ACTA O P H T H A L M O L O G I C A 64 (1986) 499-503

Some components affecting the precision of corneal thickness measurement performed by

optical pac homet ry

Carsten Edmund and Morten la Cour

Department of Ophthalmology (Head: H.-W. Larsen), Gentofte Hospital, University of Copenhagen, Denmark

Abstract. With the Haag-Streit pachometer attached to a Haag-Streit 900 slit-lamp, 29 normal individuals were examined by repeated measurements on two sep- arate days by the same observer. A statistical variance component model admitted three components of vari- ance to be separated and estimated as SD: The biological day to day variation (0.006 mm), the variation attri- buted to the slit-lamp adjustment (0.005 mm), and the variation derived from the adjustment of the pacho- meter (0.013 mm). Knowing these components an epti- mum practical procedure of examination can be estab- lished.

Key words: cornea - corneal thickness - pachometry - measurement precision.

Within the last few years in vivo measurements of human corneal thickness has been increasingly employed for physiological as well as clinical pur- poses. In consequence, various methodological problems have attracted attention (Arner & Rengstorff 1972; Olsen et al. 1980; Patel 1981). Methodological studies involve a distinction be- tween the accuracy and the precision of a method. Precision denotes the conformity between re- peated measurements, while accuracy expresses the conformity between the measured and the true value. Consequently, the accuracy of a pacho- metrical method can only be determined if the true thickness of the object measured is known.

The purpose of the clinical studies may either be to indicate any changes in corneal thickness from one day to another or to state if values measured on a certain day are within or outside

the normal range. In both cases the ability to discriminate between two measured values de- pends on the precision rather than the accuracy of the method.

Most pachometric studies apply repeated meas- urements to refine the precision of the method. However, the optimum precision of this method is limited by the biological day to day variation within the corneal thickness. Knowledge of this variance is thus an important prerequisite for the establishment of an optimal procedure of meas- urement.

The aim of this study is to estimate the biologi- cal intra-individual day-to-day variation of the central corneal thickness. A further purpose is to analyze quantitatively the influence of the adjust- ment of the slit-lamp and the pachometer separ- ately. What is outside the scope of this investiga- tion are discussions on aligning principles of the optical sections of the pachometer, the influence of slit width, the dependence of age and sex, individual corneal curvature of refractive index as determinants for the accuracy of measurements.

Materials and Methods

The central corneal thickness was measured in both eyes of 29 normal healthy individuals (16 men and 13 women, median age of 26 years and range 22-39). All individuals had normal eyes with ametropies below f 3 diopters. The corneal

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Tabb 1. For one individual the table shows the design of the study. (:olumn IV contains all the individual pachometer readings. Column 111 contains the means of 3 measure- menis with one adjustment of the slit-lamp. Column I1 conlains the means of 6 measurements employed on the samr eye (right or left). Column I contains the means of 12 nieasurements performed the same day. The bottom line denotes the variances estimated from data in each particular column. The first index digit refers to the day, the s c u d to the eye, the third to the number of slit-lamp adjubtnients, and the fourth to the number of pacho-

meter readings within each series.

Eye 1 )ay Slit-lamp Pachometer

adjustments readings

Tii..

Tiiz.

I 1. ..

Tizi.

Tiz . .

T i z z .

Ti2 11

Tiziz Ti213

T21..

Tzz..

SfV

thickness was measured with a Haag-Streit 900 slit-lamp equipped with a Haag-Streit pachometer modified as described by Ehlers & Sperling (1977). The instrument was further equipped with an automatic recording device, calibrated to the third decimal of the linear reading scale of the pachometer .

The measurement procedure was as follows. The light beam of the slit-lamp was focused per- pendicular to the central part of the cornea using as narrow a slit as possible. Further, the pacho- meter was adjusted 3 times, and each time the corneal thickness was recorded automatically, and blind for the observer, by activation of a foot switch. The alignment used was an end to end touch between the optical sections of the back of the endothelium and the front of the epithelium. The procedure was repeated on the fellow eye and finally again on both eyes. Six measurements were thus obtained on each eye by two adjust- ments of the slit-lamp each time with three adjust- ments of the pachometer.

The above specified procedure was carried out two different days with a median interval of 12 days (range 1-57). All measurements were per- formed between 10.00 h and 12.00 h by one observer (CE).

