Doctor of Philosophy. Troy O. McBride

Transcription

1 Spetrosop Reonstruted Near Infrared Tomograph Imagng for Breast Caner Dagnoss A Thess submtted to the Faulty n partal fulfllment of the requrements for the degree of Dotor of Phlosophy by Troy O. MBrde Thayer Shool of Engneerng Dartmouth College Hanover, New Hampshre May 200 Examnng Commttee Ulf Österberg, Ph. D., Char Keth Paulsen, Ph. D., Member Bran Pogue, Ph. D., Member Dean of Graduate Studes 200 Trustees of Dartmouth College Mhael Patterson, Ph. D., Member Sgnature of Author

2 Abstrat Near-nfrared NIR lght has the potental to be used as a non-nvasve means of dagnost magng wthn the human breast. Due to the dffusve nature of lght n tssue, omputatonal model-based methods are requred for funtonal magng wthn the breast. These methods an be used to reonstrut tomograph mages of absorpton and satterng propertes of the nteror of the breast from lght measurements at the skn's surfae. The work presented here desrbes mprovements n both the data aquston system and mage reonstruton algorthm of NIR tomograph magng for breast aner dagnoss. Spefally, the desgn, onstruton, and testng of a frequeny-doman paralleldeteton NIR data aquston system s presented. Data aquston from the system requres under 30 seonds for a sngle tomograph sle at one optal wavelength wth a measurement repeatablty for a sngle phantom on average of 0.5% n AC Intensty and 0.4 degrees n phase. In addton, methods for mproved reonstruton n the areas of magng addtonal tssue hromophores and the separaton of absorpton and satterng heterogenety are desrbed. The mproved system and reonstruton methods have been tested extensvely wth omputer smulaton and tssue-smulatng 'phantoms'. In addton, fortyfve healthy volunteers, and fve women wth breast abnormaltes have been maged. Moderate-resoluton quanttatve tomograph mages of absorpton and satterng are reonstruted from data aqured at the breast tssue surfae, and the quanttatve absorpton mages are ombned at multple optal wavelengths to generate mages of oxygenated and de-oxygenated hemoglobn, lpd, and water onentraton. Ths researh has led to an mproved novel magng system whh s potentally useful n the dagnoss and deteton of breast aner.

3 Aknowledgements I have been truly blessed wth the fnest group of advsors ever assembled. I quote an anonymous grant revewer: "Ths s a hghly aomplshed group. Dr. Pogue... s a keenly adept member". I owe my greatest grattude to Bran Pogue, for patently sharng hs abundane of knowledge, leadng by example wth hs treless work eth, and always fndng the tme to talk wth me and read my work. I ould not have found a better researh advsor. I also am partularly ndebted to the magan Keth Paulsen, who an smultaneously teah three ourses, run four grant programs, wrte ompetng renewals, read four theses, sour fve journal artles, mentor twenty researhers, and stll fnd tme to be a generous and knd ndvdual. There are few heads of large researh programs of hs alber. My offal thess advsor, Ulf Österberg, has been extremely helpful throughout my studes. I truly appreate the many onversatons that we have had spannng general sene and theory, teahng, runnng, polts, hansaws, and even optal tomography. He has been for me what few Ph.D. students ever atually have -- a true "advsor". It s hard to magne wth ths exellent ombnaton of nternal advsors, that I would also have a great external advsor n Mhael Patterson, untl you realze that he was Bran Pogue's Ph.D. advsor. I only hope that I an mantan ths han of exellene as Bran's frst Ph.D. advsee. I am grateful for the omments and suggestons from Dr. Patterson durng hs vsts to Dartmouth and for hs thorough readng and omments on ths thess. I would lke to aknowledge lnal ollaboraton and help from Steven Poplak, Sandra Soho, Wendy Wells and Sunshne Osterman; prevous researh by Huabe Jang and Davd Rnehart; valuable student work by Clare Wllsher, Elzabeth Whte, and Sean Stauth; expermental ad from Shudong Jang and Greg Burke; tehnal expertse from Davd Stratton, and patene and onversaton from offemates, Eljah Evenstar Wallae Van Houten, Yong Yang, Dnse Wllams, Karen Lunn, and Ha Sun. Fnanal support was provded by the Natonal Insttutes of Health and the Alma Hass Mlham Fellowshp. I would also lke to aknowledge professors Martha and Holls MBrde and ther hldren Andrew and Kar for years of enouragement towards ths degree and other more broad ntangbles. Fnally, Lots Of Valuable Enouragement from my wfe Jeanne makes t all worth whle! I wll forever gve you my lots of valuable enouragement...! And to Shaylee! I dedate ths thess to the true embodment of the Ph.D., Bors Katsen, 997, and to Quon Chuk Tam, 2000, a good father and a good man.

4 Contents Abstrat Aknowledgements Table of Contents Lst of Fgures Lst of Tables Chapter. Overvew A. Introduton B. Bakground and Sgnfane C. NIR Tomograph Imagng at Dartmouth Chapter 2: FEM reonstruton algorthm A. Introduton B. Dffuson Approxmaton C. Fnte element soluton C.. Forward solver C.2. Levenberg-Marquardt nverse soluton C.3. Normalzaton of the senstvty matrx Chapter 3: Smulaton A. Introduton B. Smulaton proedure at Dartmouth Chapter 4: Instrumentaton A. Introduton B. Manual aquston C. Intal automated aquston setup D. Current parallel deteton system Chapter 5: Phantom testng A. Introduton B. Phantom studes at Dartmouth B.. Lqud phantoms B.2. Resn sold phantoms B.3. Compressble sem-sold phantoms B.4. Gelatn phantoms Chapter 6: Calbraton and homogeneous fttng algorthm A. Introduton B. Pratal Consderatons v v xv v

5 6.C. Homogeneous Fttng Algorthm C.. Motvaton and prevous method Method A C.2 Current homogeneous fttng algorthm Method B D. Results Chapter 7: Separaton of satterng and absorbng heterogenety... 7.A. Introduton B. Hstoral motvaton C. Improved algorthm D. Phantom studes Chapter 8: Heterogeneous and Contnually-varyng phantoms A. Introduton B. Contnuously varyng and rregularly shaped objets C. Heterogeneous Bakground and Inlusons Chapter 9: Funtonal Imagng A. Introduton B. Theory B.. Tssue Charatersts B.2. Determnaton of [Hb-T] and SO C. Smulaton of Breast Caner Lesons D. Homogeneous Measurements E. Heterogeneous phantom studes E.. Phantom wth nreasng blood onentraton E.2. Phantom wth ontrast n [Hb-T] and SO Chapter 0: Patent Imagng A. Introduton B. Intal automated system B.. Patent 5: 3 m fbroadenoma B.2. Patent 6: 0.8 m nvasve aner B.3. Comparson wth early normal values C. Current automated system C.. Normal patent study C.2. Study of Lpd and Water ompensaton Chapter : Conludng remarks a. Conluson B. Future studes Appendx A: Itemzed Components Lst Appendx B: Fle namng onventons Referenes v

6 Lst of Fgures Fgure.: Shemat of the funtonal magng proess Fgure.2: a Dagram of data aquston system, b photograph of fber-opt nterfae Fgure.3: Flow hart of fnte element based mage reonstruton algorthm for a sngle wavelength Fgure.4: a Plot of NIR absorpton spetra for water, lpds, Hb-O 2 and Hb-R. Values for absorpton oeffent are dsplayed for anatomally relevant onentratons for breast tssue. b Mathematal dagram of onverson of absorpton mages to funtonal mages of breast tssue hromophores Fgure.5. Shemat for mage reonstruton showng requrements left and steps for testng rght mage reonstruton methods Fgure.6. Smulatons showng mproved reonstruton of satterng and absorbng nlusons for nose-free data. a Orgnal smulated mage wth three embedded objets. Fgure b shows the reonstruted absorpton oeffent mage and the reonstruted satterng oeffent mage Fgure.7. Smulatons of heterogeneous objet wth heterogeneous nluson wth an average 2: ontrast n absorpton and :2 absorpton n satterng. The frst two olumns are the orgnal absorpton and satterng dstrbutons pror to smulaton. The seond two olumns are the reonstruted absorpton and satterng mages. Eah suessve row represents an nreasng level of added heterogenety to the orgnal dstrbuton n the frst row. All absorpton and satterng mages are dsplayed on the dental sale Fgure.8: Smulatons showng mprovement of oxygen saturaton mages wth nreasng number of wavelengths n the presene of sgnfant nose. a Orgnal smulated oxygen saturaton mage wth embedded objet wth 20% derease n oxygen saturaton, whh was used to generate smulated data wth 0% added nose. Fgure b shows the reonstruted oxygen saturaton mage usng only 2 wavelengths and the reonstruted oxygen saturaton mage usng 4 wavelengths Fgure.9: Hemoglobn onentraton and oxygen saturaton mages of a phantom ontanng two targets -- one wth a 4: hemoglobn onentraton ontrast ompared wth the bakground and the other had a 00% derease n oxygen saturaton ontrast ompared to the bakground. The fgure a shows a shemat of the phantom, b reonstruted hemoglobn Hb onentraton mage, oxygen saturaton mage. d and e are one-dmensonal profle plots horzontal through the enter of b and respetvely. Ideal profles are plotted for omparson Fgure.0: Images of patent wth bengn fbroadenoma. Shown n the fgure are the a x-ray mammograph, b representaton of loaton of tumor taken from a sketh by radologst based on x-ray mammography mages and palpaton, hemoglobn onentraton mage reonstruted from near nfrared absorpton mages at 750 and 800 nm Fgure.: Images of patent wth malgnant dutal nvasve arnoma. Fgure dsplays a x-ray mammograph, b representaton of loaton of tumor taken from a sketh by radologst based on x-ray mammography mages and palpaton, and v

7 hemoglobn onentraton mage reonstruted from near nfrared absorpton mages at 750 and 800 nm Fgure.2: Plot of average hemoglobn onentraton from near-nfrared mages of volunteers. Also plotted are two loalzed values for hemoglobn onentraton for a malgnant tumor and a bengn tumor Fgure.3: Plot of average hemoglobn onentraton from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms Fgure 2.: Fnte element fne mesh 425 nodes, 777 elements used n the forward solver for ths thess. The letter S and D represent soure and detetor loatons respetvely Fgure 3.: Shemat of Matlab program to generate optal property dstrbutons and map them onto the fnte element mesh. a A 200x200 pxel mage of the dstrbuton s reated n Matlab. b The mage s blurred by an averagng flter wth sze equal to the average node spang. The mesh s overlayed on the mage and the values of the pxel nearest to eah node s wrtten to fle. Ths proess effetvely uses lnear nterpolaton to map the dstrbuton onto the nodes Fgure 3.2: Shemat of the forward smulator. Node-based mages of a a and b s ' generated from Matlab program. Ampltude and phase measurement data from the forward smulaton for mages a and b labeled "experment" n ths graph. Plotted for referene s the measurement data for a homogeneous dstrbuton wth the same bakground propertes as a and b Fgure 3.3: Reovered mages from smulated measurement data plotted n Fgure 3.2. usng the FEM reonstruton program. Dsplayed are the node-based mages of a a and b a '. No nose was added to the measurement data n ths ase..... Fgure 4.: An early phantom magng setup. The ylndral phantom s n the enter of the mage. Two fber opts lead to holes drlled n the phantom, one from a laser soure and the other leadng to a PMT detetor. The nlusons n the phantom an be arefully postoned usng the setup attahed to the top of the ylnder, and phantoms were maged wth and wthout the nluson present Fgure 4.2: Some phantom mages obtaned from the frst expermental setup. The ontents of the phantoms are summarzed below the mages and further detals an be found n the orgnal paper by Jang et al Fgure 4.3: Shemat of the frst-automated magng setup showng the onnetons to and from the laser soure and PMT on translaton stages Fgure 4.4: Photograph of the automated setup. Note that for ths early setup, fbers were postoned ndvdually by loosenng of the thumb srew and manual reloaton Fgure 4.5: Heterodynng shemat from Davd Rnehart thess, where n our ase,?=2p00 MHz s the loal osllator sgnal,?+d=2p00.00 MHz s the frequeny of the nput and deteted sgnal, and d=2p khz s the heterodyne or "beat" frequeny. A 0 khz low-pass flter n the data aquston blok removes the hgh-frequeny sgnals Fgure 4.6: Photograph of laboratory setup, where TS laser, Argon on pump laser, and eletro-opt modulator are mounted on optal benh on the rght. The frst patent bed setup s shown at the left sde of the photograph Fgure 4.7: Photographs of assembled lathe-huk fber postonng system. By rotatng the metal spokes n red below the lathe huk, the fber opts are moved v

8 radally. The photographs on the rght show the fbers at a lose poston dameter of openng = 6 m and at a ompletely open poston dameter = 0 m. A "labjak" s mounted below the lathe huk to allow for vertal postonng of the array Fgure 4.8: a Top vew and b utaway sde vew of ntal radal postoner desgn Fgure 4.9: Image of Laser dode array. The dode lasers A-5 are mounted n fber launh modules. A omputer ontrolled RF swth B provdes the dode wth eletral urrent. The output of the lasers s nput nto a 6: fber opt ombner C Fgure 4.0: Image of rak mounted system. The four labeled levels house A the omputer, B the stage ontroller and PMT voltage soure, C the fve laser dodes, RF swth, and urrent soure, D the frequeny generators Fgure 4.: The parallel deteton assembly. a The 6 RF mxers are mounted on a rular alumnum ds, whh s attahed to a rotary stage fxed to a square alumnum plate. A DC spltter box s also mounted on the enter of ths plate. b The 6 PMTs are mounted on the perphery of a seond rular ds. The RF spltter and soure fber are also mounted to ths ds. The fully assembled deteton array nludes the PMT ds mounted above the mxer ds. A fxed square alumnum plate for the fber opt lght delvery s mounted above the PMTs Fgure 4.2: The fber opt/patent nterfae for dret fber ontat wth the breast n a rular geometry. Fber opt bundles at the tssue nterfae A are mounted to sxteen radally-algned horzontal translaton stages B. The nterfae s attahed to a vertal translaton stage C. The motor ontrollers D and the deteton array E are mounted to an alumnum base below the patent nterfae. The vertal and horzontal stages are ontrolled by a sngle push button ontroller. Fgure 4.3: The ustom bult patent table. The woman les prone on the table wth her breast pendant through the openng. The fber-opt nterfae s loated below the openng. An nexpensve PC vdeo-am s plaed below and updated mages are vewed on a omputer sreen suh that the nurse an easly poston the fbers n ontat wth the breast usng the push-button ontroller Fgure 4.4: a AC ampltude and b phase of deteted sgnal for the same optal sgnal for all 6 PMT detetors Fgure 4:5: a Relatve AC power level for the same measured voltage 0. V at dfferent gan settngs. b Phase shft measured for the dental optal phase but at dfferent gan levels. Both measurements are reported for detetor number one.. Fgure 4:6: a AC Voltage plotted aganst relatve optal power and b measured phase shft for the same optal sgnals for eght representatve detetors D - D8 at a sngle gan settng of 0.7 V. A log sale s used for the power of the optal sgnal n plot b Fgure 4.7: Calbraton urves for PMT response at dfferent gan settngs. A fxed optal sgnal ntensty was vared wth neutral densty flters for all gan settngs. A regresson to the deteted log ampltude at eah detetor was performed versus log of nput optal power. The onstant term of the regresson s related to the lnear slope ampltude/nput power and s plotted n fgure a versus gan level for eght representatve detetors D - D8. The phase shft s approxmately onstant for deteted sgnals below saturaton level and above the nose floor. The v

9 average phase shft for eght detetors D - D8 s plotted n fgure b for dfferent gan settngs Fgure 4.8: a Plot of the deteted AC ntensty sgnal versus the nput power at the gan settng of 0.95 of the maxmum gan. The long dashed lne s the system nose level and the short dashed lne s the nose level of the eletrons. The sold lne ndates the lnear response of the detetor pror to reahng the nose floor. b Plot of phase error wth respet to nput power. The phase error dereases wth nreasng sgnal to a onstant RMS level of less than a degree at typal power levels Fgure 4.9: a Absorpton and b satterng mage of a homogeneous phantom wth albraton and expermental data aqured by manual postonng setup. Absorpton and d satterng mage from automated postonng setup. The x and y axes of the mages are unts of mllmeters and the sale bar unts are nverse mllmeters Fgure 5.: Reovered values for a a and b s ' at 785 nm for Intralpd per unt onentraton for homogeneous soluton based on data aqured wth urrent deteton system and proessed wth the homogeneous fttng algorthm Fgure 5.2: Reovered values for a a and b s ' at 785 nm for 2% Ink per unt onentraton. Note a nterept s mm - nstead of expeted value for water of mm Fgure 5.3: Photographs of resn sold phantoms. a homogeneous phantom, b phantom wth holes drlled for addton of nlusons Fgure 6.: Plot of entre 256 measurement a lnintensty and b phase shft data set. Ths data s averaged over all soures and homogeneous fttng algorthm appled to fnd best ft. Also dsplayed s lnintensty and d phase data averaged over all soures and the alulated data for the best ft homogeneous optal propertes Fgure 6.2: Shemat desrbng two homogeneous fttng algorthms Fgure 6.3: Plot of measured and alulated a log of dstane tmes AC ntensty, lnri, and b phase,?, versus soure to detetor dstane, r Fgure 6.4: Plot of a lnintensty data at 6 detetor stes showng offset due to algnment dfferenes, b alulated data from fnte element soluton, and dfferene between a and b. Dfferene data s used as the 'albraton' fator Fgure 6.5: Image after frst teraton of reonstruton of absorbng objet wth Gaussan profle wth a ntal estmate equal to average optal propertes, b 0% error n ntal estmate, and 50% error n ntal estmate. The vertal axs unts are n mm -. d, e, and f are profle plots along a vertal lne through the enter of mages a, b, and respetvely Fgure 6.6: Plot demonstratng measured data wth overall offset due to long term drft of laser ntensty. The average dfferene s used to orret ths offset Fgure 6.7: Homogeneous fts to measured data for the two methods desrbed n Fgure 6.2: a Method A satterng oeffent data, b Method B satterng oeffent data, Method A absorpton oeffent data, d Method B absorpton oeffent data. Eah onentraton was measured three tmes at eah of three wavelengths Fgure 6.8: Shemat of nputs to mage reonstruton algorthm from homogeneous albraton and ntal estmate alulaton. Inputs from albraton methods are dsplayed n bold boxes x

10 Fgure 7.: Dagram of senstvty matrx, J T J. The parttons llustrate the satterng and absorpton seton of the matrx for NN number of nodes and NM measurement stes. ln I θ and are the dervatve of the ampltude wth D j a j respet to dffuson oeffent D and the dervatve of phase shft wth respet to absorpton oeffent a, respetvely, for measurement ste at node j Fgure 7.2: One teraton reonstrutons for a smulated absorbng-only nluson 2: ontrast n a. The absorpton and redued satterng oeffent mages are presented respetvely usng a,b the orgnal non-normalzed phase-andampltude method,,d the method wth normalzed J T J matrx, and e,f the urrent method where the J T J matrx s normalzed and the phase terms are weghted Fgure 7.3: One teraton reonstrutons for a smulated nluson wth 2: ontrast n both a and s '. The absorpton and redued satterng oeffent mages are presented respetvely usng a,b the orgnal non-normalzed phaseand-ampltude method,,d the method wth normalzed J T J matrx, and e,f the urrent method where the J T J matrx s normalzed and the phase terms are weghted Fgure 7.4: a Orgnal absorpton oeffent a and b the redued satterng oeffent s ' smulated mage wth three embedded objets. Fgure shows the reonstruted a mage and d the s ' mage Fgure 7.5: An 86 mm dameter sold ylndral tssue-smulatng phantom wth three 7 mm dameter ylndral holes s shown. Absorbng-only ontrast was added to hole A, satterng-only ontrast to hole B, and absorbng and satterng ontrast to C. Bakground optal propertes were estmated to be a =0.006 mm - and s '=.0 mm Fgure 7.6: Reonstruted mages of a,,e a and b,d,f s ' for ontrast levels of a,b ½:,,d ½:, and e,f 2½: for both oeffents are dsplayed. In the upper entral hole C, both a and s ' are nreased together, whereas n the left hole A only a s nreased, and n the rght hole B only s ' s hanged. The x and y axes are poston n mllmeters and the unts of the sale bars are nverse mllmeters Fgure 7.7: Comparson of reonstruted and expeted ontrast at the enter of the reonstruted objets n Fgure 7.6. The reonstruted values for a absorpton and b satterng oeffent are plotted versus the expeted results for embedded objets wth ontrast n A absorpton-only, B satterng-only, and C absorpton and satterng. The reonstruted rosstalk n terms of absorpton ontrast for the satterng-only objet and d satterng ontrast for the absorptononly objet are also dsplayed Fgure 8.: Orgnal and reonstruted absorpton oeffent mm - mages of an objet wth a Gaussan profle and a rular step nluson. 3% nose was added to the smulated measurement data pror to mage reonstruton. a Orgnal rular step objet; b orgnal Gaussan objet; horzontal profle of a; d horzontal profle of b; e reonstruted mage of a; f reonstruted mage of b; g horzontal profle of e; h horzontal profle of f. X-Y oordnates are n unts of mm x

11 Fgure 8.2: Smulaton of objets wth dfferng rregularly shaped nlusons n a and s '. The orgnal a and s ' property dstrbuton s shown n a and b, wth the reonstruted mages n and d. The sale bars are n unts of mm Fgure 8.3: Exsed breast tssue ontaned n a thn plast bag s plaed wthn the fber opt nterfae. The sxteen soure and detetor fbers are radally postoned n dret ontat wth the sample Fgure 8.4: The frst two olumns are the orgnal absorpton and satterng dstrbutons pror to smulaton. The seond two olumns are the reonstruted absorpton and satterng mages. Eah suessve row represents an nreasng level of added heterogenety to the orgnal dstrbuton n the frst row. All absorpton and satterng mages are dsplayed on the dental sale Fgure 8.5: a Reonstruted absorpton and b satterng mages of embedded pork heterogenety wthn exsed breast tssue. and d are the profle graphs through a and b respetvely. e-h are dental mages for the ase where the sample was rotated 90 degrees ounterlokwse Fgure 9.: Plot of near-nfrared absorpton spetra for water, lpds, oxygenated Hb-O 2, and de-oxygenated hemoglobnhb-r. Values taken from Wray et al. for Hb-O 2 and Hb-R, from Hale and Querry for water, and from Quaresma et al. for lpds Fgure 9.2: a Absorpton oeffent mm - mage at 750 nm of a smulated normal tomograph seton of breast tssue ontanng a anerous leson. b Vertal profle graph through the enter of a. Hemoglobn onentraton M mage and d hemoglobn oxygen saturaton % mage of the smulated breast and anerous leson. e and f are vertal profle graphs through the enter of mages and d respetvely. X-Y oordnates are n unts of mm Fgure 9.3: Results for 0% nose mage reonstrutons of a smulated breast aner leson wthn a tomograph ross seton of normal breast tssue. The orgnal mages and values are shown n Fgure bakground of 0 M hemoglobn onentraton and 70% oxygen saturaton ontanng a rng of 40 M hemoglobn onentraton wth 50% oxygen saturaton. a Hemoglobn onentraton mage and b hemoglobn oxygen saturaton mage for the regresson usng two wavelengths. and d are vertal profle graphs through the enter of a and b respetvely. e and f are the hemoglobn onentraton and oxygen saturaton mages usng three wavelengths. g and h are profle graphs through the enter of e and f., j, k, and l are the mages and profle graphs for the regresson usng four wavelengths Fgure 9.4: Comparson of measured values and those predted by Staveren et al. for the redued satterng oeffent s of a phantom ontanng 0.5% Intralpd n water. Expermental estmates are reahed by fttng the data from a homogeneous phantom to the fnte element model usng Method A desrbed n Chapter Fgure 9.5: Plot of expermentally measured absorpton oeffent versus onentraton of blood for three wavelengths: ahb-r and bhb-o 2. Measurements were reorded from a homogeneous satterng medum of 0.5% Intralpd n a 72 mm dameter ylndral phantom. Homogeneous fttng Method A was used for ths data Fgure 9.6: Comparson of absorpton oeffent alulated from expeted values for blood and water and measured values: a 0 M de-oxygenated hemoglobn n 0.5% Intralpd and water soluton; b 0 M oxygenated hemoglobn n 0.5% x

12 Intralpd and water soluton. Homogeneous fttng Method A was used for ths data Fgure 9.7: Comparson of absorpton oeffent values from Hale and Querry wth the absorpton oeffent of water measured n a plast beaker versus a thnwalled balloon. Note that the offset s not apparent n the thn-walled balloon ase. Homogeneous fttng Method A was used for ths data Fgure 9.8: Comparson of absorpton oeffent alulated from expeted values for blood and water and measured values: a 24 M de-oxygenated hemoglobn and b 24 M oxygenated hemoglobn n 0.5% Intralpd and water soluton. Homogeneous fttng Method B was used for ths data Fgure 9.9: NIR spetra and graphal results of least squares fts to determne hemoglobn onentraton and hemoglobn oxygen saturaton level for a 33 year old woman, and b 62 year old woman Fgure 9.0: Colleton of absorpton oeffent mages for a 25mm rular nluson n a 72 mm rular phantom. The bakground s 0.5% blood n 0.5% Intralpd and water. The nluson n the frst row has no blood. The nluson n the seond row ontans % blood, the thrd row.5% blood and the fourth row 2% blood. Column a s measured at 750 nm, olumn b at 800 nm, and olumn 830 nm Fgure 9.: Comparson of absorpton oeffent taken from the enter of the nluson n the mages n Fgure 9.0 wth absorpton oeffent values alulated from expeted values for blood and water Fgure 9.2: Absorpton oeffent a, hemoglobn onentraton [Hb-T], and hemoglobn oxygen saturaton SO 2 mages of an nreased [Hb-T] nluson left off-enter and a de-oxygenated blood nluson rght off-enter n a oxygenated blood bakground. a Depton of orgnal phantom, b 750 nm a mm - mage, 802 nm a mage, d [Hb-T] M mage, e SO 2 mage. f and g are onedmensonal transets through mages d and e respetvely. Ideal profles are plotted for omparson Fgure 0.: Reonstruted mages for a woman wth a bengn fbroadenoma Patent 5. Dsplayed are the absorpton oeffent a mages sale bar unt of [mm - ] at a 750 nm and b 800 nm and the hemoglobn onentraton [Hb-T] mage sale bar unt of [M]. The x and y axes of the mages are poston n unts of mm. Also dsplayed are the values for a vertal transet through the mddle of the [Hb-T] mage. y-axs s [M] and x-axs s vertal poston n mm Fgure 0.2: Reonstruted mages for the ontralateral mammographally normal breast for patent 5. Dsplayed are a the hemoglobn onentraton [Hb-T] mage and b vertal transet through the mddle of the [Hb-T] mage. sale bars and axes are dental to Fgure 0. and d Fgure 0.3: Reonstruted mages for a woman wth an nvasve arnoma Patent 6. Dsplayed are the absorpton oeffent a mages sale bar unt of [mm - ] at a 750 nm and b 800 nm and the hemoglobn onentraton [Hb-T] mage sale bar unt of [M]. The x and y axes of the mages are poston n unts of mm. Also dsplayed s the values for a vertal transet at x = 42 mm of the [Hb- T] mage. y-axs s [M] and x-axs s vertal poston n mm Fgure 0.4: Reonstruted mages for the ontralateral mammographally normal breast for patent 6. Dsplayed are a the hemoglobn onentraton [Hb-T] mage and b vertal transet through the mddle of the [Hb-T] mage. sale bars and axes are dental to Fgure 0.3 and d x

13 Fgure 0.5: Plot of average hemoglobn onentraton from near-nfrared mages of volunteers. Also plotted are two loalzed values for hemoglobn onentraton for a malgnant tumor and a bengn tumor Fgure 0.6: Plot of average a hemoglobn onentraton, b oxygen saturaton, absorpton oeffent at 785 nm, and d redued satterng oeffent at 785 nm versus age from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms. Error bars represent dfferene n mean value between the two breasts Fgure 0.7: Plot of average hemoglobn onentraton versus a body mass ndex kg/m 2 and b radograph densty from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms. The error bars represent the standard devaton between multple measurements, suh as left and rght breast or multple planes wthn a sngle breast. In b, the error bars are based on values from multple subjets Fgure 0.8: Tomograph NIR mages of female breast wth 3 m leson loated at 3 o'lok presented n the manner used by our lnal database. a. - d. and. - l. are a and s ' mages n graysale unts of /mm at the four wavelengths ndated. e. and g. are Hb-T and SO 2 mages determned usng method as desrbed n the text assumpton of 30% and 60% bulk water and lpd ontent. The x and y axes of the mages are poston n unts of mm. The average values and standard devaton of all pxels are ndated below eah mage. f. and h. are horzontal transets through the enter of mages e. and g Fgure 0.9: Images of a. water, b. lpds,. Hb-T and e. SO 2 are reovered usng a least squares ft to determne all four parameters method 2 from the a mages presented n Fgure 0.8. The x and y axes of the mages are poston n unts of mm. d. and f. are horzontal transets through the enter of mages. and e Fgure 0.0: Images of a. satterng power b. water,. lpds, d. Hb-T and f. SO 2 are reovered usng method 3. The satterng power mage s alulated from a ft to ln s ' for the sequene of mages n Fgure 0.8 versus lnλ. The water and lpd mages are then determned from equatons 2.a. and 2.b. The x and y axes of the mages are poston n unts of mm. e. and g. are horzontal transets through the enter of mages d. and f Fgure 0.: Tomograph NIR mages of the ontralateral normal female breast. a. - b. and. - d. are a and s ' mages n graysale unts of /mm at the two wavelengths ndated. 785 and 826 nm mages are omtted. e. and g. are Hb-T and SO 2 mages determned usng method as desrbed n the text assumpton of 30% and 60% bulk water and lpd ontent. The x and y axes of the mages are poston n unts of mm. f. and h. are horzontal transets through the enter of mages e. and g x

14 Lst of Tables Table.: Results for average hemoglobn onentraton of the bakground and lesons for two women maged usng the expermental data aquston set-up..... Table 5.: Repe for resn phantom mxng proedure developed by Elzabeth Whte Table 5.2: Repe for slone soft phantom Shudong Jang mxng proedure... Table 5.3: Repe for gelatn phantom Dun L/Todd Kerner/Elzabeth Whte proedure Table 6.: Comparson of molar extnton oeffent for oxygenated hemoglobn measured by Wray et al. wth results from use of homogeneous fttng algorthm Method B. based on data from phantoms nreasng hemoglobn onentraton Fgure 6.7.d Table 8.: The normalzed standard devaton dvded by the mean of the spatal propertes of the mages n Fgure 0.4 are tabulated. These values are ompared wth the reonstruted ontrast of the embedded objet for dfferent levels of added heterogenety. The normalzed standard devaton s the same untless sale as the reonstruted ontrast, thus, for a devaton of 0.20, an objet wth.2 or 0.8 ontrast would be at the level of plus or mnus one standard devaton Table 8.2: Values from homogeneous ft ompared wth reovered entral values of embedded pork. Also, the normalzed standard devaton desrbed n Table 8. of the entre mage s reported Table 9.: Comparson of the expermental determnaton of the molar absorpton oeffent slope of a lnear regresson to data wth the Wray et al. and Hale and Querry values: ahb-r and bhb-o Table 9.2: Results of least squares fts to alulate Hb-O 2 and Hb-R ontent of known 0 M hemoglobn onentraton, 0.5% Intralpd and water homogeneous phantom Table 9.3: Numeral results of least squares fts to determne hemoglobn onentraton and hemoglobn oxygen saturaton level for a 33 year old woman, and b 62 year old woman. Water and lpd onentratons were onstraned to the approxmate values dsplayed Table 9.4: Lnear regresson results from data plotted n Fgure 9. A slope of ndates a : orrespondene between the absorpton oeffent values from the enter of the nluson n the mages n Fgure 9.0 and the absorpton oeffent results alulated from expeted values for hemoglobn and water Table 0.: Results for average hemoglobn onentraton of the bakground and peak onentraton for patents 5 and Table 0.2: Values for SO 2 and Hb-T for dfferent methods of ompensatng for water and lpd ontent. Method, the assumpton of a fxed bulk water and lpd ontent, orresponds to Fgure 0.8. Method 2 Fgure 0.9 nvolves a leastsquares ft to all four hromophores. Method 3 Fgure 0.0 uses the satterng power mage to mage water and lpds. Method 4 assumes no lpd and water ontent xv

15 Chapter : Overvew.A. Introduton Ths thess desrbes the development and mprovement of both the data aquston system and mage reonstruton algorthm for near-nfrared NIR tomograph magng for breast aner dagnoss. Spefally, the data aquston system was mproved n both speed and auray through the mplementaton of parallel aquston, and several avenues were explored for mprovng reonstruton n the areas of magng tssue hromophores and separaton of absorpton and satterng heterogenety. The mproved system and reonstruton methods were tested extensvely n omputer smulatons and tssuesmulatng 'phantoms', as well as healthy volunteers and some breast aner patents. The thess s organzed nto hapters: Overvew 2 Reonstruton algorthm: The dervaton and formulaton of the model and reonstruton program are presented. 3 Computer smulatons: The methods and tools used for omputer smulaton of NIR tomograph magng are summarzed. 4 Imagng system: The entre magng system nludng data aquston system, fber-opt nterfae, laser soures, and omputer ontrols s presented. The desgn, onstruton, and testng of a sxteen hannel parallel deteton system s detaled. Some hstoral data are provded on past data aquston systems. 5 Phantom studes: The materals and methods for onstrutng and testng wth tssue-smulatng phantoms are presented. 6 Calbraton and homogeneous fttng algorthm: The albraton of the DAQ system s desrbed. Of partular mportane to albraton, the homogeneous fttng algorthm s detaled.

