of performance is the signal-to-noise ratio (SNR) of the resulting data. This paper ... calculate the ¯ uorescence ef®ciency of tissue from in vivo measure- ments of tissue ..... after all Fresnel losses at the air/glass interfaces, and Tf represents the ...
M eth o d to D eterm in e T issu e F lu o rescen ce E f® cien cy in Vivo a n d P red ict S ig n al-to -N o ise R a tio fo r S p ectro m eters E . V . T R U J IL L O , D . R . S A N D IS O N , U . U T Z IN G E R , N . R A M A N U J A M , M . F O L L E N M IT C H E L L , a n d R . R IC H A R D S -K O R T U M * D ep artm en t of E lectrica l an d C o m p u ter E ngin eerin g, T he U niversit y of T exa s, A u stin, T exa s, 7871 2. (E .V .T ., U .U ., N .R . an d R .R - K .); D epartm ent 2 6 65, S an dia Nation al L abora tories, A lbuqu erq ue, N ew M exico, 8718 5 (D .R .S .); and D ep artm en t of G yn eco logic O n cology, U T M D A nderso n C ancer C enter, H ousto n, T exas, 7 70 35 (M .F .M .)
R ecen t clinica l tria ls h a ve d em on str at ed th e p oten tial of ¯ u o rescen ce sp ect rosc op y f o r in vivo d iag n osis of p ath ology . Th ere is sig n i® can t p ot en tia l to red u ce t h e co st an d com p lex ity of in st ru m en ta tion t o m easu re tissu e sp ect ra ; h o w ever, carefu l a n alysis is req u ired t o m ax im ize p erfo rm an ce an d m inim ize co st . O n e m easu re of p erfo rm a n ce is t h e sig n al-to - n o ise rat io ( S N R ) o f t h e resu ltin g d at a. T h is p ap er d escribes a m eth od t o p red ict th e S N R of a given op t ical d esig n f or a p a rticu lar tissu e ap p lica t ion . In ord er t o calcu la te th e exp ected S N R , t w o p ieces o f in fo rm a t ion a re req u ired : (1 ) th e t h ro u gh p u t a n d inh eren t n oise of th e sy ste m an d ( 2) a q u an tita t ive relat ion sh ip b etw een t h e illu m inat ion en ergy an d t h e resu lting t issu e ¯ u oresc en ce ava ilab le f or co llect ion , w h ich w e d e® n e as th e tissu e ¯ u o rescen ce ef® cien cy (F E ). W e p rese n t a m eth od to calcu late th e ¯ u o resc en ce ef® cien cy o f tissu e f rom in vivo m ea su rem en ts of tissu e ¯ u oresc en ce. W e rep o rt F E m easu rem en ts of t h e n orm al an d p recan cero u s h u m an cerv ix in vivo a t 337, 3 80, a n d 46 0 n m excita tio n . W e also p rese n t an d evalu ate a m et h o d t o est im ate th e t h rou g h p u t a n d n o ise of v ariou s sp ect ro m et ers an d p red ict t h e exp ect ed S N R fo r t issu e sp ectra b y u sin g t h e m easu red t issu e F E . F or sq u am ou s cerv ica l tissu e, as t h e d egree o f t h e d ise a se in crease s, F E d ecrea se s, an d a s t h e excitat ion w av elen g th increases, F E d ecrease s. C ervica l tissu e F E va ries m ore th a n tw o ord ers of m ag n itu d e, d ep en d ing o n t h e t issu e t yp e a n d on th e excitat ion w a v elen gt h u se d . O u r S N R ca lcu latio n s, b ased o n m easu red va lues of tissu e F E, d em on str at e ag reem en t w ith in a fa ct or o f 1 .3 o f t h e m ea su red S N R on average. T h is m eth od can b e u se d t o est im a te th e p erfo rm an ce of d iff eren t sp ect ro m eter d esig n s f or clin ica l u se . In dex H eading s: C ost- effect iven ess an a lysis; C ervix; P recan cer ; F lu oresc en ce sp ectro sc op y ; S ign al-t o -n oise ra t io.
IN T R O D U C T IO N R ecen t clinical trials h av e dem o nstrated th e p o ten tial o f ¯ u orescen ce sp ectro scop y fo r in vivo diag no sis o f patho lo gy. 1,2 T issu e ¯ u orescence sp ectro sco py can b e u sed to im age larg e areas o f tissue to id entify areas su spiciou s for d isease an d ex tract diag no stically relev an t stru ctu ral an d h isto ch em ical in form atio n . 3 T his is an im p o rtan t ad v antag e w ith resp ect to m any tradition al m etho d s th at requ ire clin ical ex pertise to id entify areas to b io p sy fo r su bseq u ent h isto lo gic analy sis. In particu lar, ¯ u o rescen ce h as sho w n p ro m ise for the d iagn o sis o f p recan cero u s an d cancero us lesio ns of th e b reast, 4 lun g , 5 bro nch u s, 6 oral cavity, 7 cer v ix, 8 g astro in testin al tract, 1 ,9 an d b rain . 10 A ltho u gh spectro sco pic m easu rem ents o ffer several ad van tages, in stru m en tatio n d escrib ed in the literatu re is ex pen sive relativ e to cu rrent d iag n ostic to o ls, an d, in o ur ex perien ce, d if® cult fo r clin ical staff to u se w ith ou t tech n ical assistan ce. T h ere is sign i® can t p oten tial to red uce R eceived 3 N ov em ber 1 997 ; accepted 3 M ar ch 1 998. * A uth or to w h om corr esp ond ence sh ould be se nt.
