Five g ME applanation tonometry Pt to P0 conversion nomogram and table

Exp. Eye Res. (1973) 15, 509-512 LETTER

TO

THE

EDITOR

Five g ME Applanation Tonometry Pt to PO Conversion Nomogram

and Table

The Goldmann applanation tonometer (Schmidt, 1960) is the first clinical tonometer to be developed that measuresintraocular pressurewith a degreeof accuracy required for the confident diagnosis and management of glaucoma. In addition to the use of the principle of applanation, the accuracy of this tonometer depends on factors such as a constant small volumetric displacement of the aqueous, the use of microscopic magnification in the measurementof the applanation diameter, and a sound mechanical construction. The Goldmann tonometer is not self-recording, and there has been a revival of interest in the construction of applanation tonometers, both mechanical and electronic, which do this. Sometonometers, such as the “Tonomat” (Posner and Inglima, 1967) and the “Tonair” (Steinberg, 1965) use a constant weight of 5 g with a variable volume displacement, so that the difference between the steady-state intraocular pressure (PO) and the pressure with the tonometer applied (P,) varies significantly (seeFig. 1). Applanation

345 -II

diometer

6 I

I

Coefficient

5

(mm)

I 5

I IO

I 15 Volume

I 25

I 20

of indentation

of

I 30

I 35

I 40

I 45

I 50

(mm 3,

FIG. 1. The standard Friedenwald nomogram showing the relation of the Sohiotz tonometer readings (0 to about 20), in curves for four plunger weights (5.5, 7.5, 10. and 15 g), to the tonometric intraocular pressure (Pt) and the volume (V,) displaced by the cornea1 indentation. As the relation of Pt to V, is logarithmic [V, = (log,,P,-log,,P,)/K], the ordinate is a logarithmic scale and the coefficient of rigidity (K) can then be represented as the gradient of a straight line. The 5 g applanation curve has been added to show the relation of VC to P, for an applanation tonometer, the corresponding diameters of applanation being read on the top abscissa. A straight line from the 5 mm diameter position shows that at a value of 6 = 0.040, a Pt = 18.7 mmHg corresponds to a steady-state intraocular pressure (P,) of 12.8 mmHg.

This paper outlines the method used for calculating this difference (P, -PO) and provides a nomogram and table of values for clinical application. The results of intraocular measurementswith a “Tonair” tonometer and Goldmann tonometer are compared and discussed. 509

510

1).

P.

WOODHOUSE

calculation of intraocu7ar pressure Clinical tonometry is based on the Imbert-Pick principle, which is a special application of Newton’s third law that “Action and reaction are equal and opposite” :

The

Intraocular

pressure

Force of applanation tonometer ( W g-wt) (P,) = ~ Area of applanation (A cmz) -

(1)

In Goldmann tonometry the force is varied until the diameter of the circle of appanation is 3.06 mm. At this diameter, the area of applanation (O-074 cm2) is numerically equivalent of the reciprocal of the specific gravity of mercury so that the measured applanation force (W g-wt) is equal to the intraocular pressure (P,) in cm Hg. The volume displacement is small and constant (O-56 mm3) so the P, can be taken as equivalent to P, for all clinical purposes. In those methods of applanation tonometry using a constant weight, the area of applanation varies and the tonometric intraocular pressure (P,) must be calculated using the Imbert-Pick Equation (1) : p

= _w = w xg3.6

tA

(2)

D2

where the diameter of applanation is D mm. A nested computer program was used to calculate a table relating the pressure (P,), the displacement volume (V,) and the applanation diameter (D) for an applanation weight of 5 g and cornea1 curvatures with radii of 7.6, 7.8, and 8.0 mm, and from this table applanation nomogram curves were drawn for the three curvatures (Fig. 2). The displacement volume (V,) was calculated in mm3 using the following equation (Woodhouse, 1968) : 422 J7,

=

n[T

42

-n2)]

x

9 Y2 i

+r

tr

-;

) +cr2

-q2)

1

(3)

where r = radius of cornea1 curvature in mm, where q = radius of applanation circle in mm. The nomogram curve demonstrates the increasing volume displacement at lower intraocdar pressures, which results in an increasing error in the estimation of the steady-state intraocular pressure. Assuming an average value for the coescient of ocular rigidity (K = 0*0215), the difference between the measured pressure (P,) and the steady-state pressure (P,,) may be estimated:

