DIFFERENTIATION OF MALIGNANT FROM BENIGN BREAST LESIONS BASED ON FUNCTIONAL DIFFUSE OPTICAL TOMOGRAPHY

Transcription

1 DIFFERENTIATION OF MALIGNANT FROM BENIGN BREAST LESIONS BASED ON FUNCTIONAL DIFFUSE OPTICAL TOMOGRAPHY By LIN CHEN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

2 Copyright 2006 by Lin Chen

3 This document is dedicted to the grdute students of the University of Florid.

4 ACKNOWLEDGMENTS I would like to thnk Dr. Hubei Jing, my thesis dvisor, for his guidnce. I would like to express pprecition to ll the members in the Biomedicl Optics Lbortory of Florid. My specil thnksgiving goes to Chngqing Li nd Xioping Ling, for mny discussions nd dvices in this project. I pprecite Qizhi Zhng nd Hongzhi Zho in their help for the procedure of clinic experiments. The Oconee Memoril Hospitl nd the Greenville Hospitl hve been gret help to our clinic experiments in introducing ptients nd guidnce on the lesion position. I thnk my prents for their cre, love nd support on my study. iv

5 TABLE OF CONTENTS pge ACKNOWLEDGMENTS... iv LIST OF TABLES... vii LIST OF FIGURES... viii ABSTRACT... ix CHAPTER 1 INTRODUCTION THEORY...4 Introduction...4 Reconstruction Algorithm...5 Chrcteriztion of Spectr in Brest Tissue MATERIALS AND METHODS...15 Generl Approch...15 Instrument nd Clibrtion...17 System Setup...17 System Clibrtion Method...19 Phntom Experiments for System Clibrtion...20 Results of Clibrtion Experiments...20 Clinicl Experiments...24 Fitting Considertion...25 Absorption Fitting...25 Scttering Fitting RESULTS AND DISCUSSIONS...28 Tumor Result-Imges for Selected Exmples...28 Discussions...41 Hemoglobin Concentrtion...41 Represented cses Cses...43 v

6 Wter Content...51 Scttering Spectr...53 Conclusion...55 LIST OF REFERENCES...57 BIOGRAPHICAL SKETCH...60 vi

7 LIST OF TABLES Tble pge 2-1 The Opticl Properties of Humn Femle Brest The Extinction Coefficients of All the Wvelengths in the Experiments The Number of Lesions Selected for Experiment nd Anlysis...25 vii

8 LIST OF FIGURES Figure pge 2-1 Flow chrt of the Newton-type itertion for estimting the distribution of the opticl properties Schemtic of 2 experimentl systems Geometry of the phntom configurtion Comprison between the reconstructed bsorption imges of originl dt nd of clibrted dt for cses of 2:1 bsorption contrst Reconstructed bsorption imges for heterogeneous phntoms with or without clibrtion from different dimeters in the cse of 1.4:1 bsorption contrst Corresponding position from report to opticl 2D imges The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected nodule cse The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected clcifiction cse The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected cyst cse The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected cncer cse Grph illustrtes the quntittive vlue for the rw de-oxy hemoglobin concentrtion nd oxy-hemoglobin concentrtion Men hemoglobin concentrtions of reported disesed lesion Grph illustrtes the quntittive vlue for the mximum hemoglobin concentrtion nd the corresponding oxygen sturtions Grph illustrtes the men vlue of scttering power with the totl hemoglobin concentrtion. nd the ptient ge b in reported disesed lesion...54 viii

9 Abstrct of Thesis Presented to the Grdute School of the University of Florid in Prtil Fulfillment of the Requirements for the Degree of Mster of Science DIFFERENTIATION OF MALIGNANT FROM BENIGN BREAST LESIONS BASED ON FUNCTIONAL DIFFUSE OPTICAL TOMOGRAPHY By Lin Chen August 2006 Chir: Hubei Jing Mjor Deprtment: Biomedicl Engineering In this thesis, opticl imges bsed on clinicl study with ptients including 11 cncer nd 30 benign cses were processed nd nlyzed. Using multi-spectrl diffuse opticl tomogrphy systems coupled with finite element reconstruction lgorithms, we first obtined opticl bsorption nd scttering mps of the brest nd then derived tissue functionl imges from the recovered bsorption nd scttering imges t multiwvelengths. In order to obtin ccurte in vivo imges, clibrtion dtbse ws developed which ws bsed on series of homogenous phntom mesurements with rnge of phntom dimensions. Hemoglobin (both oxy nd de-oxy) concentrtions nd wter content imges were obtined from the multi-spectrl bsorption imges, nd Mie scttering theory pproximtion ws pplied to extrct scttering mplitude nd power. Functionl prmeter imges of the 41 cses were investigted, nd correltion plots of different function prmeters were illustrted nd compred mong 4 disese ctegories including cncer, cyst, nodule nd clcultion. We found tht the mjority of the ix

10 crcinoms exhibited incresed totl hemoglobin concentrtion compred to the helthy nd other benign tissues, nd the correltion between totl hemoglobin concentrtion nd oxygen sturtion of these disesed tissues showed cler seprtion between mlignnt nd benign lesions, while the seprtion mong the benign lesions is not pprent for the cses exmined. x

11 CHAPTER 1 INTRODUCTION Opticl methods for the detection of brest cncer, especilly for the erly detection of cncer, cn be trced bck to s erly s 1929 [1], when it ws introduced by Mx Culter. Decdes of studies improved the diffuse opticl tomogrphy (DOT) s noninvsive imging technique tht could provide quntittive bsorption nd lso scttering distribution. In the 1980s, Crlsen [2] introduced spectrl brest imging by restricting the light source of medicl trnsillumintion imger. Becuse of the introduction of these technologies, opticl imging of humn tissue using ner-infrred (NIR) light provides the possibility of obtining new types of physiologicl informtion from the tissue in vivo, while the trditionl method, using conventionl x-ry mmmogrphy techniques could only provide structurl informtion. The ner-infrred light pssing through brest tissues is sensitive to severl physiologicl components such s hemoglobin, wter, lipid, melnin, crotene, proteins, DNA, nd so forth. Thus NIR bsorption in brest tissue is influenced by hemoglobin concentrtion, oxygen sturtion, wter content, nd to lesser extent by lipid. Therefore, NIR techniques could be fshioned into n inexpensive nd portble lterntive solution for distinguishing mlignnt (even in n erly stge) from benign disesed or helth tissues. NIR cn ccomplish this by obtining quntittive hemoglobin concentrtion, oxygen sturtion, wter frction nd other functionl informtion from bsorption distribution of tissue. The gol of the studies described in this thesis is pilot pproch to evlute the possibility from substntive ptient cses. 1