Volume 52, Number 7, 1998
the co st an d co m plex ity of th is in stru m en tatio n ; h ow ev er, carefu l an aly sis is requ ired to m ax im ize p erform ance an d m in im ize cost of in stru m en tatio n . O n e m easure o f th e p erfo rm ance o f an o p tical system is th e sign al-to -n o ise ratio (S N R ) o f th e resu ltin g d ata. In g eneral, as th e S N R is redu ced , the classi® cation accu racy d rop sÐ as d o the sy stem co sts. 11 ±1 3 T his p aper d escrib es a m eth od to p red ict th e S N R o f a g iv en op tical d esig n fo r a particu lar tissu e ap p licatio n an d sh o uld ser ve as a g u ide in th e d esig n and ev alu atio n o f m o re co steffectiv e ¯ u orescence diag no stic system s. We illu strate an d v alid ate th is m etho d w ith th e p articu lar ex am p le o f d etection o f cer vical precancer. M ETH O D S In o rd er to calcu late th e exp ected S N R fo r a g iven sy stem desig n, tw o p ieces o f in form atio n are req uired : (1) th e th ro u gh p u t and inh eren t n oise o f the sy stem an d (2) a q uan titative relatio nsh ip betw een th e illu m in atio n en erg y an d th e resu ltin g tissu e ¯ u orescence available fo r co llectio n . In o p tically d ilute sam p les, the q uan tu m ef® ciency (Q E ) p rov id es th is relatio nsh ip , an d m etho d s to m easu re Q E are w ell k no w n . 3 H ow ev er, in tu rb id , m ultico m po n ent sam p les (su ch as tissu e), th ese m eth od s are n ot app rop riate. To rem o v e th ese lim itation s, w e hav e d evelo ped a m eth o d to calculate th e ¯ u orescence ef® ciency (F E ) o f tissu e from in vivo m easurem en ts o f tissu e ¯ uo rescen ce. W e rep o rt ¯ u o rescen ce ef® ciency m easurem en ts of th e no rm al an d precancerou s h u m an cer vix in vivo at th ree ex citation w avelen gth s. W e also p resen t a m eth o d to estim ate the thro ug h pu t an d n oise o f v ario u s sp ectro m eters an d p redict th e exp ected S N R fo r tissu e sp ectra b y u sing th e m easu red ¯ uo rescen ce ef® cien cy of tissue. W e validate th is m etho d fo r cer vical tissue ¯ u orescen ce spectra. F E T h eo ry. In a d ilu te, h om og en eou s, no n scattering so lution o f p ath leng th L , E q . 1 d escrib es th e relatio n sh ip b etw een th e ex citation en ergy (P 0 ( l x )) an d the ¯ u orescence en erg y arriv in g at the detector (P ( l x , l m )), as a fun ctio n o f ex citation an d em issio n w av elen g th . P (l
x, l
m) 5
E
L
d z P 0 (l
x
)m
a
(l
x
)f (l
m
) b (z).
(1 )
0
In th is form ula m a ( l x ) rep resen ts th e ab so rp tion co ef® cien t o f th e ¯ u oro p ho re at th e ex citatio n w avelen gth , f ( l m ) is th e fraction o f ab sorb ed en erg y co nv erted to ¯ uo rescen ce at th e em issio n w av elen g th, an d b (z) is th e co llectio n ef® ciency of th e sy stem , w h ich d ep en ds on th e
0003 -7 028 / 98 / 52 07-0943$ 2.00 / 0 q 199 8 S ociety for A pp lied S pectros co py
APPLIED SPECTROSCOPY
943
F IG . 2 . S ch em atic d iagram of th e ¯ uor im eter u se d to m easu re ¯ u orescen ce sp ectra.
F IG . 1. G eo m etr y o f the ® ber- op tic p r o be use d to m easu re ¯ uoresc en ce sp ectra of (a) stan dar d so lutions and ( b ) tissu e.
dep th alo ng the o ptical ax is, z. In the case w h ere th e collectio n ef® cien cy is in dep en den t o f z and h as the v alue of b 0 , E q . 1 red u ces to the fam iliar resu lt: P ( l x, l
m
) 5
P 0( l
x
)b
0
m a(l x )f ( l
m
)L .
(2)
S um m in g f ( l m ) o v er all em issio n w avelen gth s y ield s th e qu an tum ef® cien cy o f th e ¯ u oro ph o re. T he p ro d uct of the ab so rp tion coef® cien t an d th e Q E o f an u n kn o w n ¯ u o ro p ho re can b e calcu lated fro m ¯ uo rescen ce m easurem en ts o f th e u n kn o w n sam ple an d m easurem en ts fro m a sam ple w ith k n ow n abso rptio n co ef® cien t an d Q E ; th e m easu rem en ts m u st be d o ne w ith th e sam e system un d er th e sam e co n dition s. D eriv ed fro m E q. 1 , th e pro duct of m a and the Q E o f th e u n kn o w n is g iven by
m
aÐ un kn ow n
5
m
(l
x
)Q E u nk no w n
aÐ k no w n
(l
x
O
)Q E kn ow n l
O
l
P kn ow n ( l
P un kn ow n ( l m
x
, l
m
)
x
, l
m
) .
(3)
m
If th e ab sorp tio n co ef® cien t of th e u n kn o w n is m easured , th e Q E o f th e u n kn o w n can b e co m p uted . 3 T he pro blem w ith this ap p roach fo r tissu e is th at E q . 1 is n o t valid fo r tu rb id m edia, since it do es n o t in clud e th e effects o f scattering an d reab so rp tion p resen t in tu rbid m e-
944
Volume 52, Number 7, 1998
dia. In a tu rb id sam p le, th e ¯ u o rescen ce p ro d u ced depen d s n ot o n ly o n th e p rod u ct o f th e ab so rp tion coef® cien t an d th e Q E bu t also on th e attenu atio n o f excitatio n lig h t p rop ag atin g in to th e sam ple an d the atten u atio n o f ¯ u o rescen t lig h t pro pag atin g o ut o f th e sam p le. F u rth erm o re, in m o st tu rbid m ed ia, th e id en tity of ¯ u o rescen t m o lecu les is u n kn o w n . T h e ab sorp tio n coef® cien t con tain s co n tribu tion s fro m th ese ¯ u o ro p ho res as w ell as o th er n o n¯ u orescent chro m o ph o res. A s a resu lt, m a of the ¯ u o ro p ho re cann o t b e determ in ed easily in turb id m ed ia, in co n trast to m o st d ilu te solu tio n s w h ere just o ne ¯ uo ro p ho re in¯ u ences th is valu e. F in ally, m an y tissu es hav e a lay ered stru cture, and ¯ u o ro p ho res and ab so rb ers are no t d istribu ted ho m o g eneo u sly alo ng the op tical ax is (z). A lth o ug h th e Q E is dif® cu lt to m easu re for tu rbid sam ples, it is relatively easy to m easu re th e ¯ u o rescen ce ef® ciency, w h ich d escribes th e ratio o f to tal em itted ¯ uo rescen ce en ergy to ex citatio n energy. T h e ¯ u orescen ce available to th e detector fro m a turb id m ed iu m (P t ) con tain ing a sin g le ¯ u oro ph o re w ith ab so rp tion co ef® cien t m a can b e w ritten as P t (l
x, l
m) 5
P 0 (l
3
x)
E
`
d z H in ( l
x
, z) m
a
(l
x
, z) f ( l
m
, z)
0
H o ut ( l
m
, z) b (z)
(4)
w h ere (H in ( l x , z)) an d (H o ut ( l m , z)) rep resent th e sam p le atten uation o f th e excitatio n an d em issio n lig ht, resp ectiv ely. F or a tu rbid m ed iu m co ntain in g m u ltip le ¯ uo rop h o res, E q . 4 can b e gen eralized to P t(l
x, l
m) 5
3
P 0 (l
O
x)
[m k
E
`
d z H in ( l
x
, z)
0 ak
(l
x
, z) f
k
(l
m
, z)]H ou t ( l
m
, z) b (z) (5)
w h ere the ind ex k refers to ind iv id u al ¯ u o ro p ho res. W e de® ne the F E as
E E `
FE 5
`
dl
dz
l
0
3
m
H in ( l
x
O
, z)
H o ut ( l
x
m
[m
ak
k
(l
x
, z) f
k
(l
m
b
, z)]
, z).
