Download Experimental tonography on enucleated human eyes. I. The

Experimental tonography on enucleated
human eyes. I. The validity of
Grant's tonography formula
7. Hclland-Eriksen and Tor Odberg
When newer tables for parameters in Grant's formula for tonography are used, one obtains
far higher values for the outflow facility than those generally accepted. The aim of this investigation has, therefore, been to test the validity of the tonography formula. The outflow
facility determined by constant-rate perfusion in enucleated eyes has been compared with the
results of tonography on the same eyes in the steady-state condition. Loss of intraocular fluid
during tonography has been measured directly by means of a new techni(jiie. Outfloiu facilities
determined according to the two methods show very good agreement. Thus, when the production of (HJUCOUS is held at a constant rate, and when there is no change in intraocular blood
volume. Grant's tonography formula is found valid, provided absolute values for P,,, P,, and
<IV are used.
Key words: tonography, tonography loimula, constant-rate peilusion, outflow
facility, facility of aijiicous outflow, enucleated eyes.
I
ably that values for outflow facility (C)
calculated according to the tonograpliic
method are in good agreement with values
ol G determined by perfusion in vivo on
the same eyes.1- ' Moreover, there is good
agreement between aqueous outflow calculated tonograpliieally and by turnover of
test substances."
This is, in tact, rather surprising, considering that Friedenwald's tables for
corneal indentation, V,., do not completely
express the total volume displacement in
the eye by tonometry,7''' and that the P,,
calibration tables (1955 scale)"' are too low
compared to applanation tonometry in the
lying position."1 '-' Furthermore, it is known
that aqueous production may decrease during tonography,''1 and that viscoelastic
characteristics ol the eye" and change in
t is commonly accepted that the tonographie method, originally developed by
Grant,1 slitters from many sources of error. -•' Nevertheless, it lias been stated that
"the tonographie technique is the most useful available for estimating the facility ol
outflow of the aqueous." 1 Becker and
Shatter1 state as well that, "in spite of the
many possible errors, careful tonography
provides a reasonable estimate of the
facility of outflow in the living eye." A
fundamental reason for saying this is prob-
From the Department of Ophthalmology, University of Oslo, Ulleval Hospital, Oslo, Norway.
This investigation was supported in pail by Anders
Jalirc's Fund for the Promotion of Science.
Submitted for publication Aug. 16, 1974.
199
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200
Hctland-Erikscn
and Odbcrg
intraocular blood volume 1 ' may influence
the tonogram.
One of us (H-E) has worked out new
calibration tallies for the total volume displacement of the eye during tonometry,
V|,s and tallies for P,, based on applanation
tonometry," together with values for the
rigidity coefficient, K, in living eyes. Using
these tables and values for K in the conventional tonography formula, one obtains
considerably higher values for C than those
commonly accepted.1" We find it justified
to search for an explanation of this, and
there are several possibilities: (1) One or
more of the new tables or values for K are
incorrect. (2) The tonography formula is
not valid. If this is true, the good agreement between outflow facility determined
tonographically and by other methods must
be due more or less to chance. (3) The
new tallies are correct and the formula
valid. This would give an outflow facility
higher than that commonly stated. It has
been calculated that C increases about 50
per cent when correction is made for K and
change in intraocular blood volume during
tonography.11' A possible decreased production of aqueous will give a measured outflow facility which is greater than the true
one. The problem of this pseudofacility is
discussed by several authors.1 '• 1T Moreover, a viscoelastic effect following application of the tonometer on the eye would
add to this error."
The aim of this investigation has been
to obtain a direct experimental test of the
validity of the tonography formula as
Grant originally wrote it:
dV
T(P,, 1 V -
I in :csti native Ofilithalmnlogy
March 1975
in the formula are known? To our knowledge, dV has ne^er been determined experimentally. Both the volume and the
pressure components in the formula are
usually calculated according to Friedenwald's formulas and tables.'" Thus, in the
experiments of Becker and Constant/' the
tonographically calculated. C is compared
to C determined by perfusion. By analysis
of pressure decay curves, Langham 18 determined C by means of the pressure-volume
relationships based on injections of fluid
into the eye, and not by means of pressure
change due to fluid displacement as in
tonography.
In an experimental model used for testing the validity of the tonography formula,
it is necessary to control the assumptions
made. The most important of these are that
the rate of aqueous production, the intraocular blood volume, and the episcleral
venous pressure do not change as a consequence of tonography.1'' It is also necessary to determine (and not calculate) all the
factors in the formula.
By building a model on enucleated eyes,
the production of aqueous can be replaced
by a continuous constant-rate perfusion, the
change in blood volume is negligible, and
the episcleral venous pressure is O. By
means of continuous registration of the
intraocular pressure the values of P,, and
P, are determined and dV can be measured
directly according to the present technique.
When the eye is in steady-state, the outflow facility is given by P,, and injected
volume per minute, and this C can be
compared to the facility calculated according to Giant's formula for tonography in
which all factors are known.