12 2 Our experimentl device ws developed s silicon photodiodes-bsed DOT system, nd employed finite element lgorithm for the frequent-domin opticl dt reconstruction bsed on well-known diffusion eqution. In Chpter 2, we review the reconstruction lgorithm for bsorption nd reduced scttering coefficients in detil. Also, it includes generl review on the spectr chrcteriztion of brest tissue. The experimentl system nd the preprtion for clinicl exmintion re covered in Chpter 3. In order to ssist in obtining the first quntittive reconstructed dt of both bsorption nd reduced scttering coefficients, the clibrtion method ws employed. We built dtbse bsed on series of homogenous phntom with rnge of dimensions (from 60mm to 11cm with n increment of 10mm) to fit with vrious sizes of clinicl humn brests. Menwhile, clinicl experiments were performed on more thn 100 volunteers including those with mlignnt cncer, benign disesed nd helthy brest conditions. Typicl cses with both mmmogrphy nd ultrsound reports (nd biopsy reports if they exist) were selected, reconstructed nd evluted. We lso introduced our fitting methods on both bsorption nd sctting spectr bsed on the simplified models in Chpter 3. Results of the clinicl experiments re presented in Chpter 4. With comprison to the mmmogrphy nd ultrsound reports, we were ble to recognize the tumors in the corresponding position, nd evlute the functionl informtion. We noticed specific differences for totl hemoglobin, corresponding to physiologicl nd pthologicl knowledge, with different kinds of tumors. A series of nlyses were crried out for the purpose of investigting these visible imges nd quntittive vlues.

13 3 These nlyses ttempt to provide bsis for the id of dignosing mlignnt cncer nd other brest diseses.

14 CHAPTER 2 THEORY Introduction Yerly mmmogrms re recommended strting t ge 40 nd continuing for s long s womn is in good helth; nd clinicl brest exm should be tken s prt of periodic helth exm, preferbly t lest every three yers for women in their 20s nd 30s, nd every yer for women, for the presence of brest cncer which is one in eight women in the United Sttes. Thus, diffuse opticl tomogrphy (DOT), tries to investigte n lterntive method for the erly detection of preclinicl brest cncer. Currently, conventionl x-ry mmmogrphy nd plption re the most common method for brest cncer detection. However, obvious limittions to conventionl x-ry mmmogrphy hve been recognized. For exmple, conventionl x-ry mmmogrphy is not suitble for young women in erly pre-menopusl stge, by reson of their incresed cellulrity nd subsequent rdiodense tissue structure. Tht is to sy, due to hormone fluctutions, the pre-menopusl women with preclinicl brest cncer re t incresed risk of more rpid tumor growth. In ddition, the positive predictive vlue of conventionl x-ry mmmogrphy is quite low in both medicl nd economic terms, nd s result, numerous biopsies re required to be performed ech yer. Moreover, women with the fmilil gene for brest cncer (e.g., fmily history, genetic tendency, pst brest cncer) might experience risk when subjected to the x-irrdition. As result, DOT, non-ionizing, non-invsive ner-infrred opticl imging holds gret promise to become n lterntive for brest cncer screening, especilly for cncer 4

15 5 in erly stge. Using lser light source, this opticl method ttempts to produce n imge of the inside of the brest, with unique cpbility for screening high rdiodense brests usully for premenopusl women. Recent studies hve suggested tht biomedicl opticl imging of brest tissue hs significnt dvntges for brest cncer detection nd dignosis, which helps lot for retining the corresponding tretment to be keeping pce with the incresed incidence of the brest cncer. Menwhile, this method hs no hrm to humn body even for ptients with fmilil gene for brest cncer; nd the instrumenttion for opticl imging is much lower in cost thn tht for x-ry mmmogrphy. Further, the DOT could obtin quntittive bsorption nd scttering distributions from brest tissue, which cn not be mesured by conventionl x-ry mmmogrphy or other rdiologic techniques. The spectrl dependence of quntittive tissue bsorption µ nd reduced scttering µ ' distributions could provide tissue functionl informtion in s brest with the introduction of ner-infrred (NIR) migrtion spectroscopy. Multi-spectrl mesurements helps for determintion of the concentrtions of de-oxy nd oxyhemoglobin, wter, nd other components in brest; nd the scttering properties of the tissue could lso yield importnt physiologicl informtion, such s the scttering mplitude nd scttering power. These typicl vlues within the brest re believed to help doctors for better dignoses on brest diseses. Reconstruction Algorithm Our reconstruction lgorithm for bsorption nd reduced scttering coefficients, previously described in detil [3, 4], is n itertive finite element lgorithm bsed on the well-known diffusion eqution

16 i ( ω ) 6 D Φ(, r ω ) µ Φ (, r ω) = S(, r ω) (1) c where D is the diffusion coefficient, Φ (, r ω) is the rdince, µ is the bsorption coefficient, c is the wve speed in the medium, Srω (, ) is the source term s n time vrition is ssumed. And the diffusion coefficient D cn be expressed s i t e ω 1 D = 3[ µ + µ (1 g)] s (2) where µ s is the scttering coefficient nd g is the verge cosine of the scttering ngle. And the reduced scttering coefficient is defined s µ s ' = (1 g) µ s.with known µ nd µ s distribution, the diffusion eqution becomes stndrd boundry vlue problem for sptilly vrying rdince subject to pproprite boundry conditions (BC s). There re three clssicl boundry conditions for this diffusion eqution: i) specifiction of the field, Φ (Dirichlet or Type I); ii) specifiction of its flux, D Φ nˆ (Neumnn or Type II); iii) specifiction of reltionship between field nd flux (mixed or Type III) In our study, we employed Type III BC s in the reconstruction lgorithm, tht is D Φ nˆ = αφ, where ˆn is the unit vector norml to the boundry surfce, nd α is relted to the internl reflection, which cn be derived from the Fresnel reflection coefficient. For the finite element forwrd solution, Φ nd F = D Φ nˆ re expnded s the sum of coefficients multiplied by set of loclly sptilly vrying Lgrngin bsis functions N jφ j (3) j= 1 Φ= Φ

