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New methods of measuring the rate of aqueous flow in man with fluorescein
Eze2tl Eye Res. (1966) 5, 208-220
N e w M e t h o d s o f measuring the R a t e o f Aqueous F l o w in M a n with Fluorescein ]-~. F . JON-ES AND D , M. MAURICE
De2ag't,ncnt of Physiology, I~stztute of Ophth.almology, J~ald Street, Lon~ton IV.O.1, En!Ila.nd (Received d A't),il .1966) Two methods of dete,'lniaing the rate of loss of fluorescein from the ~queous humour in lno~n are described. The dye is introduced into the cornee~ by mesas of iontophoresis ~md estimated in the eye with the slit.lamp fiuorophotomoter. In the first mcthod'l, he time course of the fluorescein coneen~rat[oll .in the ,%ntcrior chaunter is obse~wed, from which its turnover rate in t h e ehr~mber is derived.-.] n the second me,,hod measurements of/the ratio of the total fluorescence of tl~e eye to tha.t of the aqueous humo~,r le~d to a direct, evMudtion of the aqueous flow r~te. The errors and limibr~gions of t.he methods arc discussed and it is cottelucled that. the seemtd method, though generally more reliable, is inapplicable to blue-eyed s u b j e c t . In ot.her cases vhcre is good accordance b e t w e e n t,l~e results obtained by t.he gwo metho(Ls. I n a smMt group of young norm,M volunteers the mean turnover rate found by l,hc first method wan 0-015 rain and t h e niean rate o f flow by the second, method 2.5 td~tnin.
I. Introduction T h e idea of using t i l e changes with time of the concentration of fluorescein in the anterior chamber as s. Ineasure of the rate of flow of the aque0u.s hltmour has had a long currency; It-was first 13ut on ~ sound theoretic~d ba~is by O o l d m m ~ n (1950), w h o injected iluorescein intravenously Jn r~bbits and man, and measured the time course of th.e.fluorescence in t/he blood" a.ud t~|m a,tterio~ chamber using his slit-lamp flu0rophotometer. This ,nethod, though it results in satisfactory estimates of the flow rate in man, suffers from two disadvant;tges--frequent blood samples have to be obtained f r o m the patient, and a rather complex nlathematical treatment of the results is necessary to derive-the required value. A shnilar method published by L a n g h a m and Taylor (1960)is. open t.o the same objections. L a n g l e y a n d M a c D o n a l d (1952) a p p e a r t o b e t h e f i r s t to ]lave s u g g e s t e d s t a i n i n g t h e c o r n e a so t h a t %he d y e e n t e r e d t h e a q u e o u s h u m o u r a c r o s s t h e c o r n e a l e n d o t b e l h n n . T h o u g h t h e y s h o w e d t h a t q u a l i t a t i v e l y , t h e f l u o r e s e e n 0 e o f tile a q u e o u s h u m o u r c h a n g e d in t h e m a n n e r t o b e e x p e c t e d , t h e y d i d n o t i n v e s t i g a t e t,h e p o t e n t i alit.ies o f t h e i n e t h o d v e r y i n t e ~ s i v e t y n o r d i d t h e y a t t e m p t t o p u t it o n a q u a n t i t a t i v e basis. ~ V e e k e r s a n d D e l m a r c e l l e ( 1 9 5 3 ) a t t e m p J c e d a q u a n t i t a t i v e t r e a t m e n t b u t - l e f t i t v e r y i n c o m p l e t e . A m o r e t h o r o u g h st.udy s h o w s t h a t t h e v a l u e s t h e y e x t r a c t e d r e l a t e m o r e t o t h e P e r m e a b i l i t y o f t h e . e n d o t b e l l u m t h a n t o t h e r a t e o f tlm a q u e o u s f l o w . I n t h i s p a p e r , t w o d i s t i n c ~ m e t h o d s o f m e a s u r i n g t h e r a t e Of a q u e o u s f l o w i n m a n b y m e a n s o f f l u o r e s c e i n a p p l i e d t o p i c a l l y a r e d e s c r i b e d . B o t h d e t e r m i n a t i o n s m a y be c a r r i e d o u t in. t h e c o u r s e o f a s i n g l e e x p e r i m e n t ; One g-ires t h e t~urnover r a t e o f f l u o r e s r e i n in t h e a n t e r i o r c l m m b e r , a n d t h e o t h e r l e a d s d i r e c t l y t o t h e flow r a t e o f t h e a q u e o u s h u m o u r . T h e i n v e s t i g a t i o n h a s b e e n c o n c e r n e d so f a r o n l y i n e s t a b l i s h i n g t h e va.l~ditv and limitations of the methods, and has been restricted to normal vohmteers. 208
A Q U E O U S F L O W I N MAN
209
2. Theory
Method .1 I t will be assumed that, t h e excha.nges of fluorescein b e t w e e n t h e c o r s e s a n d tlie blood at the l i m b u s . a r e ,egligib]e, and t h a t the e x c h a n g e s b e t w e e n the c o r n e a and a q u e o u s h u m o u r and b e t w e e n Qle aqueous h u l u o u r ~md t h e blood obey simple first-order d y n a m i c s . Then we m a y write for t h e e x c h a n g e b e t w e e n t h e cornea and "aqueous h u m o u r : dC° - - l%.c,,(Ca - C~) dt
(l)
where k c,~,. is tile transfer coefficient fi'Olll the c o r n e a ~o the aqueous, referred to the v o l u m e of the cornea [ D u k e - E i d e r a.nd Mauriee, 1957), a.nd C a a~ld Cc a r e . t h e effective a q u e o u s and corneal c o n c e n t r a t i o n s of fluorescein. If it is assumed t h e c o n c e n t r a t i o n in t h e blood is negligible, t h e c o r r e s p o n d i n g e q u a t i o n for t h e aqueous h u m o u r is: cl C~,£
.,
-
--
l
t
.
~.oC,,+.k~.~,,(O~-- C,)
,
dz
(2)
-where/"o is t h e loss coetficient from tile a n t e r i o r c h a m b e r and k,.c~~ is t h e corneM trafisfer coefficieut referred to t h e x-olume of *.Ira a n t e r i o r c h a m b e r . If the a q u e o u s h u m o u r is free of fluorescein at. zero ~ilne, the solution of these differential equations has t h e form:
C',
=
C.~(e.--"'--e-~")
(31
where t is the time, C.~ is a. c o n s t a n t d e p e n d i n g on the initial degree of s t a i n i n g of t h e cornea, and A and B are given by: (4).
A ÷ B = k o . , . + ~;,. ~,,'. ko
and
A.B = Z-o I,,~.~.
(5)
For the c o r n e a t}l~ e q u i v a l e n t e q u a t i o n is:
C~--
Ca ~tl J O.¢t
~(B_k~.,,.o)e_.,,_(A_kc.c,,)e_n,~.
[
(6)
J
The shape of these curves: ,as plo~ted, on semi-logarithmi 0 paper, is shown in Fig.-i. The
C,, curve is built "up of two s t r a i g h t lines of slopes A and B in t h e nit%Ill-tot SllOWlI. i long time a R e r beginning of t h e e x p e r i m e n t , w h e n t h e effect of the B e x p o n e n t i a l has died out, the s l o p e A is g i v e s by: A - - --,.lO~ _ C6dt
-d6'~ (?odg
(7)
At, the s a m e t i m e t h e ratio Ce/C,,~ becomes c o n s t a n t a n d will b e d e n o t e d d~a. D i v i d i n g -equation (1) b y Cc t h e n , i t follows: A k.c.c~- 1--(1./de.)' Finally, from e q u ~ i o n s (5) a n d (8):
(8)
,.o--O(,-;)
If B ariel a~c~ can be experimentally d e t e r m i n e d it,-is possible to find
k o,
L e t F a and F c
210
R.F.
JONES
AND
D.
M.
MAURICE
be the actuM fluorometer readings corresponding to Ca and C~. At equilibrium when C, = Co, let the ratio F J F a be denoted rta, so t h a t
Fa__ F° ca c o "r a. On t h e d e s o e n d i n g p a r t of the curve, when Cc/C ~ takes up the value dca, let F d F a correspondingly take up t h e value go,. Then: d c~:
- -
(l;)
~ca
by equation (10). F r o m equations (11) and (9)
(12)
k o ----- B ( l _ _ r ~ . \ g*~/ I000
100
IO
%
o
t
1
t
I
I
r
,
2
3
4
5
6
Time'
F I Q . I . C u r v e s s h 0 w i n g ~ h e o r e t i c a l c h a n g e s iR f l u o r e ~ c e i n c o u o e r t S r a t i o n wi~h t i m e , a f t e r [Ls i n t r o d u c t i o n i n t o t h e c o r n e a . Ca a n d C, r e p r e s e n t e f f e c t i v e e o n c e n t r a t l o u s in t h e a q u e o u s h u m o u r mad c o r n e a a n d m t t h e t o t a l a m o u n t i n t h e e y e . Ordinate: l o g a r i t h m o f c o n c e n t r a t i o n o r m a s s o f f l u o r e s c e i n in a r b i g r - r y u n i t s . Abscissa: t i m e a f t e r d y e e n t e r s c o r n e a . :Each c u r v e is m a d e UP o f t w o e x p o n e n t i a l c o m p o n e n t s : a s l o w o n e (A) a n d a f a s t o n e (B). T h e B c o m p o n e n ~ is r e l a t i v e l y l a r g e s t in t h e a q u e o u s h u m o u r c u r v e a n d is d e r i v e d in p r a c t i c a l b y s u b t r a c t i n g t h e c u r v e o f C,, f r o m t h e b a c k w a r d p r o l o n g a t i o n o f t h e A l i n e .
The tr~mfer coefficient out of the eye /co has two parts, one the outflow coefficient kI w h i c h represents the loss of fluorescein from the anterior c h a m b e r by drainage of aqueous humour, a n d the other, t h e diffusion coeific[ent k d which represeuts t h e exclmnge by diffusion a c r o ~ the iris, s o t h a t ko-~ k1+.k,i. (13) :FrOm t h e experiments of G o l d m a n n (1950) it appears t h a t ilx the n o r m a l eye ~:a is, at most,, o n l y o n e : t e n t h p a r t of ]co and probably a considerably smaIler fracLion. For this reason l%will be referred to as t h e flow c o n s t a n t in w h a t follows, a n d 1%V,,, where V a is the volume of the anterior chamber, will be Called the rate of flow, t h o u g h it m u s t be borne in m i n d t h a t this is an approximation.
AQUEOUS
:FLOW
IN
MAN
211
Method 2. If,m~ is t h e t o t a l m a s s o f fluorescein in t h e a q u e o u s a n d c o r n e a , t h e r a t e a t w h i c h it leaves t h e e y e is g i v e n b y dmt/dt. S i n c e it is a s s u m e d t h a t t h e d y e is lost f r o m t h e cornea 0nly b y w a y of a q u e o u s h u m o u r , a n M t e r n a t i v e e x p r e s s i o n for t h e r a t e of loss o f i~s mass is - - C , V , k o. T h e r e f o r e drn~ __ dt
(14)
. C.V.4,
D i v i d i n g b o t h sides b y m~ leads to: A
--
C
V.ko
after the B e x p o n e n t i a l has d e c a y e d . T h e n :
V~ko ~ A m t
o.
Am~
or
(15)
w h e n f is t h e a q u e o u s flow r~te, Therefore, b y m e a s u r i n g t h e slope, A, a n d t h e ratio, mffCa, t h e flow r a t e m a y be o b t a i n e d directly. I t is of i n t e r e s t f u r t k e r m o r e t h a t : mt
--~ Tr~Oa-b VcOc
(16)
where Vc is t h e effective v o l u m e of t h e c o r n e a , so t h a t f r o m e q u a t i o n s (3), (6) a n d (16), and r e m e m b e r i n g : it follows:
V,~CA (Be_A~
Ae_~: )
(17)
This c a r v e is p l o t t e d in :Fig. 1.