16 7 Separaton of satterng and absorpton heterogenety: Methods and results for mprovng separaton of absorbng and satterng heterogenety are presented and dsussed. 8 Heterogeneous Phantoms and Contnually-varyng objets: Typal phantom and smulaton studes are performed wth step objets n a homogeneous bakground. Both normal and anerous breast tssue s heterogeneous. Smulaton and phantom studes are presented whh nvolve heterogeneous bakground and objets wthout step hanges n optal propertes. 9 Imagng of tssue hromophores: Usng omputer smulatons and NIR measurement of phantoms, least squares fttng tehnques and the use of multple optal wavelengths are explored as a means to extrat spatal maps of oxygenated Hb-O 2 and de-oxygenated hemoglobn Hb-R as well as water and lpds. 0 Patent Imagng: Data has been aqured from both healthy human volunteers and patents wth known breast malgnanes usng the parallel data aquston system. These data are reonstruted n attempt to better separate and understand the role of satterng, absorpton, and tssue hromophore heterogenety wthn the healthy human breast and breast aner tumors. Conlusons/ Future Dretons The work presented here bulds on mportant researh n NIR magng and photon mgraton at other nsttutons and prevously at Dartmouth College. The followng seton attempts to provde the hstory of researh n the feld and provde the reader wth a better dea of the orgn of the researh desrbed heren..b. Bakground and Sgnfane.B.. Bakground of Optal Imagng 2

17 As early as 929, Cutler et al. reported utlzng a lght for magng through the breast. Ths orgnal optal projeton magng, or transllumnaton, was arred out n a dark room by vsually lookng for shadows ast by large breast tumors. Improvements n transllumnaton followed, nludng the use of two wavelength regons as well as olor flm and vdeo ameras for deteton. For ths ontnuous-wave projeton magng, senstvty has been found to be smlar to x-ray mammography for large tumors, but senstvty for small tumors under m 2 and spefty for all tumor szes s substantally lower 3. Several developments have led to renewed nterest n optal magng of the breast, spefally, n vvo NIR spetrosopy, photon mgraton theory, mprovements n lght generaton and deteton, and vnumeral modelng tehnques oupled wth the avalablty of nreasng omputng power. These spef areas are dsussed below for ther relevane to ths thess. The understandng that hemoglobn onentraton and oxygen saturaton an be reovered from non-nvasve NIR spetrosop measurements through several entmeters of tssue arose over the past entury. As early as the turn of the entury, measurements of hemoglobn dervatves at two wavelengths were dsussed as a method for assessng oxygenaton, 4,5 however, lnal and ommeral oxmeters were not developed untl the 930s 6,7 and 970s 8 respetvely. A study by Jobss 9 reported n 977 usng NIR wavelengths to determne onentratons of oxygenated and de-oxygenated hemoglobn s onsdered a pvotal demonstraton of the potental of NIR spetrosop measurements for tssue volumes 5. Hemoglobn ontrast n the breast between anerous and normal tssue was estmated to be 4: by Profo et al. 0 usng exsed tssue and performng vessel ounts. Further haraterzaton of ontrast n the NIR was shown by Peters et al. and Troy et al. 2 usng optal measurements of exsed tssue. In the late 990's, ths hemoglobn ontrast 3

18 has been onfrmed from n vvo NIR measurements 3-5 and estmated to be wthn the range of 2: to 3:. The understandng of lght propagaton n tssue, spefally the development of photon mgraton theory and the dffuson approxmaton to lght travel n a hghly satterng medum has generated an entrely new feld of study. The applaton of the dffuson approxmaton appled to laser pulses n hghly satterng meda s assoated wth researh by Ishmaru n Whle dffuson theory s useful for modelng CW lght propagaton, the use of tme-resolved measurements provdes nformaton on the nreased pathlength of lght n tssue due to multple satterng events, thus mprovng the ablty to separately reover absorpton and satterng propertes. The use of tme-doman measurements -- reordng the pont spread of a poseond pulse of lght after passng through a tssue volume -- was ntated n several groups nludng measurements by Chane et al. 7,8 Applaton of analyt solutons from dffuson theory were frst presented by Patterson et al. 9 allowng quanttatve reovery of optal propertes from tme-resolved measurements. Frequeny-doman measurements, where the phase shft of a snusodal wave passng through a tssue volume s reorded, provde a more nexpensve and perhaps stable manner of aqurng tme-based nformaton. Fshkn et al. 20 and Patterson et al. 2 developed smlar analyt solutons n the frequeny-doman and performed some of the frst frequenydoman measurements to non-nvasvely reover optal propertes. The development of fber opts, lasers, and photomultpler tube PMT detetors has been essental n the ablty to buld nexpensve buld NIR data aquston systems. Clad fber opts were developed n the 950s, wth the frst low-loss fbers 7 db/km reported by Cornng n Commeral use of fber opts has taken off only durng the past 20 years n onert wth the wdespread avalablty of semondutor lasers. Sne the development of the frst laser n 960 by Theodore Maman, the feld of lasers n 4

19 medne has taken off rapdly. Wth the avalablty of nexpensve and stable semondutor lasers at many wavelengths throughout the NIR, CW and frequeny-doman setups an be run off smple wall outlets for power. Tme-doman systems requre modeloked lasers whh surfaed n the 970s and tend to be more expensve and senstve to moton. 23,24 PMTs were developed n the late 930s and have sne been the standard for applatons requrng both senstvty and speed of response. 25 Whle sold-state detetors, suh as harged-oupled deves CCD and photododes PD, were developed later and tend to be more stable for CW and low frequeny applatons, nether has yet to rval the PMT n senstvty at hgh frequeny. v Exponental nreases n omputatonal power have led to an exploson of the applaton of numeral methods to nverse problems. Fnte element FEM based algorthms appled to optal magng whh would have been unsolvable only a few deades ago due to memory and speed onstrants, an urrently be solved n two-dmensons n a matter of mnutes. Even wth the hgh power omputng avalable at the turn of the 2st entury, however, full 3-dmesonal solutons stll an requre many hours. Many of the ntal applatons of the dffuson approxmaton to lght travel n tssue were based on analyt solutons usng smplfyng assumptons, suh as sem-nfnte or perturbaton theores, 9-2 to better estmate absorpton and satterng propertes from pont measurements. For more general magng, numeral methods whh an aurately model the lght propagaton for arbtrary geometres and property dstrbutons have been appled. Snger et al. 26 desrbed model-based mage reonstruton methods as appled to objets that "dffuse radaton" n 990. Arrdge et al. 27,28 appled fnte element FEM modelng to lght propagaton n tssue based on the tme-resolved dffuson approxmaton. Inverse solutons whh mnmze the dfferene between alulated and measured data suh as Newton mnmzaton or onjugate gradent methods have been appled n both tme-doman 29 and 5

20 frequeny-doman 30,3 to reover mages of absorpton and satterng based on smulated measurements at the perphery of a hghly satterng objet. The ombnaton of all of these developments has led to the urrent potental of NIR spetrosop magng for quanttatvely reoverng spatally-resolved maps of funtonal parameters suh as hemoglobn. Dffuse optal magng s beng examned for applatons suh as breast magng, 4,32-36 neo-natal bran montorng, 37 and mappng bran funton. 38 Ths thess onentrates on breast magng applatons, but many of the developments desrbed apply n general to the feld of dffuse optal magng..b.2. Health-related sgnfane Quanttatve measurements of hemoglobn related parameters n human tssue have been demonstrated wth non-nvasve tehnques usng near nfrared lght. 3,4,38-42 Wth the use of model-based omputatonal methods near nfrared dffuse optal tomography an generate spatally-resolved absolute mages of hemoglobn onentraton and oxygen saturaton. 5,35 These quanttatve mages are obtaned non-nvasvely and at low ost. These hemoglobn based mages may be useful for both breast aner dagnoss and deteton. Loalzed nreases n blood vessel growth angogeness and therefore blood volume are observed at the loaton of anerous tumors; ths nrease has been estmated to orrespond to a two to four fold nrease n hemoglobn onentraton wthn breast aner tumors relatve to healthy tssue. 0,42,43 Also, t has been reported that a loalzed.4 to 4.4 derease n oxygen partal pressure s present wthn breast aners. 44,45 Ths dereased oxygen pressure may orrespond to a measurable derease n hemoglobn oxygen saturaton. These two physologal fators suggest that there s onsderable potental for quanttatve hemoglobn magng as a method of haraterzng breast tumors non-nvasvely. 6

21 The urrent method of breast sreenng, x-ray mammography, s wdely aepted and prated. X-ray mammography s hgh resoluton and very good at detetng abnormaltes n older women. In fat, t s estmated that 85%-90% of breast aner tumors are deteted n ths populaton. 46 However, x-ray mammography has a low postve predtve value -- about 60% to 85% of bopses are performed on bengn tumors. 47 X-ray methods have lower senstvty for dense breast tssue whle also havng rsk n ndung aners and there usage for sreenng for women under 50 years of age wthout a hstory of breast aner has been a subjet of ontroversy. 48 Ultrasound magng s urrently a useful adjunt to dstngush ysts from other masses, however, there s no non-nvasve magng modalty for relably dstngushng bengn and malgnant tumors. 49 Near nfrared magng has the potental to derease the number of unneessary bopses, by dstngushng tumors based on hemoglobn related parameters, as well as to mprove early deteton and dagnoss of breast dsease n younger women. Further, there may be a potental nhe n followng up women's breast aners to trak the response to treatment, or n stagng the tumor development n order to hoose the optmal treatment. Ths exploratory study s desgned to buld and refne a system whh an be used to address some of these potental lnal applatons..b.3. Quanttatve Hemoglobn Imagng De-oxygenated and oxygenated blood spefally hemoglobn, water, and lpds have dfferent absorpton spetra n the vsble and near-nfrared, allowng separaton of these omponents by measurements at multple wavelengths Tssue s hghly absorbng at vsble wavelengths, however, a low absorpton wndow n the near-nfrared, spefally nm, allows for measurements through many entmeters of tssue. Imagng breast tumors wth lght has been performed as far bak as 929. The dffulty, however, s that tssue s hghly satterng at vsble and near-nfrared wavelengths. Therefore, an mage 7

22 based on unproessed data s hghly blurred and the effets of satterng and absorpton an not be dstngushed. Reent developments n the measurement of photon mgraton and omputatonal methods have allowed for the realzaton of a system at Dartmouth College whh s apable of moderate resoluton 5-0 mm quanttatve magng of hemoglobn related parameters. Important to the onept of quanttatve near-nfrared magng n breast tssue, pont measurements of hemoglobn related parameters have been demonstrated by several groups. 3,39,40 Tromberg et al. 3,42 have reported pont measurements of hemoglobn onentraton and oxygen saturaton n vvo for normal and anerous breast tssue. In order to redue the blurred nature of mages obtaned by near-nfrared lght, several groups have exploted tmeresolved measurements and approxmatons to lght propagaton n a hghly satterng medum to generate mproved qualtatve n vvo mages of breast tssue. 38,53 In the ommeral settng, the Phllps magng deve uses lnear perturbaton theory for mage reonstruton 32,54 whh has been shown to be unable to quanttatvely reonstrut the optal propertes requred for hemoglobn magng. 55 Smlarly, the Carl Zess magng system uses only parallel projeton data whh also lmts the quanttatve nformaton ontaned n the resultng mages. Several groups have shown mproved qualtatve mages havng an nreased absorpton at the loaton of known breast aners, but as of yet have not demonstrated spatally-resolved quanttatve mages. In ths ven, however, Fantn et al. 4 were able to haraterze the hemoglobn onentraton and oxygen saturaton of the tumor usng the assumpton of a known spheral shape and sze of the mass. Arrdge and Shweger 29 have theorzed that sne the lght travels n a hghly satterng medum, quanttatvely aurate spatally-resolved near-nfrared magng requres a method whh utlzes and preserves the non-lnear relatonshp between tssue optal propertes and the measured optal data at the tssue surfae. Usng omputer smulatons and smple phantom 8

23 experments, t has been shown that model-based omputatonal methods whh enfore ths non-lnear relatonshp an be used to quanttatvely mage absorpton and satterng propertes n a hghly satterng medum. 56 Jang et al obtaned quanttatve spatally-resolved mages of nlusons wth equal elevated ontrast n absorpton and satterng based on smulatons and tssue-lke phantoms through a fnte element based reonstruton algorthm whh utlzes the frequeny doman dffuson equaton. Through modfaton of ths algorthm, Pogue et al. 59 were able to quanttatvely reover mages of absorpton-only objets. Further modfaton of the reonstruton algorthm has allowed for quanttatve separaton of objets wth heterogenety n both absorpton and satterng. Usng ths algorthm and an automated magng system, the group at Dartmouth College demonstrated near-nfrared tomograph spatally-resolved quanttatve mages of hemoglobn onentraton and oxygen saturaton derved from expermental data. MBrde et al. 5 reported these quanttatve mages of hemoglobn onentraton and oxygen saturaton n tssue-lke phantoms ontanng oxygenated and de-oxygenated blood n a hghly satterng medum. Studes wth volunteers have shown ths ablty n vvo for two patents wth known breast pathologes. These quanttatve mages have been obtaned from multple-wavelength frequeny-doman measurements wth a rularly symmetr magng geometry where model-based omputatonal mage reonstruton has been used..c. NIR Tomograph Imagng at Dartmouth.C.. Imagng System at Dartmouth The expermental setup onstruted at Dartmouth an be summarzed by lookng at three dfferent portons of the magng proess: Data aquston, 2 Image reonstruton, and 3 Funtonal mage formaton. The overall proedure s summarzed n Fgure. wth 9

24 more detal provded n the followng subsetons. For more detaled desrptons, see the referenes provded n eah subseton. Fgure.: Shemat of the funtonal magng proess.c... Data aquston The urrent data aquston system at Dartmouth Fgure.2 s desgned for rosssetonal magng of breast tssue. It onssts of 6 soure and 6 detetor optal fbers postoned n a rular array. 59,60 The optal fbers wthn the array are attahed to a radal postonng system that allows for varable dameter fber movement, whh provdes dretontat ouplng wth the breast. The poston of the rular array an also be vared vertally to allow for seletve or multple ross-setonal sles. a 0

25 b Fgure.2: a Dagram of data aquston system, b photograph of fber-opt nterfae A seres of ampltude-modulated 00 MHz laser dodes are used as lght soures. Deteton s aheved by eletral heterodynng the output of sxteen photomultpler tubes PMT wth a referene sgnal at MHz. The sgnal ampltude and phase shft of the 500 Hz beat sgnal are reorded wth a omputer. Both ths data aquston system and a prevous sngle detetor verson are desrbed n Chapter 3. The measured data s nput nto a FEM program for reonstruton nto mages of absorpton and satterng..c..2. Image reonstruton Currently, a 2-d FEM reonstruton program s used. The 256 data ponts aqured for a sngle wavelength are reonstruted Fgure.3 nto an mage of tssue optal propertes absorpton and redued satterng oeffents usng a fnte element based alulaton of the dffuson equaton. 3,56-58,6 The soluton s obtaned through a least squares mnmzaton of the dfferene between the measured lght flux ampltude and phase shft at eah detetor and the alulated fluene rate ampltude and phase shft determned from an estmated set of tssue optal propertes. Newton's method s employed to teratvely solve the non-lnear mnmzaton problem whh results from the fnte element soluton of the dffuson equaton.

26 Fgure.3: Flow hart of fnte element based mage reonstruton algorthm for a sngle wavelength. equaton, Spefally, the fnte element soluton s based on the frequeny doman dffuson ω D r Φ r, ω a + Φ r, ω = S r, ω. where Φ s the optal lght fluene rate [W/mm 2 ] at loaton r for modulaton frequeny ω. The optal propertes of the tssue are n terms of absorpton oeffent a [mm - ] and transport satterng oeffent s / [mm - ], whh s related to the sotrop dffuson 2

27 oeffent D by the equaton D = [3 / s + a ] -. The lght soure n ths ase s onsdered a pont soure S = s 0 d r-r 0 [W/mm 3 ] d s the dra delta funton at pont r 0 of strength s 0. Gven a dstrbuton of optal propertes,, a dstrbuton of the optal fluene rate, F, s readly determned through a fnte element based forward soluton. The true optal property soluton s obtaned teratvely through a Newton's method least squares mnmzaton mnmzaton of χ 2 n equaton.2 of the dfferene between the Φ and Φ o summed over the total number M of observatons. 2 χ = M o o Φ Φ Φ Φ =.2 where * represents onjugaton of the omplex-valued fluene rate. The mnmzaton results n a Levenberg-Marquardt type soluton to the nverse problem, = T T J J + ρi J Φ Φ o.3 where Φ J = s the Jaoban matrx and = - 0 s the update vetor defnng the dfferene between the true and estmated optal propertes. The soluton s onsdered llposed and the J T J matrx s generally ll-ondtoned 62 and therefore the ommon treatment s regularzaton 3,6 -- typally done by addng some fator,?, to the dagonal usng the dentty matrx, I. The reonstruton algorthm s desrbed n Chapter 2..C..3. Homogeneous Fttng Algorthm In dervng the Levenberg-Marquardt nverse soluton, 63,64 hgher order dervatve terms are dsarded usng the assumpton that ther ontrbuton s small. Ths assumpton breaks down for ntal estmates whh are not suffently lose to the true dstrbuton. For 3

28 data aqured from a real system, the ntal optal property estmate s determned based on a homogeneous fttng algorthm appled to the measurement data, 65 assurng onvergene wthout the need for a pror knowledge of the tssue optal propertes. Ths homogeneous fttng algorthm, desrbed n detal n Chapter 6, s essental to fndng an aurate ntal estmate and s used n system albraton. The algorthm uses the same FEM forward solver, but the mnmzaton s based on measured and alulated data averaged over all soures and ft to a lne based on dstane..c..4. Funtonal Image Formaton For a sngle set of data measured at one wavelength, a quanttatve mage of absorpton and satterng oeffent are reonstruted. The satterng oeffent mages generated are not used n the alulaton of hemoglobn onentraton or hemoglobn oxygen saturaton level. Hemoglobn onentraton an be approxmately mapped solely based on the absorpton oeffent of tssue alulated at one wavelength, 800 nm, and an assumed level of water wth other absorbers. These latter onentraton assumptons are based upon pror physolog data and ther valdty wll be dsussed later. Hemoglobn oxygen saturaton mappng requres the alulaton of the absorpton oeffent at a mnmum of two wavelengths. Generally, the Dartmouth experments nvolve the reonstruton of quanttatve absorpton mages at two to sx wavelengths followed by a least squares regresson to derve the hemoglobn onentraton and oxygen saturaton mages usng an assumed level of water and lpds. The use of addtonal wavelengths tends to mnmze the effet of nose and has also been analyzed for magng of water and lpds. For breast tssue, the alulated absorpton oeffent an be assumed to be a ombnaton of absorpton due to water, oxygenated hemoglobn Hb-O 2, de-oxygenated hemoglobn Hb-R, and lpds. 66 For theoretal absorpton oeffents measured values 4

29 from Wray et al. 52 for Hb-O 2 and Hb-R, from Hale and Querry 50 for water, and from Quaresma et al. 5 for lpds an be used. The plots of absorpton oeffent for water, lpds, Hb-O 2, and Hb-R taken from the data n these papers are shown n Fgure.4 a. The onverson from absorpton mages to hemoglobn-based mages s depted n Fgure.4 b. Lpd and water onentraton mages n addton to the hemoglobn mages ould n theory be alulated n the same manner, but would requre absorpton mages at addtonal optal wavelengths. a 5

30 b Fgure.4: a Plot of NIR absorpton spetra for water, lpds, Hb-O 2 and Hb-R Values for absorpton oeffent are dsplayed for anatomally relevant onentratons for breast tssue. b Mathematal dagram of onverson of absorpton mages to funtonal mages of breast tssue hromophores..c.2. Expermental studes.c.2.. Computer smulaton The frst step n testng any mage reonstruton algorthm s omputer smulaton. "Measured" data s generated from solvng the forward FEM problem for a known smulated dstrbuton of optal propertes. Nose an be added to ether the smulated measured data or optal property dstrbuton. The reonstruton program s then appled n the usual fashon to attempt to reover the ntal mages. The optal magng algorthm s ll-posed, suh that smulaton s used to test both the feasblty of the nverse soluton and to test methods to mprove the results of the algorthm. The effet of regularzaton s omplex and an be appled n a large number of manners. Computer smulaton allows the optmzaton of the regularzaton tehnque and mage reonstruton algorthm. 6

31 Relevant studes that have been tested n smulaton, nlude the magng of multple nlusons, nlusons of dfferng sze and ontrast, ablty to separate and quanttatvely mage absorpton and satterng nlusons, reover funtonal nformaton from absorpton mages at multple wavelengths, effet of heterogenety on mage reonstruton, effet of geometry and number of soures and detetors, and possble mprovements from addtonal modulaton frequenes. Chapter 3 ntrodues the relevant programs used for smulaton and dsusses the methods used for results presented n later hapters. In addton, studes not presented n ths manusrpt are referened. In general, one an expet to do no better expermentally than n a nose-free smulaton. For the urrent setup and reonstruton program, resoluton and mage qualty does not seem to be lmted by nstrumentaton but n the reonstruton proess. Fgure.5. Shemat for mage reonstruton showng requrements left and steps for testng rght mage reonstruton methods..c.2.2. Phantom Studes Followng omputer smulaton, phantom expermentaton s the seond step n testng mage reonstruton, as shown ptorally n Fgure.5. Objets whh mm the satterng and 7

32 absorbng propertes of the breast have been onstruted n lquds, rgd plasts, and plable slone and gelatns. Satterng ontrast an be added usng varyng onentratons of lpd emulsons, suh as Intralpd, n lqud phantoms or ttanum doxde powder to other mxtures. Absorpton ontrast s most often aheved by Inda nk or through the use of whole blood. Lqud phantoms are easy, fast to make and apable of testng wth lve blood, but requre an external ontaner whh an effet the measurements n unknown ways. Sold phantoms are more permanent and extremely useful for repeat measurements. Holes an be drlled for addton of lqud nlusons, or nlusons an be embedded permanently durng fabraton. Whle there s no needed ontaner, msmath n refratve ndex when usng lqud nlusons an lead to unertantes n nterpretaton. These phantoms have been used extensvely n haraterzaton of the data aquston system and n assessng the valdty of the FEM reonstruton program. Smlar to smulaton, the phantom studes have been used to study the magng of multple nlusons, nlusons of dfferng sze and ontrast, ablty to separate and quanttatvely mage absorpton and satterng nlusons, reover hemoglobn mages from absorpton mages at multple wavelengths, as well as the effet of bakground heterogenety. Followng proper albraton, t appears that the expermental reovery of absorpton and satterng mages mathes qute well wth the expeted results from omputer smulatons. The materals and methods for these phantom studes s overed n Chapter 5..C.2.3. Separaton of absorbng and satterng heterogenety Separaton of absorpton and satterng heterogenety s requred for quanttatve magng of absorbng onsttuents suh as hemoglobn, lpds, and water n the breast. The ablty to fully separate absorpton and satterng heterogenety n tssue provdes not only the purest mage of the absorpton oeffent, but also a means of magng satterng heterogenety 8

33 whh ould ontan nformaton relevant to tssue struture. Usng both omputer smulatons and phantom studes, a method to better mage absorpton and satterng nlusons ndependently was mplemented. The mproved algorthm nvolved three steps: frst the adopton of log ampltude and phase data versus the orgnal use of real and magnary data. Seond, the matrx dagonal was normalzed to one usng a standard Marquardt sheme. In addton, further weghtng of phase wth respet to log ampltude based on modulaton frequeny has been found to sgnfantly mprove separaton of absorpton and satterng. A omputer smulaton showng good separaton of absorpton and satterng heterogenety s shown n Fgure.6. The mplementaton of ths method and the results of omputer smulaton and phantom magng s presented n Chapter 7. a Smulated mage b Reonstruted Reonstruted Absorpton Image Satterng Image Fgure.6. Smulatons showng mproved reonstruton of satterng and absorbng nlusons for nose-free data. a Orgnal smulated mage wth three embedded objets. Fgure b shows the reonstruted absorpton oeffent mage and the reonstruted satterng oeffent mage..c.2.4. Heterogeneous and ontnually varyng objets Phantom studes are generally tested usng one to three nlusons wthn a homogeneous bakground. In vvo magng of abnormaltes n the breast does not math ths model as both normal and dseased breast tssue s generally heterogeneous. The onstruton of heterogeneous phantom materals s dffult and the knowledge of atual optal propertes 9

34 a, s ' of the breast an be hallengng. One method of embeddng objets wthn a heterogeneous bakground s to use exsed tssue. A study was done 67 where a seres of exsed breast tssue samples were measured for average optal propertes and pork musle tssue was aqured and embedded n the breast tssue as a moderate ontrast objet smlar to that of tumors n the breast. Pror to these phantom studes, omputer smulatons of embedded objets n heterogeneous meda were performed as shown n Fgure.7. As well, dffuson tomography s generally tested n numeral smulatons usng a step hange between bakground and embedded objets. Ths abrupt hange may not realstally smulate breast tssue optal property hanges. Smulatons were also performed on several dfferent ontnuously varyng optal property dstrbutons and ompared wth those obtaned from dsrete step hange objets. 68 Spefally, a Gaussan profle, an rregularly shaped objet, a rng objet, and a rular step hange objet were used n the numeral smulatons. The methods and results for these studes are presented n Chapter 8. 20