17 7 M F = Fφ (3b) j= 1 j j where φ j is the known bsis nd Φ j, F j re the respective rdince nd flux t node j. Similrly, µ nd D re expnded s collection of unknown prmeters multiplied by known sptilly vrying expnsion function K D= Dψ (4) k = 1 k k L µ = µϕ (4b) l l l= 1 As result, the diffusion eqution becomes iω Φ D ψ φ φ µϕ φφ N K L j k k j i l l i j j= 1 k= 1 l= 1 c M = Sφ + F φ φds i j j i j= 1 (5) which could be express in the mtrix form s [ A]{ } { b} Φ = (6) where the elements of mtrix [ A ] re K L iω = Dψ φ φ µϕ φφ (7) ij k k j i l l i j k= 1 l= 1 c s indicting integrtion over the problem domin. The column vector { Φ } is composed of the photon density And { b } is filled with elements tht Φ i t node i. b = Sφ + α Φ φ φds i i j j i j= 1 M (7b)

18 8 where expresses integrtion over the boundry surfce with j F replced by αφ j s Type III BC defined, nd M is the number of boundry nodes. With finite element discretiztion, the photon density (computed opticl dt) is obtined s the solution of the diffusion eqution. Then regulrized Newton s method is exploited here to updte the initilly guessed opticl property distribution itertively in order to minimize n object function composed of weighted sum of the squred difference between computed nd mesured opticl dt t the medium surfce. We ssume tht the computed nd/or mesured vlues of Φ or F re nlytic functions of D nd µ, nd D nd µ re independent since µ s µ. Then Φ nd F could be Tylor expnded s n ssumed ( D, µ ) distribution, which is perturbtion wy from some other distribution, ( D, µ ) be expressed s (, ) (, ) D µ, such tht discrete set of rdince nd flux vlues cn Φ Φ Φ D µ =Φ D µ + D+ µ + (8) F F F D µ = F D µ + D+ µ + (8b) (, ) (, ) D µ where D= D D nd µ = µ µ. If the ssumed opticl property distribution is close to the true profile, the left-hnd side of (8) cn be considered s true dt (either imposed or observed), nd the reltionship truncted to produce where o c =Ψ Ψ (9) J χ o Ψ nd c Ψ re observed nd clculted [bsed on the estimted ( D, µ ) distribution] dt, either Φ or F, depending on boundry conditions for i= 1, 2,, M

19 9 loctions nd D k for k = 1, 2, K nd µ l for l = 1,2,, L; nd J is Jcobin mtrix consisting of derivtives of Ψ with respect to D or µ t ech boundry observtion node. J Ψ1 Ψ1 Ψ1 Ψ1 Ψ1 Ψ1 D1 D2 DK µ 1 µ 2 µ L Ψ 2 Ψ 2 Ψ 2 Ψ 2 Ψ 2 Ψ 2 = D1 D2 DK µ 1 µ 2 µ L Ψ M Ψ M Ψ M Ψ M Ψ M Ψ M D1 D2 D K µ 1 µ 2 µ L (9b) And χ is the vector tht gives the perturbtion of µ nd D D1 D 2 D, µ 2 µ L K χ = µ 1 Ψ Ψ Ψ o Ψ = o 1 o 2 o M, Ψ Ψ Ψ c Ψ = c 1 c 2 c M (9c) In order to relize n invertible system of equtions for multiplied by T J on both sides to obtin ( ) χ, the Eq. (9) could be J T J χ = J T Ψ o Ψ c (10) which cn be used for updting the opticl property distribution. As the mtrix T J J is known to be ill conditioned, techniques should be performed to regulrize or stbilize the decomposition of digonl of T J J in prctice, nd the problem trnsformed to T J J. Thus, quntity is dding to the

20 ( J T J λi) χ J T ( o c ) 10 + = Ψ Ψ (11) where I is the identity mtrix nd λ my be sclr or digonl mtrix. START Initil Vlue( D, µ ) Forwrd Computtion FEM solution of Diffusion Eqution iω D Φ(, r ω ) µ Φ (, r ω) = S(, r ω) Mesured dt Φ o i ( ) c Converged? M c o ( ) 2 i i χ = Φ Φ i= 1 STOP Inverse Computtion Build Jcobin Mtrix: I= Φ χ Solve mtrix Eqution: ( I T I+ λi ) χ =I T ( Φ o Φ c ) Updte Opticl Property Vlues ( D, µ ) D ' = D + D µ ' = µ + µ i i i i i i Figure 2-1 Flow chrt of the Newton-type itertion for estimting the distribution of the opticl properties

21 11 By dding contribution to the digonl terms in Eq. (11), the mtrix T J J is mde more digonlly dominnt, which improves its invertibility. Hence, there is no need for ny exct solution from Eq. (10), which is lredy n pproximtion. The flow chrt in Fig. 2-1 describes the itertive updte of µ nd D to pproch the true profile strting from uniform initil guess. Chrcteriztion of Spectr in Brest Tissue Physiologiclly, the brest is turbid, light scttering medium combined with different shpes of bsorbers, sctterers, fluorophores nd nisotropic interfces [5]. For biomedicl opticl imging, the techniques iding for cncer dignosis depend primrily on detection for the berrtions of reflected, trnsmitted nd emitted light tht due to the physiologicl chrcteriztion or cellulr growth of cncer nd the host response to the cncer. Thus, it is importnt for us to get to the bottom of physiologicl nd pthologicl fctors of humn brest disese tht cn influence opticl dignosis. There re two primry opticl properties, the bsorption coefficient µ nd the reduced scttering coefficient µ ', which determine the propgtion of the diffusive light s through the brest. The diffuse opticl tomogrphy llows for mesuring quntittive bsorption nd scttering distribution of tissues t ny wvelength of interest, hence it is possible to use the spectr of which to obtin tissue functionl informtion, such s quntify typicl vlues of hemoglobin concentrtion, oxygen sturtion, wter content, scttering power, scttering mplitude nd so forth within the brest tissue. With single integrting sphere technique, few mesurements of opticl properties hve been done in vitro on both norml nd disesed brest tissues shown in Tble 2-1 [6]. The opticl coefficients for the tissues with fibrocystic dises, fibrodenoms nd