3. Methods ln~roduction of fl~m~'escein B y m e a n s of i o n t o p h o r e s i s , a d e p o t of fluorescein w i t h s h a r p l y defined b o u n d a r i e s was inl;roduced i n t o t h e cornea, o f t h e e y e to be examimed. T h e e l e c t r o d e c o n s i s t e d of a w i c k Of 2 ~/~ a g a r gel, 4 m m in d i a m e t e r , m a d e u p a s e p t i c a l l y in 10 ~/o f l u o r e s c e i n Solution a n d c o n t a i n i n g 0"1~/o m e t h y l h y d r 0 x y - b e n z o a t e as a p r e s e r v a t i v e . T h e a g a r w a s e x t r u d e d from a plastic t u b e b y c o m p r e s s i 0 g i t w i t h a c l a m p (Fig. 2). T h e e n d of t h e e l e c t r o d e was blotted w i t h sterile filter p a p e r to a b s o r b all free fluid. T h e c o r n e a w a s anaesthetized, w i t h novesine, a n d t h e e l e c t r o d e w a s a p p l i e d to t h e u p p e r h a l f of its surface, s o m e 3 m m c l e a r of the limbus. A c u r r e n t of a b o u t 200/~n w a s p a s s e d f o r 10-15 scc. Several a d v a n t a g e s a c c r u e f r o m r e s t r i c t i n g She s t a i n e d a r e a in t h i s way. :First; an u n s t a i n e d a r e a o f c o r n e a is l e f t in t h e l o w e r h a l f t h r o u g h )vhich o b s e r v a t i o n s on t h e initial weak fluorescence of t h e a n t e r i o r c h a m b e r m a y be m a d e w i t h o u t d i s t u r b a n c e f r o m t h e strong g l a r e of t h e reservoir of d y e. S e c o n d , a n y e x c h a n g e of f l u o r e s c e i n : w i t h t h e l i m b a [ circnlation will be v e r y m u c h r e s t r i c t e d i n t h e first few h o u r s of t h e e x p e r i r n e n t . T h i r d , there is no s t a i n i n g o f t h e lid m a r g i n s , a n o c c u r r e n c e which can give rise to difficulty in m e a s u r i n g t h e t o t a l fluorescence of t h e e y e i n t h e l a t e r s t a g e s .
212
g.
F.
JONES
Al~D
D.
)17. ] ~ [ A U R I C E
N o n e of t h e s u b j e c t s suffered aI~y discomfort, or h a r m f r o m t h e ~ p p l i c a t i o n of the elect r o d e . C o n c e n t r a t i o n s of fluoreseein m o r e t h a n 100 t i m e s grea~er t h a n t h o s e d e s c r i b e d h e r e h a v e r e g u l a r l y been p r o d u c e d in t h e c o r n e a s of rabbits w i t h o u t a n y e v i d e n t r e a c t i o n to t h e dye. I t was also n e c e s s a r y t o establish t h e r a t i o .of t h e tluorescein c o n c e n t r a t i o n s in t h e c o r n e a a n d a q u e o u s h u m o u r in t h e s t a t e of e q u i l i b r i u m , rc~. F l u o r e s c e i n was s w a l l o w e d in capsules of 200 rag, u s u a l l y a t b e d t i m e , on .rising, a n d e v e r y s u b s e q u e n t h o u r for several hours. To a c c e l e r a t e t h e d e t e r m i n a t i o n of t h e e q u i l i b r i u m value, a d r o p of 10 °/~ ltuorescein was i n s t i l l e d once or tWiCE i n t o one eye, so t h a t t h e c o r n e a l c o a e e a t r a t . i o n a p p r o a c h e d t h e c o r r e c t level f r o m a b o v e on one side a n d below on t h e o t h e r . T h e i n g e s t e d d y e app e a r e d to b e e x c r e t e d q u a n t i t a t i v e l y in t h e u r i n e . S
220K - - ~
45V +
1"~'io. 2 . . ~ I e c t r o d e a n d circuit u s e d for i n t r o d u c t i o n o f fluorescein into the eve by iontophorcsis. F, :Fluorescein-saturatcd a g a r gol; .S, silver wire; .[, indifferent electcode; C, c l a m p e.xbruding get f r o m plasgic tube.
Measurements of fl~oresceqace T h e determ~nut.ions w e r e m a d e w i t h t h e f l u o r o p h o t o m e t e r of M a u r i c e (19(~3), a n d r e a d i n g s t a k e n from t h e a q u e o u s h u m o u r a n d c o r n e ~ as d e s c r i b e d in that, paper. :I1~ t h e f o r m e r case t h e w i n d o w w a s placed on t.he l o w e r halt~ of tile i a l a g e of t h e c h a m b e r , m i d w a y b e t w e e n t h e c o r n e a alxd lens. F o r d e t e r m i n a t i o n s of t h e t o t a l fluorescence of t h e a n t e r i o r s e g m e n t , t h e i n s t r u m e n t was m o d i f i e d to p r o j e c t a 12 m m d i a m e t e r circle of blue light o n t o t h e eye. T h e slit of t h e l a m p was r e p l a c e d b y a c i r c u l a r a p e r t u r e a~ld t h e o b j e c t i v e by a s u i t a b l e l o w - p o w e r e d lens. C o r r c s p o n d i u g i y : t h e p h o t o m e t r i c m i c r o s c o p e was c o I l v e r t c d to a telescope b y t h e USE of a l o w - p o w e r e d o b j e c t i v e lens, a n d in this case the largc s q u a r e w i n d o w was f o u n d to be t h e c o r r e c t size, t h a t w h i c h exa.ctly f r a m e d t h e imn.ge of 5lie circle of light. T h e a n g l e b e t w e m l t h e a r m s of ).he s l i t - l a m p wa.~ r e d u c e d as far as possible so t l m t both optical s y s t e m s w e r e a l m o s t paralle], point:ing a t t.he eye. T h e s u b j e c t res~ed his h e a d a g a i n s t a n a d j u s t a b l e suplaort so t h a t t h e corneal s u r f a c e was fLxed a.t a s t a n d a r d dist, ancc, a p p r o x i m a t e l y 0-5 m, froln t h e i n s t r u m e n t . T h e e n t i r e c o r n e a was exposed, e i t h e r b y t h e s u b j e c t ' o p e n i n g his eyes v e r y ~dde or, m o r g u s u a l l y , b y t h e lids being h e l d a p a r t . T h e circle of l i g h t was t h e n s h o n e onto t h e c o r n e a an¢]~ if ii h a d p r e v i o u s l y b e e n ' b r o u g h ~ into register with I/be w i n d o w , t h e r e a d i n g could be t a k e n ill a few seconds. :Readings of t h e t o t a l fluorescence a n d t h a t o f t h e a q u e o u s h u m o u r w e r e taken, before the- i o n t o p h o r e s i s t o e s t a b l i s h t h e b a s e l i n e , t h e n g e n e r a l l y a.t e v e r y 15 mi.n for t h e f i r s t h o u r or two, a n d t h e r e a f t e r a t longer i n t e r v a l s . T h e r e a d i n g s were c o n t i n u e d u n t i l t h e e n d of t h e w o r k i n g d a y , a n d t h e r e was u s u a l l y sufficient fluorescein p r e s e n t in tlm eye for t h e m to be r e c o m m e n c e d t~he n e x t m o r n i n g a n d carried, on, a t l e a s t a s far as t h e a q u e o u s w a s c o n c e r n e d , t h r o u g h o u t t h e s e c o n d d a y . T h e d y e was n o t sufficiently u n i f o r m in dist r i b u t i o n t h r o u g h o u t t h e c o r n e a for m e a n i n g f u l r e a d i n g s to be t a k e n f r o m it u n t i l t h e end o f t h e first d a y . D e t e r m i n a t i o n s of t h e v o l u m e of ~he a n t e r i o r c}mmber w e r e m a d e by a p h o t o g r a p h i c m e t h o d ( t o n e s a n d M a u r i c e , 1963).
A Q U E O U S :FLOW I1N" M:AN
°13
Sta~dardization The ratio of t h e fluorometer readings obtaialed for t h e total a n d aqueous fluorescence at any m o m e n t , Ft and Fo, must, be converted to the ratio of the values of ,nt and Ca for use in equation (15) of t h e second m e t h o d . A conversion factor S is introduced So t h a t
mt C~,
S Ft -if-,"
To obtain the value of ,~, readings are t a k e n by the ~taad.ard procedure on a solution of fluorescein c o n t a i n e d in an artificiM anterior c h a m b e r formed anteriorly by a ~ra~sparent plastic contact lens of 8 m m radius of cuxvature arid l I m m diameter, and posteriorly by a sheet of black plastic. For such a shell ~n' __dt_.= lrs Co where V~ is the volume contained within it, which can readiiy be d e t e r m i n e d by weiglfing. Then:
for the readings, F,~ and F~, taker, on the shell. Two chambers were constructed, one with a flat, a n d one with a hollowed o u t rear wall, t.hat c o n t a i n e d 115 and 180/xl. They were filled with fluorescein solutious of various concentrations and, after subtracting the background fluorescence when filled with water, S was found to be the same for both shells and c o n s t a n t up to a concentration of nearly 10 -s g/ml. A~y difference in the distribution of the dye within the artificial c h a m b e r and the eye should not be important, for it is found t h a t the reading given by a fluorescen6 spot does not. vary m a r k e d l y according to its position within the illuminated circle. Again, different refract.ire indices of the plastic a n d the cornea should n o t create arx error in c,q as was shown both by theoretical considerations, a n d b y wetting the outer surface of the artificial chamber when no changes in F~ or F~ tool< place. 4. Results
Ge~wral The p r o c e d u r e h a s been t e s t e d on n u m e r o u s subjects, n o n e of w h o m has f o u n d i t troublesome. Occasionally, diffieulby has b e e n e x p e r i e n c e d in o b t a i a l n g r e a d i n g s when t h e r e was a v e r y n a r r o w p a l p e b r a t fissure or p o o r m a i n t e n a n c e of fixation. I n t h e b c s t cases (Fig. 3) t h e con s! s t e u c y of t h e re~ulgs was r e m a r k a b l e ; irt ttm worst, the readings, p a r t i c u l a r l y o f t h e a q u e o u s fluorescence, w e r e so v a r i a b l e t h a t t h e r e s u l t s were Unusabte--Zin o n e s u b j e c t F , : d o u b l e d i t s v a l u e ia 5 rain. T h e i m p r e s s i o n was gah~ed, t h o u g h ' i t is b y n o m e a n s c e r t a i n , t h a t t h e b e t t e r c u r v e s w e r e o b t a i n e d w i t h subjects of p!a:cid t e m p e r a m e n t a n d w i t h eyes h a v i n g d e e p a n t e r i o r chambers.
