CRITICAL ANALYSIS OF PRECISION IN TONOMETRY

KARLIS APINIS, M.D. Pendleton, Oregon

The most fundamental problem in the vegetative physiology of the eye, as Duke-Elder points out in one of his recent papers, is the formation and elimination of the intra­ocular fluid and the control of the ocular ten­sion.

Investigation of the physiochemical ques­tions of this problem has become, due to the latest advances and development of the tech­nical research methods of that branch of science, quite inaccessible to the ophthal­mologist in practice and must remain the domain of a pure scientist with a technically well-equipped laboratory.

The control of the ocular tension, a result of the balance of the two vegetative func­tions of the eye, is equally important to both the scientist and the ophthalmologist.

The scientist will fail to recognize the causes influencing the maintenance of a bal­ance in the formation and elimination of the intraocular fluid, when he cannot depend on sufficient precision in the method of regis­tering the variations of ocular tension.

Without such a precise instrument, the ophthalmologist will fail to detect the early stages of glaucoma or will be unable to ap­preciate the efficacy of the applied treatment.

The device for this purpose, well known to every ophthalmologist, is the tonometer. What is missing after the many years of its use is a critical attitude toward its precision in registering the variations of ocular tension.

LIMITATIONS OF IMPRESSION TONOMETRY

The impression tonometer most widely used in Europe is that of Schijzftz; in the United States, the Schijzftz and its modifica­tions. The past decades have brought an im­provement in the technical aspect and per­fection of this instrument but have left in the same state of imperfection its precision in registering the variations of ocular ten­sion.

The basic principle of an impression to­nometer is to produce an impression in the center of cornea with a metallic rod of a constant diameter and concavity. The weight of the rod changes from 5.5 to 7.5; 10.0 and 15.0 gm. An increase of ocular tension re­quires the use of an accordingly greater weight for producing the same depth of im­pression.

An impression tonometer expresses, in reality, only the depth of the obtained im­pression in 0.1-mm. units. The height of ocu­lar tension in mm. Hg corresponding to each impression depth is supplied by a table of inversion based on experimental data fur­nished by Schijzftz a long time ago. A critical study of this table points out the disadvan­tage of the impression tonometer. Contrary to the basic maxim that every measurement requires the use of a constant invariable unit of measurement, the table of inversion operates with exceedingly variable units. (Chart 1).

The unit of measurement for the impres­sion tonometer changes (1) for each weight of the impression rod used with increasing impression depth (maximal impression pro­duces the smallest obtainable unit of meas­ure, and as the impression depth decreases the unit increases) ; (2) for each change to a greater weight of the impression rod.

Even with the use of an impression rod of one weight, according to Schijzftz an un-advisable procedure, an invariable unit of measurement of the ocular tension cannot be obtained. The unit of ocular tension for the weight 5.5 gm. is 2 mm. Hg within the im­pression depths from 0.6 to 1.0 mm.; 3 mm. Hg—from 0.5 to 0.6 mm.; 4 mm. Hg—from 0.3 to 0.5 mm.; 5 mm. Hg—from 0.2 to 0.3 mm.; 6 mm. Hg—from 0.1 to 0.2 mm.; and 7 mm. Hg for the impression depth of 0.1 mm. from the 0 point. The difference be­tween the smallest unit of measurement,

398

ANALYSIS OF PRECISION IN TONOMETRY 399

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2 mm. Hg, and the largest of 7 mm. Hg is 5 mm. Hg.

These variations in ocular-tension meas­urement units increase with the change to the next greater weight of the impression rod.

Inaccuracies in impression tonometer read­ings are obscured because the ocular tension is expressed in mm. Hg without the used weight of the impression rod being men­tioned. For example, an intraocular pressure of 20 mm. Hg can be the result of an appli­cation of 5.5-gm. weight, an impression depth of 0.6 mm., the unit of measurement being in that case, 3 mm. Hg. The same tension (20 mm. Hg) can be the result of the applica­tion of a 7.5-gm. weight and an impression depth of 0.8 mm., or, as another example: an ocular tension of 40 mm. Hg can be meas­ured with a weight of 7.5 gm., an impression depth of 0.3 mm., a unit of measurement of 7 mm. Hg, as well as with the weight, 10.0 gm., impression depth, 0.5 mm., measurement unit, 7 mm. Hg. A record of the used weight and the depth of the obtained impression should never be omitted, since only these data reveal the precision of each measure­ment.

It must also be remembered that the read­ings of the impression tonometer are based on the mathematical average of many differ­ent findings. It is possible that the ocular tension deduced on the basis of the impres­sion depth coincides with the real ocular ten­sion. The possibility (proved experimen­tally) remains, however, that the tonometric readings are lower than the actual ocular tension. This could be overlooked if the unit of measurement was very small, but that cannot be said of the impression tonometer with an average unit of measurement of 5 mm. Hg.

