Outflow Characteristics of Isolated Anterior Segments of Human Eyes

Transcription

1 Outflow Characteristics of Isolated Anterior Segments of Human Eyes Berlinde G. Dijkstra,* Jan M. Ruijter,\ and Philip F. Hoyng* Purpose. To evaluate the relationship between intraocular pressure (IOP) and flow through the trabecular meshwork in isolated anterior segments of human eyes. Outflow facility (C) is thought to decrease proportionally with increasing IOP in human eyes in vivo and in vitro. Methods. Twenty-nine eviscerated human anterior segments were perfused with ascending and descending pressure sequences in a stepwise fashion (range, 4 to 40 mm Hg); 11 of the 29 eyes were treated similarly after 20 hours of perfusion at 12 mm Hg. Pressure-flow sequences of individual eyes were evaluated with a linear (constant C) and a nonlinear regression method (C decreasing with increasing IOP). In addition, in eight intact postmortem eyes, pressureflow characteristics were determined, followed by perfusion of their isolated anterior segments. Results. Pressure-flow sequences as determined by linear regression had an average correlation coefficient of Average C (slope of the plot) was /xl minute" 1 mm Hg" 1. There was no influence of direction of pressure sequence or time on C. To test for linearity, the hypothetical outflow obstruction coefficient (Q) was determined for each plot. Median Qof 29 eyes was mm Hg" 1, and in 45% (13 eyes) Qwas negative, suggesting facilitation instead of obstruction. This indicates that the outflow obstruction coefficient is not a physiological parameter in isolated anterior segments. Conclusions. The relationship between IOP and flow through perfused isolated anterior segments of human eyes is linear between 4 and 40 mm Hg, indicating that within this range outflow facility is constant and does not decrease with increasing IOP. Invest Ophthalmol Vis Sci. 1996;37: X he introduction of the perfusion organ culture model of isolated ocular anterior segments provided a valuable tool for studies of trabecular flow.'" 3 Its main advantage over enucleated eyes is that anterior segments can be kept viable for a longer period of time.' 1 Anterior segment perfusion focuses on the flow through the trabecular meshwork. The drainage of aqueous humor can be described by the relationship between perfusion pressure and flow. Initially, this relationship was thought to be linear, represented by the classic Goldmann equation: F = C X (IOP P c ), where F is the flow through the trabecular route, C is the facility of outflow, IOP is intraocular pressure, and P c is episcleral venous pressure. 5 In enucleated eyes, P c is supposed to be zero, simplifying the equation to: F= CX IOP, (1) Further work in the field of aqueous outflow dynamics led to the observation that outflow facility is pressure dependent, that is, it decreases with increasing perfusion pressure. 5 " 7 Linearity was thought to occur if no provision had been made to prevent anterior chamber deepening during perfusion. Anterior chamber deepening is a mechanism suggested to antagonize the decrease of the facility of outflow (that is, increase of resistance) with increasing perfusion pressure. 8 For intact enucleated eyes, it was then analyzed that: R= X IOP, 7 (2) h'rom the *l)ejmrtmmt of Experimental Ophthalmology and f Visual System Analysis, The Netherlands Ophthalmic Research Institute, Amsterdam, The Netherlands. Submitted for publication January 24, 1996; accepted May 9, Proprietary interest category: N. Reprint requests: lierlinde C. Dijkstra, The Netherlands Ophthalmic Research Institute, P.O. Box 12141, Amslmlam, 1100 AC, The Netherlands. R, resistance of outflow, was determined at each perfusion pressure using (the linear) equation 1 (F = C X IOP) and R = \/C. R., was interpreted as resistance at IOP = 0 mm Hg, and Q, the outflow obstruction Investigative Ophthalmology & Visual Science, September 1996, Vol. 37, No. 10 Copyright Association for Research in Vision and Ophthalmology 2015

2 2016 Investigative Ophthalmology & Visual Science, September 1996, Vol. 37, No. 10 Perfusion Apparatus The perfusion apparatus used was comparable with earlier described types,13 but it had a modified sealing mechanism to minimize distortion of the corneoscleral shells (Fig. 1). The clamping ring rather than the central column was fixed to the base of the apparatus; the movable central column was part of a lever system. A sufficient number of weights was added to ensure a leakproof seal at the highest pressures applied. In the central column, an additional, tiny canal was made to allow injection of fluorescein to check for leakage. FIGURE l. Design of the apparatus. coefficient, was interpreted as the obligatory positive constant factor characterizing the increase in resistance (that is, decrease in outflow facility) with increasing perfusion pressure. A constant outflow obstruction coefficient implies a curvilinear nature of the relationship between pressure and flow. This study was designed to investigate the relationship between pressure and flow in anterior segment perfusion of human eyes by analyzing the shape of the pressure-flow graphs of individual eyes and by extrapolation