Method J The a q u e o u s c u r v e in t h e b e s t c a s e s c o n f o r m e d v e r y w e t l to t h e d o u b l e e x p o n e n t i a l e q u a t i o n (3), as s h o w n b y t h e fig of t h e s t r a i g h t lines to t h e ~TMues Of/7~ (Fig. 3(a)). This s u p p o r t s t h e v a t i d i t y of t h e assuxnptiorm m a d e i n d e r i v i n g tiffs equatioll, a n d justifies t h e a p p l i c a t i o n of t h e s a m e a n a l y s i s to leas p e r f e c t e x p e r i m e n t a l d a t a . .Mos t s u b j e c t s s h o w e d a r a t h e r e r r a t i c cou~.se in F~, p a r t i c u l a r l y i n t h e earl)5 m o r e ~mportant, stages. MucJa of t h i s was d u e t o u n e q u a l d i s t r i b u t i o n of t h e d y e - - w h i c h
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was seen to be more concentrated in the aqueous humour failing down the inner face of the cornea through convection. I n some subjecLs, Vigorous shaldng of the head, or side to side movements of the eyes, produced a more uniform distribution and ~ better reading. E v e n when this was successful, unexplained variations from the smooth theoretical curve frequently occurred. To carry out the exponential analysis, it was effort better to obtain the value of ~he slope A from the//'t curve and adjust the line t o / i v among the/P~ points. The point of intersection of the two straight lines, A and B, may be fixed without difficulvy, and
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F~o. 3. E x p e r i m e n t a l v a l u e s o b t a i n e d f r o m d a r k e r - e y e d subjee~ (l~.K:~ in T a b l e 1). (a) F l u o r e s e e i n i o n t o p h o r e Z s i n t o l e f t c o r n e a ~ 10.0 a.na. T r i a n g l e s r e p r e s e n t •-readings o f tot,M f l u o r e s c e n c e o f t h e e y e . Circles a n d s q u a r e s r e p r e s e n t r e a d i n g s o f fluorescemee in t h e a q u e o u s h u m o u r a n d c o r n e a l s t r o m a , r e s p e c t i v e l y , a s c o m p a r e d t o a s o l u t i o n o f S t a n d a r d c o n c e n t r a t i o n . Crosses d e r i v e d b y subtrz/c~ion o f e x p e r i m e n t a l a q u e o u s humottr, v a l u e s f r o m s t r a i g h t l i n e t h r o u g h p o i n t s a~ l a t e r t i m e s . 'Pae e u r ~ e d r a w n t h r o u g h ~he rn~ p o i n t s ha~ a . s h a p o d e t e r m i n e d b y e q u a t i o n (17) u s i n g t h e coe~t~unts d e r i v e d f r 0 m t h e _wa c u r v e . {b) C o n t i n u a t i o n o£ previoa~s e x p e r i m e n t or, s e c o n d d a y . I n o r d e r to d e t e r m i n e s t e a d y s t a t e , s u b j e c t s ~ a i . l o w e d 200 r a g . c a p s u l e s o f fltmreseeiu a p p r o x i m a t e l y hotlrl~- f r o m 8.0 a . m . F i l l e d i a s y m b o l s cortes. p o n d to v a l u e s o b t a i n e d fro m r i g h t e y e . S y m b o l s d i v i d e d h o r i z o n t a l l y represenV differer, ee o f ~ a t u e s f r e t s t w o e y e s , t h o s e d i v i d e d v e r t i c a l l y t h e a v e r a g e v a l u e o f &we. eyes. L i n e s a r e p r o l o n g a t i o n o f t h o s e d r a w n in (a). T h e y f a l l a m o n g d i f f e r e n c e p o i n t s a s w o H d b e p r e d i c t e d .
to establish the slope 13 i t is necessary only to determine one:other p o i n t upon •it with accuracy, f o r th]~ ireason; particular attention was paid t o the readings Jn t h e period 1--2 hr after the iontophoresis, I n spite of the irreb~llarities, i_n nearly every case a stra4ght tine:couldbe drawn through: the different p o i n t s ; at least t o the satisfaction of the experimen~r, and the independent:estimates of the two authors were i n good agreement.
A Q U E O U S J~'I.,OW JN 3[AN
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To o b t a i n ~he value of X:o from the slope B ~t m u s t be mul~ipli6d b y the f a c t o r ( 1 - r,,/dc,,) a c c o r d i n g to e q u a t i o n (12). Since the fl'action .rc,,/g~, is f o u n d to h a v e a value, a b o u t 0'1, s m a l t c o m p a r e d w i t h u n i t y , n e i t h e r go,, nor re,, need be m e a s u r e d w k h ~neat acc, uracy. T h e formcr is o b t a i n e d d u r i n g t h e course of t|m e x p e r i m e n t ; but sops.rate d e t e r m i n a t i o n s ~re n e c e s s a r y for the latter. ~Vben the d y e is h~geste& according to the schedule described curlier, t h e p l a s m a level oscillates b u r ~he conc e n t r a t i o n in the a n t e r i o r c h a m b e r a t t a i n s a. level which does not, undecgo measur~tbt.e v~,riations. T h e a c l d e v e m e n t of c o m p l e t e e q u i l i b r i m n between aqueous ]:tttraoilr a,n d co,'ne~t is v e r y slow, b u t by a p p r o a c h i n g it .from botlt sides a sumcienzly close ~tpproximat.ion m a y be obtaitled i n a few hours (Fig. 3(b)). i n four subjects, the v a l u e of re,, was fottPxl to lie between 1-1 a n d 1.3; it was not. considered necessary to c a r r y o u t t:he d e t e r m i n a t i o n s in all cases, bu.t a value of 1..2 was d e e m e d to be appropriate.
Method 2 The b a c k g r o u n d t o t a l fluoresc, enee of l~he hun~tatl a n t e r i o r segment, was of the order of 0-02 /zg of fluoresce|n, a n d a b o u t 50 t i m e s t h i s a m o u n t was inbroduced b y iont, ophoresis. T h e aurofluorescence of t h e selera was v e r y mucia higher t,han of tim cornea, so t h a t f r e q u e n t l y t h e r e a d i n g w i t h l;he circle of l i g h t c o r r e c t l y in posit;ion o~z the eye was a m i a i m m r t x,alue r a t h e r t h a n a m a x i m u m . J?or tocsin-dark-eyed people, tam I'~ x,a.lues followed a smoovh curve thai, h a d a s h a p e am'cein_- with t h a t given by e q u a t i o n (17), ii~ which Values of A a n d B dec{veal f r o m the ~':,, c u r v e were i n s e r t e d (Fig. 300)- 'J?he d c t e r m i n a t i o ~ of t,he slope. A a n d t~he ral~io t'jF~ p r e s e n t e d tittle diffienlty i n - m o s t cases. .Be~bre t h e values of t h e flow r a t e could be c a l c u l a t e d t h e effect of three possible sources of error h a d to be assessed. These were (1) Lhe r e t u r n of t.ight f r o m t h e iris, (2) a c h a n g e in t.he fluorescence of fluoreseein caused b y t h e c o r n e a l tissue, a n d (3} t},c loss of t h e d y e d i r e c t l y from tim cornea to ~he blood a t t h e limbus. (1) Y.ris ~'ejtecta¢we. The r e a d i n g Ft m a y be increased a b o v e its t r u e v a t a e because the posterior .lace of the a n t e r i o r c h a m b e r does n o t absort? all t h e 4ight. falling a p o a it, as in the case of the c a l i b r a t i n g ch ambers. The green l i g h t e m i t t e d b y t h e fluore~seein rna.y be s e a t t e r e d by t h e iris d i r e c t l y to t h e p h o t o m e t e r , or some of the i n c i d e n t blue ligh~ m a y be .returned t h r o u g h t h e a q u e o u s h u m o u r - a n d cornea to e x e i t e f t u : t ; h e r fludreseen.ee. Whe~a t h e fluorescein is first io.troduced in.to the e y e b y iont.ophoresk% it is remote f r o m t h e iris a n d ~he influence of this bissue s h o u l d be small; as it diffases thi-oughou6 t h e a n t e r i o r c h a m b e r a n d to t h e p e r i p h e r y of t h e cornea, t h e effect of t h e s c a t t e r i n g s h o u l d rise to a maxinxtma. A n init.ial rise o r a.n e x t e n d e d flat p o r t i o n to t | i e ]~', curve is, in fact, feared irt b l u e - e y e d s u b j e c t s (Fig. 4).'Browr~ eves a n d i n t e r mediate s h a d e s (grey: green, h a z e l ) : d o n o t a p p e a r to be seriousl,,- affected b y this source of error, as show~ by" t h e eouformit.) o f t h e F~ Curves t o e q u a t i o n (17) a n d by: other evidence to be discussed later. No p r a c t i c a b | e w a y was f o u n d of e v a d i n g this source of error in pate-eyed subjects, and t h e m e t h o d , insofar as it m e a s u r e s the a.bso) lute rate of flow~ is i n a p p l i c a b l e to t h e m . {2) Corneal que.nchi~ 9. [[1~is possible ~hat t h e cornea} tissue e x e r t s a n e f f e c t on t h e fluoresce~n w h i c h p e r m e a t e s i t so ~;hat its fluorescence is s o m e w h a t quencfied, This would Iead t0. an u n d e r e s t i m a t e of t h e v a l u e of F~ a n d a c c o r d i n g l y of:/'. This., w a s invest-igated, in. a n i m a l eyes, b y c o m p a r i n g t h e t0t~al fluorescence of a s t a i n e d corneal disc w i t h t h a ~ ; of t h e fluoreseein after it h a d been le-ached Out of t h e tissue. The e x p e r i m e n t was carried o u t as folloWs (l?ig. 5). T h e f l u 0 r 0 m e t e z w a s a d a p t e d as if to measure/~'t i n t h e eye a n d was foot'sea, by" m e a n s o f reflect'lenin t~he hypot, e n a s e
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was held in ]t h. e correct p o. s i t i o n by moans of a b l a c k e n e d ring cemented to t h e sm'faee. • . . . W a t e r wad"placed w i t h i n t h e ring to r e d u c e d reflections from t h e b o t t o m of t h e 15ube. T h e tissue ~ a s o b t a i n e d from t h e eye of a rabbih whose corn.ca h a d been s t a i n e d w i t h f l u o r e s e e i n t h e pre%,ious evening. The a n i m a l was Mlled, ~he corneal e p i t h e l i u m
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F r o . 4. Exl)erimer~t,M v a l u e s o b t a i n e d f r o m b l n e - e y e d s u b j e c t (M.t'4. i n T ~ b l c . l ) . Dei~ails a s in .Fig, 3(a),
scraped 0ffi t h e cornea excised and ~ disc of tissue, 6 ram. in d i a m e t e r , quickly p u n c h e d f r o m it. T h i s was pliieed in .the b o t t o m of a t u b e u n d e r 0.2-0-5 ml of physiological Saline b u f f e r e d at p H 7. Measurements. of t h e t o t a l fluorescence, were m a d e immedia t e l y a n d ~fter 24 hr, w h e n t h e d y e had leached o u t i n t o t h e b a t h i n g fluid. I d e n t i c a l m e a s u r e m e n t s were c a r r i e d o u t on all u n s t a i n e d disc of cornea from ~he obher.eye, submergqd in an equal v o l u m e o f dilute buffered flu0rescein solu~;ion. T h e t o t a l fluorescence of. b o t h s p e c i m e n s w a s f o u n d to h a v e increased a~ t h e end of 24 hr, a n d this could be ascribed %o a n a v e r a g e lengtt,ening of the p a t h of the |ighg t h r o u g h t h e fluoreseentisolu~ion a.s a result of its s c a t t e r i n g b y the swollen, cloudy, cornea, l n five stained c o r n e a l discs the tots.1 fluorescence rose t o . l t 4 ° / o of its o.rigin~l vahie, and. in t h e fix;e unstrained controls to 112.%. A.s a f u r t h e r c.heck, e a c h c o r n e a was. d i s s o l v e d b y a d d i n g a small drop of c o n c e n t r a t e d t e t r a m e t h y l a m m o n h ~ m hNdroxide to t h e t u b e a n d a.llowing it to s t a n d for a f u r t h e r 24 hr. The fluorescence
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of t h e c l e a r s o l u t i o n o b t a i n e d in t h i s w a y was 97~/o of t h e o r i g i n a l r v a l u e in ~ h e case of t h e five s~,4ined discs, and 96~/o m t h e five cow,trois. Since t h e s t a i n e d disc l~y a~ t h e bo6torn of t h e t u b e a t t h e b e g i n n i n g of t h e experim e n t a n d t h e fluorescein s o l u t i o n l a y a b o v e t h e cornea in t h e control, a d d i t i o n a l experimei~ts Xverc c a r r i e d o u t on t h e effect of t h e dist, r i b u t i o n el" t h e d y e w i t h i n t h e t:~be on t h e r e a d i n g of t h e f l u o r o m e t e r . Some glucose was a d d e d to ~ s o l u t i o n of fluorescein to increase i t s d e n s i t y , a n d a. £ew #] were c a r e f u l l y r u n u n d e r 0-2~-D.5 mL of clear buffered saline so t h a t a t h i n l a y e r of d y e ]a.y a t t h e b o t t o m of t h e tube. T h e
Fro. 5. E x p e r i m e n t a l a r r a n g e m e n t for e s t i m a t i t l g t h e quenching of fluo,'esec~aec of fluorescein b y t h e corneal s t r o m a . C, :Disc of corneal s t r o m ~ .
