ELWIN MARG, Ph.D.; R. STUART MACKAY, Ph.D., and RAYMOND OECHSLI, A.B., Berkeley, Calif.

[Submitted for publication Aug. 1, 1960.

School of Optometry, University of California.

Supported in part by a grant from the Arcadia Lions Club of California.]

The response of our new tonometer, as it is applied to the cornea, traces a typical curve shown in Figure 1. It rises sharply to a first maximum or crest, dips to a first minimum or trough, and then rises again to a central bump or maximum, all as a progressively greater force is applied to the probe to flatten a larger area of the cornea. As the probe is withdrawn, the curve continues essentially symmetrically. This is observed in both human and rabbit eyes. The curve can be interpreted in either or both of 2 ways.

Fig. 1.-Typical tonogram of the human eye. Time, t, is almost one second. C=crest, T=trough, and M=maximum.

One explanation is that the first maximum or crest is an expression of the bending of the cornea at the limit of the applanated area. The height of the first minimum or trough then would give the intraocular pressure for the degree of applanation used. The depth of the trough would be a measure of corneal rigidity or stiffness. The maximum at the center of the double curve represents the raised pressure resulting from the applanation.

Another explanation is apparent if the cornea is assumed suddenly to buckle mechanically as does the bottom of an oil can in reaction to the force applied against it. In other words, the above curve is analogous to that of a negative resistance in electronics, that is, the cornea demonstrates a mechanically regenerative effect.⁵ The buckling-in would form a potential or real vault in the space between the cornea and the tonometer. If this hypothesis were exclusively true, the first maximum or crest of the curve would represent the pressure at the moment of buckling when the corneal forces were just balanced, and the actual intraocular pressure could be measured at this instant. Here the first maximum rather than the trough would yield the intraocular pressure.

It was essential to determine the phenomena which generated the crest and trough curve in order to determine the intraocular pressure accurately. Furthermore, clarification of the phenomena would provide more basic information on corneal me chanics and help interpret the results and degree of error due to corneal mechanics of classical applanation tonometers.

In order to make the above discussion clearer, it would be well to review briefly the theory of our new tonometers.

New Tonometer

If a transducer (of mechanical displacement or force into electrical signal) of about 1 mm. diameter circle is set flush on a plate, it forms the basis of a new tonometer which is superior to previous tonometers (Fig. 2). As the plate is increasingly pressed against the cornea a curve results which shows a crest, a trough, and a central maximum (Fig. 1). When the sensitive spot or transducer surface is just more than covered by the cornea, then following first order theory the pressure against the spot is the intraocular pressure alone, assuming that corneal buckling does not occur. Errors which are inherent in applanation tonometers are eliminated. The surface tension of lacrimal fluid pulling the plate to the eye is not registered by the transducer surface because the tension is at the margin of the plate-corneal junction beyond the spot at the center. Likewise, forces at this margin caused by the bending of the cornea are not recorded because they act beyond the sensitive area. Hence, corneal stiffness, astigmatism, and the size of the globe are of no importance in the measurement. Flattening the cornea 1.5 mm. does not raise the pressure significantly unlike any other tonometer. The tonometer was constructed by using a special variable inductance transducer with mechanical negative feedback. The latter made it possible to maintain flatness against the cornea over and beyond the centrally sensitive area which is the condition for an exact reading that only these tonometers fulfill. This tonometer has shown less scatter of readings than other types of tonometers in relatively inexperienced hands. Furthermore, it can be used without topical anesthesia since only a flat surface covered by a fine, aseptic, rubber film is gently touched against the eye for less than a second.

Fig. 2.-Principle of the tonometer. The cornea of the eye is flattened against the tonometer probe to beyond the sensitive transducer surf ace. The only force recorded is the intraocular pressure since such extraneous factors as corneal stiffness exercise their forces beyond the limits of the sensitive transducer surface. Any tendency towards motion in the displacement transducer is detected and amplified to produce a restoring force which holds the transducer surface coplanar with the surrounding region. The restoring force current shown on the indicator is recorded as a measure of the intraocular pressure.