These disadvantages, characteristic of every impression tonometer, inspired me to a manometric and clinical investigation of the use of the applanation principle in tonom-etry.

400 KARLIS APINIS

L I M I T A T I O N S OF APPLANATION TONOMETRY

The use of the applanation principle in tonometry permits two different procedures. The amount of ocular tension can be cal­culated (1) by the size of the applanation diameter under a constant weight or (2) by the weight necessary to obtain an applanation diameter of a constant invariable size.

Chart 2 (Apinis). The relationship of tonometric readings and manometric tension. The weights used (reading from bottom to top) S gm., 7.5 gm., 10 gm., 25 gm., and 30 gm.

While all the readings in the use of the impression principle are based on the mathe­matical average of experimentally found data, the applanation principle gives re­sults based on pure mathematical calcula­tions. Imbert, Fick, Maklakow, and others are convinced that by the use of the applana­tion principle, mathematical calculations can express the real ocular tension, and that the influence of such factors as the elasticity of cornea and sclera are practically negligible.

DETERMINATION OF OCULAR TENSION BY SIZE OF APPLANATION DIAMETER

When the size of the applanation diameter is used to determine ocular tension, the to­nometer of Maklakow is used. Manometric investigations on cadaver eyes in situ prove a very interesting fact—under certain condi­

tions, the mathematically calculated ocular tension coincides in reality with the mano­metric controlled ocular tension. For the 10.0 gm. weight of the Maklakow tonometer, this occurs when the size of the applanation diameter reaches the limit of 5.6 mm. In that case, the tonometric ocular tension coincides with the actual tension of 30 mm. Hg con­trolled by manometer (Chart 2) .

From this point of coincidence upward, the difference between the tonometric and manometric ocular tension increases progres­sively, the tonometric readings being less than the actual ocular tension. Downward from this point, the tonometric readings are higher than the manometric-controlled ocular tension.

Such an intersection of the curve of tono­metric readings with the manometric curve suggests that it might be possible to obtain a coincidence of the tonometric with the manometric-controlled ocular tension at every level, using a gradually increasing weight of the tonometer (Kalfa, Apin).

Manometric investigations (Apin) proved that such a coincidence can be obtained. Some examples from those studies confirm this. Chart 2 reveals the evidence that for every weight of the tonometer such a point of coincidence with the manometric con­trolled ocular tension can be reached. The intersections of the tonometric curve with that of manometer are given for several weights (Chart 2) . For the weight 5.0 gm., the point of coincidence lies at 12 mm. Hg; for 7.5 gm. at 20 mm. Hg; for 10.0 gm., at 30 mm. H g ; for 25.0 gm., at 46 mm. Hg; and for 30.0 gm., at 56 mm. Hg.

Observations made during these researches emphasized the necessity of using an increas­ing weight of the tonometer for an increase in ocular tension. The size of the applanation diameter should not be less than 6.0 mm. at low ocular tension and not exceed 7.0 mm. at high ocular tension. Within these limits, the size of the applanation diameter should be gradually increased in conformity

ANALYSIS OF PRECISION IN TONOMETRY 401

with increasing ocular tension. In practice it is, therefore, unnecessary to use a table for inversion of the tonometric readings in mm. Hg based on experimental average find­ings ; that can be done using data furnished by mathematical calculations.

Weight (in gm.)

The precision of this method for the de­termination of ocular tension, as compared with that of impression tonometry, is con­siderable. The same measure unit of 0.1 mm. is used to determine the size of the applana-tion diameter. All attention during the to­nometry can be fixed on the correct applica­tion of the tonometer. The applanation di­ameter obtained is always printed on paper as soon as the instrument is taken off the eye. The printed diameter can be measured later at ease with every devise necessary to in­crease accuracy.

The inversion of the size of the applana­tion diameter into the corresponding mm. Hg of ocular tension requires an inversion table whose data are mathematically calculated. The measure units of ocular tension for every size of the applanation diameter and

every used weight are shown in Chart 3. It is true that this method has the same disad­vantages of variable measure units for (1) every change in the size of applanation di­ameter for each weight and (2) every change to another weight for each size of the ap­planation diameter that impression tonometry has.

The actual value of this method for the de­termination of ocular tension lies in a con­siderably higher precision. The variations of the measure units with a change of the size of applanation diameter are minimal and can

Chart 3 (Apinis). The units of measure of the applanation tonometer with determination of tension by the size of the applanation diameter (in mm.).