35 Fgure.7. Smulatons of heterogeneous objet wth heterogeneous nluson wth an average 2: ontrast n absorpton and :2 absorpton n satterng. The frst two olumns are the orgnal absorpton and satterng dstrbutons pror to smulaton. The seond two olumns are the reonstruted absorpton and satterng mages. Eah suessve row represents an nreasng level of added heterogenety to the orgnal dstrbuton n the frst row. All absorpton and satterng mages are dsplayed on the dental sale..c.2.5. Imagng of tssue hromophores The ablty to reover funtonal mages from absorpton mages at multple wavelengths as summarzed n C.2.2. has been studed n omputer smulaton, phantom studes, and n patent magng. In omputer smulaton, studes ndated that an nreased number of optal wavelengths ould mprove reovered mages of oxygen saturaton n the presene of 2

36 nose as summarzed n Fgure In phantom studes usng human blood mxed wth Intralpd, t was shown that mages of hemoglobn onentraton and oxygen saturaton an be reovered quanttatvely usng these methods. 5 The results of one suh phantom study are presented n Fgure.9. Furthermore, n patent magng, the nfluene of lpds and water has been explored. 69 The methods and results of these funtonal magng studes are presented n Chapter 9. a smulated mage b 2 wavelengths 4 wavelengths Fgure.8: Smulatons showng mprovement of oxygen saturaton mages wth nreasng number of wavelengths n the presene of sgnfant nose. a Orgnal smulated oxygen saturaton mage wth embedded objet wth 20% derease n oxygen saturaton, whh was used to generate smulated data wth 0% added nose. Fgure b shows the reonstruted oxygen saturaton mage usng only 2 wavelengths and the reonstruted oxygen saturaton mage usng 4 wavelengths

37 a b Hb-onentraton mage O 2 saturaton mage d Hb-onentraton profle e O 2 saturaton profle Fgure.9: Hemoglobn onentraton and oxygen saturaton mages of a phantom ontanng two targets -- one wth a 4: hemoglobn onentraton ontrast no oxygen saturaton ontrast ompared wth the bakground and the other had a 00% derease n oxygen saturaton ontrast no hemoglobn onentraton ontrast ompared to the bakground. The fgure a shows a shemat of the phantom, b reonstruted hemoglobn Hb onentraton mage, oxygen saturaton mage. d and e are onedmensonal profle plots horzontal through the enter of b and respetvely. Ideal profles are plotted for omparson. 5.C.2.6. Patent Imagng Followng an ntal set of suessful phantom studes, a seres of female volunteers have been maged. The magng of volunteers at the date of ths thess an be dvded nto two tme perods based on the nstrumentaton. The frst set of volunteers approxmately 8 women numbered patents 3 through 2 were maged wth a sngle detetor setup usng a Ttanum Sapphre TS wavelength-tunable laser pumped by an Argon Ion laser. Of partular nterest from ths group are two volunteers wth onfrmed breast pathologes. Both volunteers have sne had surgery and the tumor was lassfed by hstology. Patent 5 had an approxmately three entmeter bengn fbroadenoma; the estmated sze and loaton as 23

38 drawn by the radologst s shown n Fgure.0b. Near-nfrared magng of ths patent through the plane of the tumor showed a approxmately 2.0 tmes ontrast n hemoglobn onentraton at the ste of the tumor Table. and Fgure.0. Patent 6 had an approxmately eght mllmeter malgnant nvasve dutal arnoma. An approxmately 3.5 tmes ontrast n hemoglobn onentraton was observed at the ste of the tumor Table 0. and Fgure.. Whle the system was undergong hanges wthn ths ntal study perod and not all reonstruted mages seem relable, the average hemoglobn onentraton reovered s assumed to be approxmately aurate. Fgure.2 shows the average hemoglobn onentraton for the frst ffteen volunteers maged, as well as the measured hemoglobn onentraton of the abnormaltes of nterest from two patents wth known pathology. The mages for ths ntal group of volunteers were obtaned from measurements at two wavelengths 750 and 800 nm n most ases. ax-ray mammograph b sketh of geometry Hb onentraton mage Fgure.0: Images of patent wth bengn fbroadenoma. Shown n the fgure are the a x-ray mammograph top ranoaudal vew, b representaton of loaton of tumor taken from a sketh by radologst based on x-ray mammography mages and palpaton, hemoglobn onentraton mage reonstruted from near nfrared absorpton mages at 750 and 800 nm. 24

39 Patent 5 Patent 6 Bakground Hb Conentraton M Tumor Hb Conentraton M Approxmate Tumor Sze m Table.: Results for average hemoglobn onentraton of the bakground and lesons for two women maged usng the expermental data aquston set-up. ax-ray mammograph b sketh of geometry Hb onentraton mage Fgure.: Images of patent wth malgnant nvasve dutal arnoma. Fgure dsplays a x-ray mammograph.5x photograph zoom of oblque medolateral vew, b representaton of loaton of tumor taken from a sketh by radologst based on x-ray mammography mages and palpaton, and hemoglobn onentraton mage reonstruted from near nfrared absorpton mages at 750 and 800 nm. Fgure.2: Plot of average hemoglobn onentraton from near-nfrared mages of volunteers. Also plotted are two loalzed values for hemoglobn onentraton for a malgnant tumor and a bengn tumor. The error bars represent the standard devaton between multple measurements, suh as left and rght breast. The results wth no error bar orrespond to a patent where only one measurement was made. 25

40 Followng ths ntal set of volunteers, the sxteen detetor data aquston system was onstruted. Ths system s desgned for sx dode lasers wth wavelengths rangng from 660 to 850 nm. At present approxmately 23 addtonal volunteers numbered patents have been maged wth ths new deteton setup. The data for average hemoglobn onentraton s presented n Fgure.3 for a group of these women. Further detals and results are nluded n Chapter 0. Fgure.3: Plot of average hemoglobn onentraton from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms. The error bars represent the standard devaton between multple measurements, suh as left and rght breast or multple planes wthn a sngle breast..d. Future dretons Ths thess attempts to summarze many of the prevous studes n addton to the past four years of researh desrbed n detal heren. Several extng results have ourred durng these past four years nludng the frst n vvo spatally-resolved magng of 26

41 hemoglobn onentraton 35 and demonstraton of n vvo satterng mages. 67 These results just touh at the surfae of an extng and stll growng feld of dffuse optal tomography. The fnal hapter, n addton to onludng remarks, dsusses some of the future dretons and nomplete studes partularly relevant to dffuse optal tomography and the program at Dartmouth. 27

42 Chapter 2: FEM reonstruton algorthm 2.A. Introduton Ths hapter revews the development and formulaton of the fnte element method FEM reonstruton algorthm. Spefally, the dervaton of the dffuson approxmaton to lght propagaton n tssue s presented as well as the FEM formulaton. The nverse soluton s derved and the detals of the reonstruton program are desrbed. Other features of the reonstruton algorthm spef to the urrent program, suh as normalzaton and weghtngs shemes, are ntrodued at the end of ths hapter. The foundaton for these weghtngs s dsussed n later hapters. 2.B. Dffuson Approxmaton Lght transport n hghly satterng meda suh as breast tssue s well modeled by the radatve transport equaton, usng the assumptons that satterng s elast no hange n energy suh as fluoresene and that polarzaton and oherene are not sgnfant. As well, nterferene effets are assumed to average out. The transport of photons for a gven tssue s desrbed by three oeffents -- the absorpton a and satterng s oeffents unts of [/mm] desrbng the lkelhood of a photon beng absorbed or sattered over a gven dstane, and the phase funton? whh defnes the probablty of angular dstrbuton of probabltes for a satterng event. The Boltzmann transport equaton, L r, sˆ, t + t L r, sˆ, tˆ s + + L r, sˆ, t = L r, sˆ', t ψˆ, s sˆ' dω+ ' S r, sˆ, t 2., a s s 4π desrbes the radane L, as a funton of poston r, dreton ŝ, and tme t, for a gven soure S, speed of lght n the medum, and set of oeffents a, s,?. The radane s n unts of [Watts/m 2 srad] where ŝ s the unt vetor n the dreton of nterest and O s sold angle. 28

43 The transport proess an be approxmated by a Monte Carlo smulaton of photon propagaton, where eah photon s treated probablstally and the sum of the effets of a large number of smulated photon hstores s an aurate representaton of the radane n the medum. These smulatons are aurate, but extremely tme-onsumng and less desrable for nverse solutons beause of the need to serally smulate eah photon. FEM mplementatons of the radaton transport equaton are omplex due to angular terms and an also be omputatonally exhaustng. Analyt solutons to the transport equaton are avalable for only a selet few smplfed ases. Thus, smplfyng assumptons are sought, suh as the dffuson approxmaton, whh serve to redue or elmnate the angular dependene of ths equaton. The standard method for smplfyng the radatve transport equaton s to expand radane L usng spheral harmons In the P approxmaton, only the frst two terms of the expanson are retaned, resultng n the equaton, 3 L r, sˆ, t = Φ r, t + J r, t sˆ 4π 4π 2.2, where fluene rate and flux are ntegrals of the radane over all sold angles, Φ r, t = L r, sˆ, t dω J r, t = L r, sˆ, t sˆ dω 2.3, 2.4. The fluene rate F s defned as the number of photons passng through the surfae of a unt sphere per unt tme and the flux J as the number of photons passng through a unt area but n a partular dreton ŝ. Ths P approxmaton s only true when the radane s domnated by the sotrop term F mplyng that the satterng s muh greater than absorpton s >> a and no boundares are present. The P expanson of the soure term s 29

44 30 s t S t S t S ˆ, 4 3, 4, 0 + = r r r π π 2.5 where S 0 s an sotrop soure of photons and S s a lnearly ansotrop soure. The substtuton of the P approxmaton for L eq. 2.2 and S eq. 2.5 nto the radatve transfer equaton, 2., s t S t S d s s s t t s t t s s t t s t t t s s a ˆ, 3, ' ˆ' ˆ, ˆ, 3, ˆ, 3, ˆ ˆ, 3, ˆ, 3, Ω+ + Φ = + Φ Φ + + Φ r r r J r r J r r J r r J r π ψ 2.6 results n an equaton n terms F and J. By ntegratng ths equaton over all sold angles, the ontnuty equaton an be derved. Note the dentty that the ntegral over all sold angles for a vetor ŝ dotted wth another arbtrary ndependent vetor A s zero: 0 ˆ 4 = Ω d s π A. 7 Term by term, the ntegraton yelds,,,,, S 0 t t t t t t s s a r r r r J r + Φ = Φ Φ 2.7, whh smplfes to the ontnuty equaton 2.5,,,,, S 0 t t t t t a r r r J r = Φ + + Φ 2.8, where S 0 s an sotrop soure term. By multplyng equaton 2.6 by ŝ and ntegratng over all sold angles, a seond equaton an be obtaned:,,,, 3, S t t g t t t t s s a r r J r J r r J + = + + Φ + 2.9, where g s the average osne of the satterng angle. Ths an be smplfed to,, ', 3, S t t t t t s a r r J r r J = + + Φ + 2.0

45 where s ' = -g s and s termed the redued satterng oeffent. To further smplfy ths equaton, the assumpton s made that the tme dervatve of the flux Jr, t s muh smaller t than the nteraton rate of photons + ' J r, t. In addton, f we assume only sotrop soures, equaton 2.0 an be redued to Fk's law: a s J r, t = Φ r, t 3 + ' a s 2.. The tme-doman dffuson equaton an now be formulated by substtutng Fk's law 2. nto the ontnuty equaton 2.8: Φ r, t t 3 a Φ r, t + + ' s Φ r, t = S 0 r, t a 2.2. By performng the Fourer transform n tme t ω of ths equaton 2.2, the frequeny doman dffuson equaton s obtaned, ω Φ r, t Φ r, t + aφ r, t = S0 r, t 3 + ' a s 2.3 where? s the angular modulaton frequeny n radans. The frequeny doman dffuson equaton s generally wrtten D r, t ω Φ + a Φ r, t = S0 r, t 2.4 where D = 3 + a s ' s the dffuson oeffent n mm. One way of nterpretng ths equaton s to state that the nrease n photons due to spatal flux hanges and soure terms s balaned by the loss of photons due to absorpton and related to ampltude hanges at the modulated frequeny. 3

46 The assumptons that must be made to go from the radatve transport equaton 2. to the dffuson equaton 2.2 are: a << s ' 2 Jr, t << a + s ' J r, t t 3 S r, =0 t 3 4 L r, sˆ, t = Φ r, t + J r, t sˆ. 4π 4π For assumpton, t an be debated whether the a term n D an be negleted suh that D=/3 s '. 76,77 The debate s ongong, however, the urrent reonstruton program makes ths assumpton. In the breast, typal values for a are between and 0.0 mm - and s ' from 0.5 to 2.0 mm -. In general, assumpton s true n most body tssues for musle and bran a s as hgh as 0.04 mm -, but stll muh less than s ' 78, however, t breaks down n several body regons suh as ar pokets and flud-flled areas e.g. erebral spnal flud, water flled ysts. Non-dffusng regons an be ompensated n some ases by hybrd models whh use lght ray propagaton for suh areas and dffuson models elsewhere. 79 Assumpton 2 s generally onsdered vald for modulaton frequenes less than GHz. 80 Assumpton 3, sotrop soure, s learly nvald for ponts near a laser lght soure. The radane from a laser soure s hghly dretonal as t enters a hghly satterng medum, however, outsde of three to fve redued satterng lengths / s ' ~ mm for tssue the soure an generally be modeled as sotrop. For ths reason, measurements <3-5 mm lose to a soure rarely math dffuson theory, however, dffuson theory appears to be vald farther away from the soure. In the method desrbed n ths thess, the soure s taken to be an sotrop pont soure loated several mllmeters nteror to the atual soure poston. 32

47 Assumpton 4 states that the radane s only lnearly ansotrop whh mples that the angular dependene of the radane s small. As long as assumpton s true, ths assumpton also tends to be vald. Smlar to assumpton 3, however, near boundares suh as ar-to-tssue the radane s more hghly dretonal. Dffuson theory has been shown n prate to math well wth Monte Carlo smulatons and has been shown to math measurements from tssue and tssue-smulatng phantoms as long as they are taken a suffent dstane from the soure.e. 3-5 redued satterng lengths. 8 33

48 2.C. Fnte element soluton 2.C.. Forward solver The use of FEM to model the dffuson equaton s attratve due to the flexblty n terms of geometry and the ablty to preserve the non-lnear relatonshp between the measurements and propertes n the partal dfferental equaton 2.4. Whle FEM s not lmted n geometry, for smplfaton a sngle set of 2-d rular meshes s used throughout ths thess. The mesh shown n Fgure 2. dsretzes a 2-d plane of the breast nto a seres of nodes; these nodes are onneted wth lnes to adjaent nodes to form trangular elements. A lnear bass funton relates the value everywhere n eah element based on the values at the three nodes defnng the element. In ths fashon, the soluton s defned everywhere n the regon, unlke a fnte dfferene method where the soluton s not onstraned between grd ponts. Fgure 2.: Fnte element fne mesh 425 nodes, 777 elements used n the forward solver for ths thess. The letters S and D represent soure and detetor loatons respetvely. 34

49 In order to model the lght propagaton wth the dffuson equaton, the soure term S 0, boundary ondtons, and propertes s, a need to be defned. Whle more general soure models an be mplemented n FEM, a pont approxmaton loated slghtly nteror of the boundary s used to defne the soure term.e. S r, t = S δ r, where d s the delta t funton loated at r 0. Patterson et al. 9 and Farrell et al. 8 have shown that loatng r o at / s ' provdes a good approxmaton for the soure term. Type III or mxed boundary ondtons are used at all boundary nodes, where the extng flux J nˆ normal to the boundary s equal to some number a tmes the fluene rate F at the boundary, nˆ = D Φ nˆ = αφ J, 2.5 where nˆs the unt vetor normal to the boundary and a s n theory a real postve number related to the nternal refleton. 8 For our expermental studes, ths a term s a omplex number for aurate mathng to frequeny doman data. The addton of the magnary part of a s emprally requred to aurately math both the phase and ampltude of the measured data. The forward soluton to the frequeny-doman dffuson equaton 2.4 provdes the fluene rate F everywhere based on known values for a and s ' at eah FEM node for a gven set of boundary ondtons and a partular soure. 3,82,83 The frst step n the FEM formulaton s to generate the weak form of the dffuson equaton. Ths s aomplshed by multplyng equaton 2.4 by a weghtng funton f and ntegratng over the entre problem doman. For the 2-dmensonal ase, ths an be wrtten as an ntegral over the problem doman area A, ω D Φϕ da a + Φ da= S da ϕ 0ϕ

50 To smplfy the frst part of ths equaton, we need to defne Green's theorem also termed ntegraton by parts whh states that V u da = V nˆ u ds V u da 2.7 for some arbtrary funtons V and u. s the losed ntegral over the surfae s. Usng ths theorem where V = D Φ and u = f, equaton 2.6 an be rewrtten D n ds D da ω Φ ˆϕ Φ ϕ + Φ da= S da a ϕ 0 ϕ 2.8 Rearrangng terms and usng to represent ntegraton over the problem doman, the weak form an be wrtten n ts more famlar form, ω D Φ ϕ a + Φ = S D n ds ϕ ϕ Φ ˆ 0 ϕ 2.9 For the FEM formulaton, we dsretze the area nto a set of ponts or nodes. Thus, the weghtng funton an be expressed at eah node as a funton f. The nodes are onneted n a mesh nto a set of trangular elements. The relaton between nodes n an element s defned by a bass funton at eah node. For the Galerkn method, the weghtng funton s also used as the bass funton. The fluene rate an then be dsretzed usng ths bass funton f where Φ = N j= Φ j ϕ j 2.20 and N s the total number of nodes. The FEM dsretzaton of the frequeny doman dffuson equaton for a homogeneous medum beomes: N j= Φ j D ϕ j ϕ + a ω ϕ j ϕ = S ϕ 0 M j= D Φ j nˆ ϕ ϕ ds 2.2 j 36

51 37 where we are solvng for F j, the fluene rate at eah node j, - j D Φ =J j eq. 2.5 s the flux at eah boundary node, and M s the number of boundary nodes. represents ntegraton over the problem doman, whh for lnear elements orresponds to ntegraton over all neghborng nodes. s the losed ntegral over all boundary nodes. For a nhomogeneous regon, the absorpton and dffuson oeffent are also dsretzed, suh that j N j aj a ϕ = = 2.22 j N j D j D ϕ = = In ths ase, we assume that a sngle mesh s used and that the same lnear bass funton s used throughout Galerkn method. The FEM dsretzaton then beomes ds n D S D j M j j j N k k ak j N k k k N j j = = = = Φ = + Φ ϕ ϕ ϕ ϕ ϕ ω ϕ ϕ ϕ ϕ 0 ˆ Substtutng n type III boundary ondtons 2.5 for the flux boundary term, the equaton an be rewrtten n terms of only the fluene rate: ds S D j M j j j N k k ak j N k k k N j j = = = = Φ + = + Φ ϕ ϕ α ϕ ϕ ϕ ω ϕ ϕ ϕ ϕ The boundary term ontans the unknown fluene rate and s therefore brought to the left hand sde of the equaton:

52 38 j N k k ak j N k k k N M j j j j N k k ak j N k k k M j j S D ds D ϕ ϕ ϕ ω ϕ ϕ ϕ ϕ ϕ ϕ α ϕ ϕ ω ϕ ϕ ϕ ϕ 0 = + Φ + + Φ = = + = = = = In prate ths beomes a matrx soluton where = Φ Φ I b I b II Ib bi bb S S A A A A 2.27 where the subsrpt b denotes portons of the matrx or vetor assoated wth boundary nodes and subsrpt I denotes nteror nodes. The matrx terms are: I b j N k k ak j N k k k II j Ib j bi j j j N k k ak j N k k k bb j S S S D a a a ds D a ϕ ϕ ϕ ω ϕ ϕ ϕ ϕ ϕ ϕ α ϕ ϕ ω ϕ ϕ ϕ ϕ 0 = = + = = = + = = = = = In prate, the soure term s defned as a pont soure and therefore s only atve on one element or three nodes. Other soure mplementatons an be appled wth ths FEM algorthm suh as the dstrbuted soure desrbed by Paulsen et al. 84 Wth the use of lnear elements, the matrx A s banded sne for eah node only the neghborng nodes are nonzero. For the 420 node mesh used n ths researh, a forward soluton for all soures as desrbed by the equatons above, requres approxmately one seond.

53 2.C.2. Levenberg-Marquardt nverse soluton In magng, the goal s reovery of a and s ' at eah FEM node based on measurements of lght fluene at the tssue surfae. In absene of an analyt nverse soluton, the numeral way of ahevng ths nverse soluton s to mnmze the dfferene between measured observed fluene, Φ, at the tssue surfae and alulated data, Φ, o from the forward solver. In mathematal terms, ths s a mnmzaton of? 2 : χ 2 = NM = Φ Φ o where NM s the number of measurements. One method of dervng the nverse soluton, the so-alled Tkhonov approah, 85 s to set up a mnmzaton of χ n whh a penalzed term s added to the? 2 term, χ = NM = NN o 2 Φ Φ + ρ j= j where? s an arbtrary weghtng fator of the dfferene between the urrent estmate of the optal propertes at eah node j subtrated from the ntal estmate o. Ths term an be thought of as a dampng term whh tends to keep the urrent optal property estmate from strayng too far from the ntal estmate. As the value of? dereases, the effet of ths term s lessened. The? term beomes the regularzaton parameter n the dervaton, so smlar to ts effet n stablzaton of the matrx nverson, as? reahes zero the true mnmzaton of? 2 and the true matrx relaton are reahed. In general, χ wll not equal zero, but nstead we are nterested n fndng the value of for whh χ s lose to zero. Followng the Taylor seres expanson method for dervng Newton's method, we expand χ based on for some nearby pont 0 : 39

54 = χ χ χ d d 2.3 and throw out hgher order terms. We are nterested n the value of a and s ' where equaton 2.30 s a mnmum, suh that 0 = χ. In ths ase, we fnd that χ χ d d 2.32 We now hange ths to an teratve sheme where = + 0. Solvng for +, we arrve at the standard Newton-Raphson teratve form: d d χ χ + = Usng eq we an solve for the dervatve terms, where ρ χ + Φ Φ Φ = o T 2.34 sne F o and o are known onstants based on the measurement data. In prate, o s alulated usng the homogeneous fttng algorthm desrbed n Chapter 6. Takng the dervatve of eq 2.34, we fnd the seond dervatve term where ρ χ Φ Φ Φ + Φ Φ = o T T 2.35 The ontrbuton of seond dervatve term, o T Φ Φ Φ, s onsdered small and dsarded. Refer to Numeral Repes 64 p. 523 n 986 edton for dsusson. In fat, the text states that ths term an be destablzng f nluded. Dsardng ths term, eq an be rewrtten:

55 T χ Φ Φ = + 2 ρi 2.36 where I s the dentty matrx. Dvdng by two, these terms are now nserted nto the Newton-Raphson eq. 2.33: T T Φ Φ Φ ρ Φ Φ + ρ 0 + o + = + I 2.37 Φ Usng the standard termnology, the dervatve matrx,, s alled the Jaoban matrx, J, and = + s alled the update vetor. Insertng ths standard notaton, we see the famlar form of the Levenberg-Marquardt sheme, where? s the regularzaton parameter, T T o [ J J + ρi] J Φ Φ + ρ = and the extra term s the penalzed term from the Tkhonov defnton of χ n eq The values for Φ are determned by dfferentatng by parts the forward soluton [ A ] Φ = S eq. 2.27, suh that A Φ + [ ] = Φ S A 2.39 Solvng for the varable of nterest, Φ S A = A 2.40 [ ] Φ where both A - and F have already been determned n the forward soluton. The dervatve of the soure term, S, wth respet to s learly zero. Ths leaves the alulaton of the A whh an be determned at eah matrx element usng the defntons from the forward soluton eq. 2.28, 4

56 a j ak = ϕ k ϕ j ϕ 2.4 a j D k = ϕ ϕ k j ϕ 2.42 In prate, the Jaoban s bult on a olumn by olumn bass the dervatve for all measurement stes are alulated on a node by node bass. The a j k terms are only non-zero for lnear elements at the neghborng nodes suh that the multplaton a j k Φ s alulated dretly and the matrx A s never onstruted. The Jaoban matrx dmensons are two tmes the number of nodes 2NN by the number of measurements NM Φ D Φ 2 J = D M Φ D NM Φ D2 Φ 2 D2 M Φ D NM 2 L L O L Φ DNN Φ 2 DNN M Φ D NM NN Φ a Φ 2 a M Φ NM a Φ a2 Φ 2 a2 M Φ NM a2 L L O L Φ Φ 2 M Φ ann ann NM ann 2.43 where F s omplex valued. The dffuson oeffent D s used nstead of s ' n the fnte element alulatons, but we report s ' = /3D at the end of the reonstruton. In prate, however, we do not use a omplex solver but nstead buld the Jaoban wth separate lnes for phase,?, and ampltude data, ln I, suh that the sze s 2NN by 2NM: 42

57 43 = ann NM a NM a NM ann NM a NM a NM NN NM NM NM NN NM NM NM ann a a ann a a ann a a ann a a NN NN NN NN I I I D D D D I D I D I I I I I I I D D D D I D I D I D D D D I D I D I θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ L O M O M M L O M O M M L L L L L L L L ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln J Ths arhteture s leftover from prevous studes and ould be replaed by a omplex solver, however, t s relatvely effent for the purpose of ths work. 2.C.3. Normalzaton of the senstvty matrx Regularzaton of the senstvty matrx, J T J, onssts of the addton of an arbtrary value,?, to the dagonal to make the matrx more dagonally domnant, dereasng the ondton number and makng the nverson numerally stable. The unfortunate onsequene of ths stablzaton s an arbtrary hange n the relatonshps defned n The Levenberg-Marquardt sheme 63 smplfes the effet of the regularzaton by normalzng J T J to the same value along the dagonal suh that a onstant value of? has the same relatve effet throughout the matrx n ths ase at every node. Ths normalzaton relates to the reaton of a new matrx, J J T, by normalzng by the square-root of the olumn and row dagonal.