total fluorescence was m e a s u r e d in t h i s eondit.ion a n d a f t e r m i x i n g t h e content, s of the tube. No difference in t h e r e a d i n g w~s n o t e d in n u m e r o u s triMs, a n d i t w a s e v i d e n t t h a t t h e effect u p o n i t o f t h e ohange ii~ d i s t r i b u t i o n m u s t b e l e s s t h a n 1 % . ]?he conclusion d r a w ~ £rom nil t h e s e o b s e r v a t i o n s w a s t h a b t h e s t r o m ~ l tissue has no m e a s u r a b l e influence on t h e fluorescence of fluorescein h~ t h e r a b b i t . No m a r k e d differences in t h e chemica.1 c o m p o s i t i o n of m a m m a l i a . u corneas h a v e been r e p o r t e d , and Jr, was considered u n l i k e l y t h a t t h e b e h a v i o u r of t h e h u m a n cornea, was different in this respect. (3) Loss at l'imbus. I f fluoi'escein passes d i r e c t l y from t h e cornea to t h e blood a t t h e limbus, t h e m e a s u r e d v a l u e of A will be h i g h e r t h a n t h a t a p p r o p r i a t e t o equatior,. (15). A ca.lcuIntioa b a s e d on t h e a s s u m p t i o n of ~ s i m p l e g e o m e t r i c a l s h a p e for t h e cornea. and a r a t e ~f s p r d a d of fluorescein w i t h i n t h e s t r o m ~ eqllM to t h a t f o u n d iu t h e r a b b i t (M~urice, :1960) suggested t h a t it m i g h t u l t i m a t e l y a m o u n t to 3 0 % of A. H o w e v e r , ignorance b o t h of t h e t r u e r~xte of diffusion a n d of t h e e x c h a n g e rela.tionships a t Vhe limbus in man~ m a k e s a n e x a c t e s t i m a t e ~mpossible. Owing to t h e i u t r o d u a t i o n of t h e fluorescein into u circumse, ribecl a.rea n e a r t h e c e n t r e of t h e cornea, i t is to be e x p e c t e d t h a t the loss across 6 h c p c r i p h e r y ~ l l be xmgligibte a t t h e b c g h m i n g o f t h e measure± n~ents, b u t i t m a y a . ~ n m e i m p o r t a n c e towa.rds t h e end of t h e initial 8 hr period over which 21 is e s t i m a t e d .
218
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hl. I ~ I A U R I C l g
A n at.tempt was m a d e to d e t e r m i n e e x p e r i m e n t a l l y t h e g r e a t e s t possible c h a n g e i~ A resultd~g from p e r i p h e r a l losses, b y c b m p a r i n g the value o b t a i n e d f r o m a n eye s t a i n e d eelatrally w i t h t h a t f r o m its fellow eye s t a i n e d p e r i p h e r a l l y . Ii'luoreseein was i n t r o d u c e d m the n o r m a l maxmer b y i o n t o p h o r e s i s e x a c t l y c e n t r a l l y in one c o r n e a and a t the u p p e r l i m b u s in t h e other, t~eadingg of t h e fall of t h e fluorescence in the two eyes were carried o u t from 1 or 2 hr l a t e r for a f u r t h e r 6 hr. Ilt t.he o r d i n a r y s l i t - l a m p a clear zone a p p e a r e d to rmmtin between the c e n t r a l s p o t a n d the p e r i p h e r y a t t h e e n d of this p e r i o d , suggesting t h a t no significant loss h a d occurred across the limbus. ConMstent a n d m e a n i n g ~ t l m e a s u r e m e n t s of t h e t o t a l fluorescence of the eccentricMly s t a i n e d eye were diffienlt to o b t a i n . R e c o u r s e was t h e r e f o r e h a d to c o m p a r i n g t h e a q u e o u s b u r n o u t s of t h e two eyes; five subjects with deep a n t e r i o r c h a m b e r s were c h o s e n tbr this purpose. T h e a q u e o u s h u m o a r of t h e p e r i p h e r a l l y s t a i n e d eye d r o p p e d 4 a n d l~/o/hr t~ster t h a n t h a t of t h e c e n t r a l l y st.ained in two cases, t h e y fell ~t t h e s a m e r a t e in a n o t h e r ease,, and, in t h e r e m a i n i n g two, t h e p e r i p h e r a l l y st,Mned a q u e o u s fell a t a r a t e slower by :~ a n d 1-5~/o/hr. I n each of the l a s t four cases the proba b i l i t y t h a t the r a t e of fall in the p e r i p h e r a l l y s t a i n e d eye could h a v e been gn'e,~ter by a n a m o u n t su[t~lcicnt ~o give a 10°/o or m o r e increase in A was tested s t a t i s t i c a l l y ; these p r o b a b i l i t i e s were a b o u t 5, 1, 0-5 a n d 0-15/o, ,'espeetively. This e v i d e n c e suggests that., e v e n in the e x t r e m e c o n d i t i o n s where the c o r n e a was s t a b l e d at t,}ie lirnbus, the loss f r o m t h e c o r n e a d i r e c t l y t o the blood is n o t of a n y i m p o r t a n c e in. m o s t eyes. Some u n c e r t a i n t y m u s t remMn, however, since regional va,.iations h~ cornea 1 thie.kness a n d , possibly, in e n d o t h e l i a l p e r m e a b i l i t y can r e s u l t in the d r o p in fluo,.escein conc e n t r a t i o n in t h e cornea n o t being parallel t:o t/hat in the aqueous h n m o u r .
Ea'dperimental values T h e wxlnes o b t a i n e d f r o m 16 s a t i s f a c t o r y curves are s h o w n in Table: 1, where tile 3are a r r a n g e d according to t h e co]our of the iris. T h e subjects were n o r m a l v o l u n t e e r s of b o t h sexes from 20-40 y e a r s old. T h e m e a n of t h e vatues of £'o in I 1 s u b j e c t s is 0.015/rain with a s t a n d a r d d e v i a t i o n of 0,0037/rain. This is s i g n i f i c a n t l y higher a t tile 1~/o ]ex.el t h a n the d i s t r i b u t i o n f m m d bv G o l d m a n n ia l 0 s u b j e c t s : a m e a n of 0.011/rain a n d s s t a n d a r d d e v i a t i o n of 0-0022/ mil'l. T h e m e a n of t h e v a l u e of f i n t h e 10 d a r k e r eyed subject,s is 2,5 t~l/min with a deviat i o n of 0-50/xi/min: T h e p e r c e n t a g e v a r i a t i o n o f f a p p e a r s to be slightly smaller t h a n t h a t of/co, bug n o t e n o u g h to suggest t h a t t h e f o r m e r m i g h t be t h e m o r e c o n s t a n t quantity. T h e values o f Va g i v e n b y the p h o t o g r a p h i c m e t h o d p r e v i o u s l y described a p p e a r t o be s i g n i f i c a n t l y Iower t h a n those f o u n d b y I-Ieim (1941). A g r o u p of I 8 gubjects gave a m e a n v a l u e of 175/M with a s t a n d a r d d e v i a t i o n of 33 t~l. T h e 53 of ~ e i m ' s s u b j e c t s in tt~e s a m e age group, 20-40 years, h a v e an aver~,ge v a l u e of 220 p.i w i t h a s t a n d a r d d e v i a t i o n of 51 t~l. I t Should be e m p h a s i z e d t h a t t h e t h r e e q t t a n t i t i e s f , ]%, a n d V . are estim~t~zc!, b y c o m p l e t e l y independerLt m e t h o d s , t h o u g h it has been c o n v e n i e n t to c a r r y our, the d e t e r m i n a t i o m s of t h e first two in the com~se of ~ single e x p e r i m e n t . T h e s e q u a n t i t i e s are c o n n e c t e d b y t h e t h e o r e t i c a l rela,tionship:
.f
Mean &E.M.
R.K. a b V.N. J.K. M,P~,
M.K.
I-T.K.
D.M... b
A,I,',
M, B . ~
.[~,.~,
R.L k[.8. D.J~.
Subject
Blue-grey Blue Bloc
]Lazei l[azcl Groy
Haze/ Hazel
Dark brown Dark brown Dark brou'a Brown Brown
Eye cohmr
1.55 t. 15 1.7 1.9 1.7 1.9 2,3 1.5 1.45 2-4 2,4 2,3 2.1 3. l 2.1 2'6
FdFo
0.0J53§ 0,0011
0-011 0"014 0'018
0"014
10
26 9 10
0"012 0.018 0"0ll.-14 0'023 0'032 0'017 0"013 O.OI t 0-012 0-010 0-015 0,012
k, (rain -t)
9 11.5 14 14 16 10 16 8.5 8 12 15 10
~ ~o
2-4st
0"014 0.020 0.01~15+, 0"025 0.035 0.0Ill 0.014 0.013 0.0135 0-02I 0.010 0,0t,1 0.016 0-011 0"016 0.020
il (rain-I)
0"17
2.3 t.75 2.1 3.2 2,45 2.75 2,9 t.8 1.75 2.9 2.9 2.5 2-3 3.0 2-8 4'6
,f * (/dJ)nin)
R, L, ]light and loft eyes of same subjcck a, b, Same subject on two different occasions. *Va]ue of 8 365/zl in some on.sos, 410 gl in othors. Uncertain value hecausv, of large scatbr .f oxperimental points. f I0 subjects, excluding V.N., J.K. and 51'.12, § 11 subjectS, exohlding D.R,. and M.B.
0.0032 0.0033 0.0029 0.0029 0.0030 0,0030 0,0026 0'00'37 0'0048
0'003~
0,0041 0,0042 0"0034 0.004 t 0,0035 0'0035
A Onin-1}
T:'t BI.I~ [
174 190
tg!)
')% ""
162 190 214
I89 100 153 l(i0 122 }12 200
1:~ (~.l)
1.0 1.05 0.8-1.0 1"15" 1,6 0,7 9.9 1,0 l'I 1.2 1.1 .I-1 !.4 0.75 0-9 0'75
1,'.Tr,~Jf
).J
),¢
0
0
220
1~. F, J O N E S
AND
D.M.
MAUP~ICE
:In view of this it is gratifying, though no doubt fortuitous, that the ratio k,, V,/f for the experimental values, showu in the last column of the table, is close to unity in fanny, of the cases. The low w~tue for the two blue-eyed subjects is additional evidence thatJ' is overestimated by method 2 in these cases. One m a y conclude that either method is capable of giving ,m accurate estimate of the absolute value of tim outtlow of tiuoresccin from the ~mtcrior ch~tmbcr in man. Experience has st)own that method 2 is much more reliable ~md convenient in cycs of thc darker hues to which it is applicable. I t is, in theory, ouly necessary to make readings on the subjecl~ on t,wo occasions m order to derive A and 1,',[F,, thougil additional checks are advisable. The dye may be insl;illed on tim previous evening which often adds to the convenience of t.hc experimental schedulc. By co,m'as~;, method t requires readings to bc made frequently throughout the d~):, and commonly does not permit a valae of ko to be derived to an ,~cce~,i~abic degree of precision. It is tlsually satAsfactorv in eyes wit}t (leep anterior chambers, however, and may be used with irides of anv co]otlr. ]?requcatly, when t:he effect of a drug is being ~:ested, for example, a comparison of the outflow of the two eves of one [)crson or of t;hc same eve on two different occasions is all that is required. For r.his purpose a simple modific'ltion of method 2 can be employed in which either -f~,fF,. or F,,/F~ is measured; these developments will be described elsewhere. ,.
R.J~FERENCES Duke-Elder, Sir W. S. and Mauricc. D. :~,I.(1957). Brit. J. 01fl~thalm(J, 41,702. Goldmann, H. (1950). Ophtludmologica, ]2,t,~el 119, 65. I]:eim, M. ( 1941). Ophtludmoloyica. f3(t.~el.102, 19:}. Jones. R. F. and M~urice. D. M. (19fi3). Exptl Eye Re~'. 2, 233. Ll,.ngham, 5'17.F~. and Taylor, C. B. (1960). d. Physiol. 152, 447. Langley, D. artd 3Iael)onald, R. K. (1952}. Brit. J. Ophth,dmoI. 36, 432. ~Iaurice, D. M:. (1960). Am. J. Ophthalmol. 49, I0[[. ~rctttrice: D. M. (19(;2,1. Exptl Eye Rcs. 2, 33. Weekers, K. and Dcbm, rc~tle. Y. (1953)~ Ol~hthab~wlogica, Basel 125, 425.
