I t is generally accepted that the hydraulic

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1 The effect of intraocular pressure on conventional outflow resistance in the enucleated human eye Richard F. Brubaker A technique for measuring resistance to outflow in enucleated eyes is described. The technique minimizes the artifactual effects of ocular stretching and anterior chamber deepening. Using this perfusion technique, it was found that the resistance to outflow in normal, enucleated human eyes increases directly and linearly with intraocular pressure. This phenomenon, termed the outflow obstruction effect, was defined as the fractional increase in baseline outflow resistance (outflow resistance at an outflow pressure of zero) per millimeter of Hg intraocular pressure rise above baseline and was designated by the letter Q. The value of Q was found to be mm. Hg-' ± indicating that the outflow resistance rises above its baseline value approximately 1 per cent per millimeter of Hg rise in intraocular pressure. Estimates of Q, calculated from data published by other investigators over the past two decades, are also included. I t is generally accepted that the hydraulic resistance to outflow of aqueous humor through the "conventional" outflow pathways from the eye is not influenced by intraocular pressure. 1 ' 1 That is, changes in intraocular pressure brought about by tonometry, ophthalmodynamometry, or anterior chamber infusion are not suspected to cause a change in outflow resistance. There is accumulating evidence, however, that changes in intraocular pressure do cause significant changes in outflow resistance. Weekers, Watillon, and de Rudder 7 found that tonographic resistance values calculated from the 1954 tables were From the Department of Ophthalmology, Mayo Clinic, Rochester, Minn Supported by Crant No. EY00634 of the National Eye Institute, National Institutes of Health, Department of Health, Education, and Welfare, Bethesda, Md. Submitted for publication Aug. 29, higher in man when heavier weights were used and that enucleated bovine eyes had higher outflow resistance when perfused at higher intraocular pressures. Francois and co-workers 8 noted that increasing the depth of the anterior chamber in enucleated human eyes caused a decrease in outflow resistance but that increasing the pressure in the eye without changing the anterior chamber depth caused an increase in outflow resistance. Langham"- "' observed that the steady-state intraocular pressure in living and dead cat and rabbit eyes was not a linear function of the rate of infusion of saline into the anterior chamber but rose more rapidly as the infusion rate was increased. Macri 11 observed that some living cat eyes exhibited higher outflow resistance values when perfused at higher pressures. Armaly ( reported that in living cat eyes and in enucleated cat and rabbit eyes, the resistance to aqueous outflow was a

2 Volume 14 Number 4 Effect of 10? on outflow resistance 287 Wick Stone Fig. 1. Diagram showing relation between eye, paper wick, needle, and embedding stone. Entire block immersed in 37 C. water bath. linear function of intraocular pressure. Kleinert14 made a similar observation in living human eyes utilizing anterior chamber perfusion techniques as did Nihard15 in enucleated human and porcine eyes. Goldmann,10 using differential Schi0tz tonography, observed that facility of outflow in man was lower at higher intraocular pressures. This finding was confirmed by Moses17 using applanation tonography and by Levene and Hyman18 using modified Schi0tz tonography. Ellingsen and Grant19 observed that enucleated human eyes, when provision was made for free communication between the anterior and posterior chamber, exhibited increased outflow resistance at higher perfusion pressures. Johnstone and Grant,20 Kayes,21 and Grierson and Lee22 have described morphologic differences in the trabecular meshwork and Schlemm's canal in rhesus eyes enucleated at different intraocular pressures. Worthen23 has made similar observa- tions in trabulectomy specimens in human eyes. These physiologic and morphologic data appear to indicate that elevation in intraocular pressure per se may alter the conventional