x, l
m) 5
E
x
, l
m
dz H in Ð t ( l
H o utÐ t ( l
P0
E
) 5
3
x
, z) m
aÐ t
(l
x
)f
t
(l
m
)
0
3 an d P std ( l
`
P0
`
m
, z) b t (z)
d z H in Ð std ( l
x
(7 a)
, z) m
aÐ std
(l
x
)f
std
(l
m
)
0
H o utÐ std ( l
m
, z) b
std
(z)
(7 b )
w here the su b scrip t t refers to a tu rb id sam p le, in th is case cer v ical tissu e, an d th e su bscript std refers to th e reference stand ard u sed fo r th e m easu rem en ts. A ssu m in g an isotrop ic ¯ u o rescen ce em issio n , 11 th e collectio n ef® ciencies can be ex pressed as
b
t
5
std
5
b
0
(z 1
sh ield t ) 2
(z 1
sh ield t 1
(8 a)
an d
b
b
0
(8 b )
z 0) 2
w here b 0 is a co n stan t that in clu d es th e d etecto r ef® cien cy. W e fu rth er assu m ed that th e tissu e co llection ef® cien cy ( b t ) w as in d epen d ent of z, since the dep th s fro m w h ich m o st o f th e ¯ uo rescence is co llected are v er y sh o rt ( , 3 00 m m ) 1 5 co m p ared to th e shield th ickn ess (1 .7 m m ) (E q . 9 ).
F E t(l
x
)
êE é
êE 5
` l
ë
ê
, l
x
m
) dl
ú ´ê P std ( l
x
ú êE úê ù é
m
x
` l
P t (l
x
, l
m
) dl
m
û ë
`
dz 0
E l
`
dl
m
H in Ð std ( l
x
b 5
0
(sh ield t ) 2
.
(9 )
In teg ratin g b o th sides o f the E q s. 7 a an d 7 b w ith resp ect to th e em issio n w avelen gth , ex p ressin g their ratio, an d u sing the co llectio n ef® cien cies of E q s. 8 b and 9 p ro v ides a w ay to calculate th e tissue F E , g iven th e ¯ uo rescen ce sp ectru m of th e tissu e and a stan d ard w ith k no w n op tical p rop erties and co llectio n g eo m etr y (see E q . 1 0 belo w ). T h e F E o f cer v ical tissu e w as estim ated fro m in vivo m easu rem en ts of tissu e an d su bseq u ent m easu rem en ts of a n o ntu rb id stand ard , speci® cally, a R h od am in e 6 10 solutio n (2 m g /L in ethy lene g ly co l), by usin g E q . 10 . T h e m easu rem en t tech n iqu es u tilized for b o th th e cer vical tissu e an d the referen ce stand ard are described ® rst, an d then th e F E calculation is p resen ted . In stru m en ta tion . A schem atic diag ram o f th e p ortable ¯ uo rim eter, w h ich w as u sed to acq u ire the cer v ical tissu e ¯ uo rescen ce an d th e referen ce stan d ard sp ectra at three ex citatio n w avelen gth s, is sho w n in F ig . 2. T h is system h as b een d escrib ed in detail p revio usly 1 6 an d is b rie¯ y review ed here. Tw o n itro g en-p um ped d y e lasers w ere u sed to pro vid e illu m in atio n at three differen t ex citatio n w avelen gth s: 3 3 7 , 3 80 , an d 4 60 n m . L aser illu m in atio n at each ex citation w av eleng th w as cou p led in to the ex citatio n ® b ers o f th e p ro b e. E x citatio n ligh t w as d elivered to the sam p le th rou g h a tran sp aren t o p tical sh ield w ith a thick n ess o f 1 .7 m m . T h e av erag e tran sm itted pu lse en ergies at the 33 7 , 3 8 0, an d 4 6 0 nm excitatio n w av eleng th s w ere 12 , 9 , an d 1 4 m J, resp ectiv ely. T h e laser ch aracteristics w ere a 5 n s p ulse du ratio n an d a 30 H z repetitio n rate. T h e pro xim al end s of th e fo ur em ission co llectio n ® b ers w ere arran g ed in a circu lar array an d w ere im ag ed at th e en tran ce slit o f a p oly chro m ato r, w hich w as co u pled to a 1 02 4 in ten si® ed d io d e array th at w as co ntrolled by a m ultich an nel analy zer. L o n g-p ass ® lters at 3 60 , 4 0 0, an d 47 0 nm w ere u sed to b lock th e scattered lig ht resulting fro m th e 3 37 , 3 8 0 , an d 4 6 0 n m e x c i t a t i o n so u r c e s, r e sp e c t i v e l y . D u r i n g ¯ u o re sc e n c e m easu rem en ts, a 2 05 n s co llectio n g ate, w h ich w as sy nch ro n ized to the lead ing ed ge of th e laser p ulse w ith a p ulser (P rin ceto n In stru m en ts P G 2 00 ), elim inated th e effects o f th e w h ite lig ht used fo r v isual ex am in atio n. C lin ica l M ea su rem en ts. C lin ical ¯ u orescence spectra w ere m easu red fro m 3 7 4 cer v ical sites in a rand o m ly selected g rou p o f 92 n o np regn an t patients referred to th e co lp o scop y clin ic o f th e U n iv ersity o f Te x as M D A n derso n C an cer C en ter o n th e basis o f ab no rm al cer v ical cy tolo g y. In fo rm ed co nsen t w as ob tained fro m each p atien t w ho p articipated, and the stu dy w as review ed an d app ro v ed by th e In stitu tion al R ev iew B o ard s of th e U ni-
(6 )
A s w ill b e sho w n, th e F E o f an u n kn o w n turb id sam ple can b e calcu lated from m easurem en ts of th e u n kn o w n an d m easu rem en ts o f a h o m o g eneo u s sam ple w ith k n ow n o ptical pro p erties ( m a , Q E ) ob tain ed by u sing a ® b er-o ptic p ro b e u nd er sim ilar con d itio n s. F ig u re 1 sh o w s a sch em atic d iagram o f th e o p tical ® ber pro be used in th ese stu dies; m u ltip le ® bers w ere u sed to d eliver ex citatio n ligh t and co llect ¯ u orescence th rou g h a tran sp aren t o p tical sh ield , w ith th ick ness sh ield t . F o r tu rbid tissu e m easu rem ents, th e shield w as p laced d irectly in co ntact w ith the tissu e. F o r stan dard m easurem en ts, th e sh ield w as p laced in co ntact w ith th e w all o f a 1 cm th ick q uartz cu vette, w ith w all th ick n ess z 0 . U n der th ese co n dition s, the ¯ u o rescen ce pro du ced b y an un k no w n tu rbid sam p le (P t) an d by a ho m o g eneo u s stan d ard ( P std ) co ntain ed in a cu vette w ith w all th ick ness z 0 an d p ath leng th `, are g iven b y E qs. 7 a an d 7b , respectively, P t(l
t
, z) m
aÐ std
(l
x
)f
std
(l
m
x
)H o utÐ std ( l
m
, z)
ù
ú
1 (z 1
sh ield t 1
z0)
2
ú .
