A C T A O P H T H A L M O L O G I C A V O L . 5 3 1 9 7 5

Department of Ophthalmology, Kommunehospitalet, University of Arhus, Denmark.

(Heads: Niels Ehlers, Viggo A . Jensen)

APP LAN AT10 N TON OM ETRY AND CENTRAL CORNEAL THICKNESS

BY

NlELS EHLERS, THORKILD BRAMSEN and STEFFEN SPERLING

Readings with the Goldmann applanation tonometer were made at various intraocular hydrostatic pressures and compared with central corneal thick- ness and radius in rabbit and in man. Linear correlations were established between hydrostatic pressure and applanation readings, with correlation coefficients close to 1.0. In rabbits the tonometer readings were generally too low. In human eyes with a normal corneal thickness tonometer readings and hydrostatic pressure coincided, with thick corneas the readings were too high, with thin corneas too low. The correlation between corneal thick- ness and the error of applanation tonometry (LIP) was statistically highly significant (P < 0.001). No statistical correlation could be established be- tween corneal radius and AP. Multiple regression, taking thickness as well as corneal radius into consideration, revealed only slightly higher corre- lation coefficients. It is concluded that the central corneal thickness is a parameter which should be taken into consideration when evaluating applanation tonometer readings. A Table is presented showing the correc- tion to be added to the applanation reading at differing corneal thickness.

Key words: applanatian tonometry - central corneal thickness - corneal radius - intraocular pressure - glaucoma.

In previous publications an increased central corneal thickness was demonstrated in monosymptomatic ocular hypertension (Kruse Hansen & Ehlers 197 1 , Ehlers, Kruse Hansen & Aasved 1975), and a reduced central corneal thickness in low-

Supported by grant no. 512-1578 from the Danish State Research Foundation. Presented at the 15th Meeting of the Association for Eye Research, Wiirzburg October 1974.

34

Afifilanation Tonometry and Central Corneal Thickness

tension glaucoma (Ehlers &: Kruse Hansen 1974). These findings suggested that the corneal thickness influenced the reading obtained by applanation tonometry. In the calibration of the applanation tonometer Goldmann assumed a corneal thickness of 0.5 mm and emphasized that theoretically the corneal thickness would influence the reading (Goldmann & Schmidt 1957). However, a t that time there were no data available on the variation of corneal thickness. In the present report experimental data on the influence of corneal thickness and radius upon the applanation tonometer reading are reported for rabbit and man. The findings were presented at the 15th Meeting of the Association for Eye Research, Wiirz- burg October 1974.

Material and Methods

Rabbit experimcnts. Under intravenous barbiturate anaesthesia a canula was passed through the anterior chamber in rabbits weighing between 0.5 and 3.0 kg. Openings in the canula permitted access to the aqueous. The canula was connec- ted to an adjustable saline reservoir and a Statham model P 23 pressure trans- ducer (volume displacement 0.04 /~1/100 mmHg). The transducer fed an electro- nic manometer (Ellab Blood Pressure Monitor M4 BCM) directly calibrated by water columns. The rabbit was suspended in the supine position and the head placed in a Haag-Streit slit lamp. Corneal thickness was measured as previously

to pressure

to sal ine

F i g . 1. Diagrammatic illustration of the placement of the canula in the anterior

chamber of the rabbit.

35

Niels Ehlers, Tliorkild Brumsen und Stef fen Sperling

reported (Ehlers k Kruse Hansen 1971) the pachometer being modified accord- ing to Mishima & Hedbys (1968). Intraocular tension was measured by an ordi- nary applanation tonometer, and corneal radius by the Haag-Streit keratometer.

Human experiments. Central corneal thickness and horizontal radius were mea- sured with the above mentioned instruments. Cases of astigmatism above 1.5 D were excluded. After retrobulbar anaesthesia and prior to operation for cataract or glaucoma, a small canula was passed into the anterior chamber under micro- scopical control. The intraocular pressure was determined by the height of a saline reservoir above the eye and simultaneous applanation tonometry was performed with the Perkins or the Draeger handheld applanation tonometer, calibrated against the standard Goldmann tonometer.