58 J J T T j J Jj = T T J J J J jj Ths onverson an be wrtten n matrx form where G G G G j j j j T = J J = 0 = / = 0 suh that J j T J j f = j f j f = j f j 2.46 J T T J J J = G G 2.47 The normalzaton s easest derved startng from the equaton 2.38 before the nverson of senstvty matrx suh that T T o [ J ρi] = J Φ Φ + ρ J We multply by the G matrx n several spots wthout hangng the equaton: T T o [ J J + ρi] G G = G [ J Φ Φ + ρ ] G effetvely normalzng the dagonal of the J T J matrx. We then defne a new regularzaton parameter, ρ, suh that I ρi = G ρ G 2.50 where ρi G = ρi G 2.5 Multplyng through the G - terms n eq. 2.49, we fnd T T o G [ J J] G + G [ ρi] G G = G [ J Φ Φ ] + G ρ whh an be smplfed to the form T T o J J + ρi G = G [ J Φ Φ ] + ρig

59 and solved for? T T o J J + ρi G [ J Φ Φ ] + ρig 0 = G Ths equaton basally states that f one normalzes the senstvty matrx, J T J, one must T o dvde the gradent term, J Φ Φ, multply the penalzed term, ρ, and dvde the fnal soluton eah by the square root of the dagonal of J T J. 0 2.C.4. Empral observatons The unfortunate onsequene of normalzng the matrx s that nodes on the boundary beome unstable for our stuaton where boundary values are very low n omparson to nteror nodes. The urrent soluton s to set the optal property values at boundary nodes to not hange.e.?=0. Ths has lttle pratal mpat, but s an awkward but neessary addton n the program. A fnal, but mportant empral observaton s that n the J T J matrx, the phase and ampltude terms are added together pror to regularzaton. Ths has the unfortunate onsequene of allowng the larger of the two terms to domnate the reonstruton. In ths ase, ampltude domnates phase, suh that early teratons are based towards ampltudebased reonstruton smlar to a DC mager. Thus, a weghtng fator equal to the mpat of phase versus ampltude multples the phase term at all loatons. Ths s desrbed n detal n Chapter 7. To the keen reader, t may seem that a term has been left out of ths dervaton -- the measurement varane, s 2. In some ases, the? 2 term s defned as χ Φ Φ NM o 2 2 = 2 = σ

60 Ths? 2 term s used n many dervatons and serves the mportant role of dereasng the emphass of less aurate measurements. Ths term ould be easly added to our urrent reonstruton program; the alulaton of the varane an readly be obtaned by dvdng our samplng tme nto multple setons and reportng the average and varane of the measurements. However, several arguments aganst the need to add ths term an be advaned. Frst, the random varane n measurements s urrently relatvely onstant n our measurement system due to detetor setup. Seond, the terms wth the hghest random varane are the measurements n whh the lght transverses the entre medum the far detetors. These arguably ontan the most mportant data n tomograph magng and thus dereasng ther nfluene may have detrmental effets. Fnally, model-data msmath and other systemat errors are more promnent at near detetor loatons where the random varane s lkely lowest. These lams asde, however, ths ssue has not been explored n suffent depth to lam that the varane term should or should not be nluded. Ths ssue s left for future study. 46

61 Chapter 3: Smulaton 3.A. Introduton The frst step n testng an mage reonstruton method s generally onsdered to be omputer smulaton. For NIR optal tomography, a dstrbuton of optal propertes a, s ' s generated whh s representatve of the tssue volume of nterest. In general, we use values assoated wth typal breast tssue for the bakground a = mm -, s ' = mm - and add nlusons wth varyng ontrast. For FEM, ths dstrbuton s mapped to the nodes of the mesh and the forward solver s exeuted to obtan smulated measurement data. Nose s often added to ths data to aount for the effets of expermental error. Ths smulated measurement data s then entered nto the reonstruton program and the results are ompared to the orgnal fabrated dstrbuton. In general, for a partular reonstruton program, the mages reovered n omputer smulaton for a gven dstrbuton an be onsdered the best possble results that would be obtaned expermentally. For ths reason, many of the mprovements and problems n mage reonstruton are best addressed n omputer smulatons. 3.B. Smulaton proedure at Dartmouth 3.B. Generaton of test objet The proedure for the omputer smulatons studes desrbed n ths thess s straghtforward. Images of the satterng and absorpton dstrbuton to be tested are generated at a resoluton of 200 by 200 pxels usng a Matlab program. Dstrbutons ontanng objets of arbtrary geometry were frst drawn n Photoshop and then transferred to Matlab. These 200 x 200 pxel mages are then mapped to the FEM fne mesh nodes whh are typally a rular arrangement of 425 loatons. The FEM mesh s a rle whle 47

62 the 200 x 200 pxel mage s a square. The dameter of the rle s set to be equal to the wdth of the square and eah nodal value s found by takng the value of the losest pxel to the x, y oordnates of the partular node. The 200 x 200 pxel mage s blurred by an averagng flter equal to the average node spang pror to ths mappng to effetvely lnearly nterpolate the mage onto the node struture as opposed to a nearest neghbor mappng whh has jagged edges due to the fnte node spang as shown n Fgure 3.. The man Matlab program for the mage generaton and mappng s alled "multplestepmg.m"; all fles and programs are nluded on the CD "stand alone reon". a b Fgure 3.: Shemat of Matlab program to generate optal property dstrbutons and map them onto the fnte element mesh. a A 200x200 pxel mage of the dstrbuton s reated n Matlab. b The mage s blurred by an averagng flter wth sze equal to the average node spang. The mesh s overlayed on the mage and the values of the pxel nearest to eah node s wrtten to fle. Ths proess effetvely uses lnear nterpolaton to map the dstrbuton onto the nodes. 3.B.2 Forward smulator The nodal values of the orgnal a and s ' dstrbuton are wrtten to fle. The flename of the nodal values s wrtten to a text fle "targets.dat" whh ontans the nputs to the Fortran forward smulator program "newsmu.for". The forward smulator generates a set of smulated measurements for the gven optal property dstrbuton. Ths measurement data s then wrtten to fle. The proess s llustrated n Fgure

63 a b Measurement homogeneous Measurement experment 260 Fgure 3.2: Shemat of the forward smulator. Node-based mages of a a and b s ' generated from Matlab program. Ampltude and phase measurement data from the forward smulaton for mages a and b labelled "experment" n ths graph. Plotted for referene s the measurement data for a homogeneous dstrbuton wth the same bakground propertes as a and b. 3.B.3. Reonstruton program In addton to the smulated measurement data, the reonstruton program "new5re.for" requres an ntal estmate of the optal propertes. For smulatons, the bakground optal propertes are generally used as a homogeneous ntal estmate. The reonstruton program for real data s dental to the program for smulated data, exept a albraton data set s also requred for the real system. The reonstruton program returns 49

64 mages of a and s ' whh an be ompared wth the orgnal dstrbuton as shown n Fgure 3.3. a b Fgure 3.3: Reovered mages from smulated measurement data plotted n Fgure 3.2. usng the FEM reonstruton program. Dsplayed are the node-based mages of a a and b s '. No nose was added to the measurement data n ths ase. 3.B.4. Dsusson The urrent forward solver and reonstruton program are two-dmensonal 2-d and requre approxmately seond and 45 seonds per teraton respetvely on a 500 MHz PC omputer. Bran Pogue has developed a three-dmensonal 3-d forward solver whh provdes a more aurate model of the 3-d nature of lght dffuson. For the nverse soluton, however, the Jaoban matrx see Chapter 2 s based on a sngle 2-d tomograph sle. Ths hybrd 3-d/2-d algorthm s about fve tmes slower than the standard 2-d algorthm for the same mesh densty used here n 2-d. The detals and results of hs study an be found n an Appled Opts artle. 86 For our urrent expermental setup, however, the urrent mplementaton of the hybrd 3-d/2-d algorthm appears to perform the same or slghtly worse than the standard 2-d algorthm, perhaps due to the fat that albraton s tuned to the 2-d algorthm; thus, at present the 2-d algorthm remans the standard. Full 3-d 50

65 reonstruton algorthms whh an use out of plane measurements have been developed elsewhere and generally requre on the order of 8 hours to one day for reonstruton. 87,88 Dffuse magng reonstruton methods are n general ll-posed, suh that smulaton s used not only to test the feasblty of the method, but also to mprove the results of the algorthm. In our ase, regularzaton an never be drven to zero, thus regularzaton of the senstvty matrx J T J n Chapter 2 effets the atual relatonshp between the measurements and the propertes. The effet of regularzaton s omplex and an be appled n a number of manners. Computer smulaton allows the optmzaton of the regularzaton tehnque and mage reonstruton algorthm. For our urrent expermental setup, we use a fve to seven teraton reonstruton where regularzaton s started at 00 and redued eah teraton by 0. For patent data, we urrently use a fve teraton reonstruton. Ths method s smlar to a Marquardt sheme where the regularzaton starts at a hgh value and s lowered based on the projeton error. 64 In our ase, we have hosen a fxed regularzaton sheme n order to get hghly repeatable results. We stop at fve teratons, beause we have found emprally that ths s when urrent expermental and systemat nose begn to dstort the reovered mages. In general, more aurate reonstrutons ould be obtaned by further lowerng of the regularzaton f systemat expermental nose ould be redued. For an ll-posed problem suh as ths, smulaton s an essental method to mprove the algorthm, as well as to haraterze and understand ts lmtatons. Many of the hallenges of ths sort of magng an be addressed n smulaton. Computer smulaton at Dartmouth has been wdely used to test problems suh as relatve sze of nlusons, 58,89 poston of nluson, 6 ontrast of nluson wth respet to bakground, 58,89 and number of nlusons 58, as well as ntal assessments of resoluton lmtatons. 57,89 Smulaton studes whh wll be desrbed n detal wthn ths thess nlude the effet of a heterogeneous 5

66 bakground and ontnuously varyng objets Chapter 8, the ablty to separate absorbng and satterng nlusons Chapter 7, and the reovery of funtonal nformaton from reonstrutons at multple optal wavelengths Chapter 9. These last three studes all used the programs lsted n ths hapter. 52

67 Chapter 4: Instrumentaton 4.A. Introduton The desgn and development of the data aquston system and patent nterfae s desrbed n ths hapter. The prevous generatons of data aquston setups are summarzed and used as an ntroduton to the urrent system. The urrent deve employs sxteen soure and sxteen detetor fber opt bundles arranged n a rular geometry and translated radally nto dret ontat wth the breast. Rado-frequeny RF ampltudemodulated 00 MHz lght s foussed nto the soure fber bundles from an automated seres of laser dodes. The detetor fber bundles delver lght extng the tssue to eah of sxteen photomultpler tube PMT detetors. Frequeny doman tehnques are used to obtan both ampltude and phase data at eah of the 256 measurement ombnatons. The desgn, albraton, and performane of ths tomograph magng system are detaled. Data aquston from the system requres under 30 seonds for a sngle tomograph sle at one optal wavelength wth a measurement repeatablty for a sngle phantom on average of 0.5% n AC Intensty and 0.4 degrees n phase. 4.B. Manual aquston Muh of the early expermental data aqured for the Dartmouth projet was obtaned at MMaster Unversty n Hamlton, Ontaro. 56,57,58 For one of the early setups, an opaque ylndral ontaner was used to hold lqud phantoms. Sxteen holes for aommodatng fber opts were drlled around the ontaner at one heght and overed wth lear plast 'wndows' to be watertght. An ampltude-modulated dode laser 75nm soure was foussed nto a fber opt whh dreted the lght nto one of the holes wndows. A seond fber opt bundle leadng to a PMT detetor was then manually moved to eah of the 53

68 dfferent detetor wndows. After magng all detetor postons for a partular soure, the soure fber was manually moved to a new poston and the proess repeated for all soure/detetor ombnatons. In other ases, the nluson wthn the phantom was arefully rotated and the fber postons mantaned. A photograph of the setup s shown n Fgure 4.. Detals of the setup an be found n Huabe Jang's Ph.D. thess 82 and other journal artles. 56,57,58 Ths proedure was very tme onsumng, but provded an nexpensve means of phantom testng. Some tme savngs ould be aheved by assumptons of symmetry n the measurement data. The ntal studes from ths setup showed that ths partular fnte element method FEM reonstruton based on the dffuson model ould be used to reover mages of absorpton and satterng from expermental measurements. 56 Indeed, quanttatve mages of nlusons wth equal ontrast n absorpton and satterng were demonstrated. 58 Sample mages are shown Fgure 4.2. These studes were performed usng both ontnuous-wave CW 90 and frequeny doman tehnques. 58 Whle the use of only one fber opt and one detetor smplfes albraton ssues suh as fber transmsson and detetor senstvty dfferenes, t soon beame neessary to develop a more automated aquston setup. Fgure 4.: An early phantom magng setup. 56 The ylndral phantom s n the enter of the mage. Two fber opts lead to holes drlled n the phantom, one from a laser soure and the other leadng to a PMT detetor. The nlusons n the phantom an be arefully postoned usng the setup attahed to the top of the ylnder, and phantoms were maged wth and wthout the nluson present. 54

69 Fgure 4.2: Some phantom mages obtaned from the frst expermental setup. The ontents of the phantoms are summarzed below the mages and further detals an be found n the orgnal paper by Jang et al C. Intal automated aquston setup After the ntal suesses from the manual setup, t beame essental to aqure data n an automated fashon to nrease the produtvty of phantom studes and allow for ntal n vvo testng. For ths reason, a system was onstruted at Dartmouth where the multplexng of the soure and detetor was automated usng lnear translaton stages PCLM seres SP-4, Anorad Corp., Hauppauge, NY, 20 m of travel wth <0 m repeatablty. Most of the omponents for ths system are desrbed n detal n Davd Rnehart's Master's 55

70 thess. 9 Hs thess desrbes most omponents wth the exepton of the lnear translaton stages. In addton, he dsusses a "Dartmouth"-made heterodyne rut and housng for the PMT whh was replaed by a more relable ommeral housng rutry from ISS Instruments In. Part numbers are gven below for omponents not lsted n hs thess. The frst verson of the automated deteton system was ompleted wthn the frst year of work on ths thess n 997 and s desrbed n the Pogue et al. 59 artle n Opts Express. The setup was automated through omputer ontrol usng Labvew software Natonal Instruments, Austn, TX and was able to aqure a set of 256 measurements 6 soure, 6 detetor n about 0 mnutes. The frst automated data aquston system at Dartmouth Fgure 4.3 onssted of 32 6 mm fber bundles 6 soure and 6 detetor optal fbers arranged alternately postoned n a rular array. 59 For the orgnal automated setup, the fber bundles were held n a rle by a mahned plast rng wth thumb srews over eah fber as shown n Fgure 4.4. The thumb srews were loosened and all fbers were manually moved nto ontat wth a ylndral phantom. Fgure 4.3: Shemat of the frst-automated magng setup showng the onnetons to and from the laser soure and PMT on translaton stages. 56

71 Fgure 4.4: Photograph of the automated setup. Note that for ths early setup, fbers were postoned ndvdually by loosenng of the thumb srew and manual reloaton. 59 A sngle ampltude-modulated 00 MHz 800 nm laser dode SDL, San Jose, CA was ntally used as a lght soure. The laser dode was drven by a DC urrent soure ILX Lghtwave, Bozeman, MT and frequeny generator Maron/ IFR Systems, Whta, KS. The sgnal from the urrent soure and frequeny generator are ombned wth a bas-tee Poseond Pulse Labs, Boulder, CO and nput to the laser dode. The laser dode was mounted n a fber launh module Thorlabs, Newton, NJ and the output foussed nto a fber opt. The laser soures of the present setup are ampltude modulated and launhed usng these same omponents. The fber opt led to a ollmatng lens Thorlabs, Newton, NJ whh was mounted on a lnear translaton stage. The sxteen soure fber opts were affxed to a ustom alumnum holder parallel to the moton of the translaton stage suh that the ollmated beam ould be multplexed between all soure postons. Between the ollmatng lens and the soure fbers, however, the beam was passed through an automated flter wheel Orel, Stamford, CT ontanng a seres of neutral densty ND flters OD = 0, 2., 3.2, 5.5. The frequeny-generator and urrent soure were omputer ontrolled through 57

72 a GPIB ard Natonal Instruments. The translaton stages and flter wheel were ontrolled through the seral port of the omputer. The measurement system was ompletely automated usng Labvew Natonal Instruments software. A seond translaton stage held a photomultpler tube PMT Model R-928, Hamamatsu, Hamamatsu Cty, Japan for deteton. Smlar to the soure sde, the 6 detetor bundles were mounted parallel to the moton of the stage. For every soure poston, the PMT was moved n front of eah of the sxteen detetor fbers to omplete the 256 measurement ombnatons. For the rular geometry used, the lght ntensty at detetor loatons vares over many orders of magntude between postons near the soure and postons far from the soure. The DC sgnal of the PMT was used to assess whether the lght level fell wthn the lmted dynam range of the PMT. The ND flters were used to redue the lght nput for these detetor postons whh resulted n saturaton over 5V DC sgnal. The 00 MHz sgnal from the PMT was redued n frequeny by heterodynng tehnques smlar to AM rado mxng the sgnal wth a loal osllator sgnal and measurng the beat frequeny as shown n Fgure 4.5. For ths setup, heterodynng of the sgnal was performed wthn the PMT by modulatng the frst dynode. The PMT used a spealzed housng Model K209, ISS Instruments, Champagn, IL ontanng rutry whh provded for modulaton of the frst dynode. A seond dental frequeny generator lnked wth the frst generator suh that the beat frequeny was held onstant was used n ombnaton wth a RF amplfer 7 Watt, ENI, Rohester, NY to modulate the frst dynode wth a MHz loal osllator sgnal. The output of the PMT ould then be deteted usng the sgnal ampltude and phase shft at the dfferene frequeny of khz. The sgnal was deteted wth a data-aquston ard Natonal Instruments n the omputer. 58

73 f = os ωt f 2 = os ω + δ t f* f 2 = / 2[os δ t + os2ω + δ t] Fgure 4.5: Heterodynng shemat from Davd Rnehart thess, 9 where n our ase,?=2p00 MHz s the loal osllator sgnal,?+d=2p00.00 MHz s the frequeny of the nput and deteted sgnal, and d=2p khz s the heterodyne or "beat" frequeny. A 0 khz low-pass flter n the data aquston blok removes the hgh-frequeny sgnals. Intally, a seond dental PMT was used as a referene. A small amount of the laser soure was splt off usng a bfuraton n the soure fber opt. Ths sgnal was dretly nput nto the seond PMT wth an dental heterodyne rut. The deteted sgnal was used as a phase referene as well as a referene for ampltude varaton of the laser. Later t was determned that the AC sgnal of the laser dode was more stable than the seond referene PMT and ths eletral referene was used. Ths eletral referene was obtaned by eletronally mxng the output of the two frequeny generators. A small amount of the eletral sgnal from both frequeny generators was splt off usng 99- n Power dretonal oupler ZFDC-20-3, Mn-ruts, Brooklyn, NY. The two % sgnals were mxed usng a RF mxer ZFM-50, Mn-ruts, low-pass fltered BLP-.9. Mn-ruts and dretly nput to the data aquston ard. Ths eletral referene s stll used for the urrent data aquston system. After ntal suesses wth a sngle wavelength setup, t was desred to gan spetrosop nformaton. The dode laser was replaed wth a Ttanum Sapphre T-S 59

74 laser Model 70, Lexel Laser, In., Fremont, CA, wth a Argon Ion pump laser Model Innova 90, Coherent, Palo Alto, CA. The laser s tunable between nanometers nm usng a sngle optal setup. The laser beam s ampltude modulated usng an eletroopt modulator Model , ConOpts, In., Danbury, CT drven by the 00 MHz sgnal amplfed by a 75 watt rado-frequeny amplfer Model 75A250, Amplfer Researh, Souderton, PA. The laser beam s foused nto a soure optal fber and multplexed n the same manner as the dode laser. The T-S shown n Fgure 4.6 has the advantage of allowng for measurements at a large number of optal wavelengths and was very useful n ntal spetrosop studes. Eventually, the stablty, dffulty of use, and power onsumpton warranted a return to a olleton of dode lasers eah at a dfferent dsrete wavelength. Fgure 4.6: Photograph of laboratory setup, where TS laser, Argon on pump laser, and eletro-opt modulator are mounted on optal benh on the rght. The frst patent bed setup s shown at the left sde of the photograph. The suess of phantom studes wth the automated deteton system led to the desre to mage female volunteers. The manual postonng of fbers was unaeptable, whh led to two hoes: a non-ontat system usng a ouplng medum suh as an Intralpd bath or 60

75 2 a dret ontat setup. For both setups, a hoe must also be made onernng geometry. An exellent dsusson on geometry hoes an be found n an Opts Express paper by Pogue et al. 92 For FEM magng, a rular geometry where the boundares are well defned s desrable for attemptng to quanttatvely mage the breast. Thus, we hoose a deve whh would mantan a dret ontat rular geometry. An deal deve for provdng preson rularly symmetr movement s a mult-jaw radal postonng deve. The frst adjustable nterfae used an 8-jaw preson lathe huk wth 2 m of travel J-F 50, Alna Corporaton, Swtzerland. The jaw movement s ontrolled by the rotaton of the base of the lathe huk, whh was aomplshed by rotatng a seres of metal rods nserted n holes n the base, muh lke a shp's steerng wheel. Fgure 4.7 Fgure 4.7: Photographs of assembled lathe-huk fber postonng system. By rotatng the metal spokes n red below the lathe huk, the fber opts are moved radally. The photographs on the rght show the fbers at a lose poston dameter of openng = 6 m and at a ompletely open poston dameter = 0 m. A "lab-jak" s mounted below the lathe huk to allow for vertal postonng of the array. 6

76 Attahed to eah jaw of the lathe huk was a m dameter, 6 m long rgd metal post to separate the radal postonng deve from the patent. Attahed to eah post s a mahned metal pee to hold two detetor fbers and two soure fbers "radal moton fber holder" n Fgure 4.8. A sngle 0 m nner dameter mahned plast rng "fxed nner rng" s used as a gude for the sngle level of 32 optal fbers. The fbers were attahed n plae to the "radal moton fber holder" by a olleton of heat-shrnk tubng, eletral tape, and hose lamps. In order to allow for smaller dameter breast, the 6 mm soure fber bundles were replaed wth smaller fbers. Intally nexpensve 2 mm plast fbers Edmund Sentf were used, before beng replaed by mm sla fber Thorlabs. The large ore detetor bundles are desrable to maxmze the lght olleton, but soure fber sze s not essental. a b Fgure 4.8: a Top vew and b utaway sde vew of ntal radal postoner desgn. Ths ntal automated system turned out to be qute suessful. The speed of aquston and maxmum dameter 0 m of the openng eventually neesstated a new 62

77 deteton array and patent nterfae. Ideally, multple wavelengths and multple planes should be maged for eah patent, however, wth ths setup t requred 0 mnutes per wavelength plus an addtonal 0 mnutes for any repostonng of the patent to go to another plane. We generally lmted ourselves to two wavelengths 750 and 800 nm on T-S laser at one plane on eah breast. Suh an exam would take over hour, thus, the desgn and onstruton of a parallel deteton system wth muh shorter aquston tmes and easer patent postonng was desred. 4.D. Current parallel deteton system 4.D.. Desgn The urrent frequeny doman deteton system onssts of four omponents eah of whh are desrbed n ths seton: D.. Lght delvery, D..2 Deteton array, D..3 Fber opt patent nterfae, and D..4 Computer ontrol and eletrons. 4.D... Lght delvery Ampltude modulated laser dode soures are used for ths frequeny-doman system. Typally, the nstrument s operated at 00 MHz, however, all omponents have bandwdths whh span 0 MHz to 200 MHz. Sx laser dodes are urrently used wth optal wavelengths of 660 nm 45 mw, Mtsubsh Eletr, Japan, 76 nm 30 mw, Frankfurt Laser Co., Germany, 785 nm 50 mw, Thorlabs, Newton, NJ, 808 nm 200 mw, Polarod, Cambrdge, MA, 826 nm 00 mw, SDL, San Jose, CA, and 849 nm 00 mw, SDL. The laser dodes are drven by a sngle DC urrent soure LDX-3207B, ILX Lghtwave, Bozeman, MT and frequeny generator 2023, Maron/ IFR Systems, Whta, KS. The sgnal from the urrent soure and frequeny generator are ombned wth a bas-tee 5545, Poseond Pulse Labs, Boulder, CO and nput nto a sx-way RF swth A, 63

78 DowKey, Ventura, CA. The RF swth s omputer ontrolled through sx dgtal lnes. The laser dodes are eah mounted n a fber launh module KT-2, Thorlabs and the output dreted nto the nput of a one-by-sx fber opt ombner Custom-bult, Fbergude, Strlng, NJ as shown n Fgure 4.9. The output fber leads to the parallel deteton array where t s multplexed to the soure fbers onneted to the breast through the patent nterfae Seton 2.3. The laser omponents, frequeny generators, omputer, and ontrollers are rak-mounted Fgure 4.0. Fgure 4.9: Image of Laser dode array. The dode lasers A-5 are mounted n fber launh modules. A omputer ontrolled RF swth B provdes the dode wth eletral urrent. The output of the lasers s nput nto a 6: fber opt ombner C. 64

79 Fgure 4.0: Image of rak mounted system. The four labeled levels house A the omputer, B the stage ontroller and PMT voltage soure, C the fve laser dodes, RF swth, and urrent soure, D the frequeny generators. 4.D..2. Deteton array The same rular deteton geometry s used, thus, the detetors nearest to the soure reeve orders of magntude more ndent lght than those farthest away. Beause of the lmted dynam range of the PMT, ether the lght level or response to the lght level must be adjusted. In the prevous setup, the lght level was adjusted wth ND flter wheel. In ths setup, the gan of the PMT s vared to aount for the large varaton n lght level between detetors dependng on ther dstane from the soure. The response of the PMT at dfferent gan levels requres albraton, but one haraterzed provdes a robust/stable measurement. 65

80 The deteton array s desgned to mantan the PMTs n the same poston relatve to the soure, thus the gan s adjusted one at the start of an magng sesson. The detetor poston s fxed relatve to the soure by mountng the entre deteton array on a rotary stage. The PMTs are arranged n order of senstvty wth the most senstve detetors plaed at the far sde loatons. The deteton array onssts of sxteen PMTs Housng HC20-08, PMT R6537, Hamamastu, Japan, sxteen RF mxers ZEM-2B, Mnruts, Brooklyn, NY, and two one-by-sxteen spltters mounted on a rotary stage see Fgure 4.. The deteton array also provdes the means for multplexng the laser nput to sxteen soure postons. Eletral heterodynng through RF mxers s used to down-onvert the 00 MHz PMT sgnal to a low frequeny e.g. khz whh s easly readable by the omputer. A fxed loal osllator MHz from a seond frequeny generator Maron/ IFR Systems s dvded sxteen ways wth a RF spltter ZFSC-6-2-S, Mnruts for eah mxer. The two frequeny generators are synhronzed and a small amount of sgnal from eah s splt off and mxed as a referene. The output of the mxers s run to a flter and amplfer rut at the omputer system. The RF spltter s mounted on the rotary stage n order to mnmze the number of wres leadng to the deteton system. Smlarly, a DC spltter box bult n house by Sean Stauth s used to provde power to all the PMTs from a sngle supply E360A, Hewlett Pakard, Corvalls, OR. An eght hannel rbbon able also brngs the gan settngs to the DC spltter box where eah hannel s bfurated to eah par of equdstant detetors. The gans are set by applyng voltages between 0.3 and.0 Volts that are suppled by the omputer. Ths voltage sets the PMT hgh voltage between 300 and 000 Volts. 66

81 a b Fgure 4.: The parallel deteton assembly. a The 6 RF mxers are mounted on a rular alumnum ds, whh s attahed to a rotary stage fxed to a square alumnum plate. A DC spltter box s also mounted on the enter of ths plate. b The 6 PMTs are mounted on the perphery of a seond rular ds. The RF spltter and soure fber are also mounted to ths ds. The fully assembled deteton array nludes the PMT ds mounted above the mxer ds. A fxed square alumnum plate for the fber opt lght delvery s mounted above the PMTs. 67

82 The assembled system s mounted on ten-nh dameter alumnum dss. The PMTs are attahed to one ds along wth the RF spltter whle the DC spltter and 6 mxers are fxed to the seond ds. These dss are offset by spaers and the ompleted assembly s attahed to a rotary stage B4836-TS, Velmex In., Bloomfeld, NY. All eletral wres and the fber opt laser nput lead through a hole n the enter of the rotary stage. The fber opt laser nput s onneted to a ollmatng lens F220SMA-B, Thorlabs and mounted to the top plate. The rotary stage s fxed n an alumnum box. The sxteen soure and detetor optal fbers from the breast nterfae array lead to the top of the box. All alumnum omponents are omputer mahned to hgh preson. The dmensons and omputer numeral ontrol CNC programs are loated on the CD n the "parallel system" dretory. These detetors and soures are rotated whle the breast nterfae fber opts are fxed, thus multplexng the soure whle mantanng a onstant detetor poston relatve to ts loaton at any pont durng an mage aquston. Thn plast red flters Wratten Deep Red No. 29, Kodak, Rohester, NY plaed n front of the PMTs are used to blok room lght. 4.D..3. Fber opt/patent nterfae A preson postonng system was desgned and ustom onstruted for the deteton subassembly as shown n Fgure 4.2. The nterfae s desgned for dret fber ontat wth the breast n a rular geometry. Sxteen motorzed lnear translaton stages are arranged n a rle for radal postonng of the array of fber opts. A par of synhronzed ontrollers s used for the sxteen stages allowng for preson radal moton. The sxteen translaton stages are mounted on a motorzed vertal postoner. Both the radal dameter and the vertal poston are vared by a push-button ontroller and the fnal poston reported to the omputer. The dameter of the fber opt array an be vared from 4 to 20 m, and the 68

83 vertal stage has 20 m of travel. The preson of the horzontal translaton stages s spefed as 0.5 mrons, although n prate wth our urrent fber holders our postonng auray s on the order of mm. The entre postonng setup was ustom-bult to our spefatons by Velmex, In. n Bloomfeld, NY. Fgure 4.2: The fber opt/patent nterfae for dret fber ontat wth the breast n a rular geometry. Fber opt bundles at the tssue nterfae A are mounted to sxteen radally-algned horzontal translaton stages B. The nterfae s attahed to a vertal translaton stage C. The motor ontrollers D and the deteton array E are mounted to an alumnum base below the patent nterfae. The vertal and horzontal stages are ontrolled by a sngle push button ontroller. Ths nterfae s mounted on a metal frame The frame s from MnTe Framng, LLC, Canandagua, NY, but was part of the postonng pakage from Velmex wth lokng wheels and s plaed below a ustom bed for patent magng. The patent bed Fgure 4.3 was ustom-bult by a massage table desgner, Kevn Grady of Stratford, VT. The deteton apparatus s mounted below the nterfae on the same metal frame. The patent plaes her breast through a hole n the bed nto the fully retrated array. The array s postoned vertally to the plane of nterest and then moved radally nto dret ontat wth the breast onformng t to a rular geometry. Ths slght ompresson s mld ompared wth urrent 69

84 x-ray mammography systems. The fber opts an be retrated and repostoned vertally for magng of multple planes. The urrent setup nludes one soure fber and one detetor fber onneted to eah radal translaton stage, however, addtonal planes of soures and detetors ould be added for three dmensonal magng wth no new equpment beng neessary. Fgure 4.3: The ustom bult patent table. The woman les prone on the table wth her breast pendant through the openng. The fber-opt nterfae s loated below the openng. An nexpensve PC vdeo-am s plaed below and updated mages are vewed on a omputer sreen suh that the nurse an easly poston the fbers n ontat wth the breast usng the push-button ontroller. 4.D..4. Computer System All equpment s ontrolled through a sngle PC omputer runnng Labvew software Natonal Instruments NI, Austn, TX. The urrent soure and frequeny generator parameters are set by a GPIB board AT-GPIB, NI. The rotary stage s addressed through the seral port. An analog output board s used for the gan ontrol PCI-6703, NI of the PMTs. A multpurpose data aquston DAQ board PCI-603E, NI aqures the sxteen analog nput hannels and the sngle referene hannel. Ths board also provdes sx dgtal 70

