Exp. Eye Res. (1981) 33, 141-145

Ocular Vo lume and Ocular Rigidity

E. S. P E R K I N S

Department of Ophthalmology, University of Iowa Hospitals and Clinics, Iowa City, Iowa 52242, U.S.A.

(Received 14 July 1980 and in revised form 11 November 1980, London)

The coefficient of ocular rigidity (K) was measured in enucleated human eyes by the injection of known volumes of fluid and measuring the rise in pressure. The intraocular volume of each eye was calculated from profile photographs of the globe and the scleral thickness measured by a light-scattering technique.

K showed a highly significant negative correlation with ocular volume but a coefficient of rigidity which included the volume of the individual eye did not show a significant correlation with ocular volume. There was no correlation between K and seleral thickness but K tended to be higher in older eyes. In 17 out of 20 eyes K decreased as the level of pressure at which it was measured increased.

The results suggest that the lower ocular rigidity of myopic eyes is largely due to their greater ocular volume and not to any abnormal distensibility of the sclera.

Key words: ocular rigidity; ocular volume; seleral thickness.

1. Introduct ion

I t is well r ecogn ized t h a t F r i e d e n w a l d ' s coeff icient of ocu la r r i g id i ty (K) is low in

m y o p i c eyes and i t has been p o s t u l a t e d t h a t th is is due to t he la rger v o l u m e of such

eyes (Phill ips, 1971). H o n m u r a (1968) has shown a s igni f icant n e g a t i v e cor re la t ion

b e t w e e n r ig id i ty and ax ia l l ength , and the a im of t he p r e sen t s t u d y was to see w h e t h e r

th is co r re l a t ion d e p e n d e d on ly on ocu la r v o l u m e or w h e t h e r o t h e r fac to rs such as an

a b n o r m a l d i s t ens ib i l i ty of the sclera were also invo lved .

The ocu la r r i g id i ty o f e n u c l e a t e d h u m a n eyes was m e a s u r e d and cor re la ted w i t h t he

v o l u m e of t he g lobe e s t i m a t e d f rom profi le p h o t o g r a p h s . A h igh ly s igni f icant co r re la t ion

was found b e t w e e n v o l u m e and r ig id i ty , which d i s a p p e a r e d i f a r i g id i ty coefficient was

ca l cu la t ed to inc lude the v o l u m e of t he eye.

2. Me t hods

The enucleated eyes used had been rejected as unsuitable for corneal grafting and had been stored in a moist atmosphere at 4~ from 1 to 16 days (mean 6"95 days). Eyes with evidence of intraocular surgery were not used. Any excess tissue was removed from the globe and a 7'5 mm diameter disc trephined from the centre of the cornea to allow the introduction of a Perspex footplate 10 mm in diameter and curved on the upper surface to approximate the curvature of the cornea. The footplate was mounted on the end of a metal tube threaded so that the periphery of the cornea could be clamped between the footplate and a Perspex collar. Two stainless steel tubes passed down the outer tube and penetrated the footplate to open into the anterior chamber. One tube was connected to a pressure transducer (Hewlett-Packard, 1280 c) and the other to a tuberculin syringe which was mounted vertically with the plunger resting on a rod connected to the core of a solenoid. Coiled springs round the plunger and rod ensured rapid advance and return of the plunger as the solenoid was activated. The length of the plunger movement could be changed by altering the springs, and the rate of cycling of the solenoid was controlled electronically so tha t repeated injections and withdrawals of 3-5 #l of fluid were made at approximately 1 sec intervals. The pressure

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141

142 E.S. PERKINS

level in the sys tem could be ad jus t ed by a fluid reservoir connec ted to the t ransducer . The pressure changes in the eye were recorded con t inuous ly on a recorder (Hewle t t -Packa rd 77024).

Ocular volume The eyes were m o u n t e d and allowed to equ i l ib ra te a t room t e m p e r a t u r e a t a pressure of

20 m m H g for 10 min before any m e a s u r e m e n t s were taken. The eyes were t hen p h o t o g r a p h e d aga ins t a whi te b a c k g r o u n d f rom below and f rom the side us ing a single lens reflex camera wi th a 30 m m extens ion tube and a 50 m m lens. A surface-si lvered mir ror was m o u n t e d in f ron t of the lens to fac i l i ta te t ak ing p h o t o g r a p h s from below. Several d i amete r s were measured on en la rged p r in t s of~he profile p h o t o g r a p h s and a m e a n d i a m e t e r used to ca lcula te the to ta l vo lume of the globe. The collar of the corneal c lamp (10 m m in d iameter ) was used as a guide to the magni f ica t ion of the pr in t . The eyes were no t perfect ly spherical b u t the m e a n of the m a x i m u m difference be tween the largest a n d smal les t d i ame te r for all t he eyes was less t h a n 1 m m (0"98 m m s.D. +0"44). The error in t roduced b y consider ing the eyes to be spherical for the purpose of ca lcula t ing the vo lume is therefore l ikely to be small. I n order to ob ta in the i n t r aocu la r volume the m e a n d i ame te r of each eye was reduced by twice the m e a n th ickness of the sclera of all eyes (2 x 0'55 mm). The vo lumes shown in Table I, are the a p p r o x i m a t e in te rna l vo lume of each eye.