N e w M e t h o d s o f measuring the R a t e o f Aqueous F l o w in M a n with Fluorescein ]-~. F . JON-ES AND D , M. MAURICE
De2ag't,ncnt of Physiology, I~stztute of Ophth.almology, J~ald Street, Lon~ton IV.O.1, En!Ila.nd (Received d A't),il .1966) Two methods of dete,'lniaing the rate of loss of fluorescein from the ~queous humour in lno~n are described. The dye is introduced into the cornee~ by mesas of iontophoresis ~md estimated in the eye with the slit.lamp fiuorophotomoter. In the first mcthod'l, he time course of the fluorescein coneen~rat[oll .in the ,%ntcrior chaunter is obse~wed, from which its turnover rate in t h e ehr~mber is derived.-.] n the second me,,hod measurements of/the ratio of the total fluorescence of tl~e eye to tha.t of the aqueous humo~,r le~d to a direct, evMudtion of the aqueous flow r~te. The errors and limibr~gions of t.he methods arc discussed and it is cottelucled that. the seemtd method, though generally more reliable, is inapplicable to blue-eyed s u b j e c t . In ot.her cases vhcre is good accordance b e t w e e n t,l~e results obtained by t.he gwo metho(Ls. I n a smMt group of young norm,M volunteers the mean turnover rate found by l,hc first method wan 0-015 rain and t h e niean rate o f flow by the second, method 2.5 td~tnin.
I. Introduction T h e idea of using t i l e changes with time of the concentration of fluorescein in the anterior chamber as s. Ineasure of the rate of flow of the aque0u.s hltmour has had a long currency; It-was first 13ut on ~ sound theoretic~d ba~is by O o l d m m ~ n (1950), w h o injected iluorescein intravenously Jn r~bbits and man, and measured the time course of th.e.fluorescence in t/he blood" a.ud t~|m a,tterio~ chamber using his slit-lamp flu0rophotometer. This ,nethod, though it results in satisfactory estimates of the flow rate in man, suffers from two disadvant;tges--frequent blood samples have to be obtained f r o m the patient, and a rather complex nlathematical treatment of the results is necessary to derive-the required value. A shnilar method published by L a n g h a m and Taylor (1960)is. open t.o the same objections. L a n g l e y a n d M a c D o n a l d (1952) a p p e a r t o b e t h e f i r s t to ]lave s u g g e s t e d s t a i n i n g t h e c o r n e a so t h a t %he d y e e n t e r e d t h e a q u e o u s h u m o u r a c r o s s t h e c o r n e a l e n d o t b e l h n n . T h o u g h t h e y s h o w e d t h a t q u a l i t a t i v e l y , t h e f l u o r e s e e n 0 e o f tile a q u e o u s h u m o u r c h a n g e d in t h e m a n n e r t o b e e x p e c t e d , t h e y d i d n o t i n v e s t i g a t e t,h e p o t e n t i alit.ies o f t h e i n e t h o d v e r y i n t e ~ s i v e t y n o r d i d t h e y a t t e m p t t o p u t it o n a q u a n t i t a t i v e basis. ~ V e e k e r s a n d D e l m a r c e l l e ( 1 9 5 3 ) a t t e m p J c e d a q u a n t i t a t i v e t r e a t m e n t b u t - l e f t i t v e r y i n c o m p l e t e . A m o r e t h o r o u g h st.udy s h o w s t h a t t h e v a l u e s t h e y e x t r a c t e d r e l a t e m o r e t o t h e P e r m e a b i l i t y o f t h e . e n d o t b e l l u m t h a n t o t h e r a t e o f tlm a q u e o u s f l o w . I n t h i s p a p e r , t w o d i s t i n c ~ m e t h o d s o f m e a s u r i n g t h e r a t e Of a q u e o u s f l o w i n m a n b y m e a n s o f f l u o r e s c e i n a p p l i e d t o p i c a l l y a r e d e s c r i b e d . B o t h d e t e r m i n a t i o n s m a y be c a r r i e d o u t in. t h e c o u r s e o f a s i n g l e e x p e r i m e n t ; One g-ires t h e t~urnover r a t e o f f l u o r e s r e i n in t h e a n t e r i o r c l m m b e r , a n d t h e o t h e r l e a d s d i r e c t l y t o t h e flow r a t e o f t h e a q u e o u s h u m o u r . T h e i n v e s t i g a t i o n h a s b e e n c o n c e r n e d so f a r o n l y i n e s t a b l i s h i n g t h e va.l~ditv and limitations of the methods, and has been restricted to normal vohmteers. 208
A Q U E O U S F L O W I N MAN
209
2. Theory
Method .1 I t will be assumed that, t h e excha.nges of fluorescein b e t w e e n t h e c o r s e s a n d tlie blood at the l i m b u s . a r e ,egligib]e, and t h a t the e x c h a n g e s b e t w e e n the c o r n e a and a q u e o u s h u m o u r and b e t w e e n Qle aqueous h u l u o u r ~md t h e blood obey simple first-order d y n a m i c s . Then we m a y write for t h e e x c h a n g e b e t w e e n t h e cornea and "aqueous h u m o u r : dC° - - l%.c,,(Ca - C~) dt
(l)
where k c,~,. is tile transfer coefficient fi'Olll the c o r n e a ~o the aqueous, referred to the v o l u m e of the cornea [ D u k e - E i d e r a.nd Mauriee, 1957), a.nd C a a~ld Cc a r e . t h e effective a q u e o u s and corneal c o n c e n t r a t i o n s of fluorescein. If it is assumed t h e c o n c e n t r a t i o n in t h e blood is negligible, t h e c o r r e s p o n d i n g e q u a t i o n for t h e aqueous h u m o u r is: cl C~,£
.,
-
--
l
t
.
~.oC,,+.k~.~,,(O~-- C,)
,
dz
(2)
-where/"o is t h e loss coetficient from tile a n t e r i o r c h a m b e r and k,.c~~ is t h e corneM trafisfer coefficieut referred to t h e x-olume of *.Ira a n t e r i o r c h a m b e r . If the a q u e o u s h u m o u r is free of fluorescein at. zero ~ilne, the solution of these differential equations has t h e form:
C',
=
C.~(e.--"'--e-~")
(31
where t is the time, C.~ is a. c o n s t a n t d e p e n d i n g on the initial degree of s t a i n i n g of t h e cornea, and A and B are given by: (4).
A ÷ B = k o . , . + ~;,. ~,,'. ko
and
A.B = Z-o I,,~.~.
(5)
For the c o r n e a t}l~ e q u i v a l e n t e q u a t i o n is:
C~--
Ca ~tl J O.¢t
~(B_k~.,,.o)e_.,,_(A_kc.c,,)e_n,~.
[
(6)
J
The shape of these curves: ,as plo~ted, on semi-logarithmi 0 paper, is shown in Fig.-i. The
C,, curve is built "up of two s t r a i g h t lines of slopes A and B in t h e nit%Ill-tot SllOWlI. i long time a R e r beginning of t h e e x p e r i m e n t , w h e n t h e effect of the B e x p o n e n t i a l has died out, the s l o p e A is g i v e s by: A - - --,.lO~ _ C6dt
-d6'~ (?odg
(7)
At, the s a m e t i m e t h e ratio Ce/C,,~ becomes c o n s t a n t a n d will b e d e n o t e d d~a. D i v i d i n g -equation (1) b y Cc t h e n , i t follows: A k.c.c~- 1--(1./de.)' Finally, from e q u ~ i o n s (5) a n d (8):
(8)
,.o--O(,-;)
If B ariel a~c~ can be experimentally d e t e r m i n e d it,-is possible to find
k o,
L e t F a and F c
210
R.F.
JONES
AND
D.
M.
MAURICE
be the actuM fluorometer readings corresponding to Ca and C~. At equilibrium when C, = Co, let the ratio F J F a be denoted rta, so t h a t
Fa__ F° ca c o "r a. On t h e d e s o e n d i n g p a r t of the curve, when Cc/C ~ takes up the value dca, let F d F a correspondingly take up t h e value go,. Then: d c~:
- -
(l;)
~ca
by equation (10). F r o m equations (11) and (9)
(12)
k o ----- B ( l _ _ r ~ . \ g*~/ I000
100
IO
%
o
t
1
t
I
I
r
,
2
3
4
5
6
Time'
F I Q . I . C u r v e s s h 0 w i n g ~ h e o r e t i c a l c h a n g e s iR f l u o r e ~ c e i n c o u o e r t S r a t i o n wi~h t i m e , a f t e r [Ls i n t r o d u c t i o n i n t o t h e c o r n e a . Ca a n d C, r e p r e s e n t e f f e c t i v e e o n c e n t r a t l o u s in t h e a q u e o u s h u m o u r mad c o r n e a a n d m t t h e t o t a l a m o u n t i n t h e e y e . Ordinate: l o g a r i t h m o f c o n c e n t r a t i o n o r m a s s o f f l u o r e s c e i n in a r b i g r - r y u n i t s . Abscissa: t i m e a f t e r d y e e n t e r s c o r n e a . :Each c u r v e is m a d e UP o f t w o e x p o n e n t i a l c o m p o n e n t s : a s l o w o n e (A) a n d a f a s t o n e (B). T h e B c o m p o n e n ~ is r e l a t i v e l y l a r g e s t in t h e a q u e o u s h u m o u r c u r v e a n d is d e r i v e d in p r a c t i c a l b y s u b t r a c t i n g t h e c u r v e o f C,, f r o m t h e b a c k w a r d p r o l o n g a t i o n o f t h e A l i n e .
The tr~mfer coefficient out of the eye /co has two parts, one the outflow coefficient kI w h i c h represents the loss of fluorescein from the anterior c h a m b e r by drainage of aqueous humour, a n d the other, t h e diffusion coeific[ent k d which represeuts t h e exclmnge by diffusion a c r o ~ the iris, s o t h a t ko-~ k1+.k,i. (13) :FrOm t h e experiments of G o l d m a n n (1950) it appears t h a t ilx the n o r m a l eye ~:a is, at most,, o n l y o n e : t e n t h p a r t of ]co and probably a considerably smaIler fracLion. For this reason l%will be referred to as t h e flow c o n s t a n t in w h a t follows, a n d 1%V,,, where V a is the volume of the anterior chamber, will be Called the rate of flow, t h o u g h it m u s t be borne in m i n d t h a t this is an approximation.
AQUEOUS
:FLOW
IN
MAN
211
Method 2. If,m~ is t h e t o t a l m a s s o f fluorescein in t h e a q u e o u s a n d c o r n e a , t h e r a t e a t w h i c h it leaves t h e e y e is g i v e n b y dmt/dt. S i n c e it is a s s u m e d t h a t t h e d y e is lost f r o m t h e cornea 0nly b y w a y of a q u e o u s h u m o u r , a n M t e r n a t i v e e x p r e s s i o n for t h e r a t e of loss o f i~s mass is - - C , V , k o. T h e r e f o r e drn~ __ dt
(14)
. C.V.4,
D i v i d i n g b o t h sides b y m~ leads to: A
--
C
V.ko
after the B e x p o n e n t i a l has d e c a y e d . T h e n :
V~ko ~ A m t
o.
Am~
or
(15)
w h e n f is t h e a q u e o u s flow r~te, Therefore, b y m e a s u r i n g t h e slope, A, a n d t h e ratio, mffCa, t h e flow r a t e m a y be o b t a i n e d directly. I t is of i n t e r e s t f u r t k e r m o r e t h a t : mt
--~ Tr~Oa-b VcOc
(16)
where Vc is t h e effective v o l u m e of t h e c o r n e a , so t h a t f r o m e q u a t i o n s (3), (6) a n d (16), and r e m e m b e r i n g : it follows:
V,~CA (Be_A~
Ae_~: )
(17)
This c a r v e is p l o t t e d in :Fig. 1.