85 output lnes for the RF swth for the laser soures. The sxteen sgnals from the detetor system are amplfed by a gan of 000 and low pass fltered to prevent alasng pror to the DAQ board usng a sxteen hannel amplfer and flter network mounted n a BNC oupled box FBU-6, Audon Eletrons, England. Data s aqured for /2 seond, phase and ampltude of eah sgnal s alulated and wrtten to fle for use by the FORTRAN based reonstruton program. 4.D.2. Data Aquston and Proessng The data aquston proedure nvolves two albraton steps: D.2. detetor albraton and D.2.2 homogeneous phantom albraton. For every patent or phantom to be maged, the D.2.3 gan settngs are determned for all detetors at eah wavelength. The fnal albrated phase and ampltude data s used n the D.2.4 fnte element analyss software to determne mages of absorpton and satterng. 4.D.2.. Detetor albraton Eah detetor has a dfferent ampltude and phase response to the same optal sgnal, due to PMT varaton, mxer performane, and fxed offsets n the RF spltter Fgure 4.4. As well, PMT response vares sgnfantly for the same optal sgnal deteted at dfferent gan settngs Fgure 4.5. At a sngle gan settng, however, for the AC voltage range used n our setup, phase s approxmately onstant and deteted voltage s lnear wth respet to the power of the optal sgnal Fgure

86 a b Fgure 4.4: a AC ampltude and b phase of deteted sgnal for the same optal sgnal for all 6 PMT detetors. a b Fgure 4:5: a Relatve AC power level for the same measured output AC voltage 0. V at dfferent gan settngs. b Phase shft measured for the dental optal phase but at dfferent gan levels. Both measurements are reported for detetor number one. 72

87 a b Fgure 4:6: a AC Voltage plotted aganst relatve optal power and b measured phase shft for the same optal sgnals for eght representatve detetors D - D8 at a sngle gan settng of 0.7 V. A log sale s used for the power of the optal sgnal n plot b. A one-tme albraton over the entre useful range of lght levels and gans s appled. For the detetor albraton, a sheme smlar to that of Wlson et al. 93 and Shmdt et al. 37 s used, where a sngle soure s plaed n the enter of a homogeneous dffusng objet and measurements are obtaned at eah detetor ste. Eah detetor s exposed to the same optal sgnal, thus, the dfferenes n log ampltude and phase are used as orreton fators. The lght ntensty but not phase s hanged by a seres of neutral densty flter wheels 525, New Fous, Santa Clara, CA. The log ampltude response of the PMT s plotted aganst the log of the nput power for eah gan settng. A log-log regresson s performed and the oeffents stored for eah detetor at every gan settng. Thus, the deteted PMT ampltude s albrated n terms of optal power. The exponental term of the log regresson s lose to unty, as the PMT response s approxmately lnear. The onstant term of the log regresson s related to the lnear slope and s plotted versus gan settngs for eght representatve detetors n Fgure 4.7.a. The phase does not hange sgnfantly wth hangng lght level for a sngle gan settng, but hanges dramatally wth hangng gan see Fgure 4.6. The phase shft versus gan settng urve s shown n Fgure 4.7.b. for eght of the sxteen 73

88 detetors. Ths albraton needs to be performed only one as long as the system s unhanged. a Slope of measured ntensty versus relatve power Gan Volts D D2 D3 D4 D5 D6 D7 D8 b Phase shft degrees Gan Volts D D2 D3 D4 D5 D6 D7 D8 Fgure 4.7: Calbraton urves for PMT response at dfferent gan settngs. A fxed optal sgnal ntensty was vared wth neutral densty flters for all gan settngs. A regresson to the deteted log ampltude at eah detetor was performed versus log of nput optal power. The onstant term of the regresson s related to the lnear slope ampltude/nput power and s plotted n fgure a versus gan level for eght representatve detetors D - D8. The phase shft s approxmately onstant for deteted sgnals below saturaton level and above the nose floor. The average phase shft for eght detetors D - D8 s plotted n fgure b for dfferent gan settngs. 4.D.2.2. Homogeneous Calbraton 74

89 A fnal albraton s performed to aount for offsets due to soure fber and detetor fber dfferenes n transmsson and algnment, as well as any errors n dsretzaton or data/model msmath. A homogeneous phantom s measured and a homogeneous ft s performed to the data averaged over all soures. The ft determnes the optal propertes n terms of the absorpton and redued satterng oeffents. The alulated data from the fnte element model for those optal propertes s subtrated from the measured values and used as a fnal orreton fator. The detals of ths proedure an be found n Chapter 6. 4.D.2.3. Gan settngs The gan settngs are determned automatally at eah wavelength for every new phantom or patent. The gan of eah PMT s ontrolled by a 0.35 to.00 Volt ontrol sgnal. The PMTs are pared by dstane from the soure; thus, a total of eght gan settngs are used to establsh the gan for the sxteen PMTs. The gan s set suh that the output of the PMT falls approxmately n the mddle of the dynam range whh orresponds to a measured AC voltage n the range of 0.0 to 0. Volts. The PMT saturates around.0 Volt and the nose floor s near 0.00 V. Ths also effetvely equalzes the nose level for all PMTs despte the large dfferene n lght levels present. The albraton fators for phase and ampltude are alulated from the look-up table LUT determned n seton 3.. Ths gan proedure s automat and requres less than ten seonds to exeute. 4.D.2.4. FEM analyss The albrated data aqured from the deteton system s proessed by a FEM based reonstruton algorthm Chapter 2 to generate tomograph mages of absorpton and satterng oeffent. Images of absorpton oeffent at several wavelengths an be ombned to form mages of hemoglobn parameters Chapter 9. 75

90 4.D.3. Performane 4.D.3.. Senstvty and Absolute Error The absolute senstvty and error of eah detetor has been haraterzed usng a fxed optal sgnal and neutral densty ND flters. The lght level was nrementally lowered usng the ND flters and the ampltude and phase response and error were determned by repeated half-seond long measurements. The gan of the PMT was set to 0.95 of the maxmum. The response of a representatve detetor s shown n Fgure 4.8. The lowest detetable sgnal s n the sub-powatt range. The ampltude and phase error nrease from a onstant level of approxmately 0.5% and 0.5 degree as the sgnal approahes the deteton lmt. a 76

91 b Fgure 4.8: a Plot of the deteted AC ntensty sgnal versus the nput AC power at the gan settng of 0.95 of the maxmum gan. The long dashed lne s the system nose level and the short dashed lne s the nose level of the eletrons. The sold lne ndates the lnear response of the detetor pror to reahng the nose floor. b Plot of phase nose RMS error wth respet to the mean sgnal wth respet to nput power. The phase nose dereases wth nreasng sgnal to a onstant RMS level of less than a degree at typal power levels. The AC power was determned by fndng the modulaton depth 60% measured wth a photodode and osllosope and measurng the DC power usng an optal power meter before dereasng the power wth neutral densty flters. 4.D.3.3. Imagng of repostoned objet Small errors n the fber postonng when aqurng NIR data at the perphery of an objet an lead to surfae artfats n the reonstruted mage. In order to assess ths potental problem, phantom magng results from the automated postonng system were ompared wth a prevous manual postonng approah. It s estmated that the auray n manual postonng s on the order of several mllmeters versus the mron level auray of the automated system. The same ylndral phantom was maged ten tmes n eah postonng system; the phantom was removed and repostoned between eah measurement. The average measurement error for the ten trals was 2.2% n AC ntensty and 0.5 degree for the new postonng system and 6.5% and.5 degree n the old system. For both postonng setups, the frst and seond set of measurements were entered nto the reonstruton program as a homogeneous albraton and expermental data set respetvely. The reonstruted mages from eah of the two postonng setups are ompared n Fgure

92 a Absorpton Image b Satterng Image Absorpton Image d Satterng Image Fgure 4.9: a Absorpton and b satterng mage of a homogeneous phantom wth albraton and expermental data aqured by manual postonng setup. Absorpton and d satterng mage from automated postonng setup. The x and y axes of the mages are unts of mllmeters and the sale bar unts are nverse mllmeters. 4.D.3.2. Repeatablty Measurement repeatablty n terms of phase and ampltude error was assessed by repeatedly magng a tssue-smulatng phantom. A 84 mm dameter sold phantom was onstruted wth optal propertes smlar to that of average breast tssue a = 0.007, s / = 0.7 usng the method desrbed by Frbank et al. 94 Ths phantom was plaed n the fber opt nterfae, maged repeatedly usng the albraton proedure desrbed n seton 3. The average RMS error at eah detetor ste was determned to be 0.5% n AC Intensty and 0.4 degree n phase, wth a maxmum average RMS error for one detetor of 0.8% and 0.5 degree. Ths measurement error for repeatedly magng a phantom s about 2.5 tmes lower than the AC Intensty error when repostonng the objet as desrbed n 4.D

93 4.D.4. Dsusson A novel frequeny doman magng system was developed and has been desrbed n ths Chapter. The nstrument s fully-automated, apable of mult-wavelength magng and aqures a omplete set of data 6 soure x 6 detetor n under 30 seonds. It has been tested on phantoms and has been found to be hghly senstve sub-powatt deteton lmt wth low nose RMS error <%, <0.5 degree phase. The system s omputer-ontrolled and features sx dfferent wavelength laser dodes and a hghly aurate atuator-drven rularly-symmetr fber opt nterfae. Ths setup allows for the aquston of multple wavelengths over several planes of nterest on a patent n under ten mnutes. 79

94 Chapter 5: Phantom testng 5.A. Introduton Followng omputer smulaton, the seond step n testng an mage reonstruton method an be onsdered "phantom" testng. A "phantom" refers to a onstruted objet whh mms the propertes of the tem of nterest, but for whh the true property dstrbuton s known. In the ase of optal tomography, phantoms are onstruted whh mm the optal absorpton and satterng propertes of tssue. In order to perform phantom studes, an expermental data aquston system must be onstruted. Data aqured from the expermental setup are nput nto the reonstruton program and the reovered mages are ompared wth the known propertes of the phantom. Phantom testng s essental n order to gan onfdene n the mages later aqured from real subjets where the true dstrbuton s unknown. Phantom studes are used n the same manner as smulatons to assess the ablty and lmtatons of an magng system. 5.B. Phantom studes at Dartmouth Smlar to smulatons, for phantom studes knowledge of the average property dstrbuton of breast tssue and lesons s used as a bass for the desred omposton. Bulk optal propertes for typal breast tssue generally fall wthn the range for a of to 0.02 mm - and s ' of 0.5 to 2.0 mm -. Lesons have been found to be as hgh as 4: ontrast n absorpton wth a lower unknown satterng ontrast. For the onstruton of phantoms, t s advantageous to use substanes wth prmarly absorpton ontrast blood, nk and those wth prmarly ontrast n satterng Intralpd, ttanum doxde. In optal tomography, a number of materals and methods for phantom onstruton have been used suessfully. At Dartmouth, phantoms an be dvded nto fve ategores, lqud, sold resn, gelatn, semsold, and those usng exsed tssue. 80

95 5.B.. Lqud phantoms The frst phantoms used n optal tomography were manly lqud phantoms wth suspensons of lpd partles used for satterng ontrast and nk for absorpton ontrast. A partularly-useful ommerally-avalable lpd suspenson s Intralpd 20% stok soluton, Pharmaa and Upjohn Co., Clayton, NC -- Intralpd s used ntravenously to replensh lpds n hosptals. The absorpton of the lpd partles s neglgble and the satterng has been haraterzed n the NIR range. Intralpd s used wdely n optal tomography and the satterng dependene s approxmately haraterzed by the formula from van Staveren et al., 95 s ' λ = λ λ 2.4 where? s the wavelength n mrons and s ' s n unts of [ml - L mm - ] for ml of 00% Intralpd per L of water. e.g. For % of Intralpd n soluton, s ' at 800 nm s ~.0 mm -. Eah bath of Intralpd s slghtly dfferent and a more exat value of the satterng propertes for a spef bath an be determned usng measurements at a seres of onentratons. For absorbng ontrast, ether nk or blood an be added to lqud phantoms. Both nk and blood are satterng, but n the dffuse regme the effet of ths satterng s generally neglgble n omparson to the bakground satterng.e. a << s '. Small onentratons of nk are needed for values typal of breast absorpton; due to nonsstenes n materals and mxng, eah new bath of nk should be haraterzed for absorpton per unt onentraton. In general, at Dartmouth we mx 50 ml bathes of 0.2% Inda nk e.g. Pelkan Drawng Ink A 7 Blak, Hanover, Germany for use over several months. 0.2% nk has roughly an a per onentraton of ~0.005 [mm - ml - L] at 800 nm. The a per unt onentraton s found for eah bath by measurng a of a homogeneous ontaner of nreasng 8

96 onentratons of nk. In general, measurements of ether a or s ' per onentraton an be done aurately usng the Dartmouth data aquston system Chapter 4 and homogeneous fttng algorthm Chapter 6. For these types of measurements, the lqud phantom must be n the dffuse regme for a and s ' to be aurate, thus Intralpd s added untl satterng s muh hgher than absorpton. Blood turns out to be a well-albrated absorber. The absorpton spetra for hemoglobn has been studed by several groups and s avalable n lterature see Fgure In order to use whole blood for absorbng ontrast, the moleular weght g/mole of hemoglobn and onentraton of hemoglobn n the blood mass of hemoglobn per lter must be known. In general onentraton of hemoglobn n blood s smlar n healthy adults and an be assumed to be 50 ± 20 g/l. Measurements of true onentraton of hemoglobn n a sample of blood an also be obtaned from medal tehnology labs and samples used here have ntally been onfrmed to be 56 g/l usng the DHMC lnal hemstry department systems for hematort level deteton. The spetra of the blood an also be haraterzed by the measurements wth our system as desrbed above. In addton, hemoglobn has a dfferent absorpton spetrum dependng on ts oxygen saturaton. In ar, hemoglobn mxed n water an be assumed to be fully oxygenated. Usng these assumptons, blood has a typal a per unt onentraton of ± [mm - ml - L] at 800 nm plus mm - for the water n blood at 800 nm. Studes wth de-oxygenated hemoglobn wll be dsussed n later hapters Chapter 9. A onern of lqud phantoms s that t s neessary to hold the lqud n a ontaner, whh nevtably effets the measurements and assumptons. A ontaner s often hosen whh mnmzes wall thkness and absorpton. A reasonable amount of satterng n the ontaner wall s desred, however, to prevent lght hannelng through the wall of the ontaner. Ths "wall effet" should not effet measurements of absorpton and satterng 82

97 oeffent per unt onentraton for haraterzng a bath of nk or Intralpd. In these ases, measurements of a or s ' are performed at a seres of onentratons and the slope s used to determne the value per unt onentraton. The absolute value of a and s ', as well as the nterept of ths lne wth zero onentraton, wll be effeted by ths wall effet. In the ase of absorpton oeffent, the absolute value of a for zero nk onentraton should be equal to the absorpton of water whh has been haraterzed by several groups. 50 Instead ths nterept tends to overestmate the absorpton due to water, whh we attrbute to a walleffet. Fgures 5. and 5.2 show the haraterzaton of a bath of Intralpd and a bath of nk for a and s ' per unt onentraton. Also, the addton of nlusons to a lqud phantom requres addtonal ontaners eah of whh has an unknown effet on the true phantom propertes. a b Fgure 5.: Reovered values for a a and b s ' at 785 nm for Intralpd per unt onentraton for homogeneous soluton based on data aqured wth urrent deteton system and proessed wth the homogeneous fttng algorthm. 83

98 a b Fgure 5.2: Reovered values for a a and b s ' at 785 nm for 2% Ink per unt onentraton. Note a nterept s mm - nstead of expeted value for water of mm -. In prate, we have found Nalgene [e.g. 32 oz. polypropylene, Lab Safety Supply, Janesvlle, WI] plast bottles to a be a farly good ontaner of lqud phantoms. The bottles are olorless wth a loudy appearane that prevents lght hannelng. The wall thkness s about mm. For nlusons, we use a thn lear polyester flm suh as an overhead transpareny -- wall thkness 200 mron glued nto a ylndral shape. These ylnders have an effet on the measurements, whh an be somewhat aounted for n dfferene magng setups by fllng the ylndral nluson wth frst a bakground mxture and then addng the ontrast. These problemat ssues related to the materals were a prmary motvaton for developng sold phantoms. 5.B.2. Resn sold phantoms More permanent hard-plast phantoms Fgure 5.3 an be made out of polyester n a manner desrbed by Frbank et al. 94 These materals are permanent and an be shaped and drlled usng standard mahnng equpment. Ink and ttanum doxde TO 2 are added to provde absorpton and satterng ontrast. Careful preparaton s requred for preventon of 84

99 bubbles and proper urng. A repe and mxng proedure s lsted below n Table 5.. Holes an be drlled nto these phantoms for addton of nlusons. Whle a seond resn mxture wth dfferent propertes ould be added for a permanent phantom wth a spef nluson, we generally use lqud mxtures n the holes to allow for varable ontrast studes. These phantoms are exellent for repeatablty studes as they are stable over years; n addton, they allow for multple nlusons and small szed nlusons whh are dffult to reate n lqud phantoms. A drawbak s the msmath n refratve ndex between the resn phantom and lqud nlusons. Ths msmath appears to lead to refletons whh show up as a derease n satterng from the expeted values. Smlar to the wall effet n lqud phantoms, ths msmath must be aounted for by albraton or empral adjustment of the mxtures n order to analyze for absolute quanttatve values. Resn phantom repe Ingredents: 330g resn GY502 Araldte resn, D.H. Ltter, Elmsford, NY 99g hardener HY832, D.H. Ltter.4g ttanum doxde 0.5ml 2% nk Proedure: Mx resn, nk, TO 2 well n ontaner Degas mxture n bell jar/break vauum; repeat 3-4x. Add 50% of hardener and mx well espeally bottom. Add remanng hardener; mx well. Degas agan n bell jar as before Remove from bell jar before t gets hot/ starts to reat Let ure n hood, not under vauum When hardened, mahne to fnshed ylnder. Table 5.: Repe for resn phantom mxng proedure developed by Elzabeth Whte. 85

100 a b Fgure 5.3: Photographs of resn sold phantoms. a homogeneous phantom, b phantom wth holes drlled for addton of nlusons. A dsadvantage of the resn phantoms s that they are ompletely rgd unlke tssue. One ssue s that the flat fae of the fber opts an not ontat flush wth the urved phantom surfae. A seond drawbak s that when used for albraton, msalgnments n fber postonng are orreted by the sold phantom, whereas when magng a breast, these fber poston msalgnments are mantaned due to the ompressble nature of the breast. Thus, a phantom whh mms the breast n ompressblty s desrable. 5.B.3. Compressble sem-sold phantoms A slone phantom was prevously developed 96 whh was slghtly ompressble. By redung the hardener n ths phantom mxture, a phantom wth smlar ompressblty to the breast an be generated. Wth the reduton of hardener, the urng proess takes longer on the order of week dependng on the hardener level. Ths phantom mxture appears to be the best math to the breast for albraton usng a homogeneous objet. The addton of nlusons s not as easy as the resn phantom, and ths remans an area of development urrently. A repe for ths phantom s lsted below. The detals of ths phantom wll be reported n a journal artle by Shudong Jang at a later date. 86

101 Slone soft phantom repe Ingredents: 500g Slone RTV 4, Medford Slone, Medford, NJ 7g hardener omes wth RTV 4 note 50g s the usual amount of hardener for less-ompressble phantom.7g ttanum doxde 0.8ml 2% nk Proedure: Mx Slone, Hardener, nk, TO 2 well n ontaner Degas mxture n bell jar 5 mnutes/break vauum/str Degas mxture agan 5 mnutes/break vauum/str Degas mxture 30 mnutes/break vauum/str Degas mxture hours/break vauum/str Let ure under vauum untl fully ured For ths low level of hardener, requres up to 7 days to ure. Table 5.2: Repe for slone soft phantom Shudong Jang mxng proedure. 5.B.4. Gelatn phantoms The gelatn phantom s probably the least useful of the sold phantoms, however, s lsted here due to ts low ost and ts use by other magng modaltes. The prmary use n ths projet has been the reaton of a sngle phantom for use by three magng modaltes: NIR, eletral mpedane, and mrowave magng. Ths study s beng wrtten up by Dun L. For ompleteness, a repe for a gelatn phantom s nluded n Table 5.3. The man two dsadvantages of ths gelatn phantom are ts short shelf lfe and ts fragle nature damaged by dret fber ontat, although other types of gelatn an mprove the rgdty of the fnal produt. 87

102 Gelatn phantom repe Ingredents: 200 ml water 8.g Agar Fsher Chemal 0.5g Preservatve Dowl, Dow Chemal 0.7g ttanum doxde 0.25ml 2% nk Proedure: Mx n glass beaker Autolave untl agar s dssolved 30 mnutes at 20C n stem oven over phantoms and refrgerate when not n use Table 5.3: Repe for gelatn phantom Dun L/Todd Kerner/Elzabeth Whte proedure. 5.B.5. Tssue phantoms Another method of phantom magng s to use exsed tssue samples. Ths allows for the magng of heterogeneous samples smlar to n vvo tssue, but wth the advantage of beng able to add nlusons at known loatons. The prmary dsadvantage asde from the ssues wth handlng and odor s that the true magntude of the heterogenety s unknown. In our studes, we used exsed tssue from breast reduton surgery as a bakground objet. Inlusons were added usng beef and pork produts from the supermarket. These studes are dsussed n detal n Chapter 8. 5.B.6. Dsusson Phantom studes are an essental part of the development of ths optal tomography setup. Smlar to smulaton studes, t s mportant to study the reovery of known objets n order to haraterze the expeted performane of the system. Studes at Dartmouth have been performed to analyze effets of sze, 58,89 poston, 6 ontrast, 58,89 and number of nlusons 58 wthn a phantom. In addton, resoluton lmtatons and ontrast detal analyses an be addressed wth phantom studes. 57,89 Studes whh wll be desrbed n detal wthn ths thess nlude the effet of a heterogeneous medum usng tssue phantoms Chapter 8, the ablty to separate absorbng and satterng nlusons Chapter 7, 88

103 and the reovery of funtonal nformaton from measurements at multple optal wavelengths Chapter 9. 89

104 Chapter 6: Calbraton and homogeneous fttng algorthm 6.A. Introduton An mportant but under-appreated step n an mage reonstruton method s the albraton and other pratal onsderatons neessary for the use of expermentally-aqured data. In our reonstruton algorthm, several unknowns suh as soure-strength, boundaryondtons, numeral mpreson due to fnte mesh spang, and data-model msmath an lead to domnant artfats n reonstruton f these effets are not properly ompensated. In partular, we an use a two-dmensonal algorthm wth relatvely oarse node spang qute effetvely wth proper albraton and ompensaton. The pratal onsderatons spef to our reonstruton algorthm and data aquston system are desrbed n ths hapter. In addton, a key omponent of our method, the homogeneous fttng algorthm, s desrbed n ths hapter n the ontext of ts role n albraton. 6.B. Pratal Consderatons Calbraton and other pratal onsderatons arse when usng a model-based mage reonstruton method wth data aqured from a real magng system. In the NIR dffuse tomography ontext these nlude: system-based offsets, 2 ntal optal property estmate for a heterogeneous medum, and 3 determnaton of soure strength and ntal phase offset. 6.B.. System-based offsets For the urrent magng setup, a number of system-based offsets must be albrated n order for the measured values to math the true lght ampltude and phase present at eah detetor loaton. Systemat offset n the measured data ours at varous soure and detetor loatons due to detetor responsvty, optal fber dfferenes, multplexng mpreson, and other systemat nonsstenes. Obvously, these offsets need to be removed from the data pror to mage reonstruton n order to prevent the appearane of 90

105 artfats n the resultant tssue property profles. One opton s to albrate all of these effets suh that the measured data exatly mathes the true lght levels. Instead, we albrate the detetor responsvty dfferenes usng the methods n Chapter 4 part D.2., but use a separate method for all other unknown offsets. The method adopted here measures a homogeneous phantom and subtrats dfferenes between measured and alulated values: φ albrated hetero = φ measured hetero φ measured homo φ alulated homo 6. where φ measured s the measured ampltude and phase at eah of the 256 measurement loatons for the albraton phantom homo and the atual heterogeneous objet hetero, whle φ alulated s the orrespondng alulaton for the homogeneous homo ase. A homogeneous fttng algorthm desrbed n Seton 6.C s used to determne the optal propertes for whh the alulated data best mathes the measured data from the homogeneous albraton phantom. Thus any dfferenes between the best possble ft are used as the set of albraton fator as shown n eq. 6., whh represent the set of potentally systemat errors n one set of 256 measurements. The albraton proedure for elmnatng systemat offset at dfferent soure and detetor loatons nvolves: measurement of a homogeneous phantom eah day and after equpment hanges, 2 determnaton of the satterng and absorpton oeffent for the phantom from the measured data usng the homogeneous fttng algorthm, and 3 use of the dfferene between alulated and measured values as the set of albraton fators. 6.B.2. Heterogeneous startng values The mage reonstruton algorthm starts from an estmated set of optal propertes and teratvely updates these values based on the dffuson equaton relatonshp and the dfferene between the alulated and measured data. If the ntal estmate of the optal propertes s far from the atual optal propertes of the heterogeneous objet beng maged, 9

106 ths naurate startng pont an slow onvergene and even lead to erroneous answers. In order to determne the ntal optal property estmate for patent data or a heterogeneous phantom, the measurements are averaged for eah of the sxteen soures and the homogeneous fttng algorthm s used to determne an estmate of the "bulk" or "homogeneous" propertes that best math the averaged measured data as dsplayed n Fgure 6.. In ths manner, the ntal estmate s determned solely from the heterogeneous phantom or patent measurements, yet, s lose enough to the unknown atual heterogeneous parameter dstrbuton that the algorthm wll onverge. a b d Fgure 6.: Plot of entre 256 measurement a lnintensty and b phase shft data set. Ths data s averaged over all soures and homogeneous fttng algorthm appled to fnd best ft. Also dsplayed s lnintensty and d phase data averaged over all soures and the alulated data for the best ft homogeneous optal propertes. 92

107 6.B.3. Long term drft Dfferenes between the soure strength and ntal phase at the tme of the measurement of the homogeneous albraton phantom and the atual soure strength and ntal phase observed at the tme of the heterogeneous measurement an lead to an overall offset manly due to long term drft between the albrated measured and alulated data. Ths dfferene n overall offset needs to be removed n order for the reonstruton algorthm, whh fts to the absolute ampltude and phase data, to be effetve. To aount for long term drft, the offset for both the homogeneous phantom measurements and the atual heterogeneous measurements are alulated based on the homogeneous fttng algorthm. The homogeneous fttng algorthm responds to the slope of the data and s therefore ndependent of ntal soure strength and phase shft. The offset s estmated as the average dfferene between the measured and alulated data, φ offset homo N φ measured homo φ alulated homo = = N 6.2 φ N φ measured hetero φ alulated hetero = offset hetero = φ = φ φ N offset net offset hetero offset homo where φ offsetnet s the long term drft orreton for ntal phase and soure strength. 6.C. Homogeneous Fttng Algorthm 6.C.. Motvaton and prevous method 6.C... Motvaton An mportant part of pratal magng s the homogeneous fttng algorthm. The homogeneous fttng algorthm s rtal for both albraton of the system and for provdng 93

108 the ntal optal property estmate for the mage reonstruton proess. Assumng a homogeneous medum, only one soure loaton s needed to determne the a and s ' of the materal from measurements around ts perphery. a and s ' s determned usng a Newton- Raphson mnmzaton of the dfferene between the measured and alulated data from the fnte element forward soluton of the dffuson equaton Chapter 2.2 for the relevant geometry. In prate, data s aqured at all 6 soures 256 soure/detetor ombnatons, but s averaged together as f there were only one soure based on detetor dstane from the soure loaton. 6.C..2. Method A A prevous verson of the homogeneous fttng algorthm uses a Newton-Raphson sheme where the mnmzaton was based on an estmate of the frst dervatve for the averaged data number of detetors mnus one 5 parameters; applyng the forward soluton of the dffuson equaton, we teratvely ft the omputatons to the measured data to determne the losest tssue optal propertes for a homogeneous medum. The twodmensonal ft was performed on the phase θ n radans and log of the ntensty A of the measured transmtted lght: χ o o 2 o [ A A ] [ A A ] + [ θ θ ] [ θ θ ] 2 M 2 o = = 6.5 where an approxmaton of the frst dervatve of the data s used n order to be ndependent of ntal phase angle and soure ntensty, as desrbed n equaton 6.5. χ 2 s mnmzed based on the omparatve hange n the alulated dfferene n phase θ and log of ntensty A between detetors and + and the dfferene n measured values θ o, A o for the orrespondng detetors summed over the omplete set of M- pars of detetor stes. 94

109 In ths thess, ths mnmzaton sheme s termed Method A as depted n Fgure 6.2. In prate, ths sheme was senstve to nose n the data and the mnmzaton dd not readly onverge. The urrent method, termed Method B n ths thess, mnmzes alulated and measured values for the slope of the phase wth respet to dstane from the soure loaton and slope of the log of ntensty tmes dstane wth respet to dstane determned from lnear regresson 2 parameters as desrbed n the followng seton. The two methods are ontrasted n Fgure 6.2. Fgure 6.2: Shemat desrbng two homogeneous fttng algorthms. 6.C.2 Current homogeneous fttng algorthm Method B The mnmzaton an be smplfed by redung the ft to two parameters: slope of the phase wth respet to dstane from the soure loaton and slope of the log of ntensty 95

