S:1 ince tonography is subject to a number

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1 Studies of aqueous humor dynamics in man I. Measurements in young normal subjects Carl Kupfer and Karyn Ross Aqueous humor dynamics can be defined in terms of intraocular pressure, episcleral venous pressure, true facility, pseudofacility, and aqueous flow through the eye. With the use of cooperative subjects, the measurements can be made repetitively and are reproducible with small standard errors. In addition, good agreement between right and left eyes allows examination of pharmacologic agents on one eye as compared with the other eye. Application of this technique to a study of the mechanism of the topical steroid response of intraocular pressure indicated that the elevated intraocidar pressure is related only to a significant reduction in true outfloio facility. Key words: aqueous humor dynamics, dexamethasone, pseudofacility, normal subjects, tonography. S:1 ince tonography is subject to a number of assumptions and sources of error, 1 ' 2 its acceptance as a research technique has been somewhat limited. The sources of error can be minimized if one confines a From the National Eye Institute, National Institutes of Health, United States Department of Health, Education, and Welfare, Bethesda, Md. Manuscript submitted May 6, 1971; revised manuscript accepted June 16, Symbols used in parts I and II: Pi, intraocular pressure ( Pe, episcleral venous pressure ( Pk, intraocular pressure, discussed by Goldmann, 7 for flow which net aqueous flow is zero due to balance of secretion and outward ultrafiltration ( Ctoi, total outflow facility, corrected for ocular rigidity, = Ctrue + Cps (/il/min./ Ctrue, outflow facility for flow between the anterior chamber and the episcleral venous bed (/il/min./ Cps, pseudofacility, the rate of change of ultrafiltration (and of total aqueous flow) with changes of intraocular pressure, 7 = df/d P (/i/min./ S, portion of aqueous flow due to secretion; pressure independent by definition 7 (/il/min.) U, portion of aqueous flow due to ultrafiltration; pressure dependent by definition 7 (/tl/min.) F, net aqueous flow = S + U (/il/min.) AFobs, change of aqueous flow observed experimentally AFu, change of aqueous flow due to change of ultrafiltration as intraocular pressure changes Subscripts: a (F n, Pn), ante, parameter before medication p (F P) Pp), post, parameter after medication 518 study of aqueous humor dynamics to relative changes rather than absolute values. 3 In addition, two recent developments have increased the precision in defining the parameters of intraocular pressure; these are the measurements of episcleral venous pressure and the determination of pseudofacility. 4 The purpose of this paper is to present data on the reproducibility of measurements of the parameters of intraocular pressure of the eye in a group of young normal subjects. Also, the effect of topical dexamethasone on aqueous humor dynamics will be discussed as an example of the use of these techniques. Methods Aqueous humor dynamics were studied repetitively in four normal men between the ages of 20 and 23 years. The measurements of intraocular pressure, episcleral venous pressure, and pseudofacility were made with the subjects in the sitting position. The corneas of both eyes were anesthetized with topically applied proparacaine 0.5 per cent, and the intraocular pressure (Ph) was measured for each eye with the use of the Goldmann applanation tonometer and recorded