to group level. MATERIALS AND METHODS Preparation of the Tissues Postmortem human eyes were obtained from the Cornea Bank at the Netherlands Ophthalmic Research Institute within 16 hours of enucleation. The eyes were not suitable for transplantation because of corneal pathology. Under sterile conditions, the eyes were placed on a petri dish and bisected at the equator. Conjunctiva, vitreous, and lens were removed. The uvea was dissected from its base at approximately 0.8 mm from the trabecular meshwork in order not to damage the latter structure. The remaining corneoscleral shells were placed in modified Eagle's minimum essential medium containing 2% fetal bovine serum (final protein concentration 0.4%), 100 U/ml penicillin, and 50 fxg/m\ streptomycin. TABLE Perfusion The anterior segments were mounted on the apparatus, connected to a hanging bucket system (Gould Statham P231D pressure transducer; Hato Rey, PR) (Grass FT03 force-displacement transducer; Quincy, MA), and perfused with Eagle's minimum essential medium in a 5% CO2 environment at 37 C. After a 40-minute equilibration period at 12 mm Hg, a stable flow rate was achieved. Subsequently, pressure was changed stepwise in the following sequence: mm Hg (ascending) and vice versa (descending). At each discrete perfusion pressure, flow rate was measured after 3 minutes during a period of 10 minutes or less if flow exceeded 10 //I minute"'. A proportion of the anterior segments was treated similarly after 20 hours of perfusion. After an identical equilibration procedure, another set of eyes was perfused in the opposite order first the descending, then the ascending, pressure sequence. After the experiment, the corneal endothelium was stained with trypan blue to obtain information on the quality of organ preservation. An additional group of eyes was perfused in the ascending-descending fashion, first as intact enucleated eyes and later as anterior segment preparations. The globes were embedded in hydrous calcium sulphate stone (gypsum), with the same corneoscleral portion exposed as in the anterior segment perfusion apparatus. The embedding procedure occurred in two l. Mean Outflow Facilities Direction of Pressure Sequence Initial pressure sequence 20 hours later Reverse pressure sequence Results for all anterior segments T 4 t i I t n Outflow Facility* (mean SEM) * Outflow facility was calculated using linear regression and is expressed as fa'minute mm Hg" ' per

3 Outflow Characteristics of Anterior Segments 2017 i I facility of outflow, fi\ min-1 mmhg-1 B linn Y-intercept, ^l min-1 FIGURE 2. Distribution of outflow facilities (A), Y-intercepts (B), and outflow obstruction coefficients (C). All parameters are plotted as mean per anterior segment (n = 29). n nn nn outflow obstruction coefficient, mmhg-1 stages in such a way that the gypsum could be removed easily for the preparation of the anterior segments. A 23-gauge needle with two openings (at the tip and at 4 mm from the tip) was inserted through the cornea, slipping through the pupil into the posterior chamber. Data Analysis Individual pressure-flow curves were plotted. Ascending (up) and descending (down) sequences were analyzed separately. The pressure-flow data were fitted in two ways: 1. By linear regression, using a modified version of equation 1: F = F int + C X IOP, (3) Y un, the Y-intercept, is an auxiliary parameter in case the line of linear regression does not pass through the origin. 2. By nonlinear regression, substituting R = Ro + ^ X Q X IOP through C = \/R in equation 1. A minimum least squares curve fitting procedure was used. An F-test, testing the decrease in residual variance from linear to nonlinear regression over the residual variance of the latter, was used to compare the two fittings. The Kolmogorov-Smirnov Normality test was applied to evaluate the distribution of the intercepts, outflow facilities, and outflow obstruction coefficients derived from linear and nonlinear fitting procedures, respectively. Influence of pressure sequence direction or time on outflow facility was analyzed with a repeated measure analysis of variance. Unless otherwise stated, data were expressed as mean SEM. RESULTS The mean age of the 29 donors providing the anterior segments was 73 years (range, 43 to 96 years). In the 4 40 *4 mm Hg order, 24 anterior segments were perfused. From this group, 11 anterior segments were treated in a similar fashion 20 hours later. Furthermore, five anterior segments were perfused in reverse order, that is, 40 '4 40 mm Hg. This resulted in a total of 80 pressure-flow graphs (24 up day 1, 24 down day 1; 11 up day 2, 11 down day 2; 5 down reverse, 5 up reverse) for analysis. Linear Regression Analysis Linear regression of all pressure-flow data revealed an average correlation coefficient of Three pressure-flow sequences originating from three different eyes had a correlation coefficient lower than 0.95 c "E o FIGURE 3. Pressure-flow characteristics of eight postmortem eyes, initially perfused as intact eye ( ) and subsequently perfused as anterior segment preparations (D). The difference of both curves (dashed curve) is significant (P = 0.018) in a repeated measure analysis of variance.