ú
1 (sh ield t ) 2
û (1 0 )
APPLIED SPECTROSCOPY
945
versity o f Te x as, A u stin and th e U n iv ersity o f Te x as, M D A n d erso n C ancer C enter. D etails of this clin ical stud y hav e b een described in d etail prev io u sly b u t are brie¯ y rev iew ed h ere. 16 A fter colp o sco p ic ex am in atio n o f th e cer v ix , b ut befo re tissue b io psy, ¯ u orescence sp ectra w ere acqu ired o n average fro m tw o colp o sco p ically ab n orm al sites, tw o colp osco p ically n orm al squ am o u s sites, an d o n e no rm al colu m n ar site (if co lpo sco pically visib le) fro m each p atien t. T issu e bio p sies w ere o b tain ed on ly fro m abn o rm al sites id en ti® ed by co lp o sco py and sub seq u en tly an aly zed by the p ro b e to com p ly w ith ro u tin e patient care p ro cedu res. A ll tissu e b io psies w ere su b m itted fo r h isto log ic exam in atio n by a p an el o f fou r b o ard -certi® ed p ath olo gists, and a co n sensu s diag no sis w as estab lished by usin g th e B ethesd a classi® catio n sy stem . 1 7 S am ples w ere classi® ed as n o rm al sq uam ou s (1 88 sites), n orm al colu m n ar (2 6 sites), m etaplasia (2 0 ), in ¯ am m ation (2 5), lo w -g rad e squ am o u s in tra-ep ith elial lesion (L G S IL ) (45 sites), o r hig h -g rad e sq uam ou s intra-ep ithelial lesio n (H G S IL ) (70 sites). P rio r to each p atien t stu d y, the pro b e w as d isinfected , and a back g ro u nd sp ectrum w as acqu ired at all th ree excitatio n w av eleng ths co nsecu tiv ely w ith th e pro be d ipp ed in a n o n ¯ u o rescen t b o ttle co ntain in g d istilled w ater. T he back g ro u nd spectru m w as sub tracted fro m all su b sequ en tly acqu ired sp ectra at co rresp o nd in g ex citatio n w av elen g ths fo r that p atien t. N ex t, m easu rem ents w ere tak en w ith th e pro be p laced o n the face of a qu artz cu vette co ntainin g a solu tio n of a stan dard ¯ uo rop h o re m olecu le w ith kn o w n o p tical p ro p erties an d Q E . R h o dam in e 61 0 disso lved in ethy lene g ly co l (2 m g /L ) w as selected on th e basis o f its h ig h q u an tu m yield. 1 8 T he co n cen tratio n (2 m g /L ) w as adju sted em p irically u ntil the m easured in tensity of th e R h od am in e stan dard w as th e sam e ord er of m ag nitu de as ty pical tissue ¯ uo rescence. O th er bio lo g ical stan d ard s such as FA D an d N A D H w ere ex plo red , bu t w ere fo un d n ot to b e stab le o v er lon g period s of tim e. F ifty stan d ard ¯ uo rescen ce spectra w ere m easu red at each excitatio n w av eleng th . A fter calibratio n , ¯ u o rescen ce spectra w ere acq u ired fro m th e cer vix : 1 0 spectra fo r 10 con secutiv e p ulses w ere acqu ired at 3 37 nm excitatio n ; and 5 0 sp ectra fo r 5 0 co n secu tive laser p u lses w ere m easured at 3 80 an d 46 0 n m ex citatio n. T he pro be w as dip p ed in sterile w ater p rior to m easu rin g th e ¯ uo rescen ce o f the stan d ard an d each p atien t site to p rov id e in d ex m atch ing betw een the tissu e an d the sh ield. A ll spectra w ere co rrected fo r th e n on u nifo rm sp ectral respo n se o f th e d etection system by u sin g co rrection facto rs ob tain ed by reco rdin g th e sp ectru m o f an N IS T (N atio nal In stitu te o f S tan d ard s and Tech n olo g y) traceab le calibrated tu n g sten ribb o n ® lam ent lam p . F E C alcu la tio n s. E q uatio n 10 p ro vid es a m eth o d to calcu late th e F E s o f all tissu e sam ples. T he ® rst term in E q . 10 can be calcu lated fro m the ratio of the to tal in teg rated ¯ u orescence po w er of th e tissue an d th e R h o dam in e stan dard reco rd ed before each p atien t’ s data. T h e seco n d term in E q. 1 0 req u ires k no w led g e of the op tical pro perties o f the stan d ard as w ell as th e co llection g eom etr y. S in ce th e R h o dam in e stan d ard u sed w as a n o nscatterin g so lu tio n , and the nu m erical aperture o f ex citatio n an d co llection w as sm all (N A 5 0 .22 ), the attenuation of ex citation lig ht entering an d ¯ uo rescen t lig h t
946
Volume 52, Number 7, 1998
exiting th e R h od am in e cuv ette can b e d escribed w ith th e B eer±L am b ert law (H in 5 H o ut 5 e 2 m a ( l )z ). T he w avelen g th -dep en den t ab so rp tion coef® cien ts of th e R ho d am in e stan d ard w ere calcu lated fro m th e m easured R h o dam in e ab so rban ce. T h e qu an tum y ield o f R h o dam in e 61 0 is 1 . 1 8 T h e do u ble in tegral in th e seco nd term o f E q. 10 can b e ev alu ated nu m erically by u sing m easu red v alues o f m a ( l x ), m a ( l m ), and f ( l m ). If f ( l m ) is no t k n ow n , b u t th e q u antu m y ield is kn o w n
1
E
QE 5
` l
dl
m
f (l
m
x
2
) ,
an altern ativ e m eth o d can be used to calculate th e F E . E q s. 7a an d 7 b can b e rew ritten as P t(l
x
, l
m
) 5
3 and std
E
P0
P
x
F (l
`
d z H inÐ t ( l
H o utÐ t ( l (l m
x
, z) m
aÐ t
(l
x
)f
t
(l
m
)
0
, l
m
)
)
5
m
P 0m
b
, z)
0
(1 1a)
(shield t ) 2
aÐ std
(l
)f
x
std
(l
m
)b
(1 1 b)
0
w h ere F (l
5
m
)
E
`
d z H inÐ std ( l
x
, z)H ou tÐ std ( l
, z)(z 1
m
sh ield t 1
z0)2
2
0
and can b e evalu ated n um erically at each em issio n w av elen g th . T he F E can be th en calcu lated b y in teg rating b oth sid es of E q . 1 1 , ex pressing th eir ratio , an d rep lacin g ò d l m f std ( l m ) b y th e k n ow n Q E o f the referen ce stan d ard .