3. Methods ln~roduction of fl~m~'escein B y m e a n s of i o n t o p h o r e s i s , a d e p o t of fluorescein w i t h s h a r p l y defined b o u n d a r i e s was inl;roduced i n t o t h e cornea, o f t h e e y e to be examimed. T h e e l e c t r o d e c o n s i s t e d of a w i c k Of 2 ~/~ a g a r gel, 4 m m in d i a m e t e r , m a d e u p a s e p t i c a l l y in 10 ~/o f l u o r e s c e i n Solution a n d c o n t a i n i n g 0"1~/o m e t h y l h y d r 0 x y - b e n z o a t e as a p r e s e r v a t i v e . T h e a g a r w a s e x t r u d e d from a plastic t u b e b y c o m p r e s s i 0 g i t w i t h a c l a m p (Fig. 2). T h e e n d of t h e e l e c t r o d e was blotted w i t h sterile filter p a p e r to a b s o r b all free fluid. T h e c o r n e a w a s anaesthetized, w i t h novesine, a n d t h e e l e c t r o d e w a s a p p l i e d to t h e u p p e r h a l f of its surface, s o m e 3 m m c l e a r of the limbus. A c u r r e n t of a b o u t 200/~n w a s p a s s e d f o r 10-15 scc. Several a d v a n t a g e s a c c r u e f r o m r e s t r i c t i n g She s t a i n e d a r e a in t h i s way. :First; an u n s t a i n e d a r e a o f c o r n e a is l e f t in t h e l o w e r h a l f t h r o u g h )vhich o b s e r v a t i o n s on t h e initial weak fluorescence of t h e a n t e r i o r c h a m b e r m a y be m a d e w i t h o u t d i s t u r b a n c e f r o m t h e strong g l a r e of t h e reservoir of d y e. S e c o n d , a n y e x c h a n g e of f l u o r e s c e i n : w i t h t h e l i m b a [ circnlation will be v e r y m u c h r e s t r i c t e d i n t h e first few h o u r s of t h e e x p e r i r n e n t . T h i r d , there is no s t a i n i n g o f t h e lid m a r g i n s , a n o c c u r r e n c e which can give rise to difficulty in m e a s u r i n g t h e t o t a l fluorescence of t h e e y e i n t h e l a t e r s t a g e s .
212
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N o n e of t h e s u b j e c t s suffered aI~y discomfort, or h a r m f r o m t h e ~ p p l i c a t i o n of the elect r o d e . C o n c e n t r a t i o n s of fluoreseein m o r e t h a n 100 t i m e s grea~er t h a n t h o s e d e s c r i b e d h e r e h a v e r e g u l a r l y been p r o d u c e d in t h e c o r n e a s of rabbits w i t h o u t a n y e v i d e n t r e a c t i o n to t h e dye. I t was also n e c e s s a r y t o establish t h e r a t i o .of t h e tluorescein c o n c e n t r a t i o n s in t h e c o r n e a a n d a q u e o u s h u m o u r in t h e s t a t e of e q u i l i b r i u m , rc~. F l u o r e s c e i n was s w a l l o w e d in capsules of 200 rag, u s u a l l y a t b e d t i m e , on .rising, a n d e v e r y s u b s e q u e n t h o u r for several hours. To a c c e l e r a t e t h e d e t e r m i n a t i o n of t h e e q u i l i b r i u m value, a d r o p of 10 °/~ ltuorescein was i n s t i l l e d once or tWiCE i n t o one eye, so t h a t t h e c o r n e a l c o a e e a t r a t . i o n a p p r o a c h e d t h e c o r r e c t level f r o m a b o v e on one side a n d below on t h e o t h e r . T h e i n g e s t e d d y e app e a r e d to b e e x c r e t e d q u a n t i t a t i v e l y in t h e u r i n e . S
220K - - ~
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1"~'io. 2 . . ~ I e c t r o d e a n d circuit u s e d for i n t r o d u c t i o n o f fluorescein into the eve by iontophorcsis. F, :Fluorescein-saturatcd a g a r gol; .S, silver wire; .[, indifferent electcode; C, c l a m p e.xbruding get f r o m plasgic tube.
Measurements of fl~oresceqace T h e determ~nut.ions w e r e m a d e w i t h t h e f l u o r o p h o t o m e t e r of M a u r i c e (19(~3), a n d r e a d i n g s t a k e n from t h e a q u e o u s h u m o u r a n d c o r n e ~ as d e s c r i b e d in that, paper. :I1~ t h e f o r m e r case t h e w i n d o w w a s placed on t.he l o w e r halt~ of tile i a l a g e of t h e c h a m b e r , m i d w a y b e t w e e n t h e c o r n e a alxd lens. F o r d e t e r m i n a t i o n s of t h e t o t a l fluorescence of t h e a n t e r i o r s e g m e n t , t h e i n s t r u m e n t was m o d i f i e d to p r o j e c t a 12 m m d i a m e t e r circle of blue light o n t o t h e eye. T h e slit of t h e l a m p was r e p l a c e d b y a c i r c u l a r a p e r t u r e a~ld t h e o b j e c t i v e by a s u i t a b l e l o w - p o w e r e d lens. C o r r c s p o n d i u g i y : t h e p h o t o m e t r i c m i c r o s c o p e was c o I l v e r t c d to a telescope b y t h e USE of a l o w - p o w e r e d o b j e c t i v e lens, a n d in this case the largc s q u a r e w i n d o w was f o u n d to be t h e c o r r e c t size, t h a t w h i c h exa.ctly f r a m e d t h e imn.ge of 5lie circle of light. T h e a n g l e b e t w e m l t h e a r m s of ).he s l i t - l a m p wa.~ r e d u c e d as far as possible so t l m t both optical s y s t e m s w e r e a l m o s t paralle], point:ing a t t.he eye. T h e s u b j e c t res~ed his h e a d a g a i n s t a n a d j u s t a b l e suplaort so t h a t t h e corneal s u r f a c e was fLxed a.t a s t a n d a r d dist, ancc, a p p r o x i m a t e l y 0-5 m, froln t h e i n s t r u m e n t . T h e e n t i r e c o r n e a was exposed, e i t h e r b y t h e s u b j e c t ' o p e n i n g his eyes v e r y ~dde or, m o r g u s u a l l y , b y t h e lids being h e l d a p a r t . T h e circle of l i g h t was t h e n s h o n e onto t h e c o r n e a an¢]~ if ii h a d p r e v i o u s l y b e e n ' b r o u g h ~ into register with I/be w i n d o w , t h e r e a d i n g could be t a k e n ill a few seconds. :Readings of t h e t o t a l fluorescence a n d t h a t o f t h e a q u e o u s h u m o u r w e r e taken, before the- i o n t o p h o r e s i s t o e s t a b l i s h t h e b a s e l i n e , t h e n g e n e r a l l y a.t e v e r y 15 mi.n for t h e f i r s t h o u r or two, a n d t h e r e a f t e r a t longer i n t e r v a l s . T h e r e a d i n g s were c o n t i n u e d u n t i l t h e e n d of t h e w o r k i n g d a y , a n d t h e r e was u s u a l l y sufficient fluorescein p r e s e n t in tlm eye for t h e m to be r e c o m m e n c e d t~he n e x t m o r n i n g a n d carried, on, a t l e a s t a s far as t h e a q u e o u s w a s c o n c e r n e d , t h r o u g h o u t t h e s e c o n d d a y . T h e d y e was n o t sufficiently u n i f o r m in dist r i b u t i o n t h r o u g h o u t t h e c o r n e a for m e a n i n g f u l r e a d i n g s to be t a k e n f r o m it u n t i l t h e end o f t h e first d a y . D e t e r m i n a t i o n s of t h e v o l u m e of ~he a n t e r i o r c}mmber w e r e m a d e by a p h o t o g r a p h i c m e t h o d ( t o n e s a n d M a u r i c e , 1963).
A Q U E O U S :FLOW I1N" M:AN
°13
Sta~dardization The ratio of t h e fluorometer readings obtaialed for t h e total a n d aqueous fluorescence at any m o m e n t , Ft and Fo, must, be converted to the ratio of the values of ,nt and Ca for use in equation (15) of t h e second m e t h o d . A conversion factor S is introduced So t h a t
mt C~,
S Ft -if-,"
To obtain the value of ,~, readings are t a k e n by the ~taad.ard procedure on a solution of fluorescein c o n t a i n e d in an artificiM anterior c h a m b e r formed anteriorly by a ~ra~sparent plastic contact lens of 8 m m radius of cuxvature arid l I m m diameter, and posteriorly by a sheet of black plastic. For such a shell ~n' __dt_.= lrs Co where V~ is the volume contained within it, which can readiiy be d e t e r m i n e d by weiglfing. Then:
for the readings, F,~ and F~, taker, on the shell. Two chambers were constructed, one with a flat, a n d one with a hollowed o u t rear wall, t.hat c o n t a i n e d 115 and 180/xl. They were filled with fluorescein solutious of various concentrations and, after subtracting the background fluorescence when filled with water, S was found to be the same for both shells and c o n s t a n t up to a concentration of nearly 10 -s g/ml. A~y difference in the distribution of the dye within the artificial c h a m b e r and the eye should not be important, for it is found t h a t the reading given by a fluorescen6 spot does not. vary m a r k e d l y according to its position within the illuminated circle. Again, different refract.ire indices of the plastic a n d the cornea should n o t create arx error in c,q as was shown both by theoretical considerations, a n d b y wetting the outer surface of the artificial chamber when no changes in F~ or F~ tool< place. 4. Results
Ge~wral The p r o c e d u r e h a s been t e s t e d on n u m e r o u s subjects, n o n e of w h o m has f o u n d i t troublesome. Occasionally, diffieulby has b e e n e x p e r i e n c e d in o b t a i a l n g r e a d i n g s when t h e r e was a v e r y n a r r o w p a l p e b r a t fissure or p o o r m a i n t e n a n c e of fixation. I n t h e b c s t cases (Fig. 3) t h e con s! s t e u c y of t h e re~ulgs was r e m a r k a b l e ; irt ttm worst, the readings, p a r t i c u l a r l y o f t h e a q u e o u s fluorescence, w e r e so v a r i a b l e t h a t t h e r e s u l t s were Unusabte--Zin o n e s u b j e c t F , : d o u b l e d i t s v a l u e ia 5 rain. T h e i m p r e s s i o n was gah~ed, t h o u g h ' i t is b y n o m e a n s c e r t a i n , t h a t t h e b e t t e r c u r v e s w e r e o b t a i n e d w i t h subjects of p!a:cid t e m p e r a m e n t a n d w i t h eyes h a v i n g d e e p a n t e r i o r chambers.
Method J The a q u e o u s c u r v e in t h e b e s t c a s e s c o n f o r m e d v e r y w e t l to t h e d o u b l e e x p o n e n t i a l e q u a t i o n (3), as s h o w n b y t h e fig of t h e s t r a i g h t lines to t h e ~TMues Of/7~ (Fig. 3(a)). This s u p p o r t s t h e v a t i d i t y of t h e assuxnptiorm m a d e i n d e r i v i n g tiffs equatioll, a n d justifies t h e a p p l i c a t i o n of t h e s a m e a n a l y s i s to leas p e r f e c t e x p e r i m e n t a l d a t a . .Mos t s u b j e c t s s h o w e d a r a t h e r e r r a t i c cou~.se in F~, p a r t i c u l a r l y i n t h e earl)5 m o r e ~mportant, stages. MucJa of t h i s was d u e t o u n e q u a l d i s t r i b u t i o n of t h e d y e - - w h i c h
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was seen to be more concentrated in the aqueous humour failing down the inner face of the cornea through convection. I n some subjecLs, Vigorous shaldng of the head, or side to side movements of the eyes, produced a more uniform distribution and ~ better reading. E v e n when this was successful, unexplained variations from the smooth theoretical curve frequently occurred. To carry out the exponential analysis, it was effort better to obtain the value of ~he slope A from the//'t curve and adjust the line t o / i v among the/P~ points. The point of intersection of the two straight lines, A and B, may be fixed without difficulvy, and
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F~o. 3. E x p e r i m e n t a l v a l u e s o b t a i n e d f r o m d a r k e r - e y e d subjee~ (l~.K:~ in T a b l e 1). (a) F l u o r e s e e i n i o n t o p h o r e Z s i n t o l e f t c o r n e a ~ 10.0 a.na. T r i a n g l e s r e p r e s e n t •-readings o f tot,M f l u o r e s c e n c e o f t h e e y e . Circles a n d s q u a r e s r e p r e s e n t r e a d i n g s o f fluorescemee in t h e a q u e o u s h u m o u r a n d c o r n e a l s t r o m a , r e s p e c t i v e l y , a s c o m p a r e d t o a s o l u t i o n o f S t a n d a r d c o n c e n t r a t i o n . Crosses d e r i v e d b y subtrz/c~ion o f e x p e r i m e n t a l a q u e o u s humottr, v a l u e s f r o m s t r a i g h t l i n e t h r o u g h p o i n t s a~ l a t e r t i m e s . 'Pae e u r ~ e d r a w n t h r o u g h ~he rn~ p o i n t s ha~ a . s h a p o d e t e r m i n e d b y e q u a t i o n (17) u s i n g t h e coe~t~unts d e r i v e d f r 0 m t h e _wa c u r v e . {b) C o n t i n u a t i o n o£ previoa~s e x p e r i m e n t or, s e c o n d d a y . I n o r d e r to d e t e r m i n e s t e a d y s t a t e , s u b j e c t s ~ a i . l o w e d 200 r a g . c a p s u l e s o f fltmreseeiu a p p r o x i m a t e l y hotlrl~- f r o m 8.0 a . m . F i l l e d i a s y m b o l s cortes. p o n d to v a l u e s o b t a i n e d fro m r i g h t e y e . S y m b o l s d i v i d e d h o r i z o n t a l l y represenV differer, ee o f ~ a t u e s f r e t s t w o e y e s , t h o s e d i v i d e d v e r t i c a l l y t h e a v e r a g e v a l u e o f &we. eyes. L i n e s a r e p r o l o n g a t i o n o f t h o s e d r a w n in (a). T h e y f a l l a m o n g d i f f e r e n c e p o i n t s a s w o H d b e p r e d i c t e d .