Repeatability and Accuracy

We were interested in determining the repeatability and the accuracy of our tonometer. Since the kind of eye does not matter with this instrument, we measured the eyes of 3 rabbits. A large (14- or 16-gauge) hypodermic needle was inserted into the eye behind the limbus. A water manometer with a reservoir allowed control of the pressure which was varied from 5 to 60 mm. Hg in an ascending order of 5 mm. steps. The final measurement in each run was taken back at 5 mm. Hg and indicated excellent repeatability on the same eye. The curves oobtained in this experiment with a fine rubber condom covering the tonometer tip were all simple plateaus, that is, the crest was absent. Although this occurs when the tonometer is not squarely aligned on the cornea the reason for the lack of crests here is not clear. It may be concerned with mechanical adjustment difficulties which were common in early models of the instrument. Each curve plateau provided 1 point in the calibration curves. The 6 calibration curves, 1 for each eye, were plotted together as shown in Figure 3, and they appear indistinguishable by inspection. Each point is a single reading, taken once, no values or curves being discarded. To evaluate the basic instrument without extraneous factors such as the steadiness of the hand, the tonometer probe was mounted on a manipulator and advanced to the cornea by a screw. The end point was clear; as the tonometer flattened the cornea the meter showed increasing values until suddenly it leveled off in a plateau, whose height gave the values plotted for the curves in Figure 3.

Fig. 3.-A series of 6 curves from the eyes of 3 urethanized rabbits. Each value (point) was measured only once and no points or curves were rejected or remeasured. The curves appear indistinguishable.

The Crest and Trough

In another experiment we obtained both crests and trough curves from rabbit eyes, both with and without a rubber condom cover on the tonometer. (The rabbit eye curves are indistinguishable from those of the human eye as shown in Figure 1.) Separate curves are shown in Figure 4. The pair of curves for the crest and trough measurements show no apparent difference at 5 mm. Hg, an increasing separation to about 30 mm. Hg, and then parallelism for the remainder of the curves where the difference between the curves is equivalent to about 5 mm. Hg.

Fig. 4.-The initial crests and troughs from a rabbit eye. The curves appear identical at very low pressures and parallel at higher pressures. This demonstrates that corneal stiffness is a function of the hydrostatic pressure. Hence compensation for stiffness cannot be constant for all pressures.

In still another experiment, a series of different transducer tip sizes was used, ranging 0.75, 1.5, 2, and 3 mm. in diameter. Crests and troughs were prominent under 2 mm. and almost smoothed to a plateau by 3 mm. diameter.

Rubber Balloon Eye Model

A model eye was made of a double rubber finger cot, to approximate very roughly the coats of the eye, which was filled with water and connected to the water manometer. The internal pressure of the simulated eye could be varied by adjusting the manometer water column and independently measured with the tonometer. At low pressures, about 5 mm. Hg, a curve was observed with more than a single crest and trough as the tonometer was advanced (Fig. 5) . It was evident that the crest, and the trough, T₁, were generated by the bending forces of the balloon walls whereas buckling, OC, was an oil can effect. This buckling occurred at a large area of applanation, well beyond that of the transducer surface so that it could not reasonably be ascribed to bending Furthermore if the eye model were reduced to zero (atmospheric) internal pressure, an isolated oil can effect could be demonstrated. Figure 6 shows the buckling of the model, first, in upon advancing the tonometer and then out, upon withdrawing it. Once the advancement of the probe reached a certain point, the elicitation of the effect could not be arrested by stopping the advancement of the probe. This proved the effect was caused by buckling forces and not bending forces.

Fig 5.-The tonometer probe is advanced on the rubber balloon eye model with very low internal pressure. The bending force is maximum at the crest and gone at the trough, T₁. Buckling occurs at OC, bringing the curve back to the base line.

Significance of the Crest and Trough

Fig. 6.-Isolated oil can effect. The effect of buckling forces when the rubber balloon eye model has zero (atmospheric) internal pressure. The first is buckling-in as the tonometer probe is advanced and the second buckling-out upon withdrawal. At a critical point, arrest of the advance of the probe did not stop the elicitation of the response, clearly defining it as an oil can effect.