P,,)
Here, dV is the loss of intraocular fluid
during tonography, T is the time, Ptliv is the
arithmetic mean of the intraocular pressure
during tonography, and Po is the pressure
in the undisturbed eye. Our purpose has
been to answer the question: are we able,
by means of tonography and Grant's
formula, to determine the facility of outflow
when the absolute values of all the factors
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Material and methods
The material consisted of 14 ostensibly normal
human eyes enucleated 3 to 18 hours postmortem
(mean 11.5 hours). The average age was 62 years
(51 to 82 years). The eyes were immediately
immersed in a barbital-buffered solution of saline,'-'"
where they remained at room temperature for 0.5
to 2.5 hours. Then they were put in a nest of
cotton wool, with buffer up to the muscle insertions. The temperature was kept at 35 to 37° C.
Experimental tonographij on enucleated eyes
Volume \A
Numlwr 3
201
R es ervo ir
Transducer
Micrometer
syringe
Mo t or
S
"s
-^
N
>
M ii cc rr oo bbuurr e t l e
Fig. 1. A schematic illustration of the experimental setup.
mm Hg
CO
30
20
1 0
Transducer
T i me
in mm
Tonograph
Time
in m m ,
Fig. 2. A, example of a tracing of the intraocular pressure during tonography as recorded by
the transducer (eye No. 13). B, the corresponding tonograin.
The intraocular pressure was registered by a
transducer (Statham P23De) connected to a
hypodermic needle, No. 21 gauge, in the anterior
chamber through a polyethylene tube (PE 100).
The output or the transducer was fed into a
monitor (Statham SP 1400) and a recorder
(Statham SP 2000). The needle was inserted as
far back as possible, and care was taken not to
deform the cornea. The pressure in the eye could
be regulated to any desired level up to 50 mm.
Hg by means of a lluid reservoir. This was connected to the eye and the transducer by a threeway stopcock (Fig. 1). A burette graded in
microlitcrs was inserted between the eye and the
reservoir. An air bubble could be placed in the
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burette by means of a syringe. The whole system
contained barbital buffer.
The eye was perfused at a constant rate through
a hypodermic needle, No. 25 gauge, in the posterior chamber. Via a polyethylene tube (PE 20)
the needle was connected to an "Agla" micrometer syringe driven by a stepless adjustable
motor, as described by Sears.-1
Tonography was carried out with a Mueller
electronic tonometer (No. 1574, adjusted). The
tonometer handle was held by a clamp mounted
on an adjustable carriage, which was also used to
lower and raise the tonometer.
Before each experiment the transducer and
recorder were calibrated to the lluid reservoir.
202
Hetland-Erikscn
and Odberg
March 1975
Q
P,,,
0 70
0 20
0.30
0C0
c,
Fig, 3. Diagram showing the relationship between
the outflow facilities determined by constant-rate
perfiision (Ci) and tonography (G:).
Before and after the series of experiments the
tonometer was calibrated with a micrometer. Care
was taken to avoid influence by external magnetic
forces.1-1-'
The perfiision was started with rather high
speeds, and one could follow the rise of the pressure on the recorder. Then the speed was regulated in order to obtain steady-state at the desired
intraocular pressure, Pn,. Steady-state was defined
as a stable pressure for a period of at least four
minutes. The fluid reservoir was placed at the
same level, and an air bubble inserted in the
burette. During constant-rate perfiision, and with
the connection between the eye and the fluid
reservoir closed, conventional tonography lasting
four minutes was carried out. The intraocular pressure at the beginning and end of the tonography,
Pi, and P,=, could be read from the recorder.
Three to four seconds after having raised the
tonometer, the intraocular pressure, P,,.,, was
registered. Then the connection to the fluid
reservoir was opened, and the pressure immediately
rose from P,,, to P,,,. During this procedure the
air bubble in the burette moved toward the eye
and gave a direct measurement of the volume,
dV, which was necessary to restore the pressure to
pretonographic level. After closing the connection
to the reservoir, the pressure in the eye was observed for a period of three to four minutes. A
typical registration of the intraocular pressure during the experiment is shown in Fig. 2 where the
corresponding tonogram is shown for comparison.
Results
Steady-state was reached after 25 to 90
minutes of perhision. With a constant rate
perfusion of 1.9 to 6.5 /J per minute (mean
3.S), the intraocular pressures ranged between 11 and 25 mm. Hg (mean 18.5).
Only one experiment was carried out on
each eye. The outflow facility could be
determined according to the equation
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where I is the rate of perfusion and P,,, is
the intraocular pressure. In the 14 eyes we
obtained facility values between 0.11 and
0.40 /.i.I per minute per millimeter of mercury, witli an average of 0.214 (Table I ) .
