Gundersen, 1939), however, it seems unlikely that the limbal circulation. Columbia, Missouri 65201, U.S.A. (Received 25 March 1976)

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J. Phyaiol. (1977), 270, pp. 1-8 1 With 2 text-figure8 Printed in Great Britain DIFFUSION OF OXYGEN AT THE ENDOTHELIAL SURFACE OF THE RABBIT CORNEA BY R. E. BARR, M. HENNESSEY* AND V. G. MURPHYt From the Department of Ophthalmology, University of Missouri, Columbia, Missouri 65201, U.

1 J. Phyaiol. (1977), 270, pp With 2 text-figure8 Printed in Great Britain DIFFUSION OF OXYGEN AT THE ENDOTHELIAL SURFACE OF THE RABBIT CORNEA BY R. E. BARR, M. HENNESSEY* AND V. G. MURPHYt From the Department of Ophthalmology, University of Missouri, Columbia, Missouri 65201, U.S.A. (Received 25 March 1976) SUMMARY 1. An in vitro investigation was made to determine the oxygen tension level required at the endothelial surface of rabbit cornea to produce a net oxygen flux into the cornea across this surface when the epithelial surface was exposed to air. 2. The experimental design was based on a mathematical model which showed that the direction of oxygen flux measured in an agar layer adjacent to the endothelium was the same as the direction of oxygen flux across the endothelial surface. 3. From micro-electrode measurements of oxygen tension in the agar layer, it was found that an oxygen tension greater than 102 mmhg at the endothelial surface was required to cause a net flux of oxygen into the cornea. 4. Comparing this result to the in vivo situation, it was concluded that all layers of the rabbit cornea receive oxygen from the atmosphere under open eye conditions. INTRODUCTION Under open-eye conditions there are three possible sources of oxygen for the cornea: the atmosphere, the aqueous humor and the limbal circulation. In view of the work of Gruber (1894) and others (Bullot, 1904; Gundersen, 1939), however, it seems unlikely that the limbal circulation plays a significant role. Moreover, it seems to be generally agreed (Langham, 1952; Hill & Fatt, 1963; Fatt & Bieber, 1968; Barr & Silver, 1973; Barr & Roetman, 1974, for examples) that the anterior and central regions of the cornea derive their oxygen from the atmosphere, presumably by passive diffusion down a concentration gradient. Only the source of oxygen for the posterior region of the cornea, principally the endothelium, remains * Present address: New Jersey Medical School, Newark, New Jersey. t Present address: Department of Chemical Engineering, Iowa State University, Ames, Iowa. 1-2

2 2 R. E. BARR, M. HENNESSEY AND V. G. MURPHY in question. Some studies (Riley, 1969; Fatt, Freeman & Lin, 1974) seem to indicate that this tissue is supplied by the anterior uveal circulation via the aqueous humor. However, recent in vivo investigations (Barr & Roetman, 1974) have shown that, at least in anaesthetized rabbits, there is a flow of oxygen from the endothelium into the aqueous. In the present study a novel in vitro preparation was employed to determine how the direction of oxygen transport at the posterior endothelial surface varied as a function of the boundary condition at that surface. The results were then compared with what is known about the normal in vivo state and reasonable conclusions drawn concerning the source of oxygen for the posterior region of the cornea under normal open eye conditions. Theory In order to appreciate the experimental design and protocol, an understanding of the mathematical model that was the basis for the experiments is necessary. Therefore a brief description of the model will be given here. P=Pa Cornea x=/, X=O Agar P=P ~ ~ ~ X4 Pb Fig. 1. Diagram of the model upon which the calculations were based. The boundary conditions Pa and pb are oxygen pressures at the surfaces x = 1, and x = -lo, respectively. Consider a model composed of two planar sheets, as shown in Fig. 1. One sheet represents the cornea and the second a layer of agar. The corneal endothelium lies on the agar. From Fick's laws (Crank, 1967), the differential equations describing oxygen diffusion through these layers are d2pl/dx2-q1/dlkl = 0 (11 > x > 0), (1) d2po/dx2 = 0 (0 > x > -lo)' (2) where P. Q. D and k are oxygen tension, oxygen consumption, oxygen diffusivity and oxygen solubility, respectively, and the subscripts 0 and 1 refer to the agar and corneal layers, respectively. These equations may be