110 tmes dstane wth respet to dstane. These two parameters were hosen beause they are nearly onstant and an be obtaned from the data through lnear regresson. They are onstant for the analyt nfnte medum dffuson equaton soluton as presented below. Ths method s nsenstve to nose due to the large amount of averagng whh ours 256 measurements are averaged to two terms, d ln ri o dr dθ and o. dr The urrent fttng algorthm nvolves two steps, an ntal soluton for a and s ' from a mnmzaton based on "alulated" data from an analyt soluton for an nfnte medum, and 2 the soluton for a and s ' for our geometry from a mnmzaton based on "alulated" data from the fnte element forward solver. Step 2 uses the soluton for a and s ' for the nfnte medum as a startng value. Both steps use the dental Newton-Raphson root-fndng algorthm. For eah ase, we are nterested n fndng the values of a and s ' suh that d ln ri dr d ln ri dr o = dθ dθ dr dr o = where r s the straght-lne dstane between a soure to detetor, I and I o are the alulated and observed AC ntensty level,? and? o are the alulated and deteted phase respetvely. dθ o and dr d ln ri o dr are both determned from a lnear regresson to the measured data. For an nfnte medum, analyt expressons for the alulated values an be expressed, 20,97,98 where dθ dr 2 a = + D 2 4 ω sn tan a ω a

111 ri ln 2 4 d 2 a ω ω = + ostan dr D a a see Chapter 2 for varable defntons. The Newton-Raphson root-fndng algorthm s very fast, stable, and ndependent of ntal estmate for ths analyt soluton, thus the soluton for a and s ' from ths method s used as an ntal estmate for the fnte element soluton method. For the fnte element method, the values for dθ d ln ri and dr dr are determned from a lnear regresson appled to the alulated data for the fnte element soluton for the urrent estmate of a and s '. The applaton of ths lnear regresson to the data s shown n Fgure 6.3. a b Fgure 6.3: Plot of measured and alulated a log of dstane tmes AC ntensty, lnri, and b phase,?, versus soure to detetor dstane, r. The slope of the lnear regresson to the dθ d ln data represents the and terms. The nterept terms from the regresson ndate dr drri a dfferene n ntal soure strength and ntal phase between the measured and alulated data. For both methods analyt and fnte element of determnng the alulated values, a Newton-Raphson method s used where the frst dervatve term n the mnmzaton s approxmated numerally. 64 For larty and ease of notaton, we make the substtutons: d ln ri α =, dr d ln rio α o = and 6.0 dr 97

112 dθ φ =, dr φ = o dθ o dr 6. Followng the Taylor seres expanson method for dervng Newton's method for rootfndng, we expand a and φ as funtons of for some nearby pont 0 : d α = α d α d φ = φ d φ and throw out hgher order terms. We are nterested n the value of a and s ' where equaton 6.6 and 6.7 are true, suh that α = α o and φ = φ o. In ths ase, we fnd that d 0 α 0 α d α d 0 φ 0 φ d φ We now hange ths to an teratve sheme where = 0 = +. Solvng for?, we arrve at the standard Newton-Raphson forms: α = d d 0 α α φ 0 φ =. 6.7 d φ 0 d In ths algorthm, we use the standard numer approxmaton to the dervatve terms, d d d d α α α δ = φ φ φ δ = + + δ δ

113 where d s some small value d =0.000 for a and d =0.00 for s ' for our ase. Substtuton of these terms nto eq. 6.6 and 6.7 leads to the fnal teratve forms = α [ α α ] 0 0 α 0 δ + δ 6.20 [ φ φ ] 0 δ =. 6.2 φ φ + δ 0 0 In prate, for eah teraton we mplement a d n a and alulate the update to a and s ', followed by a d n s ' and update a and s '. Ths mplementaton of the Newton-Raphson method onverges for all ases of good measurement data and s hghly repeatable. 6.D. Results 6.D.. Pratal Consderatons 6.D... Homogeneous Calbraton Fgure 6.4 shows systemat offset from a slght dfferene n algnment of two optal fbers wth the laser soure fber durng multplexng. Ths offset s onsstent over a perod of weeks and only hanges durng system modfatons/mantenane suh as re-algnment of the laser. The resultant dfferene data Fg between the measured Fg.6.4.a. and the alulated values Fg.6.4.b. are used as a albraton fator n the reonstruton algorthm. a b lnintensty lnintensty lnintensty Fgure 6.4: Plot of a lnintensty data at 6 detetor stes showng offset due to algnment dfferenes, b alulated data from fnte element soluton, and dfferene between a and b. Dfferene data s used as the 'albraton' fator

114 6.D..2. Heterogeneous Startng Value Smulatons were performed to demonstrate the effet of dfferent startng values durng reonstruton of a heterogeneous objet. Images for three dfferent ntal optal property estmates 0%, 0%, and 50% error from the atual average optal propertes are ompared n Fgure 6.5 after one teraton. The algorthm onverges to the orret mage 2: absorbng objet wth Gaussan profle durng the frst teraton for an ntal estmate whh s equal to the average optal propertes of the heterogeneous test objet Fg.6.5.a,d. When the ntal estmate s sgnfantly removed from the atual average optal propertes, the algorthm takes longer to onverge. Ths slowdown s evdent n the other mages n Fgure a b d e f Fgure 6.5: Image after frst teraton of reonstruton of absorbng objet wth Gaussan profle wth a ntal estmate equal to average optal propertes, b 0% error n ntal estmate, and 50% error n ntal estmate. The vertal axs unts are n mm -. d, e, and f are profle plots along a vertal lne through the enter of mages a, b, and respetvely. 6.D..3. Offset Offset between the natural log of ntensty profle of a alulated and measured phantom due to long term drft n the T:Sapphre laser ntensty s shown n Fgure 6.6. The offset s aounted for by omparson of the hanges n offset between the homogeneous albraton phantom and the measured heterogeneous objet. In the extreme ase shown n Fgure 6.6, 00

115 the offset n ntensty s almost two natural log unts. In general, ths offset s dfferent between the homogeneous albraton data and the expermental measurement data even wthout the presene of laser drft lnintensty Calbrated Measured data Calulated Data Fgure 6.6: Plot demonstratng measured data wth overall offset due to long term drft of laser ntensty. The average dfferene s used to orret ths offset. 6.D..4. Determnaton of boundary oeffent values The value of a equaton 2.5 for the boundary ondtons s set to provde the best ft between the measured and alulated data. The value for a n the past was set to a sngle value based on a seres of experments. In the urrent mplementaton, a s set based on the measured data from the homogeneous albraton phantom. The homogeneous ft s performed for a seres of values of a +, 3+3, 0+0,..., ; the value of a s hosen based on the mnmum squared error between the measured and alulated data for the best ft values. 6.D.2 Testng of Homogeneous Fttng Algorthm Usng repeated measurements of the same phantom, the results of the homogeneous fttng algorthm Method B n Fgure 6.2 have been shown to have an average devaton of 0.5% even n the presene of 5% measurement nose. Ths ompares very favorably wth our prevous approah Method A n Fgure 6.2, whh dd not take full advantage of the data averagng, where 5% measurement nose translated to 5% average devaton n the 0

116 homogeneous ft. Ths derease n devaton s demonstrated n Fgure 6.7 whh shows data for a phantom study nvolvng trplate measurement of objets wth nreasng amounts of blood. The absorpton oeffent nreases whle the satterng oeffent remans onstant. The study s performed at three wavelengths and the slope of the lne of nreasng absorpton wth added blood s ompared wth expeted values of the molar extnton oeffent from Wray et al. 52 n Table 6.. a b mu-s mm nm 800 nm 830 nm ml blood / lter 0.5% ntralpd mu-s mm nm 800 nm 830 nm ml blood / lter 0.5% ntralpd d mu-a mm nm 800 nm 750 nm mu-a mm nm 800 nm 750 nm ml blood / lter 0.5% ntralpd ml blood / lter 0.5% ntralpd Fgure 6.7: Homogeneous fts to measured data for the two methods desrbed n Fgure 6.2: a Method A satterng oeffent data, b Method B satterng oeffent data, Method A absorpton oeffent data, d Method B absorpton oeffent data. Eah onentraton was measured three tmes at eah of three wavelengths. 02

117 Molar Extnton Coeffent mm - mm - Wavelength Wray et al. data Method B Perent dfferene 750 nm 3.0E E % 800 nm 4.50E E % 830 nm 5.30E E % Table 6.: Comparson of molar extnton oeffent for oxygenated hemoglobn measured by Wray et al. 52 wth results from use of homogeneous fttng algorthm Method B. based on data from phantoms nreasng hemoglobn onentraton Fgure 6.7.d. 6.D.3 Modfed Imagng Algorthm The modfed mage reonstruton algorthm s shown shematally n Fgure 6.8. Ths modfed algorthm uses the three pratal magng onsderatons dsussed n ths hapter. These modfatons are denoted n the fgure by the thker border lnes. Fgure 6.8: Shemat of nputs to mage reonstruton algorthm from homogeneous albraton and ntal estmate alulaton. Inputs from albraton methods are dsplayed n bold boxes. 03

118 Chapter 7: Separaton of satterng and absorbng heterogenety 7.A. Introduton Separaton of absorpton and satterng heterogenety s requred for quanttatve magng of absorbng onsttuents suh as hemoglobn, lpds, and water n the breast. The ablty to separate fully absorpton and satterng heterogenety n tssue provdes not only the purest mage of the absorpton oeffent, but also a means of magng satterng heterogenety whh ould ontan nformaton relevant to tssue struture. In optal tomography, separaton of absorpton and satterng heterogenety s onfounded by the ll-posed nature of the mage reonstruton algorthm. Usng both omputer smulatons and phantom studes, a method to better mage absorpton and satterng nlusons ndependently was mplemented. The mproved algorthm nvolved three steps: frst the adopton of log-ampltude-and-phase data versus the orgnal use of real-and-magnary data. Seond, the matrx dagonal was normalzed to one usng a standard Marquardt sheme. In addton, further weghtng of phase wth respet to log ampltude based on modulaton frequeny was found to sgnfantly mprove separaton of absorpton and satterng heterogenety. 7.B. Hstoral motvaton 7.B.. Real and magnary algorthm In the past, the magng algorthm at Dartmouth had dffulty separatng absorpton and satterng heterogenetes. Prevous reported experments by Jang et al. 56,58 nvolved exlusvely nlusons of equal nreases n a and s '. Testng of absorpton-only or satterng-only nlusons was not reported. From the studes reported n ths hapter, t s possble that n the "real-and-magnary" algorthm, the effet of the ampltude data may have been domnant over phase nformaton. Ths orresponds to an algorthm whh would behave smlarly to one whh used DC-data only. Both satterng and absorbng nlusons have smlar attenuaton based on ther ontrast levels n the dffuse regme, suh that wth a 04

119 DC algorthm, absorbng-only, satterng-only, and absorbng-and-satterng nlusons would all reonstrut as nlusons wth satterng-and-absorbng ontrast. There were a number of speal features n the real-and-magnary algorthm e.g. total varaton mnmzaton, least-squares-vetors weghtng sheme, spatal flterng whh made dret omparson wth the urrent algorthm dffult. Instead, n ths thess there was an attempt to mprove the phase-and-ampltude algorthm as desrbed below. 7.B.2. Prevous phase and ampltude algorthm The magntude of real-and-magnary data s on the order of 0 6 tmes dfferent between near and far detetor stes; thus, t s hghly advantageous to use logarthm data n reonstruton. For ths reason, a phase-and-ampltude-based reonstruton algorthm was developed by Bran Pogue, whh mproved onvergene of the algorthm, but n ts ntal form worked exlusvely on test objets wth absorpton-only nlusons. In ths algorthm, the senstvty matrx, J T J, see seton 2.B.3 was domnated by terms n the absorpton regon as desrbed n seton 7.C. suh that wth a regularzaton parameter of equal weghtng n both the satterng and absorpton regons, all hanges n the reonstruted mage were onfned to the absorpton mage. Hene, wth ths algorthm, a satterng objet would be reonstruted as an absorbng objet, just as n a DC reonstruton algorthm a pure-satterng nluson would lkely be reonstruted as both an absorber and a satterer. For the prevous phase-and-ampltude algorthm, phantoms and smulatons where t was known that there were no satterng heterogenetes were maged aurately; however, t s unlkely that there s no satterng heterogenety n the human breast and wth ths algorthm, any suh satterng heterogenety would translate to an absorbng objet. The normalzaton and empral weghtngs desrbed n ths hapter address ths problem. 7.C. Improved algorthm 7.C. Bakground 05

120 Lght s attenuated smlarly for both absorpton and satterng heterogenetes makng quanttatve absorpton magng hallengng. In fat, Arrdge and Lonheart, 99 propose that t s mpossble to separate satterng and absorpton heterogenetes no unque soluton from tomograph DC data. The use of frequeny-doman and tme-resolved tehnques to obtan path length nformaton, n ombnaton wth model-based teratve reonstruton methods, should allow for separaton of absorpton and satterng heterogenetes 29 assumng that we know the refratve ndex and t s spatally nvarant. For the frequeny-doman magng system at Dartmouth, the omplete separaton should be pratally ahevable. For the reonstruton method used at Dartmouth Chapter 2, one major ssue s the weghtng of the absorpton and satterng setons as well as the phase and ampltude terms of the senstvty matrx, J T J, relatve to the regularzaton parameter. In our ase, regularzaton an never be drven to zero, thus regularzaton of the J T J matrx effets the atual relatonshp between the measurements and the estmated propertes. The J T J matrx an be thought of as havng a seton relatng to absorpton and a seton relatng to satterng as shown n Fgure 7.. The relatve weghtng of the two setons determnes the extent to whh dfferenes between measured and alulated data Φ o Φ n Chapter 2 s translated nto hanges n the a and s ' mages. Wthout any normalzaton of the two setons to one another, all data perturbatons are translated nto hanges n the a mage for the phase-and-ampltude reonstruton. Ths s beause for breast tssue, s ' s on average 00 tmes larger than the a. Lkewse D ~/3 s ' s about 30 tmes greater than a Small hanges n the a translate nto larger hanges n alulated data than the equvalent hange n s ' or D.e. Φ a >> Φ D, hene the absorpton seton of the Hessan s muh larger than the satterng seton. On average, the dagonal terms are 900 proportonal to D/ a 2 06

121 07 tmes larger n the absorpton seton than the satterng seton of the Hessan; thus, wth the use of a sngle regularzaton parameter, the absorpton seton s domnant. = + NM D D I 2 2 ln θ = + NM NN NN D D I 2 2 ln θ = + NM NN NN D D D I D I ln ln θ θ = + NM NN NN D D D I D I ln ln θ θ = + NM a a I 2 2 ln θ = + NM NN a NN a I 2 2 ln θ = + NM NN a a NN a a I I ln ln θ θ = + NM a NN a a NN a I I ln ln θ θ = + NM a a D I D I ln ln θ θ Satterng Seton Absorpton Seton Cross terms Seton Cross terms Seton = + NM NN a NN NN a NN D I D I ln ln θ θ = + NM NN a NN a D I D I ln ln θ θ = + NM a NN a NN D I D I ln ln θ θ = + NM a a D D I I ln ln θ θ = + NM NN NN a NN NN a D D I I ln ln θ θ = + NM NN a NN a D D I I ln ln θ θ = + NM NN a NN a D D I I ln ln θ θ Fgure 7.: Dagram of senstvty matrx, J T J. The parttons llustrate the satterng and absorpton seton of the matrx for NN number of nodes and NM measurement stes. ln j D I and j a θ are the dervatve of the ampltude wth respet to dffuson oeffent D and the dervatve of phase shft wth respet to absorpton oeffent a, respetvely, for measurement ste at node j. 7.C.2 Normalzaton Wth the normalzaton of the J T J matrx as desrbed n Seton 2.C.3, the weghtng of absorpton versus satterng based reonstruton s balaned. However, wth only ths normalzaton, separaton of the satterng and absorpton heterogenety takes many teratons

122 even n nose-free smulaton. Indeed, wth normalzaton, the phase and ampltude reonstruton tends towards reonstrutng both satterng-only and absorpton-only objets as both satterng- and-absorbng objets n early teratons smlar to a DC algorthm and wll only onverge to the true dstrbuton f the regularzaton parameter s suffently low. 7.C.3 Weghtng of phase terms For the J T J matrx, eah element of the matrx has a seres of phase and ampltude terms summed together. For the modulaton frequeny of 00 MHz, the magntude of hange n phase for a hange n optal property s muh smaller than the magntude of hange n ampltude for the same optal property hange. Wth regularzaton, the ampltude term wll domnate. Sne these terms are all summed n the J T J matrx, the normalzaton sheme does not allevate ths ssue. Indeed wthout treatment, the phase term an be overshadowed due to ths dfferene n magntude of the dervatve term dependng on the relatve sze of the regularzaton parameter. Ths explans the trend of the normalzed phase-and-ampltude algorthm to reonstrut everythng as both satterng- and-absorbng objets sze -- the algorthm s atng n the same manner as an ampltude only suh as a DC mager reonstruton where lght s attenuated smlarly for both absorpton and satterng heterogenetes. More formally, we an fnd the magntude of the dfferene n phase and ampltude terms by the root mean square RMS value of the ln I j terms and ompare t wth the RMS value of the θ j terms. We defne 2 NN NM j 2 2 j 2 ln I = ln I NN NM 7. 08

123 θ θ 2NN NM j = j NN NM 7.2 where ln I 2 and θ 2 are essentally the average magntude of the ampltude and phase terms n the Jaoban matrx. These term depends somewhat on the optal propertes of the objet beng maged, but for values typal of breast tssue, ln I θ at 00 MHz. Ths rato appears to be related prmarly to the dependene of phase shft on modulaton frequeny and dereases by about ½ at 200 MHz. Ths sx tmes dfferene n magntude between the phase and ampltude dervatve terms esalates nto an approxmately 36 tmes dfferene n the squared terms n the J T J. Wthout ompensaton, regularzaton an lead to negaton of the phase term. One soluton s to multply the phase term everywhere by ln I θ 2 2. In other words, multply all θ j terms n the Jaoban matrx by 6 and the phase terms? n the alulated and measurement data, Φ Φ o update of the optal propertes,?, n the equaton, array. Ths weghtng has no effet on the alulaton of the T T o [ J J ρi] = J Φ Φ + ρ when?=0. Ths beomes lear n rewrtng the equaton for?=0 09

124 Φ T Φ Φ = T Φ Φ o 7.5 sne the phase terms fall equally on both sdes. The effetveness of the transformaton les n the fat that? annot be drven to zero and thus t s essental that phase and ampltude terms be on the same order of magntude for regularzaton to be judous. When? s zero or suffently low, however, ths weghtng beomes unneessary. 7.C.4. Results In order to llustrate the effet of the modfatons to the phase-and-ampltude reonstruton program, the results of three smulatons are presented. The dfferenes between the last two methods are most strkng after the frst teraton of reonstruton or for hgh regularzaton. For these smulatons, two test objets are used, one wth a sngle nluson at 2: ontrast n a, and the other wth a 2: ontrast n both a and s '. In Fgure 7.2, the reonstruted a and s ' mages are shown for a one teraton reonstruton for the absorbng-only nluson usng a,b the orgnal non-normalzed phase-and-ampltude method,,d the method wth normalzed J T J matrx, and e,f the urrent method where the J T J matrx s normalzed and the phase terms are weghted wth respet to the ampltude terms. In Fgure 7.3, the results are plotted n the same manner for the nluson wth 2: ontrast n both a and s '. 0

125 a a mage b s ' mage a mage d s ' mage e a mage f s ' mage Fgure 7.2: One teraton reonstrutons for a smulated absorbng-only nluson 2: ontrast n a. The absorpton and redued satterng oeffent mages are presented respetvely usng a,b the orgnal non-normalzed phase-and-ampltude method,,d the method wth normalzed J T J matrx, and e,f the urrent method where the J T J matrx s normalzed and the phase terms are weghted.

126 a a mage b s ' mage a mage d s ' mage e a mage f s ' mage Fgure 7.3: One teraton reonstrutons for a smulated nluson wth 2: ontrast n both a and s '. The absorpton and redued satterng oeffent mages are presented respetvely usng a,b the orgnal non-normalzed phase-and-ampltude method,,d the method wth normalzed J T J matrx, and e,f the urrent method where the J T J matrx s normalzed and the phase terms are weghted. These smulatons llustrate the effet of the normalzaton and weghtng sheme. Wthout normalzaton, the phase-and-ampltude algorthm reonstruts all hange n the absorpton mage. Wth normalzaton only, ampltude terms domnate suh that the tendeny s to reonstrut everythng as both satterng- and-absorbng objet. Wth the weghtng of the phase terms, reonstruton s balaned. As the regularzaton parameter dereases, however, ths weghtng wll beome muh less mportant. An addtonal smulaton study for an objet wth three nlusons s presented n Fgure 7.4. The reonstruton s presented for the urrent reonstruton method usng both the normalzaton and weghtng. A small amount of rosstalk of the satterng nlusons 2

127 ontrast nto the absorpton mage exsts and, as s presented n later hapters, the satterng mage appears somewhat sharper than the absorpton mages. a Orgnal a mage b Orgnal s ' mage Reonstruted a mage d Reonstruted s ' mage Fgure 7.4: a Orgnal absorpton oeffent a and b the redued satterng oeffent s ' smulated mage wth three embedded objets. Fgure shows the reonstruted a mage and d the s ' mage. 7.D. Phantom studes 7.D.. Methods/materals Tssue-smulatng phantoms were onstruted to assess the ablty to quanttatvely mage objets of varyng absorpton and satterng ontrast embedded wthn a hghly satterng medum. A sold 86 mm dameter ylndral phantom Fgure 7.5 was onstruted n a manner desrbed by Frbank et al. 94 wth Inda nk added for absorpton and Ttanum doxde added as a satterer. Three ylndral holes 7 mm dameter were drlled n the phantom for studyng nlusons of dfferng ontrasts. The sold phantom was measured to have absorpton oeffent a of mm - and redued satterng oeffent s ' of.0 mm -. Inda nk absorber and Intralpd satterer n water was added to the three holes to 3

128 form embedded objets wth varyng optal propertes. For ths study, one hole was vared n absorpton ontrast A, one hole vared n satterng ontrast B, and the thrd hole vared n both satterng and absorpton ontrast C over a range of ½: to 2½:. A seond 84 mm ylndral homogeneous phantom a = and s ' =.3 was used for albraton. Fgure 7.5: An 86 mm dameter sold ylndral tssue-smulatng phantom wth three 7 mm dameter ylndral holes s shown. Absorbng-only ontrast was added to hole A, satterng-only ontrast to hole B, and absorbng and satterng ontrast to C. Bakground optal propertes were estmated to be a =0.006 mm - and s '=.0 mm -. 7.D.2. Results The reonstruted a and s ' mages for the phantom study are shown n Fgure 7.6 and the reovered value at the enter of eah embedded objet s plotted n Fgure 7.7. From the plots, t appears that both objets of nreasng satterng and absorpton an be quanttatvely reovered wthn 25% of ther expeted values. No measurable rosstalk <% of the absorbng objet appears n the satterng mage, however, a loalzed enhanement of 30% of the ontrast of the satterng objet s evdent n the absorpton mage. An erroneous regon of dereased a and s ' s reonstruted at the enter of the mages wth 2.5: ontrast nlusons; ths entral "shadow-lke" underestmaton ours next to hgh ontrast objets and would lkely appear for n vvo mages wth hgh ontrast nlusons. 4

129 y-poston mm a b 0.5 : : x-poston mm x-poston mm a /mm y-poston mm s /mm y-poston mm : x-poston mm a /mm y-poston mm d.5 : x-poston mm s /mm y-poston mm e 2.5 : x-poston mm a /mm y-poston mm f 2.5 : x-poston mm s /mm Fgure 7.6: Reonstruted mages of a,,e a and b,d,f s ' for ontrast levels of a,b ½:,,d ½:, and e,f 2½: for both oeffents are dsplayed. In the upper entral hole C, both a and s ' are nreased together, whereas n the left hole A only a s nreased, and n the rght hole B only s ' s hanged. The x and y axes are poston n mllmeters and the unts of the sale bars are nverse mllmeters. 5

130 a b Reonstruted absorpton ontrast Expeted Abs. Only A Sat. & Abs.C Expeted absoprton ontrast Reonstruted satterng ontrast Expeted Sat. Only B Sat. & Abs.C Expeted satterng ontrast d Reonstruted absorpton ontrast Expeted Sat. Only B Reonstruted satterng ontrast Expeted Abs. Only A Satterng ontrast Absorpton Contrast Fgure 7.7: Comparson of reonstruted and expeted ontrast at the enter of the reonstruted objets n Fgure 7.6. The reonstruted values for a absorpton and b satterng oeffent are plotted versus the expeted results for embedded objets wth ontrast n A absorpton-only, B satterng-only, and C absorpton and satterng. The reonstruted rosstalk n terms of absorpton ontrast for the satterng-only objet and d satterng ontrast for the absorpton-only objet are also dsplayed. 7.D.3. Dsusson The phantom studes ndate that for embedded nlusons of suffent sze n ths ase a ylnder of /25 of the bakground ross-setonal area, absorpton and satterng heterogenety an be reovered quanttatvely wthn 25% of the expeted peak value. A dsernble enhanement wthn the absorpton mage was ndued by the satterng objet. 6

131 More aurate quanttatve haraterzaton of absorbng and satterng nlusons has been aheved n sngle-nluson phantom studes, 60 however, the satterng rosstalk nto the absorpton mage remans. Ths effet s somewhat more pronouned n expermental studes than smulatons and should be explored further. Whle t s not expeted that the breast wll have satterng varatons of suffently hgh ontrast to appear as absorbers of dagnost onern, further refnements of the algorthm or data olleton ould mnmze ths effet. 7

132 Chapter 8: Heterogeneous Phantoms and Contnually-varyng objets 8.A. Introduton Computer smulaton and phantom studes are generally performed on test objets whh onsst of a homogeneous bakground wth one to three nlusons. These nlusons are also usually homogeneous, but at some level of ontrast wth the bakground.e. a step hange from the bakground. Whle these studes are essental for understandng the nature of the lmtatons of the algorthm, and provde an easy means for phantom onstruton, they do not represent the true omplex nature of tssue. For ths reason, omputer smulaton s used n ths hapter to address nlusons wthout a step hange n optal propertes or n other words "ontnuously varyng nlusons". Also n the same seton, objets wth rregular shaped nlusons are addressed. In part C., the effet of a heterogeneous bakground s addressed n both smulaton and phantom studes usng exsed tssue. 8.B. Contnuously varyng and rregularly shaped objets 8.B.. Overvew Dffuson tomography s generally tested n numeral smulatons usng a step hange between bakground and embedded objets. Ths abrupt hange does not realstally smulate breast tssue optal property hanges. Smulatons were performed on several dfferent ontnuously varyng optal property dstrbutons and ompared wth those obtaned from dsrete step hange nlusons. Spefally, a Gaussan profle, an rregularly shaped nluson, a rng nluson see Chapter 9 for results, and a rular step hange nluson are used n the numeral smulatons. The volume of the target zone s kept approxmately onstant for the varous test ases and the nlusons are normalzed to have the same maxmum and mnmum optal property values. In onstrutng the step nluson and the Gaussan nluson, the wdth at half maxmum of the Gaussan profle s approxmately equal to the dameter of the step nluson. 8

133 8.B.2. Methods and results An objet wth a Gaussan profle nluson, an rregularly shaped nluson, a rng nluson, and a rular step-hange nluson were reonstruted usng numeral smulatons. The objets were reonstruted wth varyng levels of nose added to the smulaton data. The nlusons were, n general, reonstruted as somewhat blurred versons of the orgnal. Fgure 8. ompares the reonstruton of an objet wth a Gaussan profle and a rular step hange nluson. The orgnal mages, dsplayed n Fgure 8.a step nluson and 8.b Gaussan nluson, had the same maxmum and mnmum absorpton oeffent values, the dameter of the step nluson was equal to the wdth at half maxmum of the Gaussan nluson, and the volume of the objets was approxmately the same. The orgnal values for the mages were onstruted by usng an 84 mm dameter bakground typal of normal breast tssue values ontanng a 7 mm dameter nluson wth a 3: nrease n hemoglobn onentraton smulated for a measurement at 800 nm. Fgures 8. and 8.d show horzontal profle graphs through the enter of the mages. 3% nose was added to the measurement data pror to the fnte element reonstrutons. The mages were reonstruted usng 3 teratons and a onstant regularzaton parameter. Fgures 8.e and 8.f show the reonstruted mages for the step nluson and Gaussan nluson; the horzontal profle graphs are shown n Fgures 8.g and 8.h. The average nodal error for the reonstruton of the Gaussan nluson ompared wth the orgnal values was.0% and the average nodal error for the reonstruted step nluson was.2%. 9

134 a b 00 Orgnal step objet a Orgnal Gaussan objet a d e f Reonstruted step objet a Reonstruted Gaussan objet a g h Fgure 8.: Orgnal and reonstruted absorpton oeffent mm - mages of an objet wth a Gaussan profle and a rular step nluson. 3% nose was added to the smulated measurement data pror to mage reonstruton. a Orgnal rular step objet; b orgnal Gaussan objet; horzontal profle of a; d horzontal profle of b; e reonstruted mage of a; f reonstruted mage of b; g horzontal profle of e; h horzontal profle of f. X-Y oordnates are n unts of mm. 20