22 12 ductl crcinom hve no significnt difference with the norml tissues. However, due to the mteril of their experiments, which re tissue specimens of humn brest, blood dringe cused by the surgicl nd pthologicl dissections of the brests hve gretly diminished the contributions of hemoglobin when mesuring this group of opticl properties. Tble 2-1. The Opticl Properties of Humn Femle Brest Opticl Properties λ (nm) Absorption Coefficient µ 1 ( mm ) Reduced Scttering Coefficient µ ' 1 ( s mm ) Tissue Type Fibro-denom Glndulr (3) Adipose (7) Fibrocystic (8) Crcinom (9) (6) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1.03 ± ± ± ± 0.51 ± 0.86 ± ± ± ± ± ± ± ± ± 0.26 * Modified from Peters, V. G. et l Opticl properties of norml nd disesed brest tissues in the visible nd ner-infrred. Phys. Med. Biol. 35: * The numbers in prentheses give the number of tissue specimens exmined for ech tissue type. [6] Recent studies hve demonstrted tht the ner-infrred photon migrtion is sensitive to severl importnt tissue biochemicl compositions; for instnce, especilly in the 400~600 nm rnge, hemoglobin is strong, nd could even be seen s some hemoglobin contmintion in some of the spectr. Thus, dul-wvelength ws introduced into DOT reserches for quntifying the concentrtions of de-oxy hemoglobin (reduced hemoglobin Hb R ) nd oxy-hemoglobin ( Hb O2 ) in tissue. However, reserch suggests tht the ner-infrred light bsorption in brest is produced by more thn just hemoglobin. In the intct living humn brest, the most significnt light bsorbers include hemoglobin, melnin, wter, crotene, proteins nd DNA. As reported, the bsorption increses towrd shorter wvelengths owing to the protein bsorption, nd towrd longer wvelengths due

23 13 to wter bsorption. Tht is to sy, wter nd lipid, lthough they re just wek nerinfrred light bsorbers, for their high bundnce in the brest, could shdow significnt influence on bsorption reltive to hemoglobin in the wvelength of 900~1000nm rnge, especilly wter. The scttering properties of the tissue lso yield importnt physiologic nd pthologicl informtion. However, the distribution of ner-infrred light scttering in tissue is not well understood yet. However, multi-spectrl ner-infrred light mesurements of the reduced scttering coefficient µ ' hve still shown there re s reltionship between scttering nd wvelength. The scttering decreses with the increse of wvelength. At shorter wvelengths below 600 nm, the scttering behvior is likely dominted by scttering from the periodicity nd size of refrctive index fluctutions of the collgen fibrils in the size rnge of 70 nm to hundreds of nm; wheres t longer wvelength behvior beyond 600 nm, the scttering behvior is incresingly dominted by scttering from the lrger cylinders of collgen fibers (2-3 µm dimeter) composed of collgen fibrils. Similr to other biologicl tissues, ll cellulr nd extrcellulr components within the brest tissue contribute to light scttering; thus, besides the collgen fibers t the micro nd mcro scle, other tissue components lso contribute to the overll scttering, but the collgen fibers probbly ply the min role in scttering behviors. Thus, informtion bout the types of the scttering centers within certin lesion of brest tissue could be provided by spectrl mesurements to the scttering coefficient. Recent dvnces in our experimentl studies hve provided reconstruction dtum nd imges with seprte µ nd µ ', nd phntom experiments hve presented solid s

24 14 evidence tht the reconstruction vlue hs no cler differences with the prcticl designed vlue. In this work, the principl ner-infrred light bsorbers within the brest tissue re ssumed to be de-oxy hemoglobin ( Hb R ), oxy-hemoglobin ( Hb O2 ) nd wter ( HO). 2 For the scttering coefficient µ s ', we mde use of some priori informtion, tht is, the introduction of the simple power-lw which is well known in the ner-infrred light theory. As result, the scttering mplitude nd the scttering power were reported in ech experiment.

25 CHAPTER 3 MATERIALS AND METHODS Generl Approch The chromophore concentrtion on the bsorbnce of ner-infrred light depends on [ ] µ = ε cl, where ε is the molr extinction coefficient ( M 1 1 cm ), [ ] c is the 1 concentrtion of chromophore c ( ML ), nd l is the photon pth length (cm). the pth length l is incresed by scttering nd is not known priori. As reported, the bsorption coefficients trnslte into tissue chromophore concentrtions bsed on the eqution [ c] µ = 2.303ε (12) where the fctor of origintes from the bse conversion between the logrithm for bsorbnce nd the nturl logrithm for µ [7, 8, 9]. We ssume tht the chromophores contributing to µ in the humn brest tissues re principlly de-oxy hemoglobin ( Hb R ), oxy-hemoglobin ( Hb O2 ) nd wter ( HO) 2 (Cope 1991; Sevick et l. 1991). Thus, the concentrtions of components in the tissue we need to determine for study includes the concentrtion of de-oxy hemoglobin [ Hb ] (in units of µ M ), oxy-hemoglobin [ HbO ] (in units of M 2 µ ) nd wter [ ] HO (in units of 2 λ percentge) in the tissue. The respective extinction coefficient ε for given [ chrom. ] chromophore t wvelength λ, could be obtined from literture vlues. In the λ experiments, s the bsorption coefficients µ re mesured from 3 to 10 wvelengths optionlly [10, 11], we could use t lest three equtions to determine the three unknown 15

26 quntities of the functionl concentrtions of [ Hb ], [ HbO ], nd [ ] coefficients of ll the wvelengths re listed in the following tble [12]: 16 2 HO. The extinction Tble 3-1. The Extinction Coefficients of All the Wvelengths in the Experiments λ (nm) 1 1 Opticl Absorption of Wter HbO 2 ( M cm 1 1 ) Hb ( M cm ) 1 Compendium ( cm ) The scttering spectrum of tissue yields informtion on the nture of the scttering prticles. In generl, '( ) µ λ is the sum of contributions from the vrious tissue sctterers. s Unfortuntely, the detiled informtion bout these individul sctterers ws not well understood yet. Since it hs been observed tht the reduced scttering coefficient hs generl trend to decrese s the wvelength incresed, with some priori informtion, the simple power-lw dependence were employed to fit the ner-infrred light scttering in tissue [7, 8]: SP µ ' = Aλ (13) s where A is the rbitrry model prmeters for mplitude ( constnt), λ is he wvelength (in nnometers), nd SP, the mgnitude of the exponent, is the sctter power. As known, the vlue of scttering power SP increses significntly s the decresing of the scttering center size, combined with the opticl wvelength. In the cse of Ryleigh 2