outflow channels and cause an increase in resistance to outflow. Each of the studies cited above has been criticized in one way or another as containing measurement artifacts which themselves may explain the experimental results. The purpose of this study was to measure outflow resistance in enucleated human eyes at different intraocular pressures using an experimental protocol designed to minimize the most frequently cited artifacts: anterior chamber deepening19 and viscoelastic ocular stretching.2'1 Methods Ten human eyes were studied within 24 hours of enucleation. After enucleation and prior to perfusion, all eyes were maintained in a moist chamber at refrigerator temperatures. Each eye was

3 288 Brubaker Investigative Ophthalmology April 1975 Table I. Outflow resistance as a function of intraocular pressure for all 10 eyes. Each sequence shown separately [Outflow resistance values, mm. Hg min.//j.l (mean ± S.E.)] Intraocular pressure (mm. Hg) I up-down 1 down-up Sequence 2 up-down ± ± ± ± ± : t ± : t ± ± it ± ± it ± ± it ± ± jt ± ± it ± ± it 0.52 Ro Q r t d.f. P <0.001 < <0.01 Ro = outflow resistance extrapolated to outflow pressure of O. Q = outflow obstruction coefficient, mm. HK-'. r = correlation coefficient. = " r v"(n-2)/( 1-r-) where N = number data pairs, d.f. = decrees of freedom, = i\-2. p probability that apparent correlation is due; to chance only. 2 down-tip 2.45 ± ± ± ± ± ± ± <0.001 All 2.51 ± ± ± ± ± ± ± ± ± < , Intraocular Pressure, mmhg mean ± SE Fig. 2. Relation between mean flow rate (microliters per minute) of pcrfusate into the eye versus height of open reservoir above the eye (expressed as millimeters of Hg intraocular pressure). Each value represents the mean of four determinations in all 10 eyes ± one standard error. rinsed with saline at room temperature, and the episcleral tissue and bulbar conjunctiva carefully dissected off the globe. A No. 23 needle with an opening at the tip and an opening 4 mm. from the tip was placed through the cornea near the limbus and passed under the pupillary border into the posterior chamber. This needle was connected to a PE90 tubing allowing free communication between the posterior chamber, the anterior chamber, and a perfusion reservoir. The reservoir, tubing, and needle were filled with a mammalian 60 tissue culture medium (TC199). The reservoir was placed 13.6 cm. higher than the cornea to establish a pressure of 10 mm. Hg in the anterior chamber. A moist wick of No. 40 Whatman filter paper approximately 7 mm. wide was placed over the limbal area (See Fig. 1). The eye was then placed into a paper cup and completely imbedded in hydrous calcium sulfatc stone (gypsum). During hardening of the stone, the intraocular pressure was maintained at 10 mm. Hg. The filter paper strips extended outside the stone to allow continuous outflow of the pcrfusate. After 10 minutes, the imbedded eye was submerged in a 37 C. water bath and allowed to remain for one hour before the experiment proceeded. The pressure in the eye was then changed in 5 mm. Hg steps by changing the level of the reservoir. The rate of fluid entry into the eye was measured by observing the change in weight of the reservoir. The pressure was maintained at each level until the rate of inflow into the eye appeared to have been constant for two minutes (usually about five minutes). In half of the eyes (five eyes) the pressure sequence was as follows: 10, 15, 20, 25, 30, 35, 40, 45, 50, 45, 40, 35, 30, 25, 20, 15, and 10. This sequence was then repeated. In the other half of the eyes (five eyes) the pressure sequence was: 50, 45, 40, 35, 30, 25, 20, 15, 10, 15, 20, 25, 30, 35, 40, 45, and 50. This sequence was then repeated. There were, therefore, four sequences of five eyes each: (1) first up-down sequence, (2) second up-down sequence, (3) first down-up se-