135 In addton, objets wth nlusons of rregular geometry were study usng omputer smulaton. True to the sprt of Dartmouth College, a test objet was generated wth a large 2: ontrast "D" n the a mage and a 2: ontrast "C" n the s ' mage as shown respetvely n Fgure 8.2 a and b. The reonstruted a and s ' mages for zero added nose are presented n Fgure 8.2 and d. a b d Fgure 8.2: Smulaton of objets wth dfferng rregularly shaped nlusons n a and s '. The orgnal a and s ' property dstrbuton s shown n a and b, wth the reonstruted mages n and d. The sale bars are n unts of mm -. 8.B.3. Dsusson One of the goals of ths study was to assess the ablty of our reonstruton algorthm to mage objets wth ontnuously varyng optal propertes. Even n the presene of hgh nose, ontnuously varyng nlusons and rular step nlusons an be reonstruted quanttatvely. The reonstruted nluson, however, s blurred n omparson wth the orgnal. Ths s a result of the optal dffuson proess n ombnaton wth the underdetermned system resultng from havng a lmted number of soures and detetors and 2

136 relatvely oarse mesh spang. Both the number of detetors and soures and mesh spang were hosen to math the ondtons of our urrent expermental system. Potentally, less blurred mages ould be obtaned wth future systems whh have more soures and detetors and lower measurement nose. Interestngly, a Gaussan nluson wth a wdth at half maxmum smlar to the dameter of a rular step nluson and an approxmately equal volume reonstruts smlarly. Indeed, due to the blurrng nature of dffuson tomography, the Gaussan nluson reonstruts slghtly more aurately than the step nluson. In addton, objets wth nlusons of arbtrary geometry were reonstruted. In the same manner, blurred reonstrutons of the orgnal were obtaned. It appears that less of a blurrng effet s evdent n the reovery of the satterng nluson. In general, we observe a sharper reonstruton for a satterng nluson than an absorbng nluson for the method used for ths thess. 8.C. Heterogeneous Bakground and Inlusons 8.C.. Overvew Smulatons and phantom studes are generally tested usng one to three nlusons wthn a homogeneous bakground. In vvo magng of abnormaltes n the breast does not math ths model as both normal and dseased breast tssue s generally heterogeneous. The onstruton of heterogeneous phantom materals s dffult and the knowledge of atual optal propertes a, s ' of the breast on ths level of heterogenety an be hallengng. One method of embeddng objets wthn a heterogeneous bakground s to use exsed tssue. In ths study, a seres of exsed breast tssue samples were measured for average optal propertes and pork musle tssue was aqured and embedded n the breast tssue as a moderate ontrast objet smlar to that of tumors n the breast. Images from these 22

137 experments are ompared wth omputer smulatons of embedded objets n heterogeneous meda. 8.C.2. Methods 8.C.2.. Computer smulatons Whle generatng phantoms wth known amounts of heterogenety s dffult, omputer smulatons an be performed on any dstrbuton. Smulatons were performed for a 00 mm rular objet a = mm -, s ' =.0 mm - ontanng a sngle 20 mm dameter nluson wth 2: ontrast n absorpton oeffent and a :2 ontrast n satterng oeffent. Heterogenety was ntrodued to the entre objet by addng a perentage of a unformly dstrbuted random number between one and negatve one to the optal property values at eah node. Spefally, the perentage of heterogenety was vared from 0% to 75% of the optal propertes. The nose added to the measurement data was determned from an estmate of expermental measurement nose.e. % and the reonstruton parameters were seleted from prevously determned optmal parameters for the expermental setup as desrbed n Chapter 3. 8.C.2.2 Heterogeneous tssue phantoms Exsed breast tssue was obtaned from breast reduton surgery and fresh pork musle was purhased ommerally. The breast tssue was vsbly heterogeneous and no effort was made to lean or homogenze the tssue beyond washng wth water. The samples were plaed n thn plast bags wthn the data aquston system n order to measured the "average" optal propertes as shown n Fgure 8.3. An approxmately 30 mm ube of the pork was embedded wthn a 86 mm dameter "ylnder" of breast tssue at the measurement plane. Data were aqured from the sample and mages of a and s '. were reonstruted. The sample was rotated 90 degrees and maged agan to verfy the reovered property dstrbuton. 23

138 Fgure 8.3: Exsed breast tssue ontaned n a thn plast bag s plaed wthn the fber opt nterfae. The sxteen soure and detetor fbers are radally postoned n dret ontat wth the sample. 8.C.3. Results 8.C.3. Computer smulatons The a and s ' mages from the smulatons are dsplayed n Fgure 8.4. The mages are ordered wth nreased perentage of heterogenety from 0% to 75%. The root mean square error between the orgnal and reonstruted mages s lsted n Table 8.. Also, error n the reonstruted absorpton and satterng value at the enter of the nluson s shown n the table. Normalzed Standard Devaton Reonstruted ontrast Amount of Added Orgnal Dstrbuton Reonstruted Image of embedded objet Heterogenety Absorpton Satterng Absorpton Satterng Absorpton 2: Satterng 0.5: Table 8.: The normalzed standard devaton dvded by the mean of the spatal propertes of the mages n Fgure 0.4 are tabulated. These values are ompared wth the reonstruted ontrast of the embedded objet for dfferent levels of added heterogenety. The normalzed standard devaton s the same untless sale as the reonstruted ontrast, thus, for a devaton of 0.20, an objet wth.2 or 0.8 ontrast would be at the level of plus or mnus one standard devaton. 24

139 Fgure 8.4: The frst two olumns are the orgnal absorpton and satterng dstrbutons pror to smulaton. The seond two olumns are the reonstruted absorpton and satterng mages. Eah suessve row represents an nreasng level of added heterogenety to the orgnal dstrbuton n the frst row. All absorpton and satterng mages are dsplayed on the dental sale. 8.C.3.2 Heterogeneous tssue phantoms The average optal propertes of eah sample were measured usng a homogeneous fttng algorthm see Chapter 6. For the exsed breast tssue they were measured to be a = 25

140 0.005 ±.002 mm - and s ' =.3 ± 0.2 mm -, whle for the pork they were a = 0.04 ±.004 mm - and s ' = 0.6 ± 0.2 mm -. The resultng mages for the pork sample embedded wthn the breast tssue are shown n Fgure 8.5. A seond set of mages was obtaned after the sample was rotated nnety degrees relatve to the fber opt nterfae. The standard devaton of the mage and entral value of the embedded pork are reported n Table 8.2 and ompared to the ontrast from the homogeneous ft values. Normalzed Standard Devaton Reonstruted ontrast Reonstruted Image of embedded objet Sample Absorpton Satterng Absorpton 2.8: Satterng 0.5: 0 degrees degrees Table 8.2: Values from homogeneous ft ompared wth reovered entral values of embedded pork. Also, the normalzed standard devaton desrbed n Table 8. of the entre mage s reported. 26

141 Fgure 8.5: a Reonstruted absorpton and b satterng mages of embedded pork heterogenety wthn exsed breast tssue. and d are the profle graphs through a and b respetvely. e-h are dental mages for the ase where the sample was rotated 90 degrees ounterlokwse. 27

142 8.C.4. Dsusson A prelmnary assessment of mage reovery of an objet embedded n a heterogeneous bakground was performed n smulatons and phantom experments usng freshly exsed breast tssue. The smulatons ndated that even for substantal amounts of added heterogenety approahng 75% a 20 mm 2: ontrast nluson s vsble wthn a 00 mm dameter objet. The entral value of the nluson remans outsde 2.5 tmes the standard devaton of the mage for approxmately 50% added heterogenety n absorpton and 75% n satterng for ths spef ase 2: ontrast 20 mm nluson n a 00 mm objet wth random added heterogenety. A three entmeter ube of pork embedded n exsed breast tssue was maged to smulate heterogenety n expermentally aqured data. The pork was estmated to be 2.8: ontrast n a and 0.5: n s '. The embedded pork s learly vsble n the reonstruted mages. The reonstruted ontrast of the pork s wthn 25% of expeted values. It appears from the 90 degree rotated sample that the struture n the resultng mages rotates wth the embedded objet, suggestng that the other strutures n the mage are related to the heterogenety n the tssue not an magng artfat. In ths type of experment there s onsderable potental for spatal unertanty about the pork heterogenety loaton, beause of the flud-lke movement of these tssues. A more systemat study of ths type, where the embedded heterogenety loaton s fxed n plae more rgdly, mght provde better auray. Further studes are requred for smaller and dfferent ontrast objets embedded n heterogeneous meda. For small low-ontrast nlusons, deteton by examnng a sngle mage may be dffult. Smlar to nterpretaton of x-ray mammography, however, mproved deteton of suh nlusons ould be aheved by dentfyng developng objets n mages of the same subjet olleted over tme e.g. yearly vsts. From ths prelmnary study t 28

143 appears that moderate sze objets of two tmes ontrast should be vsble from a one-tme mage. The reonstruton algorthm makes no assumpton on the homogenety of the optal property dstrbuton and thus should be apable of reoverng the optal propertes of nlusons wthn heterogeneous dstrbutons. Beause the optal propertes wthn the breast lkely are heterogeneous on a mrosop sale, reovered mages are assumed to be an averaged representaton of the true dstrbuton. In ths partular study, the reovered a and s ' of an nluson s approxmately onstant even wth 50% to 75% added heterogenety. Ths suessful reovery of objet optal propertes n the presene of heterogenety provdes promse for quanttatve haraterzaton of a and s ' and onsequently hemoglobn parameters wthn the breast. 29

144 Chapter 9: Funtonal Imagng 9.A. Introduton Absorpton of near-nfrared lght n breast tssue s prmarly related to hemoglobn blood onentraton and oxygen saturaton whle there s also nterest n estmatng lpd and water ontent. Breast aners and other tumors have been shown to have sgnfant ontrast from the surroundng healthy tssue, suh that quanttatve magng of these funtonal parameters ould potentally be useful n detetng and dstngushng bengn and malgnant breast aner tumors. In ths hapter, spetrosop magng methods are presented whh are used to demonstrate the potental for quanttatve haraterzaton and magng of hemoglobn parameters n both smulaton and phantom studes. 9.B. Theory 9.B.. Tssue Charatersts Aordng to Whte et al., 00 the average healthy human female breast s omposed of 33% mammary gland and 66% adpose tssue. From Woodard and Whte, 66 the mammary gland s omposed on average of 5% water and 3% lpds by mass; the average for adpose tssue s 2% water and 7% lpd. Usng ths data, average breast tssue an be roughly approxmated as ontanng 3% water and 57% lpds. 66,00 These parameters are approxmate and n healthy breast tssue vary from woman to woman; n addton, water and hemoglobn ontent are lkely somewhat lower on average n post-menopausal than premenopausal women. There appears to be an overall delne n breast tssue towards hgher fat lpd ontent wth age. 0,02 Breast aner tumors are presumed to have hgher blood volume than healthy tssue, due to rapd ell growth, and hene angogeness, espeally at the tumor perphery. 0,44 Several soures have onfrmed an nrease n hemoglobn onentraton wthn anerous tumors. 0,3,4,35,44 Tromberg et al. 3 measured an approxmately 2: nrease n hemoglobn 30

145 onentraton n breast tumors as ompared to healthy breast tssue. Profo et al. 0 found that an exsed breast aner tumor had a 4: nrease n blood volume at the tumor edge and lttle nrease of blood volume n the enter. Furthermore, several groups have shown that anerous tumors tend to have lower po 2 levels than healthy tssue. 44 In a summary paper by Vaupel et al., 44 breast aner tssue s stated to have.4 to 4.4 tmes lower po 2 than normal breast tssue. It an be hypotheszed that ths po 2 derease orresponds to a lower hemoglobn oxygen saturaton. It s unlear whether ths oxygenaton derease would be onfned to the entral porton of a tumor or exst n the perphery as well. In addton, Okuneff et al. 45 demonstrated that po 2 levels predt the effetveness of radaton treatment n breast tumors and Brzel et al. 03 reported that tumor po 2 levels predt the lkelhood for metastases n some aner patents. 9.B.2. Determnaton of hemoglobn onentraton and oxygen saturaton The absorpton spetra of hemoglobn n the NIR s suffently unque that spetrosop measurements of absorpton oeffent a an be used to reover values of hemoglobn onentraton and oxygen saturaton. For the Dartmouth magng setup, eah tomograph measurement results n the reonstruton of an mage of a and redued satterng oeffent s ' at one optal wavelength?, so that mages of hemoglobn may be obtaned. The s ' mages are not generally used n the alulaton of hemoglobn onentraton and oxygen saturaton. By magng a at multple wavelengths, an array of values a s reovered at eah mage pont: a a, λ a, λ 2 = M a, λ n 9.. 3

146 We assume that the alulated a s a ombnaton of absorpton due to oxygenated hemoglobn Hb-O 2, de-oxygenated hemoglobn Hb-R, water H 2 O, and lpds. These hromophores have been prevously haraterzed for molar absorpton oeffent a over the NIR spetral range, suh that a matrx of values A an be expressed? α α = α HbR, λ HbR, λ M 2 HbR, λ n α α α HbO HbO HbO 2 2 M 2, λ, λ 2, λ n α α α H O, λ 2 H O, λ 2 M H O, λ 2 2 n α α α lpds, λ lpds, λ M 2 lpds, λ n 9.2 where the unt of a are [mm - M - ]. We use a = absorpton per unt onentraton [mm - %onentraton - ] for water and lpds beause they are typally haraterzed n unts of perent onentraton. For values of a we use the measured values from Wray et al. 52 for Hb-O 2 and Hb-R, from Hale and Querry 50 for water, and from Quaresma et al. 5 for lpds as shown n Fgure 9.. The onentraton of these hromophores where [ ] represents onentraton an be expressed as an array of values. [ HbR] [ HbO 2] = [ H ] 2O [ lpds] 9.3 whh an be expressed as a matrx problem, Α = a

147 Fgure 9.: Plot of near-nfrared absorpton spetra for water, lpds, oxygenated Hb-O 2, and de-oxygenated hemoglobnhb-r. Values taken from Wray et al. 52 for Hb-O 2 and Hb-R, from Hale and Querry 50 for water, and from Quaresma et al. 5 for lpds. Hemoglobn onentraton [Hb-T]=[Hb-R]+[Hb-O 2 ] an be approxmately mapped solely based on the a of tssue alulated at 800 nm the sobest pont where the absorpton of Hb-R and Hb-O 2 are equal and an assumed level of water and lpds. Values of a at a mnmum of two wavelengths are needed to determne [Hb-O 2 ] and [Hb-R]. Thus, hemoglobn oxygen saturaton SO 2 = [Hb-O 2 ]/ [Hb-T] mappng requres the alulaton of a usng at least two wavelengths. Generally, the Dartmouth experments nvolve the reonstruton of quanttatve absorpton mages at two to sx wavelengths followed by a least squares regresson to derve the hemoglobn onentraton and oxygen saturaton mages usng an assumed level of water and lpds. The use of addtonal wavelengths tends to mnmze the effet of nose and has also been analyzed for magng of water and lpds. 33

148 Both lpds and water are sgnfant NIR absorbers 50,5 and effet the estmaton of hemoglobn onentraton. In addton both spetra have small absorpton peaks near 750 nm, smlar to de-oxygenated hemoglobn, whh an lead to an underestmaton of hemoglobn oxygen saturaton. Consequently, for most n vvo measurements and numeral smulatons, a perentage of the lpd and water absorpton spetrum, based on average lpd and water ontent, s subtrated from the a spetrum pror to performng the least squares ft to determne [Hb-T] and SO 2. 9.C. Smulaton of Breast Caner Lesons 9.C. Composton of smulated breast aner leson For the smulaton of the optal propertes of the breast, we used lterature values for hemoglobn onentraton, oxygen saturaton, water and lpd ontent for healthy breast tssue. In ths smulaton study, we use a hemoglobn onentraton of 0 M for healthy breast tssue, smlar to values of 2.2 and 5.6 M measured by Tromberg et al. 3 for normal breast tssue. Usng the nformaton n seton 9.B.., a smulated breast aner leson s onstruted. The bakground tssue s onsdered to be 57% lpds, 3% water, and 0 M hemoglobn at 70% oxygen saturaton. The smulated anerous tumor s a 50% oxygenated rng of nreased hemoglobn onentraton wth a 50% oxygenated ore. The ore of the tumor has the same hemoglobn onentraton as the bakground tssue, exept that the hemoglobn oxygen saturaton s dereased. The rng of nreased hemoglobn onentraton s smoothly varyng from a 4: 40M maxmum hemoglobn onentraton at the enter of the rng to bakground hemoglobn onentraton at the nteror and exteror of the rng. An absorpton oeffent a mage at 750 nm and a profle of the smulated breast aner leson wthn a normal tomograph seton of breast tssue are dsplayed n Fgure 9.2a. Note that the a n the nteror of the rng s nreased as ompared wth the bakground due 34

149 to the dereased oxygen saturaton of the nteror of the rng, whh for 750 nm orresponds to hgher absorpton. The tomograph seton of the smulated breast has a dameter of 84 mm and the smulated tumor has a rng struture wth an nner dameter of 5 mm and an outer dameter of 20 mm. The redued satterng oeffent s a onstant.75 mm - for all smulatons. The orgnal hemoglobn onentraton [Hb-T] mage and vertal profle graph are plotted n Fgures 9.2 and 9.2e. The hemoglobn oxygen saturaton mage SO 2 and profle are shown n Fgures 9.2d and 9.2f. 35

150 a a at 750 nm b a at 750 nm [Hb-T] d SO e [Hb-T] f SO Fgure 9.2: a Absorpton oeffent mm - mage at 750 nm of a smulated normal tomograph seton of breast tssue ontanng a anerous leson. b Vertal profle graph through the enter of a. Hemoglobn onentraton M mage and d hemoglobn oxygen saturaton % mage of the smulated breast and anerous leson. e and f are vertal profle graphs through the enter of mages and d respetvely. X-Y oordnates are n unts of mm. 36

151 9.C.2 Resultng mages from smulated breast aner leson Numeral smulatons were performed on a tomograph sle through a smulated breast ontanng a aner leson. The smulated tomograph sle was assumed to have hromophore levels equvalent to an average breast and a anerous leson wth a rng shaped nrease n hemoglobn onentraton and loalzed derease n hemoglobn oxygen saturaton as shown n Fgure 9.2. The smulatons were performed at four wavelengths 720 nm, 750 nm, 800 nm, and 830 nm at 0% added nose to the measurement data. The reonstruted mages were used to alulate hemoglobn onentraton and oxygen saturaton mages usng least squares regressons nvolvng two, three, and four wavelengths. The resultant hemoglobn onentraton and oxygen saturaton mages are dsplayed for eah ombnaton of nose level and number of wavelengths. The hemoglobn onentraton mages at 0% nose are shown n Fgures 9.3a, 9.3, and 9.3e respetvely for regressons usng two, three and four wavelengths. The orrespondng oxygen saturaton mages are dsplayed n Fgure 9.3b, 9.3d, and 9.3f. Furthermore, vertal profle graphs taken through the enter of eah of the hemoglobn onentraton mages are shown n Fgures 9.3g, 9.3, and 9.3k. Lkewse, the profle graphs for the oxygen saturaton mages an be found n Fgures 9.3h, 9.3j, and 9.3l. 37

152 a [Hb-T], 2 wavelengths b SO d e [Hb-T], 3 wavelengths f SO g h

153 00.0 [Hb-T], 4 wavelengths j SO k l Fgure 9.3: Results for 0% nose mage reonstrutons of a smulated breast aner leson wthn a tomograph ross seton of normal breast tssue. The orgnal mages and values are shown n Fgure bakground of 0 M hemoglobn onentraton and 70% oxygen saturaton ontanng a rng of 40 M hemoglobn onentraton wth 50% oxygen saturaton. a Hemoglobn onentraton mage and b hemoglobn oxygen saturaton mage for the regresson usng two wavelengths. and d are vertal profle graphs through the enter of a and b respetvely. e and f are the hemoglobn onentraton and oxygen saturaton mages usng three wavelengths. g and h are profle graphs through the enter of e and f., j, k, and l are the mages and profle graphs for the regresson usng four wavelengths. For a rng type objet, suh as the one used n the smulated breast aner leson, the reonstruted mage s blurred and the nteror of the rng s obsured. Even n the presene of 0% nose, however, the hemoglobn onentraton an be aurately determned and loalzed exept for the averagng effet wth two or even one wavelength. The fne detal of the smulated leson s obsured, but the overall hemoglobn onentraton nrease s qute vsble even at hgh nose levels. Aurate hemoglobn onentraton mages were obtaned 39

154 wth greater than 50% added nose. The hemoglobn onentraton does not reflet the 4: nrease n hemoglobn onentraton of the rng, but reovers the average value of rng objet approxmately 2:. Wth our urrent set-up, the mappng of hemoglobn oxygen saturaton requres more than two wavelengths n order to aheve quanttatvely aurate mages. Even n the presene of no added nose, the oxygen saturaton mage for two wavelengths s poor due to numeral artfats. Wth an nreased number of wavelengths, however, the oxygen saturaton mage s reonstruted aurately wth a blurrng effet. In fat wth four wavelengths and 0% added nose, the hemoglobn oxygen saturaton mage s qute aurate -- the bakground s reonstruted wth average oxygen saturaton of 72% and the rng objet wth average oxygen saturaton of 54%, smlar to the atual oxygen saturaton of 70% and 50%, respetvely. 9.D. Homogeneous Measurements 9.D.. Imagng Experments Our ntal experments were foused on verfaton of the ablty to orretly quantfy the a for oxygenated and de-oxygenated blood more spefally Hb-O 2 and Hb-R n a turbd medum. The phantoms were de-oxygenated by flushng them wth ntrogen gas. Verfaton of the de-oxygenaton status was obtaned by measurng the partal pressure of oxygen po 2 wth a o-oxmeter Model Rapdlab 800, Chron Dagnosts, Norwood, MA. Ths deve was also used to onfrm the hemoglobn ontent of our blood samples n terms of grams per lter of hemoglobn mass n blood volume; ths value was used to onvert from blood volume to hemoglobn onentraton. We found the o-oxmetry readngs to yeld useful measurements of po 2 as long as the samples were above 20 mmhg, below whh onsderable varane appeared n the po 2 due to transportaton of the samples from the phantom to the deve. Ntrogen bubblng for one half hour was apparently suffent to 40

155 effetvely de-oxygenate the hemoglobn n the phantoms. Usng our standard setup, we maged homogeneous phantoms of water, Intralpd, and blood wth soure and 6 detetors. The homogeneous fttng algorthm Chapter 6 was appled to the measured data to determne the losest tssue optal propertes for the medum. Both lpds and water are sgnfant NIR absorbers and effet the estmaton of hemoglobn onentraton. In addton, both spetra have small absorpton peaks near 750 nm, smlar to Hb-R, whh an lead to an underestmaton of hemoglobn oxygen saturaton. Consequently, for phantom studes, the absorpton due to water was subtrated from the alulated a spetrum at eah wavelength. For n vvo measurements, a perentage of the lpd and water absorpton spetrum, based on average lpd and water ontent, was subtrated from the a spetrum pror to performng the least squares ft to determne hemoglobn onentraton and hemoglobn oxygen saturaton. The absorpton and redued satterng oeffent error bars dsplayed n Fgures were expermentally determned usng the standard devaton of repeated measurements obtaned at eah wavelength and blood onentraton. The expermental unertantes reported n Tables for the measurement of molar absorpton oeffent, Hb-R and Hb-O 2 onentraton, and total hemoglobn onentraton and oxygen saturaton were determned by onsderng the worst ase senaro whh results from applyng the alulated expermental error for the absorpton oeffent. 9.D.2. Results 9.D.2.. Redued Satterng Coeffent Whle the redued satterng oeffent values are not used n the estmaton of hemoglobn onentraton or hemoglobn oxygen saturaton level, the ablty to quanttatvely reover these values s an mportant step n the valdaton of the homogeneous fttng algorthm. The quanttatve values for the redued satterng oeffent at several NIR 4

156 wavelengths for a 0.5% Intralpd soluton an be verfed usng an equaton from an artle by Staveren et al. 95 A omparson of the values alulated from the Staveren et al. equaton eq. 5. and the measured data usng our system s shown n Fgure 9.4. Fgure 9.4: Comparson of measured values and those predted by Staveren et al. 95 for the redued satterng oeffent s of a phantom ontanng 0.5% Intralpd n water. Expermental estmates are reahed by fttng the data from a homogeneous phantom to the fnte element model usng Method A desrbed n Chapter 6. 9.D.2.2. Homogeneous Phantom Studes A prelmnary verfaton of the ablty to quantfy Hb-O 2 and Hb-R ontent n a tssue-lke phantom was aomplshed through expermental determnaton of the molar absorpton oeffent of Hb-R and Hb-O 2 at dfferent wavelengths by magng dfferent onentratons of oxygenated and de-oxygenated blood n a 0.5% Intralpd and water soluton ontaned n a plast beaker. Blood volume onentratons were onverted to hemoglobn onentratons usng the hemoglobn moleular weght 64,500 grams per mole and ontent values obtaned from o-oxmetry measurements; the hemoglobn ontent of the blood was found to be roughly 56 grams per lter of hemoglobn mass n the blood volume. Ths orresponds to 0.5% blood beng equal to about 2 mro-molar M hemoglobn. The expermentally determned molar absorpton oeffent s the slope of a lnear regresson relatng the 42

157 absorpton oeffent to onentraton. The results for Hb-R and Hb-O 2 at 750 nm, 800 nm, and 830 nm are shown n Fgure 9.5 ompare wth results for Method B n Fgure 6.7 and Table 6. wth numeral values tabulated n Table 9.. The R 2 value reported for the lnear regresson s the standard orrelaton oeffent. The offset at 0% blood does not math values for water absorpton reported by Hale and Querry. 50 Ths offset appears to be due to the presene of the mllmeter thk plast beaker walls. a Molar absorpton oeffent Offset value at 0ml blood R 2 value Wray et al. 23 Expermental Hale & Querry 24 Expermental 750 nm ± ± nm ± ± nm ± ± Molar absorpton oeffent Offset value at 0ml blood R 2 value Wray et al. 23 Expermental Hale & Querry 24 Expermental 750 nm ± ± nm ± ± nm ± ± b Table 9.: Comparson of the expermental determnaton of the molar absorpton oeffent slope of a lnear regresson to data wth the Wray et al. 52 and Hale and Querry 50 values: ahb-r and bhb-o 2. a 43

158 b Fgure 9.5: Plot of expermentally measured absorpton oeffent versus onentraton of blood for three wavelengths: ahb-r and bhb-o 2. Measurements were reorded from a homogeneous satterng medum of 0.5% Intralpd n a 72 mm dameter ylndral phantom. Homogeneous fttng Method A was used for ths data. To nvestgate further the ablty to dstngush Hb-O 2 and Hb-R wthn a turbd medum, we attempted to reprodue the nfrared spetra of 0 M Hb-O 2 and 0M hemoglobn onentratons alulated from blood volume Hb-R mxed wth 0.5% Intralpd and water. The NIR absorpton oeffent spetra were agan measured usng data from soure and 6 detetors. The spetra are plotted n Fgure 9.6 and ompared to expeted values for water plus blood. Agan, the urves are relatvely aurate exept for an overall offset. 44

159 a b Fgure 9.6: Comparson of absorpton oeffent alulated from expeted values for blood 52 and water 50 and measured values: a 0 M de-oxygenated hemoglobn n 0.5% Intralpd and water soluton; b 0 M oxygenated hemoglobn n 0.5% Intralpd and water soluton. Homogeneous fttng Method A was used for these data. The offset n the absorpton oeffent appears to be due to the transluent mllmeter thk plast walls of the beakers used to ontan the tssue-lke phantoms. To verfy ths hypothess, the spetrum of the water plus 0.5% Intralpd soluton was measured n both a plast beaker and a thn-walled balloon see Fgure 9.7. The offset was not apparent n the reonstruted absorpton oeffent spetrum from the thn-walled balloon phantom data. 45

160 Fgure 9.7: Comparson of absorpton oeffent values from Hale and Querry 50 wth the absorpton oeffent of water measured n a plast beaker versus a thn-walled balloon. Note that the offset s not apparent n the thn-walled balloon ase. Homogeneous fttng Method A was used for ths data. Usng the assumpton that the observed offset s aused by the plast walls, a orreton was appled at eah wavelength for a gven plast beaker phantom. Then, usng the spetra for Hb-R, Hb-O 2, and water, a least squares ft was performed on the orreted spetral data to approxmate the onentraton of eah of the three omponents. For the data presented n Fgure 9.6, the ft results, one orreted, are shown n Table 9.2. Table 9.2: Results of least squares fts to alulate Hb-O 2 and Hb-R ontent of known 0 M hemoglobn onentraton, 0.5% Intralpd and water homogeneous phantom. Further studes have been performed where Hb-R and Hb-O 2 have been maged n thn-walled plast bags usng the TS laser. The Hb-R sample was de-oxygenated wth the addton of yeast. The homogeneous fttng was performed usng Method B as desrbed n 46

161 Chapter 6 and data was aqured at all 6 soure postons and averaged by detetor to soure dstane. The noteable offset due to the wall-effet s not evdent n the results, shown n Fgure 9.8. a b Fgure 9.8: Comparson of absorpton oeffent alulated from expeted values for blood 52 and water 50 and measured values: a 24 M de-oxygenated hemoglobn and b 24 M oxygenated hemoglobn n 0.5% Intralpd and water soluton. Homogeneous fttng Method B was used for ths data. 47