Then the outflow facility was determined
tonographically using Grant's formula. The
loss of intraocular fluid during tonograpliy,
dV, was measured from 5.5 to 22.5 /.J, with
an average of 9.5. The facility values for
the 14 eyes were between 0.11 and 0.43 /A
per minute per millimeter of mercury, with
an average of 0.216. The results are shown
in Table I. The relation between the outflow facilities determined according to the
two methods is shown graphically in Fig.
3. The correlation coefficient was found to
be 0.91, and it was highly significant (p <
0.0005).
Discussion
Constant-rate perfusion is a well established method for determining the outflow
facility in enucleated eyes. In order to
calculate C according to the equation
Cl
I
=K
it is of crucial importance that the intraocular pressure is in steady-state. We have
paid particular attention to this during the
experiments. Consequently, the time of perfusion before tonography has been rather
long. Only in two eyes did the intraocular
pressure differ by as much as 1 mm. Hg
from P,,, 3 to 4 minutes after ending
tonography, and we interpret this as a
confirmation of the fact that the eye was in
steady-state before tonography. It also
supports the assumption that tonography
has not lead to any increased leak along
the cannulas. Any possible leaks would give
estimates of C too high for both perfusion
and tonography, perhaps especially for
tonography due to the ocular distortion
and higher intraocular pressure.
Our results concerning C| show good
agreement with previous perfusion experiments on enucleated human eyes, even
Volume N
Numlirr 3
Experimental tonograplnj on enucleated ci/es
203
T a b l e I. E x p e r i m e n t a l d a t a For e a c h of t h e e y e s w i t h v a l u e s for facility of
outflow obtained by constant rate perfusion ( C i ) a n d tonography ( C ( ; )
C,
Eye no.
1
o
3
4
5
fi
7
S
9
10
11
12
13
14
Mi.1 an
Infusion
(nl/min.)
2.6
3.9
fi.8
5.2
3.9
3.1
1.9
2.9
3.2
5.7
2.9
4.5
-1.5
2.3
3.8
P..,
(mm. ll<i)
20.5
15.5
20
19
15.5
22
IS
17
Hi
25
19
11
19
21
18.5
when dilferent perfusion fluids were
used.-"1 •-•"' Grant-" Found the mean outflow
facility in 116 eyes to be 0.17 at room
temperature. This was converted to 0.22
at 37° C. which is very close to the 0.214
of our results. His experiments sliowed that,
after a long period of perfusion, the facility
increased in some eyes and decreased in
others. Ellingsen and Grant-7 found a small
decrease of C after prolonged perfusion,
whereas Nihard-'"' could not show any significant change in the facility after 1.5
hours of perfusion.
We have not been able to find previous
publications concerning tonography were
dV has been determined directly. With our
method, we measure the volume which is
necessary to raise the pressure from P,,._.,
the intraocular pressure immediately after
tonography, to P(l|, the pressure before
tonography (Fig. 2). In order to obtain a
reliable registration of the post-tonographic
pressure, we waited three to four seconds
before measuring dV. During this period
a certain amount of inflow and outflow
has taken place, but in such small quantities that collections seemed unnecessary.
In the tonography formula dV is a measure of the reduction of intraocular fluid
as a consequence of tonography. Considering the eye as viscoelastic, as discussed by
McEwen,11 tonography will cause a timedependent relaxation of the coats of the
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<IV
(4)
8
9.5
11
10.5
11
7.5
fi
7
7.5
8.5
fi.5
22.5
11.5
5.5
9.5
(til/min./
mm. H<i)
0.13
0.25
0.3-4
0.27
0.25
0.14
0.11
0.17
0.20
0.23
0.15
0.40
0.24
0.11
0.214
Co
(fil/min./
mm. Hg)
0.18
0.22
0.30
0.24
0.20
0.22
0.11
0.18
0.18
0.24
0.14
0.43
0.27
0.11
0.2 lfi
eye. This stress relaxation would act as a
leak from the eye, and our determinations
of dV would then give values which are
too high. The extent of this fault is difficult to assess, but presumably it is not
great.-'"
Ptill in the tonography formula has been
determined as the arithmetic mean of the
intraocular pressure at the beginning and
end of tonography. This seems to be permissible as long as the pressure decay
curve is approximately linear, which is the
case in our experiments on enucleated eyes.
It is also the easiest way to determine
Pi in , and the way Grant did it.
Our experiments show remarkably good
agreement between the outflow facility determined according to constant-rate perfusion and to tonography. This indicates
that one really is able, by means of tonograpliy and Giant's formula, to determine
the outflow facility in enucleated eyes,
at least in the normal range of pressures.
Thus, the tonography formula is found
valid under the particular assumptions previously mentioned, and when the absolute
values For dV, P,,, and P, are used. Recent
investigations11 '-' imply that Friedenwald s
values for P,, are too low, and if this is
true, they will give values For outflow Facility determined according to Grant's Formula which are too low. This will also be
the case if their values for dV are too
204
Hetland-Eriksen
low. Friedenwald's formula tor the loss of
intraocular fluid during tonography will be
discussed in our next paper.
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