There should now be enough evidence to allow the evaluation of the relative roles of the 2 hypotheses, bending, or alternately buckling (the oil can effect) in order to determine to which part of the curve obtained from the model the actual tonogram corresponds.

If buckling or vaulting occurred, one would expect that it would occur for a given cornea always at the same diameter of flattening. If this occurred at a diameter of say 1.5 mm., one would not find a crest and trough for the 2 and 3 mm. transducer surface diameters. However, the crest and trough were found even for the 3 mm. diameter at times which means that if buckling occurs it takes place at larger diameters than 3 mm.-an unlikely event.

The reduced or absent crest with a 3 mm. transducer surface agrees with the buckling theory. The forces that could sustain a vault are weakened as the area grows larger. Furthermore, the force (pressure × area) from the intraocular pressure increases with area making the hypothetical vaulting force relatively smaller. However, an alternate explanation is that the alignment of the transducer surface on the cornea is more critical, thus making it more difficult to obtain a crest with a larger area transducer.

It was proposed to flatten the cornea with a piece of clear plastic which had a small hole through the center filled with fluorescine solution. Buckling would then be demonstrated by the drawing of the solution into the vault. However, the buckling might be latent in terms of a distribution of forces rather than a manifest vault. This makes such an experiment inconclusive if it is negative.

If buckling occurred, it would be expected to decrease somewhat in size with increasing intraocular pressure as it did with the model. A glance at Figure 4 shows that this is not the case. On the contrary, no crest but only a plateau is found at the minimum pressure used, rather than at the maximum pressure.

As evident in the record from the model (Fig. 5), bending and buckling are not mutually exclusive. If both phenomena were to occur, one would expect to see double crests and troughs. We have never seen such a dual response from a normal eye which probably indicates that the crest and trough are generated by either bending or buckling but not both.

Decisive Experiment

It is clear that the evidence leans slightly in favor of the bending rather than the buckling hypothesis. However, a decisive experiment is required. It is simple to describe an experiment which will give the answer. If the bending theory is valid, the crest should appear at the same time the flattened area of the cornea just covers the area of the transducer surface. Hence, using the crest as a criterion, the relation between the diameter of the corneal applanation and that of the transducer surface area which can be varied in a specially made instrument should describe a straight line of unity slope. On the other hand, if the buckling theory is valid, no such relationship would be expected but rather a vertical line should result. For a given cornea, buckling would be expected to occur at a certain degree of flattening regardless of the size of the transducer surface. Hence, as long as the transducer area was initially smaller than the area at which a vault forms, the size of the transducer surface would not affect the results.

The problem with this experiment was the measurement of the diameter of flattened area. The tears prevented accurate direct visual measurement. Attempts to use transillumination and other similar techniques met with indifferent success. It was finally decided to measure the area by the amount of displacement of the tonometer. The relationship is the same as that used in a spherometer or lens gauge.

Since 2r is a constant, the formula shows that the radius of the flattened area changes in direct proportion to the square root of the displacement. When it is plotted (Figure 7) it is clear that a straight line of the proper slope results which supports the bending theory.

Fig. 7.-This curve shows that there is a direct relation between the diameter of the area of applanation, square-root x, and that of the transducer surface, 2h. Such a result would be expected if the crest were caused by the bending of the cornea. Buckling, on the other hand, would give a curve of infinite slope which is clearly not the case here.

Comment

Once it is clear that the bending theory is valid, one can discuss its implications.

The crest of the curve comes at the moment that the flattened corneal area just covers the transducer surface. This pressure reading includes errors generated by the bending of the cornea and the lacrimal fluid surface tension. It is the same kind of reading which is obtained with the Goldmann applanation tonometer; if the transducer surface is 3.06 mm. in diameter, the reading should be exactly the same as that from the Goldmann instrument without its arbitrary corrections.