OXYGEN DIFFUSION INTO CORNEA solved using the boundary conditions P1 = Pa at x = 11, PI = PO and Dlkl(dP1/dx) = Doko(dPo/dx) at x = 0, and PO = Pb at x= -l to yield the following expression for the

3 OXYGEN DIFFUSION INTO CORNEA solved using the boundary conditions P1 = Pa at x = 11, PI = PO and Dlkl(dP1/dx) = Doko(dPo/dx) at x = 0, and PO = Pb at x= -l to yield the following expression for the oxygen tension gradient in the agar layer: dp0/dx = [(Pa - Pb) - Q1J12/2Dlk1]/[10 + (D0k0/D3Lk1)l1]. (3) Recalling that flux is proportional to the negative of the gradient, we see that, if dpo/dx is greater than zero, oxygen diffusion in the agar is in the negative x-direction, i.e. from the cornea into the agar. Likewise, if dpo/dx is less than zero, the opposite is true. Examination of the right side of eqn. (3) reveals that the denominator is always positive; therefore, the sign of the gradient, and hence, the direction of the flux, is solely determined by the quantity [(Pa-Pb)-Q1J2/2D1k1]. Since DlkL(dP1/dx) = Doko(dPo/dx) at x = 0, the sign of dp1/dx must be the same as that of dpo/dx. Hence, the direction of oxygen flux at the endothelial surface is the same as the direction of flux in the agar. Suppose now that the agar layer were not present, as under in vivo conditions, and that the oxygen tension at the posterior endothelial surface (x = 0) were Pb. Under these conditions, the gradient at the surface x = 0 is given by (dp/dx)x=o = [(Pa-Pb)-Q1112/2D1k1]/11. (4) Since 1l must be positive, the sign of the gradient and hence, the direction of the oxygen flux, is again determined by the quantity [(Pa - Pb) - Q,112/2Dlkl]. Thus, for any given Pa and Pb, oxygen flux at the posterior endothelial surface in vivo will have the same direction as the flux observed in the agar layer of the in vitro situation described in Fig. 1. It can also be shown that this conclusion holds when the cornea is simulated by a three-layered model, epithelium-stroma-endothelium, each having (different) characteristic values for Q, D and k. 3 METHODS An in vitro system involving an excised cornea was developed in which oxygen fluxes either into or out of the endothelial surface could be determined. The experimental apparatus employed is diagrammed in Fig. 2. Corneas with a scleral rim were carefully extracted from eyes of New Zealand White rabbits (2-3 kg) terminated by an overdose of Nembutal or air embolism. The procedure employed to extricate the cornea and scleral rim was such that no corneal wrinkling occurred in a high percentage of the experiments. The cornea was placed on a preset, premeasured, sterile agar mould and its thickness measured using an electrode mounted to a micromanipulator. The cornea and agar mould were then mounted in the chamber as shown in Fig. 2. The upper section was filled with a Krebs bicarbonate Ringer solution adjusted to ph of 7-4. The liquid height in the column produced a pressure of about 12 mmhg at the cornea. A pointed oxygen micro-electrode, described in more detail in Barr & Silver (1973), mounted on a long glass shaft attached to a