27 17 scttering ( d λ, where d is the scttering center size, nd λ is the responsible wvelength), SP = 4 is well estblished. As scttering objects become lrger size, the sctter power SP decreses to pproximtely 1 for lrger Mie-like sctters ( d the vlue of SP decreses to zero when d System Setup λ [8, 13]. Instrument nd Clibrtion λ ); nd There re two imging systems used for the clinic experiments re utomted multichnnel frequency-domin systems, both of which employ multiple diode lsers tht provide visible nd ner-infrred light. The DOT system setups re schemticlly shown in the Following Figure. One could provide ner-infrred lser t 3 different wvelengths (785, 808, nd 830nm), nd the other t 10 different wvelengths (638, 673, 690, 733, 775, 808, 840, 915, 922 nd 965nm). The ring of the instruments holds different lyers of fibre bundles, nd ech of those lyers hs 16 source nd 16 detection fibre bundles lterntely distributed by turns. The rdio-frequency intensity-modulted ner-infrred bems re trnsmitted to the opticl switch, nd sequentilly be pssed to the source probes tht gently touched the surfce of the experiment mterils or clinic humn brests. The diffused light collected by the detection fibre bundles is then sensed by the detection Units, which convert the light intensity into voltge signls, which re collected by the computer through the dt cquisition bord. We use the mesured dt for bsorption nd scttering imges through our reconstruction lgorithm.

28 18 Source fibre bundles 10 Lsers 10 Opticl Switch Detection fibre bundles Detection Units Lser Current CCDs DC motor Dt Acquisition Bords Computer. b Figure 3-1. Schemtic of 2 experimentl systems.. Schemtic of the experimentl system with 10 wvelengths b. Schemtic of the experimentl system with 3 wvelengths

29 19 System Clibrtion Method It hs been demonstrted tht the system clibrtion could provide helpful id to the quntittive reconstructions of both bsorption nd scttering coefficients in turbid medi [14]. In clinicl experiments, the dimeters of brests vrious from person to person, dt bse for clibrtion hs better to be estblished. For 2D imging experiments, the clibrtion procedure could be described s following pproches: (1) Mke group of homogeneous phntoms with different dimeters of interest for dt bse. (2) Perform experiments individully with the homogeneous phntoms nd collect the D respectively for ech phntom. mesured dt { ij } (3) For ech set of mesured dt D ij, find the respective initil vlues of bsorption coefficient µ, reduced scttering coefficient µ s ' nd the boundry conditions coefficient α. (4) Generte 2D finite element mesh with the sme dimeter for ech phntom. Using unit source intensity for the 16 illuminted positions, simulte the 2D photon propgtion with the initil vlues of the opticl properties nd the boundry conditions coefficient α obtined in the former pproch, then new set of dt D could be generted. * ij (5) Obtin fctor mtrix f ij using the following eqution f = D D, i, j=1,2,,16 (14) * ij ij ij The fctor mtrix f ij could be dded into the clibrtion dt bse. For experimentl dt of whether heterogeneous phntom or clinicl brest, multiply f ij from the homogeneous phntom with the nerest dimeter by the experiment dt set { E ij }, finl clibrted dt set { E * ij} could be obtined, nd used for further imge reconstruction E = f E, i, j=1,2,,16 (15) * ij ij ij

30 20 Phntom Experiments for System Clibrtion Phntom is used s n object to mke in imittion of biologicl tissues in terms of bsorption nd scttering coefficients. In our study, the phntom mterils employ composition of Intrlipid s the sctterer nd Indi Ink s the bsorber, s the Intrlipid is n queous suspension consist of glycerin, lecithin, soyben nd wter. A boiled gr powder solution in concentrtion of 2% is chosen s the hrdener to solidify the queous mixture of Intrlipid nd Indi Ink, tking dvntge of its non-bsorption nd low-turbidity. Considering the vrious size of humn brest, homogeneous phntoms in different dimeters (60mm, 70mm, 90mm, 100mm, nd 110mm) were prepred for the imging experiments under the clibrtion method. The opticl properties of phntoms in 1 clibrtion experiments re the sme: µ = mm, nd µ s ' 1.0 mm 1 =. Results of Clibrtion Experiments To exmine the results of clibrtion dt bse, heterogeneous phntoms tht hve similr dimeters to the homogeneous phntoms were employed during the exmintion for clibrtion experiments. The opticl properties for the bckground of the heterogeneous phntoms re still the sme with the homogeneous phntoms: µ mm 1 = 0.005, nd µ s ' 1.0 mm 1 = ; nd single trget ws embedded in ech homogenous bckground phntom, with position deprts from the center. Thus, one 14mm dimeter hole ws cylindricl drilled in ech homogenous bckground phntom for the inclusions of the trget. As the relted reserches hve shown tht there is obvious difficulty to get quntittive opticl imges under conditions of very low bsorption contrst, nd this instnce do not hppen under conditions with just low scttering

31 21 contrst or both low bsorption nd low scttering contrst. Considering this, the opticl coefficients of the off-center trgets for the heterogeneous phntoms in the clibrtion exmine experiments were set s low bsorption contrst only, tht is µ mm 1 = 0.010, nd µ s ' 1.0 mm 1 =. The following figure depicts the geometricl configurtions for the test cses of phntom dimeter under study. R1 = d /2 R 2 = 7 mm s Figure 3-2. Geometry of the phntom configurtion Figure 3-3 present the reconstructed bsorption imges, both without clibrtion nd with clibrtion, from phntom experiments in dimeters 60mm nd 70mm, respectively, tke the imging dt from the sme itertion of reconstructed dt with the sme filter times, nd from the sme wvelength (tke λ = 922nm, in which wvelength it is lmost the most difficult thn most other wvelengths for quntittive bsorption imges). From the Fig. 3-3, the results ccords very good with our former conclusion. In other words, when the heterogeneous phntoms hs the sme dimeter s the homogenous phntom tht used for obtining clibrtion dt, the clibrtion method could improve the quntittive opticl imges in size, shpe nd vlue, even under the conditions of very low bsorption contrst.