Scleral thickness Scleral th ickness was measu red using a l igh t - sca t t e r ing technique. A probe was designed

con ta in ing a low- in tens i ty min i a tu r e incandescen t bu lb su r rounded by a Perspex cone 5 m m in ex te rna l d iameter . W h e n the probe is appl ied to the sclera, l ight is sca t t e red f rom the centra l area of the p robe and collected by the Perspex cone, which acts as a l ight guide. The in t ens i ty of the sca t t e red l ight is measu red by a photo-d iode af te r pass ing t h r o u g h a blue

TABLE I

The values shown are mean external diameter, calculated intraocular volume allowing for scleral thiclcness, the conventional ocular rigidity (K), a coe~cient of ocular rigidity incorporating ocular volume (k), the rate of rise of pressure in mmHg / sec during injection of fluid at a mean pressure of 15 mmHg, the age of the donor and the days after death

External Intraocular Rate of rise Days diameter (mm) volume (#1) K k (mmHg/sec) Age after death

22"7 5277 0"061 322 43"48 89 7 22"8 5350 0'065 348 55"55 89 7 23'47 5861 0'047 278 40"00 83 7 24"23 6479 0"055 356 45'45 69 2 24"46 6675 0"054 367 55"55 69 2 24-47 6683 0-036 240 58-82 22 4 24'63 6821 0"057 388 71"43 65 1 24"66 6847 0"056 383 71-43 62 16

"24"84 7006 0"045 315 34"48 101 7" 24"93 7086 0"056 396 83"33 62 16 25"05 7193 0"045 323 33"33 101 7 25-12 7256 0-029 210 23"25 32 9 25"29 7412 0"034 252 28"57 32 9 25-35 7467 0"046 343 38"46 50 15 25-35 7467 0"036 269 33"33 50 15 25"7 7795 0'035 273 38'46 71 1 26"0 8083 0"035 283 43"48 17 5 26"57 8651 0-026 225 18-87 17 5 26"58 8662 0'031 268 50'00 77 2 26"87 8961 0"032 287 30"30 77 2

OCULAR VOLUME AND RIGIDITY 143

filter to exclude red light. Calibration on 28 areas of four enucleated eyes showed a linear relationship between the amplified output of the photo-diode and measurements made with a measuring telescope after incising the sclera along the meridian measured. The correlation coefficient between the measured values and output of the photo-diode was + 0"94, and the slope of the regression line was used for calibration of the thickness measured by the probe.

This method allowed several measurements to be made rapidly on each globe and the mean of these measurements to be calculated for each eye.

Calculation of rigidity The volume of fluid injected into the eye at each cycle could be read from the movement

of the plunger of the syringe, and determinations of the volume-induced pressure rise were made at mean pressures from approximately I0 to 30 mmHg. K was calculated from the recordings using the formula logp2--log Pl = dv K, where Pl was the initial pressure, P2 the pressure after injecting a known volume dv. The rise in pressure was rapid (less than 0-1 sec) so that the results were not influenced by the normal slow leak from the eye.

3. R e s u l t s

Ocular volume and ocular rigidity

There was a highly significant negat ive correla t ion between in t raocular volume and ocular r ig id i ty (P < 0"001) measured a t a mean pressure of 15 mmHg. The slope of the l inear regression line in Fig. 1 is such t ha t for each 1 ml increase in volume the r ig id i ty decreased by a p p r o x i m a t e l y 0.01. The cons tan t K in F r i edenwald ' s formula for ocular r ig id i ty includes the to ta l ocular volume, which because i t is large in re la t ion to the volume changes in t o n o m e t r y is assumed to be the same for all eyes. F r i edenwald der ived his semi-log re la t ionship between pressure and volume from the assumpt ion t ha t the p ropor t iona l change in in t raocular pressure var ied d i rec t ly with the propor- t ional change in volume, i.e. (dp/p) = k(dv/v). Because v is large in re la t ion to dv i t was assumed t(~ be the same for all eyes and (k/v) was placed by K, the coefficient of ocular r igidi ty . In these exper iments the volume of the globe was known and k could

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Oculcr r ig id i t y ( K )

FIG. l.'The conventional coefficient of ocular rigidity (K) is plotted against intraocular volume. The straight line represents the linear regression calculated by the least-squares method. Correlation coefficient = --0'79.