402 KARLIS APINIS

be ignored. The difference between the mini­mal and maximal measure units for the weight 5.0 gm. is only 0.1 mm. Hg; for 10.0 gm., 0.3 mm. Hg; for 15.0 gm., 0.5 mm. Hg ; for 20.0 gm., 0.6 mm. Hg; for 25.0 gm. and 30.0 gm., 1.0 mm. Hg. The same differences for the impression tonometry are 2 mm. Hg for the weight 5.5 gm. and 3 mm. Hg for the weight 15.0 gm.

Units Of measurement for ocular tension in both methods, impression and applanation, drawn on the same scale, allow an easy com­parison of those different procedures. Table 1 shows the units for the impression tonome­ter; Chart 3, those for the applanation tonometer. The precision of applanation tonometry exceeds that of impression to­nometry many times and for scientific re­search should be the method of choice.

OBTAINING AN APPLANATION DIAMETER OF CONSTANT SIZE

The assumption that more exact tono-metric data are reached by using a progres­sively increasing weight to produce an im­pression or an applanation is recognized in die construction of the Fick-Livschitz to­nometer. The standard size (6.8 mm.) of the applanation diameter is based on mathe­matical calculations that make it possible to double the applied weight in order to express the ocular tension in mm. Hg. For example: a pressure on the eye with a weight of 10.0 gm. produces the applanation diameter of 6.8 mm. and the ocular tension in that case is 2 X 10 = 20 mm. Hg; the same applana­tion diameter with a pressure of 15.0 gm. gives an ocular tension of 2 X 15 =30 mm. Hg, and so on.

The scale graduation of the Fick-Livschitz tonometer records the increase of pressure on the eye in steps of a 1.0-gm. weight for each grade. The unit of measurement—2 mm. Hg —is, therefore, always constant and invari­able.

The application of this tonometer is very simple and can be done while the patient is seated. Its disadvantage is that the operator's

attention must be divided between considera­tion of the size of the applanation diameter and the reading of the applied weight.

The size of the applanation diameter, 6.8 mm., must be judged with the naked eye. The possibility cannot be denied that a mis­take can be made in the appreciation of the actual size of the applanation diameter which could be 6.7 or 6.9 mm. instead of 6.8 mm. Such a mistake would of course, give an in­correct reading of the ocular tension which would actually be 2 mm. Hg lower or higher, as the case might be.

These peculiarities of the Fick-Livschitz tonometer prohibit its use in precise scienti­fic researches, although it will remain in gen­eral use for recording the ocular tension in cases in which an error of 2 mm. Hg more or less is not important.

A very slight change in procedure would, however, permit its use in scientific re­searches : the size of the applanation diameter actually reached should be printed on paper —a procedure which simplifies this tonome­ter's use and increases its precision because the attention can be fixed on reading the applied weight. The size of the printed ap­planation diameter is measured afterward with ease and every desired accuracy.

This procedure also permits determination of the ocular tension either by (1) the ap­plied weight or (2) the size of applanation diameter. The precision of the measurement by the size of applanation diameter is greater and to be preferred. The measure unit is under 1 mm. Hg, if the used weight does not exceed 10.0 gm.; under 2 mm. Hg, if the weight does not exceed 20.0 gm., and 2 mm. Hg for the weights 25.0 gm. and 30.0 gm.

The construction of the Fick-Livschitz to­nometer permits an increase of the weight in 1.0 gm. steps. However, in determining ocular tension by the size of applanation di­ameter, the applied weights can be restricted to 5.0-gm. steps (5, 10, 15, 20, 25, and 30 gm. weights).

Chart 2, with its experimental data, shows that the point of coincidence between tono-

ANALYSIS OF PRECISION IN TONOMETRY 403

TABLE 1 THE VARIATIONS OF OCULAR TENSION IN A CASE OF GLAUCOMA*

Date

7/16/47 7/22/47 7/25/47 9/ 4/47 9/11/47 9/12/47 9/13/47 9/14/47 9/16/47 9/17/47 9/18/47 9/19/47 9/20/47 9/21/47 9/22/47 9/23/47 9/24/47 9/25/47 9/28/47 9/30/47

10/ 9/47 10/13/47 10/16/47 10/27/47 10/30/47

Right Eye

il U 20 15 15 20 20 20 20 20 10 15 10 10 10 10 10 10 5 5 5 5 5 5 5 5 5

Applanation Tonometer

s o "£'3' 5 v a

£55 6.8 6.8 6.9 6.6 6.8 6.9 6.7 6.8 6.8 6.8 6.4 6.4 6.8 6.8 7.0 7.1 6.3 6.2 6.4 6.3 6.3 6.3 6.4 6.3 6.2