32 22 b c d Figure 3-3 Comprison between the reconstructed bsorption imges of originl dt (left column) nd of clibrted dt (right column) for cses of 2:1 bsorption contrst. nd c re the reconstructed bsorption imge from the originl dt in dimeter 60mm (first row) nd 70mm (second row) respectively; b nd d re the corresponding bsorption imge from the dt with clibrtion compre respectively to imge nd c. In clinicl experiments, the sizes of humn brests were not the sme s the dimeters we set for clibrtion phntom experiment. Thus, nother group of experiments were performed. As the spce between different homogenous phntoms is 10mm, we could use the clibrtion dt from phntoms whose dimeters border upon the dimeter of the heterogeneous phntoms. Tke the dt from heterogeneous phntom (Absorption only, 1 = nd µ mm µ s ' 1.0 mm 1 = ) with dimeter of d 100 = mm for exmple, we use clibrtion dt from homogenous phntoms with dimeters of 90mm, 100mm,

33 23 nd 110mm respectively. Figure 3.4 present the corresponding reconstructed bsorption imges for λ = 922nm. b c d Figure 3-4 Reconstructed bsorption imges for heterogeneous phntoms with or without clibrtion from different dimeters in the cse of 1.4:1 bsorption contrst In the Figure 3-4 (where the Figure 3-4 is the reconstructed bsorption imge for originl dt without ny clibrtion, nd Figure 3-4 b, 3-4 c, nd 3-4 d re the reconstructed bsorption imges for dt with clibrtion of 100mm, 90mm, nd 110mm respectively), obviously the results re much better for clibrted dt, even with clibrtion dt from tht of homogenous phntoms with different dimeters. Compring to the reconstructed imge of 100mm-clibrted dt, there re slight shifts for the trget position for 90mm-clibrted nd 110mm-clibrted dt, nd the sizes of trget chnges lso. The mximum vlues of reconstructed dt from 90mm-clibrted dt nd 110mm-

34 24 clibrted dt hve errors round 5% compred to the mximum vlues of reconstructed dt from 100mm-clibrted dt, nd the minimum vlues do not show visible errors mong the three imges. Since 10mm is the lrgest distnce in the clibrtion dt bse, we cn conclude tht the errors of the vlues re cceptble in the experiments, nd the clibrtion dt bse we obtined is suitble for most clinicl cse. Clinicl Experiments Over the pst yers, more thn 100 volunteers, helthy or hving pthologicl lesions in their brests, rnging from 30 yers old to 80, hve been enrolled in this study of opticl clinicl humn femle brest experiments. All these cses could be divided into two sets: ptients in the first set hve strong evidence of bnormlity, nd the ptients grouped in the other set hve mmmogrms with uncler significnce. After ech ptient ws informed bout this experiment, the ptients would undergo the procedure lsting bout hlf n hour. The ring holding the opticl fibre bundles ws gently ttched to exmine the brest (only one brest) under the lesion position bsed on guidnce or suggestion from professionl doctors, without ny discomfort or even significnt pressure on the brest. When strted, the brest would be illuminted by lser bems from series of source probes, nd t the sme time, the detectors from multiple positions round the brest would collect the diffused light trnsmitted from the brest tissue. After these dtum collections, our reconstruction lgorithm could be pplied for further study. In this pper we present representtive cses from the selected subset of bnorml cses from 2 groups of ptients (from 3 wvelengths to 10 wvelengths selectively, exmined by two different system respectively), generte brest imges with comprison to the mmmogrms, obtin bsorption nd reduced scttering coefficients with

35 25 clibrtion methods, nd finlly gin nd nlyze the opticl properties nd further functionl informtion reveled by chromophore concentrtion from bsorption coefficient µ nd scttering properties from scttering coefficient µ '. s The disesed humn femle brest could be divided into two ctegories s benign nd cncer. The benign brest tumor includes Fibrodenoms, Fibrocustic Disese (Cyst) nd miscellneous lesions such s lipoms, blunt trum, mstitis tissue nd even ruptured or leky silicone implnts. These benign lesions re distinct pthologic entities, but for detection nd dignosis, they cn be nd usully re intermixed within the sme brest. Thus, we selected clinicl cses listed in the following tble. Tble 3-2 The Number of Lesions Selected for Experiment nd Anlysis Benign Lesions Cncer Lesions Cyst Clcifiction Nodules OMH Greenville The dt obtined in the OMH (Oconee Memoril Hospitl) were collected for 10, 7 or 5 wvelengths, considering the size of the brest; nd the dt obtined in the hospitl of Greenville were collected for 2 or 3 wvelengths. Absorption Fitting Fitting Considertion With the mesured bsorption coefficients µ nd reltive bsorption spectrum, weighted lest-squres problem is put forwrd for recovering the concentrtions of bsorbers in brest tissues. The dependence equtions

36 26 µ ( λ1) ε1( λ1) εm( λ1) c1 = µ ( λn) ε1( λn) εm( λn) c m (17) could be written in more generl form { µ } = [ E]{ c} (18) As { µ } is vector contining the mesured µ vlues for N wvelengths, nd { c } is the vector contining the concentrtions of M different chromophores interested in the study. And [ ] E is the reltive extinction coefficients N M mtrix, where the trditionl literture molr extinction coefficients should be convert into extinction coefficients by multiply 2.303). Hence, generl solution for this mtrix problem could be expressed s 1 T ( ) [ ] { } T {} [ ] [ ] c = E E E µ (19) To minimize clcultion errors, normlizing scheme were employed to blnce the vrition of elements in the extinction coefficients mtrix [ E ] by normlize columns of extinction coefficients for ech chromophore with their respective mximum. Assuming M, i 1,2, m i = re the mximum vlue for extinction coefficient { } the normlized extinction coefficient mtrix convert into εi( λ j), j = 1,2,, n, 1 1 ε1( λ1) εm( λ1) M1 M m E = (20) 1 1 ε1( λn) εm( λn) M1 Mm