E ê é
F E (l
x
) 5
ë
êê
l
`
dl
P t (l
m
x
b
t
x
, l
ù m
)
úú
é
úû ´êê êë
E
m
l
`
aÐ std
dl x
(l
x
P std ( l m
ù
ú.
)Q E
F (l
x
, l m
)
m
)ú
úû
(1 2)
In th is w o rk , E q. 12 w as used to calcu late th e F E o f all cer v ical tissu e sam ples at each excitatio n w av elen g th. T h e m etho d w as tested b y m easurin g th e ¯ u o rescen ce ef® cien cy o f a n o n scatterin g so lutio n w ith kn o w n o ptical pro perties (0 .1 g /L 1,1,4,4 tetrap hen y lb u tadien e in cyclo hex an e) at 3 80 nm . R ho d am in e w as used as the referen ce stan d ard . Tw o exp erim ents w ere p erform ed. In th e ® rst exp erim ent th e d ata from th e tetraph en ylb utad ien e solu tio n w as tak en by p lacin g th e p ro b e o n th e w all o f a 1 cm p ath leng th cu v ette, sim ilar to th e R h o d am ine stan dard acq u isitio n (F ig . 1 a). In th e secon d ex p erim ent, th e p rob e tip w as p laced in d irect co n tact w ith th e tetrap h eny lb utad iene solu tio n in o rder to resem b le th e cer vical tissue exp erim ent setu p. A cco rdin g to p ub lished valu es, 1 9 th e qu an tu m y ield of a 0 .1 g /L tetraph en ylb u tad iene in cyclo h exan e solu tio n w ith an excitatio n w avelen gth of 36 5 nm is 0 .6 . T he results w ere w ith in 1 % an d 20 % of th is valu e for th e ® rst an d seco nd ex perim en tal pro toco ls, respectively. S N R C alcu la tio n s. U sin g th e F E o f th e 3 74 cer v ical
tissue sites, w e calcu lated th e exp ected sig n al-to -n o ise ratio s fo r th e sp ectro m eter of F ig . 2 at each ex citatio n w avelen gth (3 3 7, 38 0 , an d 4 6 0 n m ). T h ese w ere co m p ared to m easu red S N R s o f th e 3 74 sp ectra at each ex citatio n w av elen gth . P redicted S N R . C alcu lation of th e ex p ected sig n al w as carried o u t b y estim ating th e lo sses in th ree stag es: (1 ) ex citatio n o f ¯ u orescence, (2) co nv ersio n to ¯ u o rescen ce, an d (3 ) co llection o f ¯ u o rescen ce an d con v ersio n to electro n ic sig n al. T h e associated n oise w as th en estim ated, inclu d in g read o ut n o ise, dio de array d ark charg e n o ise, an d p h oto n sho t n o ise. F in ally, th e S N R w as estim ated as the p eak sign al d iv id ed by the roo t m ean squ are (rm s) n oise estim ate. A lth o ug h w e repo rt th ese calculatio n s for the system o f F ig. 2 , th e m eth o d is g en eral in n atu re an d can b e ap p lied to m an y different ¯ u orim eters. A su m m ar y of all th e ab b rev iatio n s u sed in th e S N R calculation s, in clud ing d e® n itio n s an d ty p ical valu es for th e sy stem in F ig . 2 , is p ro v id ed in Ta ble I. E stim atin g lo sses at th e ex citatio n stag e p erm itted calcu lation o f the in ciden t en erg y o n th e tissu e after all th e tran sm issio n and co u plin g lo sses b etw een th e so urce an d the ex citatio n p rob e. T h e ex citatio n en erg y, P 0 [J], w as calcu lated as: P0 5
P o ut N f T q T fr T f [J]
(1 3 )
w here P ou t [J] represents th e en erg y fro m th e sou rce, N f is n um ber o f excitatio n ® b ers, T q rep resen ts the in ternal tran sm issio n o f th e qu artz cou p lin g len ses at the excitation w av elen gth , T fr is th e fractio n o f en erg y rem ainin g after all F resn el losses at the air/g lass in terfaces, and T f represents the in ternal ® ber transm issio n . To pred ict h ow m u ch in tegrated tissu e ¯ u o rescen ce p ow er is av ailab le for co llection (P t), it is n ecessar y to co nsid er th e energy incid en t o n th e tissu e ( P 0 ) and th e cer v ical tissu e F E : Pt 5
P 0 F E [J].
P t T q T fr T f C E
A bb reviatio n BW *C d io d e
CE DC D isp D *F E hn La
L d isp
*N n a cc um N d io d e nf Nf *N p b Nr *P d io d e *P p ro b e *P o *P o u t *P t
(1 4 )
To pred ict th e am o u nt o f th e av ailab le tissu e ¯ uo rescence collected , the co llectio n ef® cien cy (C E ) o f th e p ro b e an d th e losses in the op tics co up ling th e p ro b e to the d etector are estim ated . A ssu m in g iso trop ic ¯ u o rescence em ission fro m a p oin t sou rce, the to tal in teg rated ¯ uo rescen ce co llected at the pro be ( P pr ob e ) is giv en b y P p rob e 5
T A B LE I. S u m m ary of p a ram et er ab b rev iatio n s u se d in S N R p red iction a n d th eir t yp ical valu es at 337 n m ex cita t ion w a v elen g t h . (T h e sy m b ol * rep rese n t s valu es th at w ere calcu la ted on t h e b a sis of a p art icu lar sp ectru m .)