The design of .the study concerning one indi- vidual appears from Table 1. Column IV denotes the pachometer readings and leads to 8 contribu- tions of varience each with 2 degrees of freedom (df). Column 111 denotes averages of pachometer readings made with the same adjustment of the slit-lamp and leads to 4 contributions of variance each with 1 df. Column I1 denotes the averages of pachometer readings performed on the same eye (right or left) and leads to 2 contributions of variance each with 1 df. Column I denotes the averages of pachometer readings carried out on the same day and lead to 1 contribution of variance with 1 df. The variances attributed to each column appear in the bottom line and con- tain the following components in accordance to Tjur (1984) :

2 2 (1) SIV=sp

s b is the variance introduced by the adjustment of the pachometer. s i is the variance introduced by

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the adjustment of the slit-lamp. s; expresses the biological intra-individual eye to eye variance, and sa expresses the biological intra-individual day to day variance. Solving the above mentioned equa- tions from 1 to 4 estimates of sp, ss, s, and s2 are obtained.

s i , S ~ I , S ~ I I and siv and thereby s i are x2 distributed with 29, 58, 116 and 464 df, respec- tively. However, neither the distribution nor the df of sa, < and s', are known. Thus confidence level may only be estimated with respect to s;. By the F-tests, S ~ I I / S ~ V = F(116,464), S~I/S!II =

F(58,116), S ~ / S ~ I = F(29,58) the estimates of s i , $ and sa may be tested to be different from zero.

The precision of a method may be improved if a mean of several specific measurements is applied. The knowledge of the above mentioned variances, however, must also precede repeated pachometric procedurek.

The variance of an average (si) of i j measure- ments of corneal thickness made on the same eye on the same day can be expressed in the following equation.

2 2 2

1 j

where i is the number of adjustments of the slit-lamp, and j is the number of adjustments of the pachometer. The square root of si(S) thus denotes the precision of the determination of corneal thickness.

SD mm

Results

s2 mmz

The magnitude of the various components of variance appears from Table 2. The error (SD)

SD mm P

Table 2. The magnitude of the estimated components of variance (s2) expressed as standard deviations (sD). sp denotes the error introduced by the adjustment of the pachometer, ss the error introduced by the adjustment of the slit-lamp, se the intra-individual eye to eye variation and Sd the intra-individual day to day variation. P denotes the

probablility of the estimates to be different from zero.

introduced by adjustment of the pachometer is about twice or 3 times the error introduced by the adjustment of the slit-lamp, which again is of the same order of magnitude as the intra-individual day to day variation.

The 95% confidence level of sp is 0.0124- 0.0141. ss and sd, but not s,, are significantly different from zero. Thus no statistical difference between right and left eye could be demonstrated.

The precision of a measurement on a given day may be calculated using eq(5) and the results in Table 2. Variation in measurement routine and its influence on the precision appears from Table 3. The precision may be expressed as a standard deviation (SD) or given as e.g. a 95% confidence interval (= k 2 . SD) around the measured values. One adjustment of the slit-lamp and three adjust- ments of the pachometer, imply a 95% confidence interval of f 0.022 mm around the stipulated mean corneal thickness.

The mean central corneal thickness of the 29 individuals was found to be 0.581 mm with an inter-individual variation of 0.031 mm SD.

Discussion

Literature states the precision of the Haag-Streit pachometer to be equal to the adjustment preci- sion. Typical precision values are suggested be- tween 0.006 and 0.008 mm (Ehlers & Kruse Hansen 1971; Alsbirk 1974; Hirji & Larke 1978; Olsen 1980).

The present study estimates the precision of a single adjustment of the pachometer to be 0.013 mm. This value is presumably not directly com-

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parable with the quoted data. Alsbirk (1974) found the precision of the mean of three pacho- meter adjustments to be SD = 0.007 mm, which should be multiplied by the square root of 3 (= 0.012 mm) to be comparable with the result of the present investigation.

The reliability of a single measurement of the corneal thickness expressed as SD and including the biological day to day variation was found to be 0.0152 mm (Table 3). This reliability can be im- proved by repeated measurements. Table 2 de- monstrates that the precision expressed as vari- ance of the adjustment of the pachometer (s2,) is about 3 times the sum of the variances of the adjustment of the slit-lamp and the biological day to day variation (9, + s2d). Thus a reasonable improvement of the reliability of the instrument is three adjustments of the pachometer. Table 3 further shows that an improvement of the me- thodical precision is most suitably obtained using two adjustments of the slit-lamp each with three adjustments of the pachometer.