37 27 1 c E E 1 = E µ, nd finlly c i = ci (21) M T Then {} T { } For these cses we report four hemoglobin prmeters: [ Hb ], [ HbO ] hemoglobin concentrtion HbT, nd the hemoglobin sturtion SO t 2, where i 2, totl [ HbT ] = [ Hb] + [ HbO 2 ] (22) SO t 2 = [ HbO2 ] [ Hb] + [ HbO ] 2 (22b) Scttering Fitting The wvelength-dependent tissue reduced-scttering coefficient is ssumed to tke SP on this simplified Mie-scttering form µ ( λ) = Aλ s described in the beginning of this chpter. A nd SP re relted to the size, the index of refrction, nd the concentrtion of sctterers in the tissue s well s the index of refrction of the s surrounding medium. This Mie-scttering form is judged s robust nonliner form, nd is trnsformed into liner form ln µ s ( λ) = ln A SP ln λ (23) For every two wvelengths λ i nd λ j we could obtin reltive ln A ij nd SP ij, hence, the finl ln A nd SP were gined s the verge vlue of group of reltive ln A ij nd SP ij n 1 n 1 nn ( 1) A= exp ln Aij, s n' = (24) n ' i= 1 j= i+ 1 2 n 1 n 1 SP = SPij (24b) n ' i= 1 j= i+ 1 where n is the number of mesured wvelengths.

38 CHAPTER 4 RESULTS AND DISCUSSIONS Tumor Result-Imges for Selected Exmples All these volunteers tht were selected for our studies including benign nd cncer ptients, hve 41 bnorml lesions, which could be divided into 4 primry kinds of brest tumors: 18 benign nodules, 6 clcifictions, 6 cysts, nd 11 cncers. All lesions were exmined by professionl physicin nd showed cler signs on mmmogrphy or hve distinct evidences on other exmintion reports. Figure 4-1 shows rough reltionship between the clinic brest front views (which ws used for the brest exmintion reports) nd our 2D opticl imges. In the following section, we will discuss some selected cses (in Fig , we present one selected ptient for ech disese ctegory), in order to gin generl view before further quntittive nlysis. Nodule This ptient is 43-yer old white femle with two smooth lobulted solid nodules presented in the medil spect of the left brest t the 9:30 o clock. The more nterior nodule mesures 5.8mm 4.8mm 8.3mm, nd the mid left brest nodule mesures 6.9mm 3.6mm 9.1mm. These two nodules lsted for t lest six months before our opticl imging, nd were recommended to follow up exmintions in nother six months to ccess stbility. The opticl imge experiments were done by the 10-wvelenghsystem, nd 64 sources nd 64 detectors were distributed uniformly for four plnes long the surfce of ptient s left brest t the lesion position (the respective rdii of the four 28

39 29 lyers tht ttch the brest re: r 1 = mm, r 2 = mm, r 3 = mm, nd r4 = mm; 16 sources nd 16 detectors t ech plne). As lyer 1 ( r 1 = mm) showed the most similr results compre to the mmmogrphy nd ultrsounds report, so we took the plne 1 for further studies. And the x-ry mmmogrphy (Figure 4-2) nd our opticl imging results (Figure 4-2b 4-2e) re presented s figures 4-2. Right 12:00 12:00 Left 9:00 3:00 9:00 3:00 6:00 6:00 3:00 6:00 12:00 9:00 Vlue b Figure 4-1 Corresponding position from report to opticl 2D imges. The Front View on Brest Exmintion Report. b The 2D Imge View for Experiment Results

40 30 L_CC L_MLO 638nm 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm b [ HbO 2 ] [ ] Hb Wter (%) HbT SO t 2 (%) c Figure 4-2 The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected nodule cse.. The X-ry Mmmogrphy for this ptient. b. The Respective Absorption Coefficients Imges from Wvelength 638nm to 922nm. c The Resolved Chromophore Concentrtion Imges from Absorption Coefficients. d Respective Reduced Scttering Coefficients Imges from Wvelength 638nm to 922nm. e Scttering Amplitude nd Scttering Power Imges

41 31 638nm 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm d Sctt Ampl. Sctt Power e Figure 4-2 Continued. Hence, the two disese lesions ner the 9:30 position were distinct t the corresponding position of opticl imges for both bsorption nd reduced scttering coefficients from the shortest wvelength 638nm to 840nm. Unfortuntely, for the longest three wvelengths, we could not obtin reconstructed imges with lesions legible for further study, due to the weker signls. Therefore, we use those qulified reconstructed dtum for resolving chromophore concentrtions, scttering mplitude, nd scttering power. Those two tumors were distinct round 9:00 o clock position in imges for de-oxy hemoglobin concentrtion, oxy-hemoglobin concentrtion, nd wter content: ll the functionl informtion of the two tumors shows n increse compred to the

42 32 surrounding tissue. Totl hemoglobin concentrtion HbT, nd the hemoglobin oxygen sturtion SO t 2 were lso gined. Only the HbT shows increses t the tumors positions, but t the corresponding position, no tumor emerged in shpe. For resolved scttering mplitude nd power imges, tumors re visible, showing increses for scttering mplitude nd decreses for scttering power t their respective positions. Clcifiction This ptient ws 65-yer-old white femle with the presence of corse clcifictions which were clustered together in the upper outer right brest t 10 o clock position. No underlying soft tissue component is pprent on the spot compression views. In ddition to the ultrsound, there is firly well circumscribed slightly lobulr hypoechoic focus ssocited with the clcifictions, which mesures pproximtely 5mm 8mm in size nd could represent ft necrosis. The opticl imge experiments were lso done by the 10-wvelengh-system, with the rdii for three plnes long the surfce of ptient s right brest t the lesion position re: r 1 = mm, r 2 = mm, nd r3 = mm(the probes for the 4 th plne ws not touched fully on the brest becuse of its own shpe). Lyer 1 ( r 1 = mm) showed the best results compred to the mmmogrphy nd ultrsounds report. And the x-ry mmmogrphy (Figure 4-3) nd our opticl imging results (Figure 4-3b 4-3e) re presented s Figures 4-3.