144 E.S. PERKINS

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Corrected rigidity (k )

FIG. 2. In this graph a coefficient of ocular rigidity (k) incorporating ocular volume is plotted against ocular volume. There is no significant correlation.

be ca lcu la ted for each eye. W h e n this was done there was no signif icant corre la t ion be tween ocular vo lume and k (see Table I and Fig. 2).

Rate of rise in pressure

The ra t e a t which the in t raocu la r pressure rose as fluid was in jec ted into the eye was also measured from the recordings a t a mean pressure of 15 m m H g and, as might be expected , the r a t e showed a pos i t ive corre la t ion with K (0"01 > P > 0"001) and a nega t ive b u t not s t a t i s t i ca l ly signif icant corre la t ion wi th vo lume (r = - 0 " 3 6 , P < 0'01).

Age

The ocular r ig id i ty t ended to be higher in older eyes (age range 17 to 101 yr) and there was a s ignif icant corre la t ion be tween K and age (0"02 > P > 0"01).

Scleral thickness

There was no signif icant corre la t ion be tween K or the ocular volume and the mean scleral th ickness of each eye.

Ocular rigidity and intraocular pressure

I n two eyes there was no signif icant change in K a t different pressure levels and in one eye K increased by 26 % from 12'5 m m H g to 25-75 m m H g . In all o ther eyes K decreased as the level of pressure a t which i t was measured increased. The decrease in K was a p p r o x i m a t e l y 25 % for an increase in pressure of 10 m m H g over the range of 10-30 m m H g .

4. D i s c u s s i o n

These resul ts show t h a t in a series of p r e suma b ly non-pa tho log ica l enuc lea ted eyes ranging in d i ame te r from 22 to 27 m m there was a signif icant corre la t ion be tween the

OCULAR VOLUME AND RIGIDITY 145

intraocular volume and the coefficient of ocular rigidity as calculated from the conventional Friedenwald formula. Inclusion of the ocular volume in the calculation of rigidity gave a new constant which did not show a significant correlation with volume.

I t is probable therefore that the low coefficient of rigidity observed in myopic eyes depends only on their larger size, and that it is not necessary to postulate any scleral abnormality in the range of refractive errors (approximately + 4"0 D to - 10"0 D) of the eyes studied in these experiments.

The measurement of rigidity using small volume changes over short periods of time only involves the visco-elastic properties of the eye, and it is possible that larger stresses applied for longer periods, such as those used by Greene and McMahon (1979) to measure creep, might demonstrate abnormal findings in myopic eyes.

The rate at which the pressure rose as fluid was injected into the eye showed a significant positive correlation with ocular rigidity and a negative but not statistically significant correlation with ocular volume.

There was no significant correlation between K or ocular volume and mean scleral thickness as measured optically. I t is likely that more severe stresses than those imposed in these experiments would be needed to demonstrate any effect of scleral thickness on the distensibility of the eye.

Variations in ocular rigidity when measured at different pressure levels have been reported by previous workers, and the present results confirm that in most eyes K decreases as the pressure at which it is measured increases. There was no significant correlation between K and the length of time the eyes had been stored.

Although it Was not possible to account completely for all the differences in ocular rigidity in this series of eyes, the results show that the volume of the eye is one significant factor. The age of the donor played some part but the thickness of the sclera did not correlate with rigidity. I t is probable that the lower ocular rigidity of myopic eyes is determined principally by their larger volume and is no~ due to an abnormal distensibility of the sclera.

ACKNOWLEDGMENTS

I am most grateful to Mr J. Edwards and Mr A. L. Yerlett of the Institute of Ophthal- mology, London for the design and construction of the apparatus, and to the Eye Bank of the Corneal Centre, University of Iowa Hospitals and Clinics for the donor eyes.

R E F E R E N C E S

Greene, P. R. and McMahon, R. A. (1979). Scleral creep vs. temperature and pressure in vitro. Exp. Eye Res. 29, 527-37.

Honmura, S. (1968). Studies on the relationship between ocular tension and myopia. Part II. Ocular tension, ocular rigidity, aqueous outflow and aqueous secretion in myopic eyes. Acta Soc. Ophthal. Jap. 72, 74-82.

Phillips, C. I. (1971). The corneo-scleral envelope and glaucoma. Br. J. Physiol. Optics 25, 198-216.