4 2018 Investigative Ophthalmology & Visual Science, September 1996, Vol. 37, No FIGURE 4. Effect of neglecting a positive Y-intercept. The solid line in A represents F = C X IOP; C, slope of the plot, is a constant value independent of pressure, as shown by the solid line in B. The dashed line in A can be described as F = CX IOP + Y, nx. The slope is similar; therefore, C is similar to the solid line in B. However, if C is calculated using F = C X IOP, the dotted curve in B will result. This curve can be characterized by C = Cj rue X Y ilh /IOP. Note that if the pressures below 7 mm Hg had not been determined, the curve would have resembled a linear decline of Cwith increasing pressures. In this way, a spurious dependency of C on pressure can be observed. 30 (0.88, 0.89, and 0.91). These particular eyes had low flow characteristics and may have been glaucomatous. The mean outflow facility calculated from the slopes of the pressure-flow graphs of 24 anterior segments was 0.26 fa minute" 1 mm Hg" 1 for the ascending and 0.28 fa minute" 1 mm Hg~' for the descending pressure sequences (Table 1). The 11 anterior segments treated a second time after 20 hours of perfusion had, with increasing pressures, an outflow facility of 0.27 //I minute" 1 mm Hg" 1 and 0.28 //I minute" 1 mm Hg" 1 with decreasing pressures. In five anterior segments perfused in reverse order of pressure sequence, mean outflow facilities of ti\ minute" 1 mm Hg" 1 and //I minute" 1 mm Hg" 1 were obtained for the decreasing and increasing pressure sequences, respectively. The mean outflow facilities of increasing and decreasing pressure-flow sequences did not differ significandy. In addition, no difference was observed between mean outflow facilities of the eyes that were treated twice. The absence of differences between outflow facilities calculated from ascending and descending slopes, as well as the absence of differences between outflow facilities in time, allows averaging of these facilities for single eyes. Figure 2A depicts the distribution of outflow facilities of the 29 individual eyes (median, 0.18 fa minute" 1 mmhg" 1 ). The mean outflow facility was //I minute" 1 mm Hg" 1. Figure 2B shows the distribution of the Y-intercepts. The mean Y-intercept was /A minute" 1, normally distributed around zero. Nonlinear Regression Analysis Nonlinear analysis using the equation F= \/R X IOP, with R = RQ + Bo X Q X IOP showed an average correlation coefficient of Only four graphs (of three different eyes, two of which had also a low correlation coefficient on linear regression) had a correlation coefficient of less than 0.95 (0.83, 0.86, 0.90, and 0.94). The outflow obstruction coefficient Qwas negative in 38 of the pressure-flow graphs (48%); translated to individual eyes, in 13 of 29 anterior segments, the factor Qwas negative (45%). Figure 2C gives the distribution of outflow obstruction coefficients for single eyes. Mean outflow obstruction coefficient was mm Hg" 1. The Kolmogorov-Smirnov Normality test, however, showed a skewed distribution, with a median of mm Hg" 1. Of the 80 pressure-flow curves, only four (5%) had a significantly better fit on nonlinear regression (P < 0.05). Nevertheless, all linear correlation coefficients obtained in those four anterior segments were greater than Perfusion of Intact Eyes Versus Anterior Segment Preparations Initially, eight eyes were perfused as intact eyes; approximately 4 hours later, they were perfused as anterior segment preparations. Pressure-flow curves of intact globes and anterior segments are given in Figure 3. The intact globes had an outflow facility of /A minute" 1 mm Hg" 1, with a Y-intercept of [A minute" 1 and a correlation coefficient of on linear regression. Nonlinear regression showed an equal fit with an outflow obstruction coefficient of mm Hg" 1 (Ro was mm Hg ja~ y minute, and the correlation coefficient was 0.997). The anterior segment preparations had an out-