§a 53 g

39 31 30 41 39 38 40 39 20 31 23 23 20 20 19 19 12 12 11 12 12 12 11 12 12

-5 ft sa M i . i 0.9 0.9 1.3 1.1 1.1 1.1 1.1 0.6 0.9 0.7 0.7 0.7

0.4

0.4 0.4

Impression Tonometer

Si «og> m

10.0 7.5 7.5

10.0 10.0 10.0 10.0 10.0 7.5 7.5 7.5 7.5 7.5 7.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

? «? W—

u **

SO 5 5 5 5 5 5 5 5 8 5 7 7 8 8 6 6

10 10 10 10 10 10 10 10 10

.̂ 5| §B 3H U

Left Eye

£ a Z-S. 20 20 15 20 20 15 15 15 20 20 20

10 10 10 10 10 5 5 5 5 5 5 5 5

Applanation Tonometer

a o

*SH

6.8 6.7 6.4 6.9 6.9 6.4 6.5 6.5 6.8 6.8 6.9

7.1 6.8 6.4 6.2 6.5 6.2 6.1 6.1 6.3 6.4 6.3 6.3 6.3

60

8a 55 g H e 39 40 35 38 38 36 34 34 39 39 38

19 20 23 25 22 12 13 13 12 11 12 12 12

.ti s H sa IS

Impression Tonometer

£ a .3>B m 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

7.5 7.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

? o a 'Sx a a

5 5 6 5 5 6 6 6 5 5 5

8 8 5 4 5

10 10 10 10 10 10 10 10

^ s* 3S £H ii

7 7 4 7 7 4 4 4 7 7 7

3 3 4 4 4 2 2 2 2 2 2 2 2

* The data for applanation are actual, for impression hypothetic.

metric and manometrically controlled ocular tension shows a spread of only minus 2.0 mm. Hg, on increase of tension and of not more than plus 2.3 mm. Hg on decrease of tension. In practice, the difference will really never reach that amount, for, when the al­terations in ocular tension (increase or de­crease) exceed 5 mm. Hg, the next smaller or larger weight can be used. For very deli­cate research the applied weight can always be increased in 1.0 gm, steps.

The precision of the procedure just men­tioned is shown in Table 1. The Fick-

Livschitz tonometer was used to register the changes in ocular tension in a case of glau­coma under conservative treatment with drugs after cyclodialysis (R.E., September 14; L.E., September 18, 1947). The proce­dure of printing the applanation diameter on paper was followed, using the 5, 10, 15, and 20 gm. weights.

Table 1 gives all essential data: (1) The applied weight, (2) the size of the obtained applanation diameter, (3) ocular tension de­duced from the size of applanation diameter, and (4) the unit for each measurement. The

4.*:— \ O ~~~7 " ~-

II U -''

'! •0-*\

^ s \ —. ■ - \

N, .——

Chart 4 (Apinis). A curve of the variations in ocular tension in a case of glaucoma as constructed from the data in Table 1.

404 KARLIS APINIS

maximum measure unit does not exceed 1.3 mm. Hg in the right eye, and 1.1 mm. Hg in the left eye; the minimum measure unit is 0.4 mm. Hg.

For comparison, hypothetical data for an impression tonometer have been added to Table 1. The maximum measure unit for the

6.7 6.8 6.9 7.0

Fig. 1 (Apinis). Examples of printed applanation diameters in their original sizes (in mm.).

impression tonometer is 7 mm. Hg; the mini­mum 2 mm. Hg. Under such circumstances it can hardly be expected that, in practice, the curve of the impression tonometer will coincide with that of applanation tonometer, because the maximum measure unit of the applanation tonometer (1.3 mm. Hg) is less than the minimum measure unit of the im­pression tonometer (2 mm. Hg) . When the impression tonometer is used, subtle changes of ocular tension will remain undetected.

The graphic expression of the variations

Apin: Klin. Monatsbl. f. Augenh., 81:631, 1928. : Klin. Monatsbl. f. Augenh., 82:500, 1929.

Kalfa: Russ. Ophth. J., 6 -.1132,1927. : Russ. Ophth. J., 8:250,1928.

of ocular tension in a case of glaucoma is shown in Chart 4. Examples of printed ap­planation diameters in their original sizes are shown in Figure 1.

SUMMARY

Recent improvements in the Schij2(tz im­pression tonometer and its modifications have increased its technical perfection but left its precision at the same state of imperfection.

The use of applanation tonometry should be preferred in scientific researches because of its greater precision and because printing the size of the applanation diameter permits exact measuring.

At present the Fick-Livschitz tonometer is best for use in applanation tonometry: (1) In practice because of ease of application with the patient in a seated position, and (2) in sci­entific researches because (a) the printing of the applanation diameter increases its pre­cision and (b) the appliance of gradually increased weight in conformity with in­creased ocular tension gives more reliable readings.

Eastern Oregon State Hospital.

REFERENCES