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Experimental tonography on enucleated human eyes. I. The validity of Grant's tonography formula 7. Hclland-Eriksen and Tor Odberg When newer tables for parameters in Grant's formula for tonography are used, one obtains far higher values for the outflow facility than those generally accepted. The aim of this investigation has, therefore, been to test the validity of the tonography formula. The outflow facility determined by constant-rate perfusion in enucleated eyes has been compared with the results of tonography on the same eyes in the steady-state condition. Loss of intraocular fluid during tonography has been measured directly by means of a new techni(jiie. Outfloiu facilities determined according to the two methods show very good agreement. Thus, when the production of (HJUCOUS is held at a constant rate, and when there is no change in intraocular blood volume. Grant's tonography formula is found valid, provided absolute values for P,,, P,, and <IV are used. Key words: tonography, tonography loimula, constant-rate peilusion, outflow facility, facility of aijiicous outflow, enucleated eyes. I ably that values for outflow facility (C) calculated according to the tonograpliic method are in good agreement with values ol G determined by perfusion in vivo on the same eyes.1- ' Moreover, there is good agreement between aqueous outflow calculated tonograpliieally and by turnover of test substances." This is, in tact, rather surprising, considering that Friedenwald's tables for corneal indentation, V,., do not completely express the total volume displacement in the eye by tonometry,7''' and that the P,, calibration tables (1955 scale)"' are too low compared to applanation tonometry in the lying position."1 '-' Furthermore, it is known that aqueous production may decrease during tonography,''1 and that viscoelastic characteristics ol the eye" and change in t is commonly accepted that the tonographie method, originally developed by Grant,1 slitters from many sources of error. -•' Nevertheless, it lias been stated that "the tonographie technique is the most useful available for estimating the facility ol outflow of the aqueous." 1 Becker and Shatter1 state as well that, "in spite of the many possible errors, careful tonography provides a reasonable estimate of the facility of outflow in the living eye." A fundamental reason for saying this is prob- From the Department of Ophthalmology, University of Oslo, Ulleval Hospital, Oslo, Norway. This investigation was supported in pail by Anders Jalirc's Fund for the Promotion of Science. Submitted for publication Aug. 16, 1974. 199 Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 200 Hctland-Erikscn and Odbcrg intraocular blood volume 1 ' may influence the tonogram. One of us (H-E) has worked out new calibration tallies for the total volume displacement of the eye during tonometry, V|,s and tallies for P,, based on applanation tonometry," together with values for the rigidity coefficient, K, in living eyes. Using these tables and values for K in the conventional tonography formula, one obtains considerably higher values for C than those commonly accepted.1" We find it justified to search for an explanation of this, and there are several possibilities: (1) One or more of the new tables or values for K are incorrect. (2) The tonography formula is not valid. If this is true, the good agreement between outflow facility determined tonographically and by other methods must be due more or less to chance. (3) The new tallies are correct and the formula valid. This would give an outflow facility higher than that commonly stated. It has been calculated that C increases about 50 per cent when correction is made for K and change in intraocular blood volume during tonography.11' A possible decreased production of aqueous will give a measured outflow facility which is greater than the true one. The problem of this pseudofacility is discussed by several authors.1 '• 1T Moreover, a viscoelastic effect following application of the tonometer on the eye would add to this error." The aim of this investigation has been to obtain a direct experimental test of the validity of the tonography formula as Grant originally wrote it: dV T(P,, 1 V - I in :csti native Ofilithalmnlogy March 1975 in the formula are known? To our knowledge, dV has ne^er been determined experimentally. Both the volume and the pressure components in the formula are usually calculated according to Friedenwald's formulas and tables.'" Thus, in the experiments of Becker and Constant/' the tonographically calculated. C is compared to C determined by perfusion. By analysis of pressure decay curves, Langham 18 determined C by means of the pressure-volume relationships based on injections of fluid into the eye, and not by means of pressure change due to fluid