5 Outflow Characteristics of Anterior Segments 2019 FIGURE 5. Actual data showing the artificial effect of neglecting the Y-intercept. A and B are derived from a downward pressure sequence after 20 hours of perfusion, where C = 0.156, K im = 1.37, and r = The dashed line in A is the regression line, and the solid line in B is its slope, or C. The dotted line can be obtained by pointwise calculation of single pressure flow data couples from F = C X IOP. C and D are equivalent to A and B, but they have negative intercepts: C = 0.219, y; nl = -0.89, and r = 1 calculated from a downward pressure sequence on day 1. flow facility of fa minute" 1 mm Hg~\ a Y- interceptof //I minute" 1, and a correlation coefficient of on linear regression. Furthermore, the outflow obstruction coefficient was mm Hg" 1 (not statistically different from zero), Ro was mm Hg /LAI" 1 minute, and the correlation coefficient was on nonlinear regression. Repeated measure analysis of variance showed the pressure-flow curves of intact eyes and isolated anterior segments (Fig. 3) to be different (P = 0.018) DISCUSSION In this study, the outflow facilities calculated from the pressure-flow data using the linear model are not different for ascending and descending pressure sequences. Such differences have been reported in enucleated human eyes. 9 At least part of those differences can be explained by the viscoelastic properties of enucleated eyes. 10 Embedding of the eye in gypsum minimizes the problem of volume expansion of the globe, resulting in the absence of those differences. 7 In anterior segment perfusion, a relatively small section of the eye is pressurized and, according to the Laplacian law, there will be less stretch in the ocular tissue of anterior segments than in whole globes at comparable pressures, accounting for the apparent absence of viscoelastic effects. The absence of a difference in facilities on day 1 and 20 hours later is in agreement with the reported absence of an increase in facility in time or, more correctly, volume perfused (washout) in the human species.' 2 " Results of this study indicate that linear and nonlinear models are well applicable to all pressure-flow curves. It should be noted that the nonlinear model has a provision for the change in outflow facility with increasing pressure, known as the outflow obstruction coefficient. 7 Statistically, this parameter implies an additional degree of freedom in the procedure of curve fitting, which generally will result in a better fit of the nonlinear regression model a priori. In only 4 of 80 fitting procedures, the curvilinear model fitted significantly (P < 0.05) better. This is in agreement with

6 2020 Investigative Ophthalmology & Visual Science, September 1996, Vol. 37, No. 10 the statistical expectation under the hypothesis that both models fit equally well. However, in 3 of the 4 curves that fitted significantly better with nonlinear regression, the outflow obstruction coefficients were negative. A negative outflow obstruction coefficient is a contradiction in terms. Negative outflow obstruction is, in fact, facilitation. This study shows that, despite a positive mean of mm Hg~', negative outflow obstruction coefficients can be observed in individual curves. Because the shape of the distribution of outflow obstruction coefficients is not normal but is skewed, the median is a better measure than the mean. Hence, 50% of the outflow obstruction coefficients is lower than mm Hg" 1. In the literature, unfortunately, only mean outflow obstruction coefficients have been reported, varying from to mm Hg" 1. 7 " 9 Although the linear and the nonlinear model fitted the data equally well, the occurrence of negative outflow obstruction coefficients in approximately 50% of the data does not support its value as a relevant physiological parameter for anterior segments in vitro. Therefore, it is concluded that in the organ culture model, the relationship between pressure and flow is best approximated by the linear model. The mean Y-intercept in the linear model was not significantly different from zero. This does not imply that an intercept should not be taken into account, especially in individual eyes. Neglecting a Y-intercept may have a substantial influence on the calculated facility of outflow, as can be interpreted from Figure 4. The solid line in Figure 4A depicts a part of the pressure/flow relationship according to F = C X IOP. Extrapolation