Statistical treatment. The data were evaluated by computor applying single and multiple linear regression models. Significance levels were evaluated by the t-distribution, as the Kolmogoroff-Smirnoff test showed distributions not in- compatible with a Gaussian curve.

Results

In the single rabbit and human eye, a linear correlation was found between intraocular hydrostatic pressure and applanation tonometer reading. In all ex- periments correlation coefficients above 0.96 were found.

In the rabbit eyes the applanation readings were invariably too low. The slope of the correlation lines increased with increasing corneal thickness (Fig. 2). In rabbit eyes there is a positive correlation between corneal radius and thickness (Fig. 3), which is not manifest in human eyes (Kruse Hansen 1971, Ehlers et al. 1975). It could therefore be expected that data obtained from rabbit eyes would be of limited clinical interest, and consequently it was decided to perform the subsequent experiments on human eyes.

The linear correlation between intraocular hydrostatic pressure and tonometer reading for human eyes was much closer to proportionality than found for the rabbit. The correlation coefficients approximated 1 and it was therefore decided to restrict the applanation tonometer readings to two different pressure levels in order to establish the correlation in the individual eye. In 29 eyes with a normal cornea, more especially without any signs of oedema, three tonometer readings were taken at 10 mmHg and three at 30 mmHg intraocular hydrostatic

36

Applanation Tonometry and Central Corneal Thickness

100

50

- Applanation I

reading / , T = 0.49 r T = 0.43 r

T = 0.37 r

= 0.997 = 0.998

= 0.985

50 100 mm Hg

Fig. 2. Three experiments on rabbits with different corneal thickness. A linear correlation be- tween applanation readings and intraocular pressures is verified by the high correlation

coefficients (r). The slope of the lines increases with corneal thickness.

pressure. The differences between intraocular pressure and corresponding appla- nation reading (dP = P - appl. reading) for each eye were compared statistically with corneal thickness and corneal radius.

The results of the analysis are shown in Tables I and 11. The correlation ma- trix in Table I shows a strong linear dependence (P < 0.001) between dPl0 and

Corneal radius I in rnm .

I 1

0.3 0 4 0.5 Corneal thickness in mm

Fig. 3. Correlation between corneal thickness and corneal radius in rabbits eyes. Correlation coefficient 0.920 (P < 0.001). Regression equation R = 1.75 + 13.58 . T. A similar corre-

lation is not found in human eyes.

37

Niels Ehlers, Thorkild Bramsen and Steffen Sperling

Table I . Correlation matrix

Corneal radius

Corneal thickness 0.085 -0.707 -0.737 Corneal radius - 0.079 0.050 a PlO - - 0.853

corneal thickness, between APw and corneal thickness and between APlo and APw. No correlation exists between APlo or dP30 and corneal radius, nor between corneal thickness and corneal radius.

Table I1 shows the four calculated regression equations. The correlation coefficients are highly significant (P < 0.001). In the single regressions the re- gression coefficients are highly significant. In the multiple regressions the partial regression coefficients with respect to corneal thickness are significant (P<O.OOl) whereas the partial regression coefficients with respect to corneal radius are not

Table I I . Single and multiple regression equations and correlation coefficient

Dependent Variables Correlation coefficients

APlO = 30.97 - 60.26 . T t = 9.22 P < 0.001

= 40.01 - 76.38 * T t = 10.04 P < 0.001

= 25.11 - 61.28 * T + 0.82 . R

AP,

APlO t = 9.48 t = 1.85 P < 0.001 P < 0.06

Ap30 = 34.25 - 77.39 . T + 0.81 . R t = 1.56 P < 0.11

t = 10.23 P < 0.001

r = 0.707 P < 0.001

r = 0.737 P < 0.001

r = 0.721 P < 0.001

r = 0.745 P < 0.001

T = corneal thickness, R = corneal radius.