[J]
(1 5 a)
Q E d et ec tor R sh ield t *S N R t Tf T® l T fr
an d CE 5
b
t
5
p R 2nf
4 p shield t 2
(1 5 b )
w here sh ield t is th e d istan ce fro m the collectio n ® b er to the tissu e sur face, R is the ® b er radiu s, w hich is sm all co m p ared to th e sh ield th ickn ess, an d n f is th e n u m b er o f co llectio n ® b ers. In o rd er to calcu late th e ¯ u orescence po w er in ciden t o n each elem ent of th e linear d io de array d etecto r (P dio de ), all th e co llectio n system losses (o p tical lo sses, area m ism atch es, and disp ersio n o f th e ¯ u orescence) are co n sid ered . T h e sig nal incid ent o n each elem en t o f th e d iod e can b e estim ated acco rd ing to P diod e 5
P pro b e T ® lT g r T N A L a L d isp [J/d io d e]
(1 6 )
T gr TNA
Tq
T zo
M ean ing B andw idth over w hich ¯ uorescence is em itted S ignal coun ts g en erated at each elem ent o f the linear d iode arr ay P ro be co llection ef® ciency D ar k charg e R ecipro cal linear d isp er si o n P ixel diam eter C er vical tissu e ¯ uo rescence ef® ciency E nerg y per pho ton at th e peak em issio n w av elength S ignal f ractio n rem aining after accounting f or d ifferences in the heigh t of the d isp er se d sp ectrum and the heigh t of the linear diode ar ray F raction o f total integ r ated ¯ uo r esc ence incid en t o n each dio de Total noise N um ber of accum ulation s at each excitation w aveleng th D io de arr ay d ark charg e noise N um ber of collection ® ber s in the pr obe N um ber of excitation ® ber s in the pr obe P hoton sh ot n oise R eadout noise E nerg y incident on each elem ent o f the linear diode array Total integr ated ¯ uo r escence co llected by the pr obe E nerg y incident on tissu e E nerg y fr om th e so u rce Total ¯ u or esc ence en erg y available fo r collection fr om th e tissu e D etector quantum ef® ciency F iber r adius D istance f ro m tissu e to the pr obe S ignal-to-n o ise ratio I n teg ration tim e per accum u lation I n ter nal ® ber transm ittan ce F ilter transm ittance S ignal r em aining af ter accounting f or all F r esn el losse s at the excitation and em issio n w avelen g ths G r ating ef ® ciency S ignal r em aining af ter accounting f or m ism atch in pro be and sp ectrograph N A I n ter nal lens transm ittance at ex citation and em issi on w avelen gths I n teg ration tim e C uvette w all th ickness
S peci® catio n s fo r sy stem in F ig. 2 1 18 nm 1 .4 E 4 cou nts
0 .0 035 7 0 coun ts/sec 2 0 nm /m m 2 .2 5E -3 cm 0 .0 03 4 .5 E - 1 9 J 0 .0 56
3 .8 E - 3
1 20 cou nts 1 0 accum u lations 5 counts 4 1 1 20 cou nts 1 count 3 .2 E - 1 4 J 8 .1 E - 1 0 J 1 .2 E - 4 J 1 .7 E - 4 J 3 .6 E - 7 J
0 .2 0 .0 1 cm 0 .1 7 cm 1 20 1 0E - 3 s 0 .9 3 0 .9 0 0 .7 8, 0.7 2
0 .2 8 0 .7 45
0 .9 8, 0.9 6
0 .1 s 0 .1 27 cm
w here T ® l represen ts th e lo n g-p ass ® lter transm ittan ce, T gr represents th e g ratin g ef® cien cy, T N A d escrib es th e rem ain ing sig nal after lo sses d u e to th e m ism atched nu m erical ap ertu re o f the pro b e an d sp ectro g rap h , L a d escrib es the sig n al rem ainin g after co nsid erin g the m is-
APPLIED SPECTROSCOPY
947
TA B L E II.
C ervica l tissu e ¯ u orescen ce ef® cien cy m in im u m , m axim u m , an d averag e va lu es. 3 37 nm E x citatio n
N orm al sq uam o us N orm al colum nar M etaplasia In ¯ am m ation LG SIL H G SIL
380 nm E xcitation
m in
av g
m ax
0.0 00 1 0.0 00 4 0.0 00 5 0.0 00 5 0.0 00 2 0.0 00 4
0.0 0 42 0.0 0 27 0.0 0 21 0.0 0 22 0.0 0 30 0.0 0 26
0 .0 156 0 .0 056 0 .0 053 0 .0 105 0 .0 120 0 .0 118
m in 6.1 E -5 2.9 E -5 0.0 002 0.0 001 3.1 E -5 8.5 E -5
m atch in th e h eig h t o f th e im ag e at th e b ack fo cal p lan e of th e sp ectro g rap h and th e heig ht o f the linear d io de array, an d L d isp d escrib es th e fractio n of the to tal in tegrated ¯ u o rescen ce in ciden t o n each d io d e. L d isp w as estim ated as th e ratio o f the w id th o f a d iod e, D , to th e w id th o f th e d isp ersed spectrum , w h ich is th e p ro du ct o f th e recip ro cal lin ear d ispersion , D isp , and th e b and w id th ov er w h ich ¯ u orescence is em itted, B W, acco rd in g to L d isp 5
D D isp 2 1 B W
.
(1 7)
T h e ligh t en erg y at each dio de is th en tran sdu ced to electro n ic co u nts (C diod e ) acco rd in g to C diod e 5
P d iod e hn
QE
[cou n ts/d iod e]
(1 8)
w h ere 1 /hn pro vid es th e co nv ersio n fro m energ y to n u m ber o f ph o ton s, an d th e Q E detecto r is th e detector q u antu m ef® cien cy in cou n ts/p h oto n. F in ally, the n oise associated w ith th is sig n al detectio n m u st b e con sidered . In th is case, th ree different ty p es of no ise are im po rtan t: the sh o t n o ise associated w ith th e sig n al (N ph ) for n accu m accum ulation s, the sh o t n o ise associated w ith the dio d e array d ark charg e (N dio de ) fo r n accu m accu m u latio n s, and th e d etecto r read o u t no ise ( N r ) fo r n accum accu m u latio ns. 20 T h e p h oto n sh o t n oise per p ix el is m o d eled acco rd ing to 20 N ph 5
Ï C d iod e
[co u nts/d io d e].