Pt = l()R.Vc PO The results of these computations are indicated in Table I, which compares the pressure values of the Tonomat P,, the nomogram P,, and the estimated P, for measured values of the diameter of applanation. It is suggested that a table of values such as these should be used with this type of tonometer. If the coefficient of ocular rigidity is known, an estimate of P, can be made using the nomogram for a cornea1 curvature of 7.8 mm radius (Fig. 1). Results

and Discussion

The results of paired readings of intraocular pressure (P,) using the Goldmann applanation tonometer and the Tonair tonometer are shown in Fig. 3(a), and the expectation of higher readings with the Tonair tonometer is confirmed. In Fig. 3(b) these readings are corrected, assuming K = O-0215, with an improvement in the

LETTER

TO

THE

Applonotion

345

EDITOR

diometer

511

(mm)

6

I800 %

I” E iE 5 : al a’

60 50 40 35 30 25 20 15

I

I

5

IO

0 005 - ,\, 15 Volume

20

,

,

,

,

,

,

25

30

35

40

45

50

of indentotion

I

(mm31

FIG. 2. Shows the limits of the 5 g applanation curve of Fig. 1 if the cornea1 radius of curvature varies between 7.6 and 8.0 mm (the extremes of variation for the measurements of adult human corneae). These limits demonstrate that the consequent error in the measurement of P, would be less than 1 mmHg within the range 15 to 50 mmHg. TABLE

Diameter of applanation (mm)

3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1

5.2 5.3 5.4 5.5 5.6

pt (Posner) (mm%)

43 40 37 35 33 31 29 27 25 24 23 22 21 20 19 18 17 16 15 14 13 12

pt (Nomogram) (mm%)

38.2 36.1 34.2 32.4 30.7 29.2 27.8 26.5 25.3 24.2 23.2 22.2 21.2 20.3 19.4 18.7 18.0 17.3 16.7 16.1 15.5 14.9

I

(K 30215) (mmR4

36.4 34.2 32.2 30.3 28.5 26.9 25.4 23.9 22.6 21.4 20.3 19.2 18.1 17.0 16.0 15.2 14.4 13.6 12.9

12.2 11.5 10.8

(K =p6.040) (mm%)

35.0 32.7 30.6 28.6 26.7 25.0 23.4 21.9 20.6 19.2 18.2 17.0 15.8 14.7 13.6 12.8 11.9 11.1 10.3 9.5 8.8 8.1

1). F.

518

1

WOODHOUSE

-/“/;“I.*,~

0

IO

20

30

IO

Goldmann

applanotbn

20

30

IO

20

30

CmmHg)

FIG. 3. The effect of the value of the coefficient of ocular rigidity on the correction of an isodynamic 5 g tonometer, the “Tonair”. (a) With no correction, all the pressure values (Pr) are above the diagonal, which represents equality between Tonair and Goldmann values; (b) correction with the value of K (0.0215) used for Schiotz tonometry, has improved the relationship of equality, but a more equal relationship is obtained in (c) with K = 0.040.

equality of readings. In Fig. 3(c) K is assumedto be 0.040 and a further improvement is obtained. At low pressuresK is known to be higher (Perkins and Gloster, 1957) and it is suggestedthat the tables of values assumingthis value of K should be used, as the pressuresusedin this type of applanation tonometry are lower than in Schiotz tonometry, where the mean value of K was originally determined as O-0215(Friedenwald, 1937). Applanation tonometry can, in principle, be more accurate than indentation tonometry and is also lesslikely to causecornea1abrasion. It is, therefore, likely that improved applanation tonometers will be designed, especially if applanation tonographs is developed. The volume displaced by cornea1applanation is not necessarily negligibIe and is an essentialfeature of tonography. It is hoped that the nomograms and table included in this paper will be helpful in calculating this volume and the associatedchange in intraocular pressure.

The errors of 5 g applanation tonometry caused by the cornea1 volume displacement are described and their importance in tonography is discussed.These errors are illustrated by means of the tonography nomogram, and a correction table is used to reduce the error of a practical applanation tonometer (Tonair). I acknowledgewith gratitude the co-operation of the consultant staff of the Wolverhampton and Midland CountiesEye Infirmary, whosepatients are referred to the glaucoma clinic, and the help given with the computer programming by Miss SusanPepper of the Birmingham Regional Hospital Board and by Mr Paton, Group Photographer, Wolverhampton. REFERENCES Posner, A. and Inglima, R. (1967). Eye, Ear, Nose and, Throat Schmidt, T. (1960). Amer. J. OphthuZmoE. 49, 967. Steinberg, P. (1965). Opticul Journal-Review, June, 33. Woodhouse, D. (1968). Bit. J. Ophthalmol. 52,492.

Wolverhampton.Eye In$rmxxry Wolverhumpton, St@s, England Received15 September1972, London

Monthly 46, 996.

D. F.

WOOLGIOUSE