4 4 R. E. BARR, M. HENNESSEY AND V. G. MURPHY micromanipulator was inserted down the column and into the agar mould. The Ringer solution was equilibrated at various oxygen tensions by bubbling gases with known oxygen partial pressures through the solution. The oxygen partial pressure in the equilibrating gas was continuously monitored with a Beckman M735 oxygen analyzer placed in the gas line. Bubbling was continued until the microelectrode current reached a steady-state value, which usually required min. /Ag-gCI -Reference electrode. Fluid level * t J Bathing solution Pb. B-Rubber gasket * 0~1-Agar '- Cornea and sclera Pa a~~~~~~~p Fig. 2. Diagram of the main part of the experimental apparatus. This vessel was surrounded by a thermostatically controlled water bath. The electrode shaft at the top was attached to a micromanipulator. This indicated that the Ringer solution had equilibrated at the new oxygen tension level and that a new steady-state oxygen gradient through the agar had been established. The entire chamber was surrounded by a water-jacket maintained at 360 C, and the section below the cornea was continuously flushed with air that had passed through a water-trap at room temperature and then through a tube coiled in the 36 C water-jacket. Thus the corneal epithelium was exposed to air about 300 C with a relative humidity of about %. After the Ringer and cornea-agar system had equilibrated for a given oxygen tension in the gas permeating the Ringer, the gas was shut off and the

OXYGEN DIFFUSION INTO CORNEA 5 micro-electrode was moved down through the agar mould for a distance of about 1-2-1-6 mm in 0-4 mm steps. At each step the electrode current was recorded.

5 OXYGEN DIFFUSION INTO CORNEA 5 micro-electrode was moved down through the agar mould for a distance of about mm in 0-4 mm steps. At each step the electrode current was recorded. The direction of movement was then reversed and the set of measurements repeated in reverse order. In this way the oxygen gradient through the agar mould was determined and any drift in electrode current could be taken into account. Depending upon the direction of the observed gradient, the oxygen tension of the equilibrating gas was either increased or decreased until the value producing a zero gradient in the agar was determined (or at least closely bracketed). For most experiments, a minimum of five gradient determinations were made. When the initial choice of Pb yielded a zero gradient through the agar, two more values of Pb' one above and one below the initial value, were also included in the experiment to ensure that the system was functioning properly. Following an experimental run, the cornea and agar mould were removed from the test cell and corneal thickness remeasured. At this time a visual examination of the cornea was also made. All experiments were completed within 2 hr following excision of the cornea. RESULTS The results of the experiments, for Pa = 155 mmhg, are shown in Table 1. Fewer data points are reported for Pb at zero net flux because it was not always possible to experimentally obtain this condition. In all cases, however, values of Pb that closely bracketed this condition (i.e values that produced slightly positive and slightly negative gradients) were determined. TABLE 1. Values of Pb producing different directions of net oxygen flux at the corneal surface. Each value is the mean + 1 S.D. deviation (number of corneas contributing to the data) Oxygen flux direction Out of cornea Zero net flux Into cornea Solution Po2 (Pb in mmhg) 95-9 ± 7-1 (35) ± 5-5 (28) (35) Corneal thickness measurements indicated an average central thickness of mm. The average increase in corneal thickness during an experiment was mm. In separate experiments, the accuracy of the thickness measuring technique was determined to be mm. Visual examination of the corneas following experiments showed no corneal clouding had developed. No significant differences were seen in results obtained from animals terminated by air embolism or by an overdose of Nembutal. DISCUSSION Anytime the cornea is manipulated during an experimental procedure, the question of possible corneal damage arises. In an experiment investigating corneal metabolism, this question is paramount. There are two aspects to consider. (1) Is the corneal metabolism during the experiment