2 Volume 10 Number 7 Aqueous humor dynamics in man. I 519 when three successive identical readings were obtained. The technique for measuring episcleral venous pressure (Pe,) 5 was modified slightly by using the frog pericardium as the membrane of the pressure chamber. An episcleral vein was chosen in the lateral scleral triangle about 7 to 8 mm. from the limbus and the hydrostatic pressure in the chamber necessary to collapse the column of blood in the vein was taken as the value of P,.,. The recorded value of P Ol for each eye was the arithmetic mean of three readings. Following the measurements of Pi, and P c,, a sphygmomanometer cuff was placed around the subject's neck and inflated to 25 to 30 mm. Hg in order to elevate the episcleral venous pressure. At this pressure level, breathing and swallowing were not disturbed. After sufficient time had elapsed to establish a new steady state of intraocular pressure, usually about ten minutes, Pi 2 was measured until three successive identical readings were obtained. Following recordings of Pi,, P,. 2 was then measured with the use of the idential vein as had been used previously. The sphygmomanometer cuff was released and approximately ten minutes later, when intraocular pressure had returned to its original resting level, total facility (Ctot) was determined using the conventional tonographic technique. The tonograms were corrected for variations in the coefficient of ocular rigidity by paired (5.5 and 10.0 Cm. weights) readings using the Friedenwald table. Four young steroid-responder subjects with otherwise normal eyes, including normal intraocular pressure bilaterally, received, to one eye only, dexamethasone ophthalmic drops 0.1 per cent three times daily for a four-week period. Followings this period, the above measurements were made on both eyes repeatedly, on different days, and a comparison made between the treated and untreated eyes. The coefficient of facility of outflow (Ctot) was determined with the following modification of Grant's 1 equation (Equation 1): Ctot (:,,, - Ve t E s {log P ti - log P tf } t (P tov - P o - AP V ) (1) where E 8C h- 8 ch is ocular rigidity determined by paired Schi0tz tonometer readings and P O is the initial Schi0tz tonometer reading with the 5.5 Cm. weight. Pseudofacility was determined by using Equation 2: G AP, where AP, = P, 2 - P h and AP 0 = P C2 - P Cl ; AP, is the change in steady-state intraocular pressure brought about by AP ej a change in steady-state episcleral venous pressure. 0 Initially, P Cl is less than Pij. With venous compression, P Ol + AP O increases slightly faster than Pi, + AP,. Eventually, there would be a value of P e, + AP e which is equal to P h + AP,. At this value, P e2 = Pi 2. In this situation of no pressure differential, there would be neither inflow or outflow; therefore, net aqueous formation would be zero. Goldmann 7 has referred to this pressure value as Pk, and has discussed its derivation. 0 Since the values for Pij, Pi 2, P e j, and Pco are measured directly, P k can be determined by the formula derived by Goldmann (Equation 3): P, 2 P e, - Po 2 P., AP, - AP O (3) Finally, flow out of the eye (F) was determined by a modified Goldmannn formulation (Equation 4): F = C.ruo (P. - Pc) where, (4 ) dtrue v>total "" dps- A linear curve representing aqueous inflow versus intraocular pressure was plotted by using as two points the value of flow, F at the intraocular pressure Pi and the value of Pk. This type of plot, suggested by Goldmann, will be referred to as a flow curve. The paired t test was used for determination of significance of the changes of experimental observations. Results Table I summarizes the data from Subject L. K. in whom measurements were made on both eyes repetitively during a ten-week period. Noteworthy is the good agreement between the two eyes with respect to the parameters of intraocular pressure. Table II summarizes the data from the four normal subjects in whom measurements were made repeatedly during a ten-week period. Again the small size of both the difference between fellow eyes and the standard error of the means of the measurements supports the validity of utilizing these techniques in a clinical research study of aqueous humor dynamics. The inflow data from Table I are displayed in Fig. 1. (2) "Bulk flow through sclera is not included in these assumptions.

3 520 Kupfer and Ross Investigative Ophthalmology July 1971 Table I. Ten determinations of right and left eyes in the same subject during a ten-week period Eye ( P, ( Ctotal vim. Hg) C t run Cpseudo (pl/min./ P* ( (nl/min./ : = standard edviation; = standard error of the mean Table II. Average data on four normal subjects Subject L. K. B. W. J. O. S. C. All eye. Eye Pi, ( Pc t ( Ctotal C, ru<j (fil./min./ Cpseudo (fd/min./ P* ( (ld/min./ Each subject had at least tea measurements of the meters of intraocular pressure on each eye over a ten-week period. The data represent the means of the repetitive measurements and from these means an over-all mean value for all four subjects has been calculated. = standard deviation; = standard error of the mean. The average calculated flow values for these four subjects tended to be somewhat lower than those previously reported. 8 ' 9 This may be caused by the young age of the patient, the relatively low value of intraocular pressure, and these patients' relatively lower directly calculated value of P k.