(1 9a)
W hen th e d io de array dark ch arge is m easured , the associated no ise co ntains co n trib utio ns fro m b o th the sho t
4 60 nm E xcitation
avg
m ax
m in
0.0 011 0.0 007 0.0 005 0.0 005 0.0 008 0.0 007
0.0 0 68 0.0 0 17 0.0 0 12 0.0 0 18 0.0 0 35 0.0 0 33
6.1 E - 5 3.9 E - 5 9.0 E - 5 7.4 E - 5 0.0 001 3.3 E - 5
avg
m ax
0.0 006 0.0 003 0.0 003 0.0 004 0.0 004 0.0 003
0.0 0 38 0.0 0 09 0.0 0 10 0.0 0 26 0.0 0 26 0.0 0 19
no ise asso ciated w ith th e d ark charg e an d the read o ut no ise asso ciated w ith each accu m u latio n . T h e sh o t n o ise of th e d ark ch arg e is p rop o rtio nal to th e sq uare ro ot o f th e d ark ch arg e p er p ixel, w h ich w as calcu lated from th e detector sp eci® catio n s fo r d ark ch arg e per secon d (D C ) in co u n ts/s, an d th e to tal in teg ratio n tim e (t [s]) per accum ulation . T he read o ut no ise w as estim ated fro m th e detector sp eci® catio n s an d th e nu m b er of accu m u latio n s (n accum ). T h u s, the to tal n oise associated w ith th e dio de array dark ch arg e is d escrib ed by E q . 1 9b . N diod e 5
Ï n accu m ´(N r 2 1
D C t)
[co u nts/d io d e]. (1 9 b)
S in ce the d io d e array d ark ch arg e is sub tracted fro m each m easu rem en t, th e to tal n o ise estim ate ( N ) is th e ro ot m ean sq uare o f all n oise ty p es: N 5
Ï n accum ´N r 2 1
N diod e 2 1
N ph 2
[co u nts].
(2 0)
Ta b le I sho w s th at, fo r the sy stem in F ig. 2 (fo r cer v ical tissu e), N is sh ot n o ise d om in ated. F in ally, th e ex p ected S N R w as calculated as C diod e
SNR 5
N
.
(2 1)
In o rder to v alid ate this m etho d , the ex p ected S N R w as estim ated for th e sy stem d escrib ed p rev io usly b y u sin g m easu red F E v alu es at each excitatio n w av elen g th fo r all th e p atien t sites an d com pared to S N R results calcu lated fro m spectral m easu rem en ts. M ea su red S N R . In ord er to m easu re the S N R o f a g iv en sp ectru m , th e no ise p resent in the spectrum m ust b e separated fro m th e tru e sig n al. In th is stu dy, th e co llected data w ere ov ersam p led in 0 .5 n m in crem en ts, w h ile the reso lutio n o f the clin ical system w as o nly 1 0 nm . O n e m etho d to p rov id e an estim ate o f th e tru e sig n al is to su m adjacent p ix els an d resam p le th e sp ectru m (bin nin g ). C o n sequ en tly, in o rder to m easu re th e S N R o f th e sp ectra, a m o vin g av erag e w in d ow o f 20 d ata p o ints (1 0 nm ) w as ap p lied to each sp ectru m , p ro v id in g P bin ned , an d sub tracted fro m the origin al un b inn ed d ata, P or ig in al , p ro d ucin g an estim ate o f th e n oise: N 5
P o riginal 2
P b in ned .
(2 2)
T h e n oise w as estim ated at each em issio n w av eleng th TA B L E III. E xcitation w av elen gth (n m ) F IG . 3. A v er age F E ( 6 excitation w av elen g th.
948
stan dar d deviation ) f or each tissu e typ e at each
Volume 52, Number 7, 1998
337 nm 380 nm 460 nm
R at io o f m axim u m to m in im u m cerv ical t issu e F Es. A ver ag e ( m ax/m in) per patient 6 s 3.6 4.7 2.9
6
6
6
3.3 7.9 2.4
( M ax/m in) all p atien ts 135.8 232.4 115.9
F IG . 4.
P ro bab ility den sity fu nctions f or cer v ical tissu e F E at 33 7, 380 , an d 460 nm excitatio n.
for th e 3 74 p atien t sites spectra acq u ired at each excitation w av elen g th . To estim ate the ratio o f th e sig nal to th e roo t m ean n o ise estim ate (S N R ), th e b in ned sign al w as d iv id ed by th e lo cal stan d ard d eviation o f the n oise, com p uted fro m E q . 2 2 at each p oin t on th e sp ectru m (E q . T A B LE IV . A v erag e p red icted an d m easu red S N R s, si gn als, a n d n oise levels of sp ectra f ro m 37 4 sites. E xcitation w ave- A v erage S N R A verage S N R A v erage A v erage length p redicted m easu red (signal predicted/ ( n oise p redicted / ( nm ) sign al m easured) noise m easu r ed ) 6 s 6 s 337 380 460
10 2 98 11 2
6
6
6
43 48 61
10 5 10 5 85
6
6
6
47 64 53
0 .5 5 0 .4 3 0 .8 4
6
6
6
0 .3 0 0 .2 4 0 .5 6
0 .5 5 0 .4 6 0 .6 2
6
6
6
0.2 4 0.2 7 0.3 4
2 3). T h e stan d ard d eviation w as lo cally o btain ed in the sam e m ov in g w ind o w as th e o n e u sed to calcu late the m o v ing average. SN R 5
P binn ed
s
(2 3 )
b in ned
R E S U L T S A N D D IS C U S S IO N F E C a lcu la tio n s. T h e F E w as calcu lated at each ex citatio n w avelen gth fo r each cer v ical site m easured in all p atien ts. T h e resu lts o f th e F E calcu latio ns are sh ow n in Ta ble II an d F ig. 3 . T h e m inim um , average, and m axim u m v alues o f the F E calcu lated at th e th ree d ifferen t ex citatio n w av elen g th s fo r each ty p e of tissu e are in clu ded in Ta b le II. In F ig. 3, averag e v alues o f th e F E are
APPLIED SPECTROSCOPY
949