6 6 R. E. BARR, M. HENNESSEY AND V. G. MURPHY the same as normal in vivo corneal metabolism and (2) does this metabolism change during the experiment? There was no way the first question could be quantitatively answered for the present experiments. There was, however, quantitative evidence that corneal metabolism did not change significantly during the course of the experiments. The procedure used to find a zero oxygen gradient in the agar required sequential changes in Pb such that its value was first above, then below, then above, then below, etc., the zero gradient value of Pb by ever decreasing amounts. Had corneal metabolism been changing, the zero gradient value of Pb would have changed causing changes in the direction of observed gradients for some of the Pb values near the zero gradient Pb. This did not occur for the data reported. In the present study it was experimentally determined that, with the epithelium exposed to air (Pa = 155 mmhg), the oxygen tension at the posterior endothelial surface (Pb) had to exceed mmhg before there was a flux of oxygen into the cornea at that surface. This is consistent with the results of Freeman (1972). In this earlier work, measurements of oxygen tension at the endothelial surface of a whole cornea mounted such that the epithelium was in contact with air and the endothelium with an oxygen impermeable barrier yielded values of and mmhg in two sets of experiments. These are not significantly different from the mmhg reported here. Assuming that corneal Q and Dk under in vivo conditions are similar to what they were in the in vitro experiments, it then follows that the cornea cannot receive oxygen from the aqueous humor unless the oxygen tension in the latter is above mmhg. Since this value is equal to or greater than the oxygen tension in arterial blood (Prince, 1964), it must be concluded that under open-eye conditions all layers of the rabbit cornea receive their oxygen from the atmosphere. This is consistent with the earlier work of Barr & Roetman (1974) in which a steep oxygen gradient (sloping away from the endothelium) was found in the anterior chamber of anaesthetized rabbits. For human eyes, the situation may not be so obvious. If one assumes that the human cornea has the same overall oxygen consumption (Q) and oxygen permeability (Dk) as the rabbit cornea, then manipulation of eqn. (4) using 11 = 0 5 mmhg yields a value of Pb = 79 mmhg for the zero flux condition. Kleifeld & Neumann (1959) measured an oxygen tension of 52-6 mmhg in human aqueous humor, and Thiel (1967) obtained a value of 59.7 mmhg. Since these are about 30 % lower than the zero flux value computed above, one would expect that under open eye conditions oxygen would diffuse from the endothelium to the aqueous humor in humans as well as rabbits. However, in a recent computer study

7 OXYGEN DIFFUSION INTO CORNEA 7 (Fatt et al. 1974) an opposite flux was calculated using an assumed Pb of 55 mmhg and earlier (Freeman, 1972; Freeman & Fatt, 1972) experimentally determined values of Q and Dk for the three principal layers of the cornea. At present, it cannot be determined whether this discrepancy is due to differences in the over-all Q and Dk values for human vs. rabbit corneas or to inaccuracies in the extremely difficult measurements required to determine Q and Dk for the individual layers. Eqn. (4) above can be used to determine a value of Q/Dk for the whole cornea. For the zero flux condition at 360 C, Pa- Pb was found to be 52-5 mmhg; therefore, using the average corneal thickness of 418,um, one obtains Q/Dk = 6*0 x 104 mmhg/cm2. Analysis of the data from Freeman (1972) and Freeman & Fatt (1972) gives an over-all Q/Dk of 9-6 x 104 mmhg/cm2 at 230 C. This value would probably increase for a temperature of C, since Q approximately doubles for every 100 C increase and Dk only increases at a rate of about 1-2 % per 0 C. A still higher estimate for Q/Dk at 370 C, about 97 x 104 mmhg/cm2, can be obtained from the data of Langham (1952) and Heald & Langham (1956). This is an order of magnitude greater than the other two values and appears to be primarily due to a difference in values for DM. For example, Heald & Langham (1956) report a stromal Dk of 0 68 x (ml. 02.cm2)/(ml. tissue.mmhg.sec) at 370C; whereas, Freeman & Fatt (1972) give 30 x (ml. 02 cm2)/(ml. tissue. mmhg. sec) at 230 C. Assuming a rise of 1% per 0 C, the latter value would be about 3-5 x (ml. 02. cm2)/ (ml. tissue. mmhg. sec) at 370 C. Since, in the present study, the surface temperature at the epithelium was 300 C, the Q of the epithelium was probably somewhat lower than it would be at 360 C. This would partially explain the low Q/Dk value obtained; however, a corrected value would still be considerably below the other values presented. Further explanation of these disparities is not possible at this time. Finally, it is worth noting that the experimental technique employed in this study made use of uncalibrated oxygen micro-electrodes. The approach taken was such that it was only necessary to determine the direction of the oxygen gradient in the agar layer produced by a given oxygen tension in the Ringer. Thus, since the latter was known from the oxygen partial pressure in the equilibrating gas, the micro-electrode measurements were only used to determine the direction (rather than the magnitude) of the resulting gradient. This eliminated many of the difficulties inherent in experiments requiring stable, calibrated microelectrodes.