4 Volume 10 Number 7 Aqueous humor dynamics in man. I 521 Fig. 1. curve of data from right eye (RE) and left eye (LE), Table I. The ordinate is flow and abscissa, pressure. The value of flow (F) at the intraocular pressure (Pi) is plotted against the value of P*. It has been generally accepted that the elevation in Pi caused by the topical application of corticosteroids resembles ocular hypertension, in that the elevation in Pi is secondary to a decrease in C to t, rather than any change in inflow or episcleral venous pressure. If this is the case, then it would be expected that the elevation of Pi by topical corticosteroid administration would be accompanied by a decrease in C to t which would be caused entirely by a decrease in Ctrue and that the absolute value of C ps would remain unchanged. Table III and Fig. 2 summarize data bearing out this prediction. A paired t test comparison of the treated and untreated eyes indicates a significant elevation in Pi and a significant decrease in C tot which is associated with a decrease in C liue exclusively. There was no significant change in P e, C ps, or P k. Discussion The data presented in Table II show that the errors inherent in the techniques of tonography and the measurement of pseudofacility are not great (standard deviation less than ten per cent) on cooperative subjects. This reproducibility of measurements in a single eye makes feasible short-term experiments on effects of pharmacologic agents on aqueous humor Fig. 2. curve of data from treated and control eyes, Table III. The flow in treated eyes, when corrected for the higher value of Pi, is not significantly different from the flow in the control eye, when compared at the same intraocular pressure. dynamics. That the measurements have a degree of reliability is demonstrated when one compares the two eyes in the same young, normal subject: the average difference between the right eye (R) and the left eye (L) (^ x HX)] is about 2 per cent for determination of Pi and P e, and per cent, per cent, per cent, and 4 per cent for calculations of Ctot, Ctrue, Cp S, and F, respectively. These differences are not statistically significant. Since the measurements give reliable comparison of aqueous humor dynamics between the two eyes, another experimental design is to compare the eyes after long-term administration of a pharmacologic agent to one eye of a normal subject. This has been done with dexamethasone in the second part of this study. Comparison of the eyes indicates that the significant rise in intraocular pressure in the treated eye was caused by a decrease of true facility of outflow, while pseudofacility and episcleral venous pressure were not altered. The fall in aqueous humor flow following dexamethasone administration is caused by the higher intraocular pressure. This can be determined by multiplying the average of AP ( of 7.1 mm. Hg by the

5 522 Kupfer and Ross Investigative Ophthalmology Juhj 1971 Table III. Effect of dexamethasone on aqueous humor dynamics A. Results for control and treated eyes Subject ( ( Control eye Treated eye B. Average Subject t:idf P diflerence between APt < treated APo < C total (ftl/min./ Ctruo and control eyes AC 10, ni AC, < < ( AC ns < ( AP <0.500 AF <0.025 average value of C ps, ja per minute per millimeter Hg. The expected decrease in aqueous flow is approximately 0.3 p\ per minute which more than accounts for the measured fall in aqueous flow of 0.18 [x\ per minute. This can be seen graphically in Fig. 2. These results are consistent with previous observations. 10 ' 1L REFERENCES ' 1. Grant, W. M.: Tonographic method for measuring the facility and rate of aqueous flow in human eyes, Arch. Ophthalmol. 44: 204, Becker, B., and Friedenwald, J. S.: Clinical aqueous outflow, Arch. Ophthalmol. 50: 557, Becker, B.: Carbonic anhydrase and the formation of aqueous humor, Am. J. Ophthalmol. 47: 342, Kupfer, C, and Sanderson, P.: Determination of pseudofacility in the eye of man, Arch. Ophthalmol. 80: 194, Brubaker, R. F.: Determination of episcleral venous pressure in the eye, Arch. Ophthalmol. 77: 110, Barany, E. H.: A mathematical formulation of intraocular pressure as dependent of secretion, ultrafiltration, bulk outflow, and osmotic reabsorption of fluid, INVEST. OPHTHAL- MOL. 2: 583, Goldmann, H.: On pseudofacility, Bibl. Ophthalmol. 76: 1, Jones, R. F., and Maurice, D. M.: New methods of measuring the rate of aqueous flow in man with fluorescein, Exp. Eye Res. 5: 208, Goldmann, H.: Uber Fluorescein in Der Menschlichen Vorderkammer, Ophthalmologica 119: 5, Armaly, M. F.: Effect of corticosteroids on intraocular pressure and fluid dynamics, Arch. Ophthalmol. 70: 482, Anselmi, P., Bron, A. J., and Maurice, D. M.: Action of drugs on the aqueous flow in man measured by fluorophotometry, Exp. Eye Res. 7: 487, 1968.