4 Volume 14 S : timber 4 Effect of IOP on outflow resistance 289 _ t.w - c E 3.4- E E 2.8- o o Z 2.2- u c o Vt <7> a Ro \t000' 1 ] \ meon ±SE "R 0Q I Intraocular Pressure, mm Hq Fig. 3. Relation between resistance to outflow (mm. Hg min.//tl) and intraocular pressure (mm. Hg). Each value represents the mean of four determinations in all 10 eyes ± one standard error. Line fit to data by method of least squares. The Y intercept, R o is the outflow resistance at an outflow pressure of 0. The slope is R«Q, where Q is the fractional increase in R per millimeter of Ilg rise in outflow pressure. The correlation coefficient between resistance and intraocular pressure is Probability that this is due to chance alone is less than quence, and (4) second down-up sequence. Statistical evaluation of the results was carried out in each sequence separately and on all four sequences as a group. Results The outflow resistance data for all perfusion sequences are shown in Table I. At any given intraocular pressure level, there were no significant differences among the four sequence values of outflow resistance. Higher resistance values were consistently seen at higher intraocular pressure levels in all four sequences. In all four sequences, the rise in resistance with rising intraocular pressure was statistically significant (p < 0.01). Fig. 2 is a graphic representation of flow versus pressure, and Fig. 3 is a graphic representation of outflow resistance versus pressure. It can be.seen that outflow resistance was not constant, but a function of intraocular pressure. This relation can be represented by a linear equation of the form Y = A + BX or R = Ro + RoQ Pout (1) where R is the outflow resistance at any intraocular outflow pressure Pom, Ro is the outflow resistance at Pom = O and Q is the fractional change in R o brought about by a change in outflow pressure of 1 mm. Hg. The constant, Q, may be thought of as an "outflow obstruction coefficient" and has the units millimeters of Hg" 1. The value of Q determined in this experiment for the enucleated human eye is ± mm. Hg- 1. The value of R o is 2.2 ± 0.04 mm. Hg min. /xl" 1. The conventional facility of outflow would be 0.41 ± /xl min." 1 mm. Hg- 1 at an outflow pressure of 10 mm. Hg. Discussion The technique of imbedding the eye in hydrous calcium sulfate stone partially eliminates, but does not completely eliminate, the problem of volume expansion of the globe. The modulus of elasticity for this material is approximately 2.5 x 10 7 mm. Hg.-" 1 A spherical cavity 25 mm. in diameter surrounded by 10 mm. of hardened gypsum would be expected to expand only 0.01 [xl for a pressure change from 10 to 50 mm. Hg, the pressure range used in this experiment. In practice, we have measured the difference between the expansion of the rabbit eye with and without gypsum imbedding. Without imbedding, approximately 21 /J.L are required to inflate the eye from 10 to 50 mm. Hg,

5 290 Brubaker Investigative Ophthalmology April 1975 Table II Investigator Annaly Ellingsen and Crant Francois, et al. Nihard Weekcrs, Watillon, and Rudder Present study Source Ref. 13, Fig. 8, p. 130 Ref. 19, Table I, p. 433 Table II, p. 433 Ref. 8, Table IX, p. 690 Ref. 8, Table I, p. 712 Table II, p. 714 Ref. 15, Fig. 7, p. 19; Fig. 8, p. 21 Fig. 6, p. 19; Text, p. 22 Ref. 7, Fig. 1, p. 228 Text and Table III, p. 227 \Q, mm. Hg~ J Comment Live rabbit and cat eyes Enucleated normal human eyes Enucleated glaucomatous human eyes Enucleated human eyes Living rabbit eye Enucleated rabbit eye Enucleated porcine eyes Enucleated human eyes Enucleated bovine eyes Living human eyes (tonography) Enucleated normal human eyes whereas with imbedding, only 3 ^L are needed. The porosity of the wet stone, which we have measured as being 0.05 fj.h cm. mm. Hg" 1 min." 1 must account for the greater than expected expansion. Nevertheless, the hardened gypsum reduces by sevenfold the expansion of the globe which can take place. The effect of calcium dissolved out of the gypsum on the outflow resistance was not considered to be significant. The concentration of CaSO., would be 13 millimoles per liter in a saturated solution around the eye. Warner and Chu 2(! in studying the effect of calcium on the outflow resistance of cats found that solutions containing 80 mmolar calcium chloride had no effect on outflow resistance when perfused through the anterior chamber. Also, our values of outflow resistance, if corrected for viscosity differences of water between 37 C. and 25 C, are identical to those determined by Ellingsen and Grant 19 for the human eye. In spite of criticisms which have been