Literature gives no exhaustive clarification of the intra-individual day to day variation of the central corneal thickness. Alsbirk (1974) estima- ted the variation between repeated measurements on separate days to be 0.013 mm (sD). He made one adjustment of the slit-lamp with three adjust- ments of the pachometer on two respective days. To be compared with the present study, the variation estimated by Alsbirk must be taken as the w m of Sd, sp and s,. In this case eq(5) (setting i = 1, j = 3) will give a variation at 0.0108 mm (SD)

when the results in Table 2 are employed. The foundation of the intra-individual varia-

tion is obscure. Several investigations supported Mertz (1980) in demonstrating an overnight swel- ling of the living human cornea to be about 4.5% or 0.026 mm. Mertz suggested a logarithmic re- covery to baseline within the first hour of opening the eye. However, the measurements in the pres- ent study were performed between 10.00 h and 12.00 h, and thus overnight swelling is unable to explain the demonstrated intra-individual day-to- day variation. Fujita (1980) has described a diur- nal variation in the corneal thickness by a cosinus relation with starting point 04.83 h, a mean of 0.548 mm, and an amplitude of k 0.0085 mm. The amplitude represents the peak diurnal varia- tion expressed as a range, which is approximately equal to the day-to-day variation expressed as a 955% confidence interval: f 2 * Sd = f 0.012 mm.

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Hence, the limiting factor of a pachometrical method is rather the intra-individual day-to-day variation which exceeds the diurnal variation. Clinical corneal thickness measurement thus could be managed at any time with exception of the first hour after sleep.

Kiely et al. (1983) more qualitatively than quan- titatively demonstrated a variation of the corneal thickness in accordance with the menstrual cycle. Further, they considered a rise in the oestrogen level to be accompanied by an increases in corneal thickness. Soni (1980) also demonstrated a similar cyclic variation in the corneal thickness replicating the menstrual cycle. Soni further claimed that this cyclic thickness variation was absent in women who used oral contraceptives. It is thus reasonable to believe that the corneal thickness is influenced by the hormonal state of the body and the intra- individual day-to-day variation in the central cor- neal thickness may thus partly reflect changes in the hormonal levels.

The mean thickness value of 0.58 mm estimated in this study considerably exceeds previous re- ported values, e.g. the mean value 0.52 mm pres- ented by Mishima (1968). By the same method of measurement as used in the present study Kruse Hansen (1971), Tomlinson (1972) and Kaiser- Kupfer et al. (1981) have estimated normal values at 0.52 mm, 0.55 mm and 0.58 mm, respectively. These discrepancies may implicate a considerable variance of aligning technique or between obser- vers as also pointed out by Olsen et al. (1980). Their study demonstrated that in theory the end- to-end pachometrical alignment procedure (also used in the present study) will implicate an ex- aggeration of the corneal thickness, and further more the results depend on the slit-width used. Unfortunately, intended choice of alignment cri- teria and slit-widths led to too small thickness values in proportion to theoretical prediction, and thus they concluded that the measurement also depends on the perceptive properties of the ob- server. Using the end-to-end alignment proce- dure at 115 normal persons, Olsen & Ehlers (1984) demonstrated a mean central corneal thickness value at 0.546 mm, although their theoretical consideration had predicted a mean value of 0.576 mm, not far from the mean value at 0.58 mm demonstrated in the present study. In consequence, the reported disagreeing values of measured corneal thickness in various studies might reflect various techniques and approaches

on accuracy problems rather than a precision evaluation. In this connection it is worth observ- ing that, with respect to precision of corneal thickness measurement, Olsen et al. (1980) de- monstrated no difference between observers. In agreement with this an equivalent mean thickness value of 0.58 mm, was estimated in another study (Edmund, 1986). The operation of the Haag- Streit pachometer, however, seems to be en- cumbered with an inter-observer variance which is important to consider when more than one observer participate in comparative studies or in the examination of the same patient.

Other methods have been designed to measure corneal thickness. Employing a specular method (Olsen & Ehlers 1984) and different ultrasonic methods (Saltz et al. 1983) no inter-observer vari- ance could be demonstrated. The precisions (SD of the specular and the ultrasonic methods were estimated at 0.0041 mm and about 0.0045 mm, respectively, but presumeably ignoring the error introduced by the various adjustments of the instrument.

This study emphasizes that the limitation of the precision of a pachometrical method is the normal biological intra-individual variation. Thus the re- sults of this study conclude that tripple readings are rational when employing the Haag-Streit pachometer .

References

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13: 57-96.

Received on August 14th, 1985.

Author's address:

Carsten Edmund Kildelobet 45, 2700 Br@nsh@j, Denmark.

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