It is noteworthy that the surface tension force acts at a greater radius than the bending force which, incidentally, extends over a finite range. This tends to minimize the surf ace tension value when the bending force value is being sought. Thus the difference in height between the crest and the trough can be largely if not entirely ascribed to corneal stiffness.

It might be thought that the surface tension force is dissipated on the rubber condom cover. Actually this would be true only if the condom were lifted from the surface of the tonometer and the forces involved do not seem to be large enough to do it.

The trough gives the intraocular pressure without the above errors. The existence of a trough demonstrates that the bending and surface tension forces are no longer being recorded. For any 1 eye, the crests and troughs may or may not vary together with pressure depending on the constancy of corneal stiffness over periods of a fraction of a second. One would not necessarily expect such constancy from eye to eye in view of the variability observed in classical tonography during the first minute; thus the trough reading is the one to use. Furthermore the appearance of such a response simplifies the design of electronic storage circuits to record the indication.

It seems evident that whenever an eye is flattened there must be some rise in intraocular pressure, starting at some degree of applanation. This artificial rise can be minimized with our tonometer by using small transducer surface diameters instead of 3.06 mm. as used by Goldmann. In the present instrument no variable unwanted factors are adjusted to approximate cancellation by size choice. In fact, the raise in pressure resulting from the flattening required to obtain a trough with the 1.5 mm. tip is only about 0.1 mm. Hg.

As already mentioned, a measure of corneal stiffness can be obtained from the difference in height between the crest

and the trough. However, special precautions must be taken to place the tonometer squarely on the cornea. When this is done, the crest height varies with intraocular pressure, showing little or no stiffness up to 10 mm. Hg, then increasing to about 30 mm. Hg and remaining essentially constant to the maximum pressure used, 60 mm. Hg. Improper centering can degrade the peak into a plateau at trough height. Furthermore, ordinary 75µ thick condoms tend to degrade the crest by reducing sensitivity so that use of a thinner covering or none at all may be desirable for this purpose.

The reduction of the crest as the transducer surface is made larger from 1.5 to 3 mm. diameter is clear. This may be interpreted by assuming that the total bending force is reduced despite the increased circumference of bending. A somewhat analogous situation is seen where a small dome can support a greater weight than a large dome.

Summary

Two hypotheses are offered to explain the curve obtained from the application of our new tonometer. One suggests that the flattened cornea demonstrates an oil can or buckling effect; the other suggests that the main features of the curve are due to corneal rigidity or stiffness. Both effects are exhibited under certain conditions by a rubber balloon eye model. A critical experiment clearly shows that corneal rigidity rather than buckling is responsible for the crest and trough of the curve. Thus the height of the first crest above the trough is a measure of corneal rigidity; the first trough above the base line is the intraocular pressure, free of the sizable errors which invalidate other tonometers; the central maximum or bump is the pressure to which the eye is artificially raised after making the measurement; and the second trough and crest give the intraocular pressure and corneal stiffness after the artificial rise.

The tonometer shows excellent repeatability and validity and is quick and gentle enough to be used without anesthesia. It can be covered with a thin, disposable rubber film for asepsis and be used in any orientation.

School of Optometry, University of California, Berkeley 4, Calif.

REFERENCES

1. Mackay, R. S., and Marg, E.: Fast, Automatic, Electronic Tonometers Based on an Exact Theory, Acta ophth. 37:495-507 (Dec.) 1959.

2. Mackay, R. S., and Marg, E.: Electronic Tonometer for Glaucoma Diagnosis, Electronics 33:115-116 (Feb. 12) 1960.

3. Mackay, R. S., and Marg, E.: Fast, Automatic Ocular Pressure Measurement Based on an Exact Theory, IRE Trans. Med. Electronics ME 7:61-67 (April) 1960.

4. Mackay, R. S.; Marg, E., and Oechsli, R.: Automatic Tonometer with Exact Theory: Various Biological Applications, Science 131:1668-1669 (June 3) 1960.

5. Mackay, R. S.: Switching in Bistable Circuits, J. Appl. Physics 25:424-429 (April) 1954.