plo tted for n orm al sq u am o u s (N S ), n orm al colu m n ar (N C ), L G S IL , an d H G S IL at each ex citation w av eleng th . S tan dard d eviation s are sho w n as erro r b ars. F o r sq u am o u s cer vical tissu es, th e F E of th e tissu e d ecreases as th e d eg ree o f th e d isease p ro gresses. F ro m h igh to lo w F E , the d iag n ostic catego ries are N S , L G S IL , H G S IL , and N C . A s the excitatio n w avelen gth increases, th e F E decreases. T h e ratio o f the m ax im u m to the m in im u m cer vical tissu e F E at each ex citation w av eleng th fo r all p atien ts is in d icated in tw o w ay s. Ta b le III g ives (1) th e ratio for th e en tire d ata set of 3 7 4 spectra fro m 9 2 p atien ts (m ax / m in ), and (2 ) th e ratio o f th e m ax im um to th e m in im u m F E fo r all sites fro m a g iv en p atien t av erag ed ov er all patients (averag e(m ax /m in )). T he v ariab ility o f th e F E am o ng all p atien ts fo r a sp eci® c ex citation w av elen g th is m o re th an tw o ord ers o f m ag nitu de an d is g reatest at 38 0 nm . T h e ratio o f the m ax im u m to th e m inim um F E fo r all sites fro m a g iven patient, av eraged o v er all p atien ts, is m uch less (Ta b le III). W ith in a patient, the cer vical tissu e F E v aries less than an o rd er o f m ag n itu d e, and variatio n is greatest at 3 8 0 n m ex citatio n ag ain . T h is result in d icates th at, w h ile th e tissu e F E v aries sig n i® can tly fro m patient to p atien t, it v aries m u ch less w ithin a p atien t. R elativ e freq uen cy h isto g ram s o f th e F E fo r each typ e of tissu e at each ex citation w av elen g th are d isplay ed in F ig . 4 . In all cases, there is sig ni® cant o v erlap b etw een th e F E d istribu tio n s of variou s tissu e ty pes, ind icatin g th at th e m easurem en t of th e F E b y itself cann o t be u sed as an accurate d iagn o stic v alue. A t 3 3 7 an d 3 8 0 nm excitatio n , the S N distrib u tio n is sh ifted tow ard h igh er F E valu es relativ e to the oth er tissu e ty pes. A t 3 8 0 n m ex citatio n , th e L G S IL d istrib ution is sh ifted tow ard lo w er F E valu es relativ e to th e o th er tissu e typ es. A t 4 60 n m excitatio n, th e H G S IL distrib u tio n is shifted tow ard lo w er F E v alues relativ e to the oth er tissu e ty pes. S N R C a lcu la tio n s. Ta b le I co m bin ed w ith E q s. 13 ±21 rep resen ts the calculation o f a ty pical S N R p red ictio n . T h e listed v alues rep resen t th e system per fo rm an ce an d ¯ u o rescen ce ch aracteristics o f a p articular p atien t at 3 3 7 nm ex citation . T h e sy m b ol * d esig n ates that th e v alu e is derived from a p articu lar p atien t spectrum . T h e results of Ta b le I in d icate a pred icted S N R o f 1 20 . T he m easu red S N R fo r the sam e p atien t w as 1 24 . Ta ble IV lists th e av erag e m easured an d p redicted S N R s fo r th e sp ectra from th e 37 4 sites. T h e ratio of th e average p redicted to th e av erag e m easured S N R is 0 .97 at 33 7 n m , 0 .9 3 at 3 80 n m , an d 1 .3 at 46 0 n m ex citation . In add itio n , Ta b le IV lists th e ratio o f th e pred icted sign al to the m easu red sig nal an d th e ratio of th e p red icted n o ise to th e m easured no ise averaged for all 37 4 sites. T h e average ratio s o f th e pred icted sig nal to th e m easured sig n al an d th e p redicted n oise to th e m easu red no ise ran g e fro m 0 .5 2 to 0 .78 and fro m 0.45 to 0 .6 0 , resp ectiv ely, ind icatin g th at th e m easured sig nal an d n o ise are app rox im ately tw ice th e p red icted sign al an d n o ise. A niso tro p ic cer v ical tissue em issio n m ay con trib u te to th e d iscrep an cies b etw een m easu red an d p redicted sign al in tensities, w hich em plo y ed an isotrop ic tissu e em issio n assum ptio n. P rev io us stud ies p er fo rm ed in arterial tissu e hav e d em o n strated em p irically th at tissu e d o es no t em it iso trop ically, as a resu lt o f h ig h ly fo r w ard scatterin g . 1 4,21
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F o r arterial sp ecim en s, tissue ¯ u o rescen ce p o w er decreases w ith the d etecto r-to-sam p le sep aratio n d istan ce, R , as 1/R n , w here n 5 1 .1 . T h e F E o f cer vical tissu e in this in v estig atio n w as calcu lated u n der the assu m p tion th at n 5 2. F o r n 5 1 .1 , the p redicted sig n al is 2 .7 tim es larg er th an th e p redicted sig nal fo r n 5 2. C O N C L U S IO N W e hav e dev elop ed a m etho d to calculate th e ¯ u o rescen ce ef® cien cy of tissu e fro m in vivo m easurem en ts o f tissu e ¯ u o rescen ce. C er v ical tissu e F E v aries m o re th an tw o ord ers of m ag nitu de, d epen d in g o n th e tissu e ty p e (N S , N C , L G , o r H G ) an d on th e ex citation w av elen g th used (3 3 7, 38 0 , an d 4 6 0 n m in th is inv estigation ). A s th e excitatio n w av eleng th increases, the F E d ecreases. T he F E decreases w ith in creasin g d eg ree o f d isease fo r sq u am o u s cer vical tissu e. G eneral m eth o ds to estim ate th e S N R o f acqu ired ¯ uo rescen ce d ata an d to p redict th e exp ected S N R fo r tissu e ¯ u o rescen ce sp ectra h ave been d escrib ed in detail. T h is m etho d w as ap p lied to cer vical tissue ¯ u orescence data ob tain ed w ith a ® b er-o ptic ¯ u o rescen ce spectro m eter. T he S N R p red ictio ns, b ased on m easured v alu es of tissu e F E , dem on strate ag reem ent w ithin a facto r o f 0.97 at 33 7 nm , 0.93 at 3 80 nm , an d 1 .3 at 4 6 0 nm ex citation to th e m easured S N R s, on av erag e. T h is m eth od can b e u sed to pred ict th e S N R ex pected fo r v ario us sp ectro m eter d esig n s. A CK N O W L E D G M E N T We gratef ully acknow ledge fu nding pr ovid ed by the W hitak er F o un dation.
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