38

Afifilanation Tonometry and Central Corneal Thickness

statistically significant (P > 0.05). The differences between the y-intercepts and between the regression coefficients are not statistically significant.

I t appears from this statistical evaluation, that for an adequate description of the correlations it is sufficient to express dPlo and dP:M as functions of corneal thickness alone.

The experimentally demonstrated linear correlation between intraocular hydrostatic pressure (P) and applanation tonometer reading (Appl.) can be written:

A p p l . = a . P + b

which may be rearranged as: P -App l .= ( l - a ) . P - b

and written: d P = ( l - a ) P - b .

This last equation shows linearity between d P and P, and it is therefore possible to calculate the LIP of any intermediate pressure level from the LIP,, and LIP, by linear interpolation.

LIP?^, the error of the applanation reading at the upper limit of normal intra- ocular pressure, is a figure of clinical interest, and is illustrated in Fig. 4. Table

A P2o mm Hg

.t 5- .

. .

- 5 r I

0 45 0 50 0 55 Corneal thickness in mm

Fig. 4 . The error of the applanation tonometer reading at 20 mmHg (AP,) is correlated to central corneal thickness. Correlation coefficient 0.768 (P < 0.001). Regression equation: AP, = 35.51 - 68.33 . T. Regression coefficient highly significant (t = 6.23, P < 0.001). Including corneal radius the equation becomes: LIP,, = 29.69 - 69.34 . T + 0.82 * R. The correlation coefficient is 0.779. Partial regression with respect to T is highly significant (t = 6.32, P < 0.001), partial regression with respect to corneal radius is not significant

(t = 1.08, P < 0.28).

39

Niels Ehlers, Thorkild Bramsen and Steffen Sperling

10 15 20 25 1 30

0.450 0.460 0.470 0.480 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590

4.2 3.5 2.9 2.2 1.5 0.9 0.3

-0.4 -1.0 -1.6 -2.2 -2.8 -3.4 -3.9 -4.5

4.7 4.0 3.3 2.6 1.8 1.2 0.5

-0.2 -0.8 -1.5 -2.1 -2.8 -3.4 -4.0 -4.6

5.2 4.4 3.7 2.9 2.2 1.4 0.7 0.0

-0.7 -1.4 -2.1 -2.8 -3.4 -4.1 -4.7

5.7 4.8 4.1 3.3 2.5 1.7 0.9 0.1

-0.6 -1.3 -2.0 -2.8 -3.4 -4.1 -4.8

6.2 5.3 4.5 3.6 2.8 1.9 1.1 0.3

-0.5 -1.2 -2.0 -2.7 -3.4 -4.2 -4.9

The Table gives the correction to be added to the tonometer reading in order to obtain the intraocular hydrostatic pressure in mmHg. T is thickness of cornea. Appl. is tono- meter reading. The Table can be applied to normal corneas.

I11 shows the graphically obtained corrections, which should be added to the applanation reading at any thickness and applanation level in order to obtain the intraocular hydrostatic pressure. It is seen from Table I11 and from Fig. 4, that for a normal corneal thickness the applanation tonometer reading coincides with the intraocular pressure. However, for a thin cornea the tonometer reading is too low, and for a thick cornea it is too high.

It will also be seen from Table 111 that the difference between the corrections at 30 mmHg and 10 mmHg varies with corneal thickness. The smallest difference is not found as might be expected at the normal corneal thickness of 0.520, but at a value of about 0.56. The slope of the line connecting applanation reading to intraocular pressure is:

A p30 - A a = l - 20

The smaller the difference between AP, and APlo the more the slope approximates 1. The slope increases with corneal thickness (Fig. 5), as was also found in rabbits (Fig. 2).

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Alplanation Tonometry and Central Corneal Thickness

..

-

1 I

0.45 0 50 0.55 Corneal thickness in mrn

Fig. 5. The slope of the lines connecting applanation readings and intraocular pressures (a = 1 -

) is probably correlated to corneal thickness. Correlation coefficient 0.350 I I P ~ , - d P , ~

20 (P - 0.05). Regression equation a = 0.561 + 0.781 . T.