raised about the studies cited in the introduction, the data from this experiment are in fair agreement with the published data of other investigators. The value of Q calculated from our data are compared to the published data of others in Table II. If pressure-dependent outflow obstruction is a phenomenon which is present in the living human eye, and if the value mm. Hg" 1 can be accepted as a reasonable estimate of the outflow obstruction coefficient, it can be concluded that this phenomenon is important in certain circumstances and unimportant in others. The easiest way to understand the effects of pressure-dependent outflow obstruction on steady-state intraocular pressure is to study the relationship between the traditional Goldmann outflow equation and the outflow obstruction coefficient Q. If the pressure "baseline" for the living eye is taken to be P (!, episcleral venous pressure, then the resistance to outflow R, at any intraocular pressure, P i} is given by the relation R = R o + (p, - P 0 ) R 0 Q (2) where Ro is the resistance to outflow when Pi = P o. Likewise, resistance R t and R> at any two pressures Pu and F i2 can be related by the equation R, = R, + (P 12 - P M ) Ro Q (3) One can just as easily express in terms of facility of outflow C: Co C = (4) 1 + (Pi - Pc) Q where C o is the facility of outflow at Pi = P (; and C, C s = (5) 1 + (Pi, - P.,) (C,/Co) Q relating the C values at any two intraocular pressures. The familiar Goldmann equation relates inflow and outflow at steady-state and has the form, aqueous formation = aqueous outflow = C (P, - P e ). Substituting C for

6 Volume 14 S l umber 4 Effect of IOP on outfloiu resistance 291 =.O5,Q=.OI C o =05, Q = Aqueous Humor Formation Rate, u.l/min O.I,Q=.OI C o = 0.1,0 = 0 O.2,Q=.OI Co = 0.2,0= 0 C o = 0.4,0=01 C o = 0.4,0= 0 Fig. 4. Theoretical relation between steady-state intraocular pressure and aqueous humor formation rate for a variety of "baseline" facility of outflow values, Co: (1) assuming outflow obstruction docs not exist or Q = 0 (solid lines); (2) assuming outflow obstruction coefficient Q = 0.01 (dotted lines). All data points calculated using Goldmann's equation as modified to include Q (Equation 6). its value found in Equation 4, the Goldmann equation becomes Flow = Co (P, - P,,) 1 + (P, - P..) Q (6) The denominator may be thought of as a correction factor to account for the positive feedback effect of intraocular pressure on the outflow mechanism. The same substitution can be made in the Barany equation as well.- 7 It can be shown by substitution of normal values of flow, facility of outflow, and episcleral pressure in Equation 6 that outflow obstruction under the assumptions of this discussion is an insignificant factor in normal eyes, except when intraocular pressure is artificially raised to measure outflow resistance. However, in glaucomatous eyes, it can be shown that significant changes in steady-state intraocular pressure can result from small changes in aqueous humor formation in eyes in which pressure-dependent outflow obstruction exists. This fact is illustrated in Fig. 4. The outflow obstruction phenomenon causes an exaggeration in the effect on steady-state intraocular pressure of any other parameter change. We have not shown that pressure-dependent outflow obstruction exists in living human eyes, nor have we demonstrated the mechanism whereby it occurs in enucleated human eyes. If this phenomenon exists in the living primate eye, a possible mechanism might be partial obstruction of the canal of Schlemm by vacuolization of its inner wall. This pressure-dependent morphologic change has been demonstrated in primate eyes by four groups of investigators.- 0 "- 11 Outflow obstruction complicates the process of measuring the resistance to outflow in enucleated eyes as pointed out by Armaly. 1 - The problem can be minimized, however, by remembering two facts. First, the effect of outflow obstruction will be smaller, the smaller the increment in intraocular pressure. Second, if the perfusion needle is placed only into the anterior chamber, the deepening effect of the anterior chamber will partly or completely eliminate the outflow obstruction effect. The latter point may explain why the existence of this effect has often been disputed. Perfusion of the eye at three levels of intraocular pressure, rather than two, allows the calculation of resistance for any pressure level using Equation 3 or Equation