8 R. E. BARR, M. HENNESSEY AND V. G. MURPHY REFERENCES BARR, R. E. & ROETMAN, E. L. (1974). Oxygen gradients in the anterior chamber of rabbits. Invest. Ophthal. 13, 386-389. BARR, R. E. & SILVER, I.

8 8 R. E. BARR, M. HENNESSEY AND V. G. MURPHY REFERENCES BARR, R. E. & ROETMAN, E. L. (1974). Oxygen gradients in the anterior chamber of rabbits. Invest. Ophthal. 13, BARR, R. E. & SILVER, I. A. (1973). Effects of corneal environment on oxygen tension in the anterior chambers of rabbits. Invest. Ophthal. 12, BULLOT, G. (1904). On the action of oxygen at low and high pressure upon the corneal endothelium. J. Physiol. 31, CRANK, J. (1967). The Mathematics of Diffusion, 1st edn., pp London: Oxford Clarendon Press. FArT, I. & BIEBER, M. T. (1968). The steady-state distribution of oxygen and carbon dioxide in the in vivo cornea. I. The open eye in air and the closed eye. Expl Eye Re8. 7, FATr, I., FREEMAN, R. D. & LIN, D. (1974). Oxygen tension distributions in the cornea: A re-examination. Expl Eye Re8. 18, FREEMAN, R. D. (1972). Oxygen consumption by the component layers of the cornea. J. Physiol. 225, FREEMAN, R. D. & FATT, I. (1972). Oxygen permeability of the limiting layers of the cornea. Biophys. J. 12, GRUBER, R. (1894). tvber Rostablagerung in der Hornhaut. Albrecht v. Graefes Arch. Ophthal. 40, GUNDERSEN, T. (1939). Vascular obliteration for various types of keratitis: Its significance regarding nutrition of corneal epithelium. Albrecht v. Graefes Arch. Ophthal. 21, HEALD, D. & LANGHAM, M. E. (1956). Permeability of the cornea and the bloodaqueous barrier to oxygen. Br. J. Ophthal. 40, HILL, R. M. & FATT, I. (1963). Oxygen uptake from a reservoir of limited volume by the human cornea in vivo. Science, N.Y. 142, KLEIFELD, VON 0. & NEUMANN, H. G. (1959). Der Sauerstoffgehalt des menschlichen Kammerwassers. Klin. Mbl. Augenheilk. 135, LANGHAM, M. (1952). Utilization of oxygen by the component layers of the living cornea. J. Physiol. 117, PRINCE, J. H. (1964). The Rabbit in Eye Research, p Springfield, Illinois: Charles C. Thomas. RILEY, M. V. (1969). Glucose and oxygen utilization by the rabbit cornea. Expl Eye Res. 8, THIEL, H. J. (1967). Die gleichzeitige Bestimmung von ph, PCO2 and P02 im Kammerwasser des Menschen. Albrecht v. Graefes Arch. Ophthal. 174,

Oxygen tension under a contact lens. Kenneth A. Poise and Marianne Decker

Oxygen tension under a contact lens Kenneth A. Poise and Marianne Decker Cornea! thickness changes were measured on human subjects who wore gel lenses that varied in center thickness. Using these measurements