Discussion

In rabbits as well as in man, linear correlations are found between intraocular pressures and applanation tonometer readings of the in vivo eye, demonstrating the applicability to the eye of the Imbert-Fick law for applanation of a sphere of infinitely small thickness:

W A

p 1-

(P = pressure in sphere, W = applanating force, and A = applanated area). I t is not surprising that the calibration of the Goldmann applanation tonometer intended for human eyes does not apply to rabbit eyes. The readings were in- variably too low, although with increasing thickness the error (dP) decreased. In human eyes a closer correlation was found between intraocular pressure and applanation reading.

A statistically highly significant linear correlation was found between dP and the central corneal thickness (P < 0.001). No correlation could be demonstrated between dP and corneal radius, and by multiple regression, the correlation coefficient taking thickness as well as radius into consideration, was only slightly higher than for thickness alone. It therefore appears that the dP can be described as a function of corneal thickness.

41

Niels Ehlers, Thorkild Bramsen and Steffen Sperling

An objection to the experimental procedures could be the use of an “open” system in which the human eye is directly connected to the reservoir. An error could be introduced, for instance if “scleral rigidity” was after all of importance for applanation tonometry. The rabbit experiments, in which the pressure was measured by a transducer of small volume displacement, did not however lend any support to the importance of this error, which moreover can hardly be correlated to corneal thickness.

The importance of the corneal thickness for assessing the reliability of the applanation readings is illustrated in Fig. 4 and in Table 111. It is seen that with a normal corneal thickness of about 0.520 the Goldmann applanation tonometer gives a correct value for the pressure. When the thickness is below normal the applanation reading is too low, and when the thickness is above normal the reading is too high. This tendency was predicted by Goldmann, but the magni- tude of the error, which may reach up to k 5 mmHg within the normal range of corneal thickness (0.46-0.58 mm) is surprising. It should be noted that the given corrections are based on a series of 29 eyes. A larger series may well cause minor alterations in the figures.

The experimental data reported in this paper stress the importance of the corneal thickness in the evaluation of glaucoma patients (Kruse Hansen & Ehlers 1971, Ehlers & Kruse Hansen 1974, Ehlers et al. 1975). I t would seem possible to explain at least some cases of low tension glaucoma and of ocular hypertension on the basis of a n error of measurement caused by the abnormal corneal thick- ness.

Applanation tonometry on oedematous corneas are at present being studied. On a swollen cornea the applanation reading may be much too low. It therefore seems necessary to distinguish between a normal thickness made up of collagen fibrils, and a swollen thickness made up of interfibrillar aqueous solution.

References

Ehlers, N. & Kruse Hansen, F. (1971) On the optical measurement of corneal thickness.

Ehlers, N. & Kruse Hansen, F. (1974) Central corneal thickness in low-tension glaucoma.

Ehlers, N. Kruse Hansen, F. & Aasved, H. (1975) Biometrical correlations of the corneal

Goldmann, H. & Schmidt, T. (1957) Ober Applanationstonometrie. Ophthalmologica

Acta ophthal. (Kbh.) 49, 65-81.

Acta ophthal. (Kbh.) 52, 740-746.

thickness. Acta ofihthal. (Kbh.) 53, to be publ.

134, 221-242.

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Applanation Tonometry and Central Corneal Thickness

Kruse Hansen, F. (1971) A clinical study of the normal human central corneal thickness.

Kruse Hansen, F. PC Ehlers, N. (1971) Elevated tonometer readings caused by a thick

Mishima, S. & Hedbys, B. 0. (1968). Measurement of corneal thickness with the Haag-

Acta ophthal. ( K b h . ) 49, 82-89.

cornea. Acta ophthal. (Kbh.) 49, 775-778.

Streit pachometer. Arch. Ophthal. (Chicago) 80, 710-7 13.

Author’s address: Niels Ehlers, 0 j enaf delingen, Arhus kommunehospital, 8000 Arhus C, Denmark.

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