displacement as in tonography. In an experimental model used for testing the validity of the tonography formula, it is necessary to control the assumptions made. The most important of these are that the rate of aqueous production, the intraocular blood volume, and the episcleral venous pressure do not change as a consequence of tonography.1'' It is also necessary to determine (and not calculate) all the factors in the formula. By building a model on enucleated eyes, the production of aqueous can be replaced by a continuous constant-rate perfusion, the change in blood volume is negligible, and the episcleral venous pressure is O. By means of continuous registration of the intraocular pressure the values of P,, and P, are determined and dV can be measured directly according to the present technique. When the eye is in steady-state, the outflow facility is given by P,, and injected volume per minute, and this C can be compared to the facility calculated according to Giant's formula for tonography in which all factors are known. P,,) Here, dV is the loss of intraocular fluid during tonography, T is the time, Ptliv is the arithmetic mean of the intraocular pressure during tonography, and Po is the pressure in the undisturbed eye. Our purpose has been to answer the question: are we able, by means of tonography and Grant's formula, to determine the facility of outflow when the absolute values of all the factors Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 Material and methods The material consisted of 14 ostensibly normal human eyes enucleated 3 to 18 hours postmortem (mean 11.5 hours). The average age was 62 years (51 to 82 years). The eyes were immediately immersed in a barbital-buffered solution of saline,'-'" where they remained at room temperature for 0.5 to 2.5 hours. Then they were put in a nest of cotton wool, with buffer up to the muscle insertions. The temperature was kept at 35 to 37° C. Experimental tonographij on enucleated eyes Volume \A Numlwr 3 201 R es ervo ir Transducer Micrometer syringe Mo t or S "s -^ N > M ii cc rr oo bbuurr e t l e Fig. 1. A schematic illustration of the experimental setup. mm Hg CO 30 20 1 0 Transducer T i me in mm Tonograph Time in m m , Fig. 2. A, example of a tracing of the intraocular pressure during tonography as recorded by the transducer (eye No. 13). B, the corresponding tonograin. The intraocular pressure was registered by a transducer (Statham P23De) connected to a hypodermic needle, No. 21 gauge, in the anterior chamber through a polyethylene tube (PE 100). The output or the transducer was fed into a monitor (Statham SP 1400) and a recorder (Statham SP 2000). The needle was inserted as far back as possible, and care was taken not to deform the cornea. The pressure in the eye could be regulated to any desired level up to 50 mm. Hg by means of a lluid reservoir. This was connected to the eye and the transducer by a threeway stopcock (Fig. 1). A burette graded in microlitcrs was inserted between the eye and the reservoir. An air bubble could be placed in the Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 burette by means of a syringe. The whole system contained barbital buffer. The eye was perfused at a constant rate through a hypodermic needle, No. 25 gauge, in the posterior chamber. Via a polyethylene tube (PE 20) the needle was connected to an "Agla" micrometer syringe driven by a stepless adjustable motor, as described by Sears.-1 Tonography was carried out with a Mueller electronic tonometer (No. 1574, adjusted). The tonometer handle was held by a clamp mounted on an adjustable carriage, which was also used to lower and raise the tonometer. Before each experiment the transducer and recorder were calibrated to the lluid reservoir. 202 Hetland-Erikscn and Odberg March 1975 Q P,,, 0 70 0 20 0.30 0C0 c, Fig, 3. Diagram showing the relationship between the outflow facilities determined by constant-rate perfiision (Ci) and tonography (G:). Before and after the series of experiments the tonometer was calibrated with a micrometer. Care was taken to avoid influence by external magnetic forces.1-1-' The perfiision was started with rather high speeds, and one could follow the rise of the pressure on the recorder. Then the speed was regulated in order to obtain steady-state at the desired intraocular pressure, Pn,. Steady-state was defined as a stable pressure for a period of at least four minutes. The fluid reservoir was placed at the same level, and an air bubble inserted in the burette. During constant-rate perfiision, and with the connection between the eye and the fluid reservoir closed, conventional tonography lasting four minutes was carried out. The intraocular pressure at the beginning and end of the tonography, Pi, and P,=, could be read from the recorder. Three to four seconds after having raised the tonometer, the intraocular