7 292 Brubaker Investigative Ophthalmology April The value of Q can be determined in this way for an individual eye so long as artifacts such as secretory suppression, ocular stretching, blood volume change, and anterior chamber deepening have been eliminated or minimized. REFERENCES.1. Goldmann, H.: Abflussdruck, Minutenvolumen, und Widerstand der Kammerwasserstromung des Mcnschen, Documenta Ophthalmol. 5: 278, Barany, E. H.: In vitro studies of the resistance to flow through the angle of the anterior chamber, Acta Soc. Med. Upsaliensis 59: 59, Grant, W. M., and Trotter, R. R.: Tonogruphic measurements in enucleated eyes, Arch. Ophthalmol. 53: 191, Francois, J., Rabaey, M., and Neetens, A.: Perfusion studies on the outflow of aqueous humor in human eyes, Arch. Ophthalmol. 55: 193, Becker, B., and Constant, M. A.: Species variation in facility of aqueous outflow, Am. J. Ophthalmol. 42:' 189, Becker, B., and Constant, M. A.: The facility of outflow: a comparison of tonography and perfusion measurements in vivo and in vitro, Arch. Ophthalmol. 55: 305, Weekers, R., Watillon, M., and de Rudder, M.: Experimental and clinical investigations into the resistance to outflow of aqueous humor in normal subjects, Br. J. Ophthalmol. 40: 225, Francois, J., Rabaey, M., Neetens, A., et al.: Further perfusion studies on the outflow of aqueous humor in human eyes, Arch. Ophthalmol. 59: 683, Langham, M. E.: Influence of the intraocular pressure on the formation of the aqueous humour and the outflow resistance in the living eye, Br. J. Ophthalmol. 43: 46, Langham, M. E.: Steady-state pressure flow relationships in the living and dead eve of the cat, Am. J. Ophthalmol. 50: 950, I Macri, F. j.: Outflow patterns of the cat eye, Am. J. Ophthalmol. 47: 547, Arnialy, M. F.: Studies on intraocular effect of the orbital parasympathetic pathway. III. Effect on steady-state dynamics, Arch. Ophthalmol. 62: 817, Armaly, M. F.: The effect of intraocular pressure on outflow facility, Arch. Ophthalmol. 64: 125, Kleincrt, II.: Abflussdruck und Abflusswiderstand, Ber. Dtsch. Ophthalmol. Ges. 64: 57, 196]. 15. Nihard, P.: Influence de la pression oculaire sur la resistance a l'ecoulement de l'humeur aqueuse, Acta Ophthalmol. 40: 12, Goldmann, H.: Glaucoma: A Symposium, Duke-Elder, W., editor, Springfield, III., 1955, Charles C Thomas, Publisher, p Moses, R. A.: Constant pressure applanation tonography. III. The relationship of tonometric pressure to rate of loss of ocular volume, Arch. Ophthalmol. 77: 181, Levene, R., and Hyman, B.: The effect of intraocular pressure on the facility of outflow, Exp. Eye Res. 8: 116, Ellingsen, B. A., and Grant, VV. M. : The relationship of pressure and aqueous outflow in enucleated human eyes, INVKST. OPHTHAL- MOL. 10: 430, Johnstone, M. A., and Grant, W. M.: Pressure-dependent changes in structures of the aqueous outflow system of human and monkey eyes, Am. J. Ophthalmol. 75: 365, Kayes, J.: Anatomical changes in the trabecular ineshwork induced by pressure, ARVO meeting, Sarasota, Fla., April 25, Grierson, I., and Lee, VV. R.: Changes in the monkey outflow apparatus at graded levels of intraocular pressure: a quantitative analysis by light microscopy and scanning electron microscopy, Exp. Eye Res. 19: 21, Worthen, D. M.: Transmission and scanning electron microscopy studies of the primate trabecular ineshwork, ARVO meeting, Sarasota, Fla., April 26, Schlegel, VV. A., Lawrence, C, and Slaberg, L. G.: Viscoelastic response in the enucleated human eye, INVEST. OPHTHALMOL. 11: 593, Bolz, R. E., and Tuve, G. L., editors: Handbook of Tables for Applied Engineering Science. Ed. 2. Cleveland, 1973, Chemical Rubber Company Press, p Warner, D. M.,' and Chu, E. B.: The role of calcium in the resistance lo aqueous outflow in the cat, Canad. J. Oplithalmol. 2: 226, Barany, E. IF.: A mathematical formulation of intraocular pressure as dependent on secretion, ultrafiltration, bulk outflow, and osmotic reabsorption of fluid, INVKST. OPHTHALMOL. 2: 584, 1963.