to establish the slope 13 i t is necessary only to determine one:other p o i n t upon •it with accuracy, f o r th]~ ireason; particular attention was paid t o the readings Jn t h e period 1--2 hr after the iontophoresis, I n spite of the irreb~llarities, i_n nearly every case a stra4ght tine:couldbe drawn through: the different p o i n t s ; at least t o the satisfaction of the experimen~r, and the independent:estimates of the two authors were i n good agreement.
A Q U E O U S J~'I.,OW JN 3[AN
~.15
To o b t a i n ~he value of X:o from the slope B ~t m u s t be mul~ipli6d b y the f a c t o r ( 1 - r,,/dc,,) a c c o r d i n g to e q u a t i o n (12). Since the fl'action .rc,,/g~, is f o u n d to h a v e a value, a b o u t 0'1, s m a l t c o m p a r e d w i t h u n i t y , n e i t h e r go,, nor re,, need be m e a s u r e d w k h ~neat acc, uracy. T h e formcr is o b t a i n e d d u r i n g t h e course of t|m e x p e r i m e n t ; but sops.rate d e t e r m i n a t i o n s ~re n e c e s s a r y for the latter. ~Vben the d y e is h~geste& according to the schedule described curlier, t h e p l a s m a level oscillates b u r ~he conc e n t r a t i o n in the a n t e r i o r c h a m b e r a t t a i n s a. level which does not, undecgo measur~tbt.e v~,riations. T h e a c l d e v e m e n t of c o m p l e t e e q u i l i b r i m n between aqueous ]:tttraoilr a,n d co,'ne~t is v e r y slow, b u t by a p p r o a c h i n g it .from botlt sides a sumcienzly close ~tpproximat.ion m a y be obtaitled i n a few hours (Fig. 3(b)). i n four subjects, the v a l u e of re,, was fottPxl to lie between 1-1 a n d 1.3; it was not. considered necessary to c a r r y o u t t:he d e t e r m i n a t i o n s in all cases, bu.t a value of 1..2 was d e e m e d to be appropriate.
Method 2 The b a c k g r o u n d t o t a l fluoresc, enee of l~he hun~tatl a n t e r i o r segment, was of the order of 0-02 /zg of fluoresce|n, a n d a b o u t 50 t i m e s t h i s a m o u n t was inbroduced b y iont, ophoresis. T h e aurofluorescence of t h e selera was v e r y mucia higher t,han of tim cornea, so t h a t f r e q u e n t l y t h e r e a d i n g w i t h l;he circle of l i g h t c o r r e c t l y in posit;ion o~z the eye was a m i a i m m r t x,alue r a t h e r t h a n a m a x i m u m . J?or tocsin-dark-eyed people, tam I'~ x,a.lues followed a smoovh curve thai, h a d a s h a p e am'cein_- with t h a t given by e q u a t i o n (17), ii~ which Values of A a n d B dec{veal f r o m the ~':,, c u r v e were i n s e r t e d (Fig. 300)- 'J?he d c t e r m i n a t i o ~ of t,he slope. A a n d t~he ral~io t'jF~ p r e s e n t e d tittle diffienlty i n - m o s t cases. .Be~bre t h e values of t h e flow r a t e could be c a l c u l a t e d t h e effect of three possible sources of error h a d to be assessed. These were (1) Lhe r e t u r n of t.ight f r o m t h e iris, (2) a c h a n g e in t.he fluorescence of fluoreseein caused b y t h e c o r n e a l tissue, a n d (3} t},c loss of t h e d y e d i r e c t l y from tim cornea to ~he blood a t t h e limbus. (1) Y.ris ~'ejtecta¢we. The r e a d i n g Ft m a y be increased a b o v e its t r u e v a t a e because the posterior .lace of the a n t e r i o r c h a m b e r does n o t absort? all t h e 4ight. falling a p o a it, as in the case of the c a l i b r a t i n g ch ambers. The green l i g h t e m i t t e d b y t h e fluore~seein rna.y be s e a t t e r e d by t h e iris d i r e c t l y to t h e p h o t o m e t e r , or some of the i n c i d e n t blue ligh~ m a y be .returned t h r o u g h t h e a q u e o u s h u m o u r - a n d cornea to e x e i t e f t u : t ; h e r fludreseen.ee. Whe~a t h e fluorescein is first io.troduced in.to the e y e b y iont.ophoresk% it is remote f r o m t h e iris a n d ~he influence of this bissue s h o u l d be small; as it diffases thi-oughou6 t h e a n t e r i o r c h a m b e r a n d to t h e p e r i p h e r y of t h e cornea, t h e effect of t h e s c a t t e r i n g s h o u l d rise to a maxinxtma. A n init.ial rise o r a.n e x t e n d e d flat p o r t i o n to t | i e ]~', curve is, in fact, feared irt b l u e - e y e d s u b j e c t s (Fig. 4).'Browr~ eves a n d i n t e r mediate s h a d e s (grey: green, h a z e l ) : d o n o t a p p e a r to be seriousl,,- affected b y this source of error, as show~ by" t h e eouformit.) o f t h e F~ Curves t o e q u a t i o n (17) a n d by: other evidence to be discussed later. No p r a c t i c a b | e w a y was f o u n d of e v a d i n g this source of error in pate-eyed subjects, and t h e m e t h o d , insofar as it m e a s u r e s the a.bso) lute rate of flow~ is i n a p p l i c a b l e to t h e m . {2) Corneal que.nchi~ 9. [[1~is possible ~hat t h e cornea} tissue e x e r t s a n e f f e c t on t h e fluoresce~n w h i c h p e r m e a t e s i t so ~;hat its fluorescence is s o m e w h a t quencfied, This would Iead t0. an u n d e r e s t i m a t e of t h e v a l u e of F~ a n d a c c o r d i n g l y of:/'. This., w a s invest-igated, in. a n i m a l eyes, b y c o m p a r i n g t h e t0t~al fluorescence of a s t a i n e d corneal disc w i t h t h a ~ ; of t h e fluoreseein after it h a d been le-ached Out of t h e tissue. The e x p e r i m e n t was carried o u t as folloWs (l?ig. 5). T h e f l u 0 r 0 m e t e z w a s a d a p t e d as if to measure/~'t i n t h e eye a n d was foot'sea, by" m e a n s o f reflect'lenin t~he hypot, e n a s e
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was held in ]t h. e correct p o. s i t i o n by moans of a b l a c k e n e d ring cemented to t h e sm'faee. • . . . W a t e r wad"placed w i t h i n t h e ring to r e d u c e d reflections from t h e b o t t o m of t h e 15ube. T h e tissue ~ a s o b t a i n e d from t h e eye of a rabbih whose corn.ca h a d been s t a i n e d w i t h f l u o r e s e e i n t h e pre%,ious evening. The a n i m a l was Mlled, ~he corneal e p i t h e l i u m
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18
~9
~,, 20
i 21
Time of doy (hr)
F r o . 4. Exl)erimer~t,M v a l u e s o b t a i n e d f r o m b l n e - e y e d s u b j e c t (M.t'4. i n T ~ b l c . l ) . Dei~ails a s in .Fig, 3(a),
scraped 0ffi t h e cornea excised and ~ disc of tissue, 6 ram. in d i a m e t e r , quickly p u n c h e d f r o m it. T h i s was pliieed in .the b o t t o m of a t u b e u n d e r 0.2-0-5 ml of physiological Saline b u f f e r e d at p H 7. Measurements. of t h e t o t a l fluorescence, were m a d e immedia t e l y a n d ~fter 24 hr, w h e n t h e d y e had leached o u t i n t o t h e b a t h i n g fluid. I d e n t i c a l m e a s u r e m e n t s were c a r r i e d o u t on all u n s t a i n e d disc of cornea from ~he obher.eye, submergqd in an equal v o l u m e o f dilute buffered flu0rescein solu~;ion. T h e t o t a l fluorescence of. b o t h s p e c i m e n s w a s f o u n d to h a v e increased a~ t h e end of 24 hr, a n d this could be ascribed %o a n a v e r a g e lengtt,ening of the p a t h of the |ighg t h r o u g h t h e fluoreseentisolu~ion a.s a result of its s c a t t e r i n g b y the swollen, cloudy, cornea, l n five stained c o r n e a l discs the tots.1 fluorescence rose t o . l t 4 ° / o of its o.rigin~l vahie, and. in t h e fix;e unstrained controls to 112.%. A.s a f u r t h e r c.heck, e a c h c o r n e a was. d i s s o l v e d b y a d d i n g a small drop of c o n c e n t r a t e d t e t r a m e t h y l a m m o n h ~ m hNdroxide to t h e t u b e a n d a.llowing it to s t a n d for a f u r t h e r 24 hr. The fluorescence
AQUEO'US
]~LO]V
IN
~IAN
2t7
of t h e c l e a r s o l u t i o n o b t a i n e d in t h i s w a y was 97~/o of t h e o r i g i n a l r v a l u e in ~ h e case of t h e five s~,4ined discs, and 96~/o m t h e five cow,trois. Since t h e s t a i n e d disc l~y a~ t h e bo6torn of t h e t u b e a t t h e b e g i n n i n g of t h e experim e n t a n d t h e fluorescein s o l u t i o n l a y a b o v e t h e cornea in t h e control, a d d i t i o n a l experimei~ts Xverc c a r r i e d o u t on t h e effect of t h e dist, r i b u t i o n el" t h e d y e w i t h i n t h e t:~be on t h e r e a d i n g of t h e f l u o r o m e t e r . Some glucose was a d d e d to ~ s o l u t i o n of fluorescein to increase i t s d e n s i t y , a n d a. £ew #] were c a r e f u l l y r u n u n d e r 0-2~-D.5 mL of clear buffered saline so t h a t a t h i n l a y e r of d y e ]a.y a t t h e b o t t o m of t h e tube. T h e
Fro. 5. E x p e r i m e n t a l a r r a n g e m e n t for e s t i m a t i t l g t h e quenching of fluo,'esec~aec of fluorescein b y t h e corneal s t r o m a . C, :Disc of corneal s t r o m ~ .