pressure, P,,.,, was registered. Then the connection to the fluid reservoir was opened, and the pressure immediately rose from P,,, to P,,,. During this procedure the air bubble in the burette moved toward the eye and gave a direct measurement of the volume, dV, which was necessary to restore the pressure to pretonographic level. After closing the connection to the reservoir, the pressure in the eye was observed for a period of three to four minutes. A typical registration of the intraocular pressure during the experiment is shown in Fig. 2 where the corresponding tonogram is shown for comparison. Results Steady-state was reached after 25 to 90 minutes of perhision. With a constant rate perfusion of 1.9 to 6.5 /J per minute (mean 3.S), the intraocular pressures ranged between 11 and 25 mm. Hg (mean 18.5). Only one experiment was carried out on each eye. The outflow facility could be determined according to the equation Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 where I is the rate of perfusion and P,,, is the intraocular pressure. In the 14 eyes we obtained facility values between 0.11 and 0.40 /.i.I per minute per millimeter of mercury, witli an average of 0.214 (Table I ) . Then the outflow facility was determined tonographically using Grant's formula. The loss of intraocular fluid during tonograpliy, dV, was measured from 5.5 to 22.5 /.J, with an average of 9.5. The facility values for the 14 eyes were between 0.11 and 0.43 /A per minute per millimeter of mercury, with an average of 0.216. The results are shown in Table I. The relation between the outflow facilities determined according to the two methods is shown graphically in Fig. 3. The correlation coefficient was found to be 0.91, and it was highly significant (p < 0.0005). Discussion Constant-rate perfusion is a well established method for determining the outflow facility in enucleated eyes. In order to calculate C according to the equation Cl I =K it is of crucial importance that the intraocular pressure is in steady-state. We have paid particular attention to this during the experiments. Consequently, the time of perfusion before tonography has been rather long. Only in two eyes did the intraocular pressure differ by as much as 1 mm. Hg from P,,, 3 to 4 minutes after ending tonography, and we interpret this as a confirmation of the fact that the eye was in steady-state before tonography. It also supports the assumption that tonography has not lead to any increased leak along the cannulas. Any possible leaks would give estimates of C too high for both perfusion and tonography, perhaps especially for tonography due to the ocular distortion and higher intraocular pressure. Our results concerning C| show good agreement with previous perfusion experiments on enucleated human eyes, even Volume N Numlirr 3 Experimental tonograplnj on enucleated ci/es 203 T a b l e I. E x p e r i m e n t a l d a t a For e a c h of t h e e y e s w i t h v a l u e s for facility of outflow obtained by constant rate perfusion ( C i ) a n d tonography ( C ( ; ) C, Eye no. 1 o 3 4 5 fi 7 S 9 10 11 12 13 14 Mi.1 an Infusion (nl/min.) 2.6 3.9 fi.8 5.2 3.9 3.1 1.9 2.9 3.2 5.7 2.9 4.5 -1.5 2.3 3.8 P.., (mm. ll<i) 20.5 15.5 20 19 15.5 22 IS 17 Hi 25 19 11 19 21 18.5 when dilferent perfusion fluids were used.-"1 •-•"' Grant-" Found the mean outflow facility in 116 eyes to be 0.17 at room temperature. This was converted to 0.22 at 37° C. which is very close to the 0.214 of our results. His experiments sliowed that, after a long period of perfusion, the facility increased in some eyes and decreased in others. Ellingsen and Grant-7 found a small decrease of C after prolonged perfusion, whereas Nihard-'"' could not show any significant change in the facility after 1.5 hours of perfusion. We have not been able to find previous publications concerning tonography were dV has been determined directly. With our method, we measure the volume which is necessary to raise the pressure from P,,._., the intraocular pressure immediately after tonography, to P(l|, the pressure before tonography (Fig. 2). In order to obtain a reliable registration of the post-tonographic pressure, we waited three to four seconds before measuring dV. During this period a certain amount of inflow and outflow has taken place, but in such small quantities that collections seemed unnecessary. In the tonography formula dV is a measure of the reduction of intraocular fluid as a consequence of tonography. Considering the eye as viscoelastic, as discussed by McEwen,11 tonography will cause a timedependent relaxation of the coats of the Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 <IV (4) 8 9.5 11 10.5 11 7.5 fi 7 7.5 8.5 fi.5 22.5 11.5 5.5 9.5 (til/min./ mm. H<i) 0.13 0.25 0.3-4 0.27 0.25 0.14 0.11 0.17 0.20 0.23 0.15 0.40 0.24 0.11 0.214 Co (fil/min./ mm. Hg) 0.18 0.22 0.30 0.24 0.20 0.22 0.11 0.18 0.18 0.24 0.14 0.43 0.27 0.11 0.2 lfi eye. This stress relaxation would act as a leak from the eye, and our determinations of dV would then give values which are too high. The extent of this fault is difficult to assess, but presumably it is not great.