of this line to the lower pressures shows that it will pass through the origin. The dashed line can be represented mathematically by the formula F = C X IOP + y, nl. As mentioned in other studies, 1 ' 2 " 1 ' 1 the slope of the plot is known as the facility of outflow. Therefore, it can be concluded that both lines represent a similar outflow facility (Fig. 4B, horizontal line). However, if, in the case of the dashed line in Figure 4A, outflow facility is calculated using F = C X IOP, a curved line will be found (Fig. 4B, dotted curve). By combining equations 1 and 3, the shape of this curve can be described as C = Y lm /IOP + differential, with Ciiiie.<-.iti;ii as the slope of the plot. At low IOPs, the fraction Y lut /IOP in this equation may contribute a considerable portion to difieiei.tbi- This effect is shown in Figures 5A and 5B for the current data. In this way, a graph derived from a limited pressure range for example, 10 to 40 mm Hg can mimic a linear decrease in outflow facility at increasing IOP. The opposite effect may occur if a negative intercept is present (Figs. 5C, 5D). There is a question as to whether nonlinear relationships between pressure and flow, as described in the literature, are merely the result of not taking into account a Y-intercept of a linear pressure-flow curve or whether these observations are really nonlinear. In this study, the perfusion of intact enucleated eyes shows a nonlinear relationship. The difference with the linear fitting, however, is too small to reject the linear model (Fig. 3). Several considerations can be made concerning the Y-intercept. A systematic calibration error of the pressure transducer could result in a Y-intercept. It stands to reason why this should always result in a positive intercept. It is unlikely, however, to adjust the pressure transducer to an erroneously low zero level; collapse of the anterior chamber would be detected easily. Therefore, opposite calibration errors are more likely to occur. If no calibration error has been made, a positive Y-intercept could be interpreted as virtual flow at pressure 0, that is, at active secretion. The resolution of a conventional hanging bucket system is not high enough to detect this reliably. A more probable cause of a positive intercept in intact eyes is uveoscleral outflow. In primates, uveoscleral outflow is known to be constant between 4 and 35 mm Hg (approximately 0.5 fil minute" 1 ). 15 In this range, uveoscleral flow is able to shift the pressureflow curve to the left, as in Figure 4, thereby creating a positive intercept. In the anterior segment preparation, the removal of the uveal tissue seriously alters the uveoscleral pathways. These then can be referred to more appropriately as emissarial channels through the sclera Although there is conflicting evidence, in vivo cyclodialysis in the cynomolgus monkey has shown the uveoscleral emissarial outflow to increase substantially and to become more pressure dependent. 18 H) The question arises whether, in the enucleated eye, the iris root remains the main barrier in the uveoscleral pathways and whether the pressure head in the suprachoroidal space is approximately 2 mm Hg lower than in the IOP. If so, the dashed curve of Figure 3 represents the flow through the uveoscleral routes in enucleated human eyes. If not, the deficit of Figure 3 (dashed curve) represents the flow through emissarial routes, thereby resembling the curve in cyclodialysed monkeys in vivo. 1 " 1 A combined mechanism is proposed because it cannot be excluded that postmortem changes in the iris root will not result in a partial breakdown of the barrier in the uveoscleral pathways. The pressure-flow curve of the anterior segments in Figure 3 still has a small positive intercept. It should be noted that the anterior segment preparation is not devoid of a scleral part (a ring of approximately 2.5 mm). An average globe of 22 mm diameter, with a corneal diameter of 12 mm and an opening of the perfusion apparatus of 17 mm diameter, exposes approximately 150 mm 2 of the 1400 mm 2 scleral surface (11%). Hence, on average, 11% of potentially contributing emissarial surface will be present in ante-