total fluorescence was m e a s u r e d in t h i s eondit.ion a n d a f t e r m i x i n g t h e content, s of the tube. No difference in t h e r e a d i n g w~s n o t e d in n u m e r o u s triMs, a n d i t w a s e v i d e n t t h a t t h e effect u p o n i t o f t h e ohange ii~ d i s t r i b u t i o n m u s t b e l e s s t h a n 1 % . ]?he conclusion d r a w ~ £rom nil t h e s e o b s e r v a t i o n s w a s t h a b t h e s t r o m ~ l tissue has no m e a s u r a b l e influence on t h e fluorescence of fluorescein h~ t h e r a b b i t . No m a r k e d differences in t h e chemica.1 c o m p o s i t i o n of m a m m a l i a . u corneas h a v e been r e p o r t e d , and Jr, was considered u n l i k e l y t h a t t h e b e h a v i o u r of t h e h u m a n cornea, was different in this respect. (3) Loss at l'imbus. I f fluoi'escein passes d i r e c t l y from t h e cornea to t h e blood a t t h e limbus, t h e m e a s u r e d v a l u e of A will be h i g h e r t h a n t h a t a p p r o p r i a t e t o equatior,. (15). A ca.lcuIntioa b a s e d on t h e a s s u m p t i o n of ~ s i m p l e g e o m e t r i c a l s h a p e for t h e cornea. and a r a t e ~f s p r d a d of fluorescein w i t h i n t h e s t r o m ~ eqllM to t h a t f o u n d iu t h e r a b b i t (M~urice, :1960) suggested t h a t it m i g h t u l t i m a t e l y a m o u n t to 3 0 % of A. H o w e v e r , ignorance b o t h of t h e t r u e r~xte of diffusion a n d of t h e e x c h a n g e rela.tionships a t Vhe limbus in man~ m a k e s a n e x a c t e s t i m a t e ~mpossible. Owing to t h e i u t r o d u a t i o n of t h e fluorescein into u circumse, ribecl a.rea n e a r t h e c e n t r e of t h e cornea, i t is to be e x p e c t e d t h a t the loss across 6 h c p c r i p h e r y ~ l l be xmgligibte a t t h e b c g h m i n g o f t h e measure± n~ents, b u t i t m a y a . ~ n m e i m p o r t a n c e towa.rds t h e end of t h e initial 8 hr period over which 21 is e s t i m a t e d .
218
R.
]b'. J O N E S
AND
D.
hl. I ~ I A U R I C l g
A n at.tempt was m a d e to d e t e r m i n e e x p e r i m e n t a l l y t h e g r e a t e s t possible c h a n g e i~ A resultd~g from p e r i p h e r a l losses, b y c b m p a r i n g the value o b t a i n e d f r o m a n eye s t a i n e d eelatrally w i t h t h a t f r o m its fellow eye s t a i n e d p e r i p h e r a l l y . Ii'luoreseein was i n t r o d u c e d m the n o r m a l maxmer b y i o n t o p h o r e s i s e x a c t l y c e n t r a l l y in one c o r n e a and a t the u p p e r l i m b u s in t h e other, t~eadingg of t h e fall of t h e fluorescence in the two eyes were carried o u t from 1 or 2 hr l a t e r for a f u r t h e r 6 hr. Ilt t.he o r d i n a r y s l i t - l a m p a clear zone a p p e a r e d to rmmtin between the c e n t r a l s p o t a n d the p e r i p h e r y a t t h e e n d of this p e r i o d , suggesting t h a t no significant loss h a d occurred across the limbus. ConMstent a n d m e a n i n g ~ t l m e a s u r e m e n t s of t h e t o t a l fluorescence of the eccentricMly s t a i n e d eye were diffienlt to o b t a i n . R e c o u r s e was t h e r e f o r e h a d to c o m p a r i n g t h e a q u e o u s b u r n o u t s of t h e two eyes; five subjects with deep a n t e r i o r c h a m b e r s were c h o s e n tbr this purpose. T h e a q u e o u s h u m o a r of t h e p e r i p h e r a l l y s t a i n e d eye d r o p p e d 4 a n d l~/o/hr t~ster t h a n t h a t of t h e c e n t r a l l y st.ained in two cases, t h e y fell ~t t h e s a m e r a t e in a n o t h e r ease,, and, in t h e r e m a i n i n g two, t h e p e r i p h e r a l l y st,Mned a q u e o u s fell a t a r a t e slower by :~ a n d 1-5~/o/hr. I n each of the l a s t four cases the proba b i l i t y t h a t the r a t e of fall in the p e r i p h e r a l l y s t a i n e d eye could h a v e been gn'e,~ter by a n a m o u n t su[t~lcicnt ~o give a 10°/o or m o r e increase in A was tested s t a t i s t i c a l l y ; these p r o b a b i l i t i e s were a b o u t 5, 1, 0-5 a n d 0-15/o, ,'espeetively. This e v i d e n c e suggests that., e v e n in the e x t r e m e c o n d i t i o n s where the c o r n e a was s t a b l e d at t,}ie lirnbus, the loss f r o m t h e c o r n e a d i r e c t l y t o the blood is n o t of a n y i m p o r t a n c e in. m o s t eyes. Some u n c e r t a i n t y m u s t remMn, however, since regional va,.iations h~ cornea 1 thie.kness a n d , possibly, in e n d o t h e l i a l p e r m e a b i l i t y can r e s u l t in the d r o p in fluo,.escein conc e n t r a t i o n in t h e cornea n o t being parallel t:o t/hat in the aqueous h n m o u r .
Ea'dperimental values T h e wxlnes o b t a i n e d f r o m 16 s a t i s f a c t o r y curves are s h o w n in Table: 1, where tile 3are a r r a n g e d according to t h e co]our of the iris. T h e subjects were n o r m a l v o l u n t e e r s of b o t h sexes from 20-40 y e a r s old. T h e m e a n of t h e vatues of £'o in I 1 s u b j e c t s is 0.015/rain with a s t a n d a r d d e v i a t i o n of 0,0037/rain. This is s i g n i f i c a n t l y higher a t tile 1~/o ]ex.el t h a n the d i s t r i b u t i o n f m m d bv G o l d m a n n ia l 0 s u b j e c t s : a m e a n of 0.011/rain a n d s s t a n d a r d d e v i a t i o n of 0-0022/ mil'l. T h e m e a n of t h e v a l u e of f i n t h e 10 d a r k e r eyed subject,s is 2,5 t~l/min with a deviat i o n of 0-50/xi/min: T h e p e r c e n t a g e v a r i a t i o n o f f a p p e a r s to be slightly smaller t h a n t h a t of/co, bug n o t e n o u g h to suggest t h a t t h e f o r m e r m i g h t be t h e m o r e c o n s t a n t quantity. T h e values o f Va g i v e n b y the p h o t o g r a p h i c m e t h o d p r e v i o u s l y described a p p e a r t o be s i g n i f i c a n t l y Iower t h a n those f o u n d b y I-Ieim (1941). A g r o u p of I 8 gubjects gave a m e a n v a l u e of 175/M with a s t a n d a r d d e v i a t i o n of 33 t~l. T h e 53 of ~ e i m ' s s u b j e c t s in tt~e s a m e age group, 20-40 years, h a v e an aver~,ge v a l u e of 220 p.i w i t h a s t a n d a r d d e v i a t i o n of 51 t~l. I t Should be e m p h a s i z e d t h a t t h e t h r e e q t t a n t i t i e s f , ]%, a n d V . are estim~t~zc!, b y c o m p l e t e l y independerLt m e t h o d s , t h o u g h it has been c o n v e n i e n t to c a r r y our, the d e t e r m i n a t i o m s of t h e first two in the com~se of ~ single e x p e r i m e n t . T h e s e q u a n t i t i e s are c o n n e c t e d b y t h e t h e o r e t i c a l rela,tionship:
.f
Mean &E.M.
R.K. a b V.N. J.K. M,P~,
M.K.
I-T.K.
D.M... b
A,I,',
M, B . ~
.[~,.~,
R.L k[.8. D.J~.
Subject
Blue-grey Blue Bloc
]Lazei l[azcl Groy
Haze/ Hazel
Dark brown Dark brown Dark brou'a Brown Brown
Eye cohmr
1.55 t. 15 1.7 1.9 1.7 1.9 2,3 1.5 1.45 2-4 2,4 2,3 2.1 3. l 2.1 2'6
FdFo
0.0J53§ 0,0011
0-011 0"014 0'018
0"014
10
26 9 10
0"012 0.018 0"0ll.-14 0'023 0'032 0'017 0"013 O.OI t 0-012 0-010 0-015 0,012
k, (rain -t)
9 11.5 14 14 16 10 16 8.5 8 12 15 10
~ ~o
2-4st
0"014 0.020 0.01~15+, 0"025 0.035 0.0Ill 0.014 0.013 0.0135 0-02I 0.010 0,0t,1 0.016 0-011 0"016 0.020
il (rain-I)
0"17
2.3 t.75 2.1 3.2 2,45 2.75 2,9 t.8 1.75 2.9 2.9 2.5 2-3 3.0 2-8 4'6
,f * (/dJ)nin)
R, L, ]light and loft eyes of same subjcck a, b, Same subject on two different occasions. *Va]ue of 8 365/zl in some on.sos, 410 gl in othors. Uncertain value hecausv, of large scatbr .f oxperimental points. f I0 subjects, excluding V.N., J.K. and 51'.12, § 11 subjectS, exohlding D.R,. and M.B.
0.0032 0.0033 0.0029 0.0029 0.0030 0,0030 0,0026 0'00'37 0'0048
0'003~
0,0041 0,0042 0"0034 0.004 t 0,0035 0'0035
A Onin-1}
T:'t BI.I~ [
174 190
tg!)
')% ""
162 190 214
I89 100 153 l(i0 122 }12 200
1:~ (~.l)
1.0 1.05 0.8-1.0 1"15" 1,6 0,7 9.9 1,0 l'I 1.2 1.1 .I-1 !.4 0.75 0-9 0'75
1,'.Tr,~Jf
).J
),¢
0
0
220
1~. F, J O N E S
AND
D.M.
MAUP~ICE
:In view of this it is gratifying, though no doubt fortuitous, that the ratio k,, V,/f for the experimental values, showu in the last column of the table, is close to unity in fanny, of the cases. The low w~tue for the two blue-eyed subjects is additional evidence thatJ' is overestimated by method 2 in these cases. One m a y conclude that either method is capable of giving ,m accurate estimate of the absolute value of tim outtlow of tiuoresccin from the ~mtcrior ch~tmbcr in man. Experience has st)own that method 2 is much more reliable ~md convenient in cycs of thc darker hues to which it is applicable. I t is, in theory, ouly necessary to make readings on the subjecl~ on t,wo occasions m order to derive A and 1,',[F,, thougil additional checks are advisable. The dye may be insl;illed on tim previous evening which often adds to the convenience of t.hc experimental schedulc. By co,m'as~;, method t requires readings to bc made frequently throughout the d~):, and commonly does not permit a valae of ko to be derived to an ,~cce~,i~abic degree of precision. It is tlsually satAsfactorv in eyes wit}t (leep anterior chambers, however, and may be used with irides of anv co]otlr. ]?requcatly, when t:he effect of a drug is being ~:ested, for example, a comparison of the outflow of the two eves of one [)crson or of t;hc same eve on two different occasions is all that is required. For r.his purpose a simple modific'ltion of method 2 can be employed in which either -f~,fF,. or F,,/F~ is measured; these developments will be described elsewhere. ,.
R.J~FERENCES Duke-Elder, Sir W. S. and Mauricc. D. :~,I.(1957). Brit. J. 01fl~thalm(J, 41,702. Goldmann, H. (1950). Ophtludmologica, ]2,t,~el 119, 65. I]:eim, M. ( 1941). Ophtludmoloyica. f3(t.~el.102, 19:}. Jones. R. F. and M~urice. D. M. (19fi3). Exptl Eye Re~'. 2, 233. Ll,.ngham, 5'17.F~. and Taylor, C. B. (1960). d. Physiol. 152, 447. Langley, D. artd 3Iael)onald, R. K. (1952}. Brit. J. Ophth,dmoI. 36, 432. ~Iaurice, D. M:. (1960). Am. J. Ophthalmol. 49, I0[[. ~rctttrice: D. M. (19(;2,1. Exptl Eye Rcs. 2, 33. Weekers, K. and Dcbm, rc~tle. Y. (1953)~ Ol~hthab~wlogica, Basel 125, 425.