43 33 R_CC R_ML 638nm 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm b c Figure 4-3 The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected clcifiction cse. The X-ry Mmmogrphy for this ptient. b The Respective Absorption Coefficients Imges from Wvelength 638nm to 922nm. c The Resolved Chromophore Concentrtion Imges from Absorption Coefficients. d Respective Reduced Scttering Coefficients Imges from Wvelength 638nm to 922nm. e Scttering Amplitude nd Scttering Power Imges

44 34 638nm 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm d Sctt Ampl. Sctt Power e Figure 4-3. Continued. Still, the bsorption nd reduced scttering imges were vivid, nd the lesion position is in ccordnce with the exmintion reports, except the imges for the longest 3 wvelengths. Clerly, the clcifiction lesion t 10 o clock position is pprent on lmost ll the resolved functionl coefficients imges except for the concentrtion of SO t 2. Remrkbly, the nodule which could be ft necrosis ws not pprent on mmmogrms nd only shdowed on the ultrsound exmintion, but did pper clerly on our opticl imges for most wve lengths in terms of both bsorption nd reduced scttering coefficients. Also, the resolved imges for chromophore concentrtion (except SO t 2 ), scttering mplitude nd scttering power, shdowed this nodule ner the corresponding

45 35 loction. Both the clcifiction nd nodule lesion present in silhouette, with increses in chromophore concentrtions nd scttering mplitude, nd decreses in scttering power. Cyst This ptient ws 43-yer-old femle during our opticl brest experiments. The reports clinicl recorded tht there ws persistent 2.3cm dimeter smooth round nodulr density, which ws demonstrted to be benign cyst. The physicin indicted the cyst to be locted t the 12 o clock position. A moderte to lrge mount of dense residul fibroglndulr tissue within the left brest ws lso present on the mmmogrphy. A smll symmetric ovl re of density could be seen in the inferior hlf of the left brest on the MLO view; however, ultrsound exmintion suggested no dominnt msses in the region of the plpble bnormlity. To explin this, her ultrsound report lso pointed out tht the density of the brest ws such tht it might decrese sensitivity of mmmogrphy for detection of mlignncy. The 10-wvelengh-system gin were employed for the corresponding opticl imging experiments, performing four-plne mesurements for the lesion position, nd the respective rdii re: r 1 = mm, r2 = mm, r 3 = mm, nd r 4 = mm, nd the fourth lyer were selected out for further reserches. We could see visible tumor t the 12:00 o clock position in reconstructed bsorption nd reduced scttering coefficient imges for the middle region of wvelengths. For resolved functionl coefficients, there re corresponding increses for this tumor t the respective position in imges for de-oxy hemoglobin concentrtion [ Hb ], oxyhemoglobin concentrtion [ HbO 2 ], wter content, totl hemoglobin concentrtion HbT nd scttering power; however, no significnt decreses or increses were present t the

46 36 disesed lesion in the imge of scttering mplitude, nd neither in the oxygen sturtion SO imge. Interestingly, those tissue density tht recorded in her mmmogrphy reports, t 2 do increse the vlue contrst to the cyst vlue in the resolved chromophore concentrtion imges, compring to the imges of bsorption nd reduced scttering coefficients, which mde them more similr to the norml bckground in the chromophore concentrtion imges. L_CC L_MLO Figure 4-4 The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected cyst cse. The X-ry Mmmogrphy for this ptient b The Respective Absorption Coefficients Imges from Wvelength 673nm to 922nm c The Resolved Chromophore Concentrtion Imges from Absorption Coefficients c Respective Reduced Scttering Coefficients Imges from Wvelength 673nm to 922nm e Scttering Amplitude nd Scttering Power Imges

47 37 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm b c 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm d Figure 4-4 Continued

48 38 Sctt Ampl. Sctt Power e Figure 4-4 Continued Cncer This ptient ws 62-yer-old white femle with two cncer msses dignosed with the needle biopsy report. After our opticl imge experiment, the ptient hd surgery on her brest nd removing the lesions. In her screening mmmogrphy reports, these two cncer lesions were reported s two incresing microclcifictions, one in the inferomedil qudrnt ner the dominnt mss nd the other in the centrl spect of the mid brest. A few other smll clusters of microclcifictions re seen lterlly in the right brest, nd more likely to be relted to benign process such s sclerosing denosis or cystic hyperplsi. In ddition, there ws smll to moderte mount of dense residul fibro-glndulr tissue in the brest. This experiment ws performed on the the 10-wvelengh-system, with only two lyers of source-detector probes touch ptient s brest surfce t the lesion position nd the respective rdii re: r 1 = mm, nd r 2 = mm, nd the experiment dtum collected in the second plne showed better results. Here, the two cncer tumors were present t the correct positions ccording to the surgery reports for reconstructed bsorption imges, but were not s cler in the

49 39 reconstructed reduced scttering imges. After nlysis, the two cncer tumors were more cler-cut in silhouette s in de-oxy hemoglobin concentrtion [ Hb ], oxy-hemoglobin concentrtion [ HbO 2 ], wter content, totl hemoglobin concentrtion HbT, scttering mplitude nd scttering power. In this cse, corresponding increses were present t imges for [ Hb ], [ HbO ] 2, HbT, nd scttering power; nd decreses were present t imges for wter content nd scttering mplitude. In ddition, decreses in oxygen sturtion SO t 2 could lso be observed t the cncer tumors lesions, lthough the mrgins were not so firly well circumscribed. Agin, the uncertin tissues tht hve low contrsts compred to the cncer tumors vlues in the bsorption nd reduced scttering coefficient imges, do increse their vlue contrst in the resolved chromophore concentrtion imges. 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm Figure 4-5 The X-ry mmmogrphy, reconstructed opticl properties nd functionl informtion imges of selected cncer cse. The Respective Absorption Coefficients Imges from Wvelength 638nm to 922nm b The Resolved Chromophore Concentrtion Imges from Absorption Coefficients c Respective Reduced Scttering Coefficients Imges from Wvelength 638nm to 922nm d Scttering Amplitude nd Scttering Power Imges

50 40 [ HbO 2 ] [ ] Hb Wter (%) HbT SO t 2 (%) b 673nm 690nm 733nm 775nm 808nm 840nm 915nm 922nm c Sctt Ampl. Sctt Power d Figure 4-5 Continued