-'" Ptill in the tonography formula has been determined as the arithmetic mean of the intraocular pressure at the beginning and end of tonography. This seems to be permissible as long as the pressure decay curve is approximately linear, which is the case in our experiments on enucleated eyes. It is also the easiest way to determine Pi in , and the way Grant did it. Our experiments show remarkably good agreement between the outflow facility determined according to constant-rate perfusion and to tonography. This indicates that one really is able, by means of tonograpliy and Giant's formula, to determine the outflow facility in enucleated eyes, at least in the normal range of pressures. Thus, the tonography formula is found valid under the particular assumptions previously mentioned, and when the absolute values For dV, P,,, and P, are used. Recent investigations11 '-' imply that Friedenwald s values for P,, are too low, and if this is true, they will give values For outflow Facility determined according to Grant's Formula which are too low. This will also be the case if their values for dV are too 204 Hetland-Eriksen low. Friedenwald's formula tor the loss of intraocular fluid during tonography will be discussed in our next paper. REFERENCES 1. Grant, W. M.: Tonographie method for measuring the facility and rate of aqueous flow in human eyes, Arch. Ophthalmol. 44: 204, 1950. 2. Duke-Elder, S.: System of Ophthalmology, The Physiology of the Eye and of Vision. 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Experimental results of tonometric measurements: scale reading versus indentation volume, vi: Ophthalmology March 1975 and Odber<> INVEST. OPHTILALMOL. 10: 716, 1971. 10. Friedenwald, f. S.: Tonometer calibration: nn attempt to remove discrepancies found in the 1954 calibration scale for Schist/ tonometers, Trans. Am. Acad. Ophthalmol. Otolaryngol. C l : 108, 1957. 11. Hetland-Eriksen, J.: On tonometry. 6. Comparative tonometry with the Coldmann applanation tonometer and the Schi0tz tonometer in the lying position, Acta Ophthalmol. 44: 522, 1966. " 12. Anderson, D. R., and Grant, W. M.: Reevaluation of the Schi0t/ tonometer calibration, INVEST. O P H T H A L M O L . 9: 430, 1970. 13. Barany, E. H.: A mathematical formulation of intraocular pressure as dependent on secretion, ultrafiltration, bulk outflow, and osmotic reabsorption of fluid, INVEST. O P H T H A L M O L . 2: 584, 1963. Downloaded From: http://iovs.arvojournals.org/ on 05/12/2017 14. McEwen, VV. K.: Difficulties in measuring intraocular pressure and ocular rigidity, in Glaucoma: Tutzing Symposium, Leydhecker, VV., editor. Basel, 1967, Karger AC. 15. Eisenlohr, f. E., Lnngham, M. E., and Maumenee, A. E.: Manometric studies of the pressure-volume; relationship in living and enucleated eyes ol individual human subjects, Br. J. Ophthalmol. 40: 536, 1962. 16. Hetland-Eriksen, J.: On tonometry. 9. The pressure-volume relationship by Schi0tz tonometry. Concluding observations, Acta Ophthalmol. 44: 893, 1966. 17. Kupfer, C , and Sanderson, P.: Determination of pseudofacility in the eye of man, Arch. Ophthalmol. 80: 194, 1968'. 18. Langham, M. E.: Manometric, pressure-cup, and tonogiaphic procedures in the evaluation of intraocular dynamics, in Glaucoma: Tutzing Symposium, Leydhecker, VV., editor. Basel, 1967, Karger AC. 19. Becker, B.~ and Friedenwald, J. S.: Clinical aqueous outflow, Arch. Ophthalmol. 50: 557, 1953. 20. Barany, E. H., and Wood in, A. M.: Hyaluronic acid and hyaluronidase in the aqueous humour and the angle of the anterior chamber, Acta Physiol. Scand. 33: 257, 1955. 21. Sears, M. L.: Outflow resistance of the rabbit eye: technique and effects of acetazolamide, Arch. Ophthalmol. C4: 823, 1960. 22. H0rven, I.: Electronic tonometer calibration, Acta Ophthalmol. 4(>: 1083, 1968. 23. Grant, VV. M., and Trotter, R. R.: Tonographie measurements in enucleated eyes, Arch. Ophthalmol. 53: 191, 1955. 24. Francois, J., Rabaey, M., and Neetens, A.: Perfusion studies on the outflow of aqueous humor in human eyes, Arch. Ophthalmol. 55: 193, 1956. 25. Nihard, P.: Influence de la pression oculaire sur la resistance a l'eeoulement de I'hinneur aqueuse, Acta Ophthalmol. 40: 12, 1962. 26. Grant, W. M.: Experimental aqueous perfusion in enucleated human eyes, Arch. Ophthalmol. C9: 143, 1963. 27. Ellingsen, B. A., and Grant, VV. M. : The relationship of pressure and aqueous outflow in enucleated human eyes, INVEST. OPMTIIAL- 10: 430, 1971. 28. Viernstein, L. |., and Kitazawa, Y.: Measurements of factors allecting the precision of tonometry and tonography, Exp. Eye Res. 9: 91, 197CK MOL.