7 Outflow Characteristics of Anterior Segments 2021 rior segment preparations and may result in a small, positive Y-intercept. This contribution also may lead to an overestimation of the calculated outflow facility through the trabecular routes. Because our results indicate that both the linear and the nonlinear fitting are applicable in anterior segment perfusion, it is open to question whether the outflow obstruction coefficient indeed represents a measure for the gradually collapse of Schlemm's canal or whether it originates from the interpolation of the flow through uveoscleral and emissarial routes in intact eyes. Moreover, in this study, it should be noted that in approximately 50% of all pressure-flow sequences, outflow obstruction was, in fact, outflow facilitation (negative Q). It is concluded that the pressure-flow characteristics in the human organ culture model have linear properties. Between 4 and 40 mm Hg, the facility of outflow is independent of the perfusion pressure in anterior segment perfusion. To avoid the influence of an unexpected Y-intercept, flow data at several pressure heads are required to determine appropriately the outflow facility. In time-consuming pharmacological experiments, it is suggested that effects at the meshwork be described as change in flow rate at a certain pressure head rather than as change in outflow facility, which requires at least several pressure points. Key Wards anterior segment perfusion, human eye, organ culture, outflow resistance, trabecular flow Acknowledgments The authors thank Mrs. E. Pels and coworkers of the Cornea Bank for providing the eyes and the culture medium. References 1. Erickson Lamy K, Rohen, Grant WM. Outflow facility studies in the perfused bovine aqueous outflow pathways. CurrEyeRes. 1988; 8: Erickson Lamy K, Schroeder AM, Chu B, Epstein DL. Absence of time dependent facility increase ('washout') in the perfused enucleated human eye. Invest Ophthalmol Vis Sd. 1990; 31: Erickson Lamy K, Rohen JW, Grant WM. Outflow facility studies in the perfused human ocular anterior segment. ExpEyeRes. 1991;52: Johnson DH, Tschumper RC. Human trabecular meshwork organ culture: A new method. Invest Ophthalmol Vis Sd. 1987;28: Moses RA. The effect of intraocular pressure on resistance to outflow. Suru Ophthalmol. 1977; 22: Francois J, Rabaey M, Neetens A. Perfusion studies on the outflow of aqueous humor in human eyes. Arch Ophthalmol. 1955;55: Brubaker RF. The effect of intraocular pressure on conventional outflow resistance in the enucleated human eye. Invest Ophthalmol Vis Sd. 1975; 14: Armaly MF. The effect of intraocular pressure on outflow facility. Arch Ophthalmol. 1960;64: Ellingsen BA, Grant WM. The relationship of pressure and aqueous outflow in enucleated human eyes. Invest Ophthalmol. 1971; 10: Schlegel WA, Lawrence C, Staberg LG. Viscoelastic response in the enucleated human eye. Invest Ophthalmol. 1972; 11: Yan DB, Trope GE, Ethier CR, Menon A, Wakeham A. Effects of hydrogen peroxide-induced oxidative damage on outflow facility and washout in pig eyes. Invest Ophthalmol Vis Sd. 1991;32: Becker B, Constant MA. The facility of aqueous outflow: A comparison of tonography and perfusion measurements in vivo and in vitro. Arch Ophthalmol. 1956; 55: Macri FJ. Outflow patterns of the cat eye. Am] Ophthalmol. 1959; 47: Barany EH. Simultaneous measurement of changing intraocular pressure and outflow facility in the vervet monkey by constant pressure infusion. Invest Ophthalmol. 1964; 3: Bill A. Uveoscleral drainage of aqueous humor: Physiology and pharmacology. In: Bito LZ, Stjernschantz J, eds. The Ocular Effects of Prostaglandins and Other Eicosanoids. New York: Alan R Liss; 1989: PedersonJE. Uveoscleral outflow. In: Ritch R, Shields MB, Krupin T, eds. The Glaucomas. St. Louis: CV Mosby; 1989: Inomata H, Bill A, Smelser GK. Unconventional routes of aqueous humor outflow in cynomolgus monkey (Macaca irus). Am] Ophthalmol. 1972; 73: Grant WM. Experimental aqueous perfusion in enucleated human eyes. Arch Ophthalmol. 1963;69: Toris CB, PedersonJE. Effect of intraocular pressure on uveoscleral outflow following cyclodialysis in the monkey eye. Invest Ophthalmol Vis Sd. 1985; 26: