pressure was measured by brachial sphygmomanometry. Each subject was seated in front of a standard slide projector, with his head resting on a support. An interference filter centered at a wavelength of 430 ran, (bandwidth = 10 nm.) was mounted in front of the projection lens, and an optical diffuser was placed in front of the filter to provide a uniformly illuminated field of observation. This setup permits an optimal visualization of the leukocytes.5 The fellow eye of each subject was covered with a patch, and the room was darkened. To monitor and simultaneously measure the IOP, the probe of a Mackay-Marg tonometer was mounted on a micrometer slide and carefully
/>P(mm Hg) 25
10
20
30
40
Pi (mm Hg)
Fig. 2. Variation of 5P as a function of Pi obtained from 22 measurements in seven subjects. placed perpendicular to the sclera of the subject's eye, close to the limbus. The signal from the probe was continuously recorded by the Mackay-Marg strip chart recorder set at 1 mm./sec. The subject was asked to raise his IOP quickly by pressing the probe of the tonometer on his eye until he saw that the leukocytes moved at a reduced speed. Then he was told to adjust the pressure of the probe to maintain this speed constant for about 2 min. It has been shown that the Mackay-Marg tonometer can provide a continuous and accurate reading of IOP when the probe is applied to the cornea.7 Therefore we compared the readings taken with the probe close to the limbus with conventional Goldmann applanation tonometry on three subjects and found that when the MackayMarg probe was held against the sclera so as to produce a constant reading for 2 to 3 min., Goldmann tonometry performed every Yz minute during this time also indicated a constant IOP (t 5%). Mackay-Marg readings taken in this position were slightly higher than Goldmann mea-
570 Reports
surements, but always by a constant amount and not by more than 4 mm. Hg. Results. Fig. 1 displays a typical recording of the time course of the IOP as the subject maintained the speed of the leukocytes at a constant reduced value. The curve shows that the IOP increases abruptly when the subject first applies pressure. After some initial oscillation while the subject masters control, the IOP stabilizes around an average value, P i ; and remains constant up to a time t«i. After time t,i, the IOP increases up to a value Pi + 5p, as the subject continues to apply pressure to maintain the leukocytes at the same reduced speed as before. This increase in the IOP takes place during an interval of time t r . In most of the experiments, after the IOP reaches Pi + 8P, it remains relatively constant for the rest of the experiment. In the others, however, there is a further slow increase in IOP following t r , although the IOP usually appears to approach a maximum within 2 to *LVz min. The average values for t,i and tr are 46 ± 21 sec. and 48 ± 14 sec, respectively. A plot of 5p as a function of Pi, based on 22 measurements, is shown in Fig. 2. The IOP's of the seven subjects were between 14 and 21 mm. Hg. Their brachial artery blood pressure ranged between 110/65 and 120/85 mm. Hg. The average mean ophthalmic artery pressure, taken as two thirds of the mean systemic pressure, was about 56 mm. Hg. In two subjects we measured the brachial blood pressure before and at the end of the experiment. We found no significant difference between initial and final pressures. Discussion. The present study was undertaken to determine the effect of raised IOP on the blood flow in the parafoveal capillaries over periods of time longer than 30 seconds. For this purpose, a method based on the entoptic observation of leukocytes in the parafoveal capillaries was developed. With our method the subject raises the IOP in such a way that he sees the leukocytes moving in a pulsatile mode consisting of two phases. One is a fast forward movement (systole), and the other a slower forward movement (diastole). The latter may even become a pause at high values of Pi. Each subject is able to choose various flow speeds that he feels capable of maintaining. This explains the various initial pressure steps of Pi which range between 22 and 46 mm. Hg. In each experiment the subjects had to raise their IOP by an amount Sp in order to keep the speed of the leukocytes constant. This increase in IOP indicates that a feedback mechanism is operative, acting to increase the blood flow towards its initial rate. The effect of this mechanism is first observed at time t,i and is effective
Invest. Ophthalmol. Visual Set. June 1977
only for a time t,. The works of Dobree2 and Russell1 suggest that this mechanism reduces the vascular resistance by causing dilatation of the retinal arteries and possibly of the veins also. An estimation of the decrease in this resistance that occurs during the time interval tr can be obtained from our data. Let P(t) represent the perfusion pressure of the parafoveal vascular system and R(t) the vascular resistance of this system at time t. The corresponding rate of blood flow is given by the relation F(t) = P ( t ) / R ( t ) (1) Since the pressure in the central retinal vein is only slightly above the IOP, one can write as a good approximation, P(t) = PA - IOP(t), where P.* is the mean pressure in the parafoveal arterioles, which we assume to be practically the same as that in the larger retinal arteries and to remain constant during the experiment. The sudden increase of the IOP to a value Pi causes the rate of blood flow to decrease by an amount AF and to become F, = F.N - A F = ( P A - P I ) / R . N
(2)
where FN and R.\ are the values of F and R at normal IOP. If this vascular system autoregulates, a feedback process acts to decrease the resistance R and thus to reduce AF toward zero. As a result, the leukocytes start flowing faster. However, at time T = t,i + t r the IOP usually does not need to be raised further to maintain a constant reduced flow. At this time, R(t) has reached a minimal value R ( T ) , and the corresponding flow is F ( T ) = [PA - (P. + 8 P ) ] / R ( T ) .
Since F ( T ) = F l ; it follows that [PA - (P, + « P ) ] / R ( T ) =
(PA - P,)/Rx (3)
After rearrangement of the terms of equation 3 and expressing [ R ( T ) - RlN]/Rx as AR/RX> this equation can be rewritten as AR/RN, = -8P/(P A - P,) (4) AR/RN. represents the total relative change in the vascular resistance occurring during t r . Using, as an approximation for PA, the average ophthalmic artery pressure of our subjects, i.e., 56 mm. Hg, and for Sp an average value of 15.5 mm. Hg, one finds from equation 4 that in the range of Pi between 24 and 30 mm. Hg, the relative decrease in resistance AR/RN, that occurs during autoregulation lies between 45% and 60% of the normal value RN. Identical calculations show that for an initial elevation of IOP to a value Pi between 40 and 46 mm. Hg, this decrease is somewhat larger. Our average value of t,i is smaller than the one found by Ffytche et al.G in their experiments with pigs. The retinal vessels of these animals did not start to dilate until about 1 min. following an increase in IOP. The difference between these data and ours may be species related, but they could also be explained by the fact that the retinal vessels must dilate by at least 5% before
Volume 16 Number 6
one can detect a change in their caliber by fluorescein fundus photography. Since a 5% change in caliber represents a 20% change in flow, it is quite probable that our method is more sensitive to changes in blood flow. Our results indicate that the retinal circulation supplying the parafovea is autoregulated in relation to perfusion pressure. It provides quantitative information on the time interval between a change of perfusion pressure and the response of the autoregulation mechanism and on the duration and time course of the response. This method in its present stage does not permit the determination of the open-loop gain of the feedback mechanism; that is, how close to its initial rate does the flow of blood return after a change in perfusion pressure. This method should prove useful for investigating autoregulation in the normal retina under various physiological conditions and in the retina of patients with diseases such as vascular occlusions, systemic hypertension, diabetic retinopathy, ocular hypertension, and glaucoma. The authors wish to thank Drs. G. Feke and F. Delori for helpful suggestions concerning this work, W. P. Roberts and M. D. Gonzalez for technical help, and A. Seidman and S. F. Blackwell for editorial assistance. From the Department of Retina Research, Eye Research Institute of Retina Foundation, Boston, Massachusetts. This work was supported by the Massachusetts Lions Eye Research Fund, Inc. and by the Morton Adler Foundation. Submitted for publication Dec. 10, 1976. Reprint requests: Editorial Services Unit, Eye Research Institute of Retina Foundation, 20 Staniford St., Boston, Mass. 02114. Key words: perfusion pressure, intraocular pressure, blood flow, autoregulation, macular circulation, entoptic phenomenon, leukocytes.
REFERENCES 1. Guyton, A. C., Jones, C. E., and Coleman, T. G.: Circulatory Physiology: Cardiac Output and its Regulation,, ed. 2, Philadelphia, 1973, W. B. Saunders Co., chap. 19. 2. Dobree, J. H.: Calibre changes in retinal vessels occurring in raised ocular tension; circulatory compensation in chronic glaucoma, Br. J. Ophthalmol. 40:1, 1956. 3. Russell, R. W.: Evidence for autoregulation in human retinal circulation, Lancet 2:1048, 1973. 4. Ernest, J. T.: Pathogenesis of glaucomatous optic nerve disease, Trans. Am. Ophthalmol. Soc. 73:366, 1975. 5. Riehm, E., Podesta, H. H., and Bartsch, C : Untersuchungen iiber die Durchblutung in Netzhautkapillaren bei intraokularen Drucksteigerungen, Ophthalmologica 164:249, 1972. 6. Ffytche, T. J., Bulpitt, C. J., Kohner, E. M.,
Reports 571
et al.: Effect of changes in intraocular pressure on the retinal microcirculation, Br. J. Ophthalmol. 58:514, 1974. 7. Moses, R. A.: Constant pressure applanation tonography with the Mackay-Marg tonometer, Arch. Ophthalmol. 76:20, .1966.
Choroidal and cerebral blood flow in baboons measured by the external monitoring of radioactive inert gases. R. STRANG,* T.
M. WILSON,** AND E.
T.
MACKENZIE. * * *
Quantitative measurements of blood flow using xenon-133 to measure cerebral blood flow and krypton-85 to measure choroidal blood flow were made in 12 anesthetized baboons (Papio anubis). Analysis of tlie clearance curves of krypton from the eye and studies of the diffusion of krypton in the eye show that the inert gas-clearance method measures choroidal blood flow only. The mean choroidal blood flow at normocapnia in this group of baboons is 463 ± 44 ml./100 gm./ min., and the mean cerebral blood flow is 46 ± 5 ml./100 gm./min. (mean ± 1 S.D.). The quantitative measurement of cerebral blood flow by the external monitoring of the clearance of radioactive inert gas from the brain was established by Lassen and his co-workers.1"3 For a homogeneous tissue the clearance of inert gas is monoexponential. For tissue of unit density, blood flow is related to the exponential rate constant by the following equation: (1) F = 100 x k x p where F = blood flow (ml./lOO gm./min.), p = the partition coefficient (i.e., the ratio of the solubility of the inert gas in 1 gm. of tissue to its solubility in 1 ml. of blood), and k = exponential rate constant (min.- 1 ). The clearance of xenon-133 from the brain can be analyzed into two exponential components. The faster component is representative of gray matter flow, and the slower component representative of white matter flow. An estimate of the average blood flow through the gray and white matter can be obtained from the height-over-area method of analysis.4 Friedman, Kopald, and Smith/1 using the betaemitting inert gas krypton-85, applied the inert gas-clearance method to the measurement of ocular blood flow. They obtained clearance curves with four exponential components from both rabbits and primates. They initially believed that the exponential rate constant of the first component obtained by exponential curve stripping was representative of choroidal blood flow. However, they subsequently stated,0 without proof, that it was