162 9.D.2.3. In vvo homogeneous measurements Smlar tests an be performed wth n vvo measurements of breast tssue NIR spetra. Whle breast tssue s heterogeneous, approxmatons to bulk values an be made by assumng homogeneous tssue and usng the same measurement sheme as the homogeneous phantom studes. An nterestng omparson n terms of bulk hemoglobn onentraton and oxygen saturaton an be obtaned by magng the breasts of young and older female subjets. By performng a smlar near-nfrared spetral san of a 33 year old woman and a 62 year old woman, least squares fts were appled to the absorpton oeffent data to approxmate the bulk hemoglobn onentraton and average hemoglobn oxygen saturaton level n eah ase. The measured spetra and the orrespondng least squares urve fts generated from the alulated onentratons numeral values are shown n Table 9.3 and spetral values of HB-R, Hb-O 2, water, and lpds are plotted n Fgure 9.9 for eah subjet. Water and lpd onentraton levels were onstraned to the average anatomal values of 3% water ontent and 57% lpd ontent for breast tssue as summarzed by Woodard and Whte. 66 These values for average water and lpd ontent are approxmate and an vary sgnfantly wth age and between ndvduals. To aount for ths Table 9.3 nludes the unertanty ntrodued from a possble 50% varaton n the average water and lpd onentraton n addton to the expermental unertanty. 48

163 Results 33 year old woman 62 year old woman Calulated values Hb-O 2 onentraton M 44 ± 4 5 ± 2 Hb-R onentraton M 9 ± 3 7 ± Total Hb onentraton M 63 ± 2 22 ± 2 Perent oxygen saturaton % 70 ± 5 67 ± 7 Preset values Water ontent 3% 3% Lpd ontent 57% 57% Table 9.3: Numeral results of least squares fts to determne hemoglobn onentraton and hemoglobn oxygen saturaton level for a 33 year old woman, and b 62 year old woman. Water and lpd onentratons were onstraned to the approxmate values dsplayed. a 49

164 b Fgure 9.9: NIR spetra and graphal results of least squares fts to determne hemoglobn onentraton and hemoglobn oxygen saturaton level for a 33 year old woman, and b 62 year old woman. 9.D.3. Dsusson The molar absorpton oeffent values alulated from the urves shown n Fgure 4 are smlar to the results reported by Wray et al. 52 for Hb-R and Hb-O 2, as shown n Table 9.. Smlarly, the results for the absorpton oeffent spetra for HB-R and Hb-O 2 Fgure 9.6 are aurate when plotted aganst establshed values; however, an offset appears n both ases. Further nvestgaton led to the determnaton that ths offset was due to the presene of the plast beaker used to hold the phantom solutons. Phantom experments showed that the offset was not evdent n a thn-walled phantoms Fgure 9.7, 9.8. Ths fndng suggests that the offset s due to the effet of the beaker walls and that no suh offset should be observed for n vvo measurements. One we aounted for the offset due to the presene of the beaker walls, the results math to wthn 20% of the known ontent the oxygen saturaton of the de-oxygenated blood was known to be less than 25% of the tssue-lke phantom, as shown n Table 9.2. Ideally, future albratons would be performed wth thn- 50

165 walled balloon or plast bag phantoms; however, n prate ths makes t dffult to nlude heterogenetes and to bubble solutons wth ntrogen gas. Breast tssue absorpton oeffent has been shown to derease wth age. 04 The results, dsplayed n Fgure 9.9, show a dramat and expeted hange n overall breast tssue absorpton oeffent between the younger and older female volunteers. Smlarly, the alulated hemoglobn onentraton s sgnfantly hgher n the younger woman. Ths result orresponds well wth the known, on average, derease n breast tssue densty wth age. 0 Quanttatve results for the 62 year old subjet are smlar to data reported n artles by Tromberg et al. 3 and Fantn et al. 4 Average hemoglobn oxygen saturaton values, measured for the two healthy women, of 68% and 70% are nearly the same as the results for healthy breast tssue measured by Tromberg et al. 66% and 68%. 3 Addtonal measurements of [Hb-T] and SO 2 at fewer wavelengths are presented n Chapter 0. 9.E. Heterogeneous phantom studes A goal of these experments was to show that pont by pont mappngs wthn a tomograph ross-seton of ether breast tssue or tssue-lke phantoms s feasble. To mage hemoglobn onentraton and oxygen saturaton n ths manner, we appled the fnte element method reonstruton algorthm to data aqured at multple wavelengths. For eah wavelength, phase and ntensty data s reorded at 6 rumferental detetor loatons for eah of 6 soure loatons. An mage of absorpton oeffent and redued satterng oeffent s formed usng the reonstruton algorthm. Eah dfferent absorpton mage s then onsdered as a mappng of the absorpton oeffent for that wavelength. A least squares ft s appled to eah pont n the mage; the result s a pont by pont approxmaton of the hemoglobn onentraton and oxygen saturaton levels wthn breast tssue or tssuelke phantoms. 5

166 9.E.. Phantom wth nreasng blood onentraton To verfy the ablty to orretly quantfy the absorpton oeffent of loalzed blood at three NIR wavelengths, a seres of dfferent onentratons of blood nlusons were measured. A 72 mm phantom plast beaker ontanng 0.5% Intralpd n water and 0.5% blood was used wth a 25 mm nluson plaed just off enter. The onentraton of blood n the nluson a thn-walled lear plast ylnder was vared from 0% to 2.0%. The resultng mages at 750 nm, 800 nm, and 830 nm are shown n Fgure 9.0. The absorpton oeffent value from the enter regon of the nluson s ompared wth the expeted values alulated from the known hemoglobn alulated from blood volume usng 56 grams hemoglobn per lter of blood and water onentratons based on values from Wray et al. 52 and Hale and Querry 50 ; these data are plotted n Fgure 9. and the results of a lnear regresson on the data are presented n Table

167 Fgure 9.0: Colleton of absorpton oeffent mages for a 25mm rular nluson n a 72 mm rular phantom. The bakground s 0.5% blood n 0.5% Intralpd and water. The nluson n the frst row has no blood. The nluson n the seond row ontans % blood, the thrd row.5% blood and the fourth row 2% blood. Column a s measured at 750 nm, olumn b at 800 nm, and olumn 830 nm. 53

168 Fgure 9.: Comparson of absorpton oeffent taken from the enter of the nluson n the mages n Fgure 9.0 wth absorpton oeffent values alulated from expeted values for blood and water. 50,52 Wavelength Results 750 nm 802 nm 833 nm Slope Offset R 2 value Table 9.4: Lnear regresson results from data plotted n Fgure 9. A slope of ndates a : orrespondene between the absorpton oeffent values from the enter of the nluson n the mages n Fgure 9.0 and the absorpton oeffent results alulated from expeted values for hemoglobn and water. 50,52 The 25 mm nlusons used n the heterogeneous phantom studes are thn walled 200 mron lear plast ylnders. The effet of the 200 mron thk ylnder walls was negated by dfferene magng where for the albraton phantom the nluson was flled 54

169 wth the dental ontents as the bakground. In leu of suh dfferene magng, n ontrast wth the mllmeter thk walls of the exteror beaker, the 200 mron walls of the ylnder appear to have a mnmal effet. 9.E.2. Phantom wth nreased [Hb-T] and lowered SO 2 nlusons Absorpton oeffent mages at multple wavelengths an be used to generate an mage of hemoglobn onentraton and oxygen saturaton. The mert of ths approah was tested wth a seres of Intralpd phantoms ontanng nlusons wth varous onentratons of oxygenated and de-oxygenated blood. Fgure 9.2 shows a sample analyss of a tssuelke phantom. In ths ase an 84 mm dameter phantom onssted of a bakground of fully oxygenated 0 M hemoglobn onentraton n 0.5% Intralpd and water. The phantom ontaned two 25 mm rular nlusons embedded wthn the bakground regon. The nluson postoned off-enter to the rght ontaned the exat same ontents as the bakground, exept that the nluson was bubbled wth ntrogen gas to de-oxygenate the blood. The seond 25 mm nluson, whh ontaned fully oxygenated 40 M hemoglobn onentraton n 0.5% Intralpd and water, was postoned left of enter. Usng a least squares ft, an mage of both hemoglobn onentraton and hemoglobn oxygen saturaton s formed from mages at two wavelengths 750 nm, 802 nm as llustrated n Fgure 0. 55

170 a Setup b a nm a nm d [Hb-T] e SO 2 f [Hb-T] g SO 2 Fgure 9.2: Absorpton oeffent a, hemoglobn onentraton [Hb-T], and hemoglobn oxygen saturaton SO 2 mages of an nreased [Hb-T] nluson left offenter and a de-oxygenated blood nluson rght off-enter n a oxygenated blood bakground. a Depton of orgnal phantom, b 750 nm a mm - mage, 802 nm a mage, d [Hb-T] M mage, e SO 2 mage. f and g are one-dmensonal transets through mages d and e respetvely. Ideal profles are plotted for omparson. 56

171 9.E.3. Dsusson The mages shown n Fgure 9.0 hghlght the ablty to reover quanttatvely the absorpton oeffent of nlusons wthn a satterng medum at multple wavelengths. The absorpton oeffent at the enter of the nluson, when ompared wth known values plotted n Fgure 9. shows a nearly one to one orrelaton. The slope of a lnear regresson to the data llustrates that errors between 4% and 5% our for the dfferent wavelengths examned. The quanttatve assessment of the absorpton oeffent at multple wavelengths should lead to the ablty to quantfy the hemoglobn onentraton and hemoglobn oxygen saturaton. For objets wth known water ontent, absorpton oeffent mages at two wavelengths should be suffent to mage hemoglobn onentraton and oxygen saturaton. The hemoglobn onentraton and hemoglobn oxygen saturaton mages dsplayed n Fgure 9.2 orretly reover the nreased hemoglobn onentraton nluson n the hemoglobn onentraton mage and the de-oxygenated nluson n the hemoglobn oxygen saturaton mage. The absorpton oeffent mages at 750 nm and 800 nm are also dsplayed n Fgure 9.2 where both the nreased hemoglobn onentraton and the de-oxygenated nlusons are evdent as strong absorbers n the 750 nm mage, whle only the nreased hemoglobn onentraton nluson s reovered n the 800 nm mage. Ths result s expeted -- see Hb-O 2 and Hb-R spetral sgnatures n Fgure 9.. These results demonstrate an ablty to aurately quantfy and map hemoglobn onentraton and hemoglobn oxygen saturaton, whh may provde useful dagnost nformaton. The results presented here have reled on the assumpton that other absorbers play an nsgnfant role n the absorpton at NIR wavelengths. Ths phantom study represents a strong ndaton that hemoglobn onentraton and oxygen saturaton mages an be reovered quanttatvely. In prate, usng addtonal wavelengths wll redue the effets of 57

172 nose and other errors when dervng these funtonal parameter maps from n vvo absorpton oeffent mages as suggested n the smulatons reported earler. The effets of water and lpd absorpton are dsussed further n Chapter 0. 58

173 Chapter 0: Patent Imagng 0.A. Introduton Followng an ntal set of suessful phantom studes, a seres of female volunteers have been maged. The magng of volunteers at the date of ths thess an be dvded nto two tme perods based on the nstrumentaton. The studes to date have been foussed manly on feasblty, as well as general assessment of the nterfae, protools, and albraton proedure. A substantal amount of patent data has been aqured, however, only the full results from three nterestng ases wll be presented here wth summary data for the remanng mages. 0.B. Intal automated system 0.B.. Patent 5: 3 m fbroadenoma The frst set of volunteers approxmately 8 women numbered patents 3 through 2 were maged wth the automated sngle detetor setup usng the Ttanum Sapphre TS wavelength-tunable laser. In all patent mages presented, hemoglobn values were alulated usng an assumed onstant level of water and lpds at 30% and 60% respetvely. Of partular nterest from ths group are two volunteers wth onfrmed breast pathologes. Both volunteers have sne had surgery and the tumor was lassfed by hstology. Patent 5 had an approxmately three entmeter bengn fbroadenoma; the estmated sze and loaton taken from a sketh by the radologst s shown n hapter Fgure.0. Near-nfrared magng of ths patent through the plane of the tumor at 750 and 800 nm showed an approxmately 2.0 tmes ontrast n absorpton oeffent and hemoglobn onentraton at the ste of the tumor Fgure 0.. The ontralateral breast was also maged at the same approxmate plane Fgure 0.2. Calbraton data was aqured from a lqud phantom. The patent had a fne-needle aspraton day pror to the NIR exam. 59

174 84.0 a a mage nm b a mage nm [Hb-T] mage d [Hb-T] vertal transet Fgure 0.: Reonstruted mages for a woman wth a bengn fbroadenoma Patent 5. Dsplayed are the absorpton oeffent a mages sale bar unt of [mm - ] at a 750 nm and b 800 nm and the hemoglobn onentraton [Hb-T] mage sale bar unt of [M]. The x and y axes of the mages are poston n unts of mm. Also dsplayed are the values for a vertal transet through the mddle of the [Hb-T] mage. y-axs s [M] and x-axs s vertal poston n mm. a [Hb-T] mage b [Hb-T] vertal transet Fgure 0.2: Reonstruted mages for the ontralateral mammographally normal breast for patent 5. Dsplayed are a the hemoglobn onentraton [Hb-T] mage and b vertal transet through the mddle of the [Hb-T] mage. sale bars and axes are dental to Fgure 0. and d. 60

175 0.B.2. Patent 6: 0.8 m nvasve aner Patent 6 had an approxmately eght mllmeter malgnant dutal nvasve arnoma; the estmated sze and loaton taken from a sketh by the radologst s shown n Chapter Fgure.. Near-nfrared magng of ths patent through the plane of the tumor at 750 and 800 nm showed an approxmately 3.5 tmes ontrast n absorpton oeffent and hemoglobn onentraton at the ste of the tumor Fgure 0.3. A stereotat ore-needle bopsy was performed 6 days pror to NIR magng a a mage nm b a mage nm [Hb-T] mage d [Hb-T] vertal transet Fgure 0.3: Reonstruted mages for a woman wth an nvasve arnoma Patent 6. Dsplayed are the absorpton oeffent a mages sale bar unt of [mm - ] at a 750 nm and b 800 nm and the hemoglobn onentraton [Hb-T] mage sale bar unt of [M]. The x and y axes of the mages are poston n unts of mm. Also dsplayed s the values for a vertal transet at x = 42 mm of the [Hb-T] mage. y-axs s [M] and x-axs s vertal poston n mm. 6

176 00.0 a [Hb-T] mage b [Hb-T] vertal transet Fgure 0.4: Reonstruted mages for the ontralateral mammographally normal breast for patent 6. Dsplayed are a the hemoglobn onentraton [Hb-T] mage and b vertal transet through the mddle of the [Hb-T] mage. sale bars and axes are dental to Fgure 0.3 and d. Patent 5 Patent 6 Bakground Hb Conentraton M Tumor Hb Conentraton M Approxmate Tumor Sze m Table 0.: Results for average hemoglobn onentraton of the bakground and peak onentraton for patents 5 and 6. 0.B.3. Comparson wth early normal values Whle the system was undergong hanges wthn ths ntal study perod and not all reonstruted mages seemed relable, the average hemoglobn onentraton reovered s assumed to be approxmately aurate. Fgure 0.5 shows the average hemoglobn onentraton for the frst ffteen volunteers maged, as well as the measured hemoglobn onentraton of the lesons from patents 5 and 6. The hemoglobn values for ths ntal group of volunteers were obtaned from measurements at two wavelengths 750 and 800 nm n most ases. 62

177 Fgure 0.5: Plot of average hemoglobn onentraton from near-nfrared mages of volunteers. Also plotted are two loalzed values for hemoglobn onentraton for a malgnant tumor and a bengn tumor. The error bars represent the standard devaton between multple measurements, suh as left and rght breast. The results wth no error bar orrespond to a patent where only one measurement was made. 0.C. Current automated system 0.C.. Normal patent study Followng ths ntal set of volunteers, the sxteen detetor data aquston system was onstruted. Ths system s desgned for sx dode lasers wth wavelengths rangng from 660 to 850 nm. At present approxmately 25 addtonal volunteers numbered patents have been maged wth ths new deteton setup. A partular subset omprse a 6 subjet normal study where eah woman was maged wth not only the NIR setup, but wth the Dartmouth eletral mpedane and mrowave spetrosopy magng systems. The group of 6 was hosen to span the range of ages 40's, 50's, 60's, 70's and mammograph densty a subjetve measure of the opaty of the x-ray mammogram typal n lnal breast sreenng. Ths s a small number of patents n relaton to the populaton, but the range of measured propertes provdes an estmate of the expeted range. The data for 63

178 average absorpton and redued satterng oeffent at 785 nm, hemoglobn onentraton, and oxygen saturaton are presented n Fgure 0.6. a b d Fgure 0.6: Plot of average a hemoglobn onentraton, b oxygen saturaton, absorpton oeffent at 785 nm, and d redued satterng oeffent at 785 nm versus age from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms. The error bars represent the standard devaton between multple measurements, suh as left and rght breast or multple planes wthn a sngle breast. The mean and standard devaton for these propertes for the 6 person normal study are a 785 nm = ± mm -, s '785 nm =. ± 0.2 mm -, [Hb-T] = 22 ± 9 M, and SO 2 = 66% ± 9%. The average values for these 6 volunteers were also plotted versus body 64

179 mass ndex BMI s an approxmate measure of ftness and s equal to a person's weght n klograms dvded by the square of ther heght n meters 05. Of some nterest, there appears to be a weak orrelaton R 2 = 0.65 between measured [Hb-T] and BMI as shown n Fgure 0.7. Another parameter of nterest s the x-ray mammograph densty of the breast. The radologst ategorzes eah breast n one of four radograph densty ategores: heterogeneously dense HD, extremely dense ED, sattered S, and fatty F. Also dsplayed n Fgure 0.7 s the measured [Hb-T] plotted versus radograph densty ategory for the 6 volunteers. a b Fgure 0.7: Plot of average hemoglobn onentraton versus a body mass ndex kg/m 2 and b radograph densty from near-nfrared mages obtaned from a set of sxteen volunteers wth normal mammograms. The error bars represent the standard devaton between multple measurements, suh as left and rght breast or multple planes wthn a sngle breast. In b, the error bars are based on values from multple subjets. 0.C.2. Study of Lpd and Water ompensaton As dsussed n prevous hapters, for stat NIR magng, wthout the addton of ontrast agents, absorpton oeffent a mages are prmarly related to the spatal dstrbuton of oxygenated and de-oxygenated hemoglobn Hb-O 2 and Hb-R ontrast, 52 and to a lesser extent water and lpd ontent. 5 Measurement at multple optal wavelengths permts 65

180 magng of these omponents as ther absorpton spetra are suffently dfferent. A partular "benh to bedsde" hallenge for NIR breast hromophore magng s transtonng from two spatally varyng absorbers Hb-O 2, Hb-R to four addtonally, water and lpds. In some NIR tomograph magng onfguratons t may prove dffult to aqure a mages at a suffent number of wavelengths to reover the onentraton of these four hromophores. In a prevous smulaton study, we estmated that a mnmum of four wavelengths s needed just to reover aurate mages of Hb-R and Hb-O 2 n the presene of nose. 68 In leu of addtonal wavelengths, however, t may be possble to use satterng nformaton to estmate water and lpd ontent. 06 The wavelength λ dependene of the redued satterng oeffent s ' an be approxmated as an exponental deay. By performng a ft to ln s ' versus lnλ, mages of satterng "power" an be determned, as defned by the slope of ths data ft. From NIR pont measurements at UC-Irvne's Bekman Laser Insttute, 06 t appears that the satterng power s lnearly related to water and lpd ontent n the breast. Thus, satterng power mages mght be used to determne both water and lpd spatal ontent redung the total number of wavelengths neessary for separaton of Hb-O2, Hb-R, water, and lpds. In ths seton, we analyze a set of lnal mages to llustrate the role of water and lpds n our mult-spetral NIR tomograph magng system. Here, we dsplay mages from one woman wth a mammographally subtle 3 entmeter nvasve left breast aner as a means of presentng the urrent lnal status of the setup and further demonstratng the potental of quanttatve hemoglobn magng wth NIR lght. Wth the presentaton of these mages, we also explore some of the hallenges n ahevng quanttatve hemoglobn mages wthn the breast. In partular, we explore three methods of ompensatng for a lmted number of optal wavelengths, and the broad spetral sgnatures n the 660 to 830 nm 66

181 regon, n determnng the unknown spatal ontent of water and lpds and ts effet on hemoglobn magng. 0.C.2.. Chromophore separaton It s wdely assumed that the prmary NIR absorbers n breast tssue are Hb-O 2, Hb-R, water, and lpds Fgure 9.. In general, an mportant goal of NIR breast magng s assessng total hemoglobn onentraton [Hb-T] = [Hb-O 2 ] + [Hb-R] and oxygen saturaton SO 2 = [Hb-O 2 ] / [Hb-T]. A partular hallenge of transtonng from laboratory experments to patent magng s gong from two spatally varyng absorbers Hb-O 2, Hb-R to four addtonally, water and lpds. In past studes, we have assumed a bulk water and lpd ontent based on average values for breast tssue. Whle ths assumpton redues overall error n omparson wth gnorng water and lpd absorpton, t s lear that lpd and water ontent vary between ndvduals of the same age and n some ndvduals hange wth the agng proess 06, durng the menstrual yle 07, and s lkely spatally heterogeneous. Ideally, mages of water and lpd should be reovered from the measured NIR data as well as Hb-O 2 and Hb-R. In reoverng mages of onentraton, t s assumed that a at eah wavelength s a lnear ombnaton of the onentraton multpled by the molar extnton oeffent of eah onsttuent. A least-squares ft to the data usng sngular-value deomposton SVD s used to determne the reovered onentratons as desrbed n Chapter 9. It s not expeted that four wavelengths s suffent to aurately estmate the onentraton of these four hromophores. Based on a smulaton study Chapter 9.C., t was determned that for our setup four wavelengths were needed to reover Hb-T and SO 2 n the presene of nose. 68 Indeed, the spetra of water, lpds, Hb-R and Hb-O 2 are broad and somewhat smlar n the regon of nm. In leu of addtonal wavelengths, however, t s possble that 67

182 satterng nformaton may be used to estmate water and lpd ontent. Indeed, prelmnary results from Ceruss et al. 06 ndate that lpd and water ontent may be determned from spatally-averaged spetral satterng data. From Me theory alulatons for a dstrbuton of spheral satterers, Van Staveren et al. 95 emprally showed a lnear relaton to ln s ' versus lnλ. Ceruss et al. 06 at UC- Irvne have used ths same relatonshp wth NIR pont measurements of s ' n the breast. Equaton 0. relates satterng oeffent wavelength dependene s 'λ by a onstant "satterng ampltude" A and a "satterng power" SP, SP s ' λ = Aλ. 0. Usng data from 28 women, Ceruss et al. show a lnear relatonshp for both lpd and water ontent to SP wth a oeffent of determnaton r 2 of 0.84 and The equatons of the lnear relatons are Water % = 0.35 * SP * 00% Lpd % = * SP * 00% 0.2.a. 0.2.b. Ths relatonshp an be used to approxmate bulk water and lpd ontent or may be appled to eah pont n the mage to determne water and lpd ontent spatally. We present results from three methods of determnng Hb-T and SO 2 mages based on dfferent treatments of water and lpd ontent. These are: water and lpd ontent s assumed to be onstant at 30% and 60% respetvely; 5 2 a ft s performed to all parameters, Hb-R, Hb-O 2, water and lpds based on absorpton data at 4 wavelengths; and 3 satterng power s used to mage water and lpds before fttng for Hb-R and Hb-O 2 from absorpton data at 4 wavelengths. These results are ompared wth the assumpton of no lpd and water absorpton method 4 n Table to assess the potental varaton nvolved n the method of estmatng water and lpd ontent. 68

183 0.C.2.2. Patent Imagng Conventonal and NIR magng results are presented for a sngle 73 year old female volunteer Patent 035. The subjet underwent routne mammography, whh demonstrated a 2.5 entmeter foal ll-defned densty wth a larger approxmately 6 entmeter maxmal dameter area of assoated arhtetural dstorton stuated n the deep lateral left breast. Breast ultrasonography dreted to the lateral left breast onfrmed an rregular hypoeho mass wth aoust shadowng. The magng abnormalty orresponded to a palpable lump n the lateral left breast. An ultrasound guded gauge vauum asssted needle bopsy of the mass was performed 2 weeks pror to NIR magng, establshng the dagnoss of an nvasve dutal arnoma. A 2 mllmeter maxmal dameter x 0.2 mllmeter approxmate thkness stanless steel marker lp, Mromark 2 tm [Ethon], was plaed n the mass at the tme of the needle bopsy. Subsequent one week after NIR magng therapeut lumpetomy and left axllary sentnel lymphadenetomy revealed a 5.9 entmeter low grade nvasve dutal arnoma wthout 0/2 axllary nodal metastases. For the NIR exam, the researh nurse Sandy Soho algned the NIR magng array n the oronal plane of the palpable lump of the pendant left breast. The fber-opt array was brought n dret ontat wth the breast usng push-button ontrols. Three planes of tomograph data were aqured: at the mdlne of the leson,.3 m above, and 0.9 m below the mdlne. Data were also aqured from the ontralateral normal rght breast at a sngle oronal magng plane orrespondng to the loaton of the left breast leson based on the depth from the hest wall to the magng array. 0.C.2.3. Results The resultng mages for patent 035 aqured at the mdlne of the leson are presented n Fgure 0.8 n the typal format submtted to our lnal database. Here, a and 69

184 s ' mages at the four wavelengths are dsplayed. Intally a onstant water and lpd onentraton of 30% and 60%, respetvely, was assumed and the relevant values subtrated from the a mages pror to determnng dstrbutons of Hb-T and SO 2 from the SVD least squares ft for Hb-R and Hb-O 2. The leson s learly vsble n both the a and Hb-T mages, as well as at a lower ontrast n the s ' mages. A horzontal profle through the leson shows a peak hemoglobn onentraton of 56 mromolar um ompared wth an average Hb-T of 9 um. Fgure 0.8: Tomograph NIR mages of female breast wth 3 m leson loated at 3 o'lok presented n the manner used by our lnal database. a. - d. and. - l. are a and s ' mages n graysale unts of /mm at the four wavelengths ndated. e. and g. are Hb-T and SO 2 mages determned usng method as desrbed n the text assumpton of 30% and 60% bulk water and lpd ontent. The x and y axes of the mages are poston n unts of mm. The average values and standard devaton of all pxels are ndated below eah mage. f. and h. are horzontal transets through the enter of mages e. and g. A seond ft was performed to the a mages wth all four quanttes, Hb-O 2, Hb-R, lpds, and water, as free parameters. The results are presented n Fgure 0.9. Values of 70

185 lpd ontent range as low as -200% and as hgh as 500%, whle water ontent values also range well below 0%. Though the ft faled to produe meanngful results for lpds and water, the hemoglobn mages fall wthn a reasonable range of values. Fgure 0.9: Images of a. water, b. lpds,. Hb-T and e. SO 2 are reovered usng a least squares ft to determne all four parameters method 2 from the a mages presented n Fgure 0.8. The x and y axes of the mages are poston n unts of mm. d. and f. are horzontal transets through the enter of mages. and e. In the thrd method, satterng power mages were determned by performng a lnear regresson to ln s ' and lnλ for eah mage pont. The resultng map of SP s dsplayed n Fgure 0.0. In addton, mages of lpd and water were determned from the relatonshps n equaton 0.2.a and 0.2.b. Smlar to the frst method, the orrespondng water and lpd values are subtrated and Hb-T and SO 2 determned from the a mages. The mages for Hb-T and SO 2 are also presented n Fgure 0.0. Table 0.2 summarzes the results for the 3 methods, whle also presentng data from a ft that gnores water and lpd ontent altogether. 7

186 Fgure 0.0: Images of a. satterng power b. water,. lpds, d. Hb-T and f. SO 2 are reovered usng method 3. The satterng power mage s alulated from a ft to ln s ' for the sequene of mages n Fgure 0.8 versus lnλ. The water and lpd mages are then determned from equatons 2.a. and 2.b. The x and y axes of the mages are poston n unts of mm. e. and g. are horzontal transets through the enter of mages d. and f. Average Values Value at enter of leson Method Hb-T um SaO2 % Water % Lpd % Hb-T um SaO2 % Table 0.2: Values for SO 2 and Hb-T for dfferent methods of ompensatng for water and lpd ontent. Method, the assumpton of a fxed bulk water and lpd ontent, orresponds to Fgure 0.8. Method 2 Fgure 0.9 nvolves a least-squares ft to all four hromophores. Method 3 Fgure 0.0 uses the satterng power mage to mage water and lpds. Method 4 assumes no lpd and water ontent. In Fgure 0., the mages of the ontralateral normal breast are presented. Only the 76 and 808 nm a and s ' are shown as they are representatve of the other wavelengths. Also dsplayed are the Hb-T, SO 2 mages usng method wth a fxed water and lpd ontent of 30% and 60%. 72

187 Fgure 0.: Tomograph NIR mages of the ontralateral normal female breast. a. - b. and. - d. are a and s ' mages n graysale unts of /mm at the two wavelengths ndated. 785 and 826 nm mages are omtted. e. and g. are Hb-T and SO 2 mages determned usng method as desrbed n the text assumpton of 30% and 60% bulk water and lpd ontent. The x and y axes of the mages are poston n unts of mm. f. and h. are horzontal transets through the enter of mages e. and g. 0.C.2.4. Dsusson Three methods of ompensatng for lpd and water absorpton wth a lmted number of wavelengths were desrbed n ths seton. Eah method results n a smlar hemoglobn onentraton mage wth a ontrast of approxmately 3: at the loaton of the 3 m leson. Values for both oxygen saturaton and hemoglobn onentraton hange by less than 5% between method assumed bulk water and lpd ontent and 3 mages of water and lpd obtaned from satterng power, but by as muh as 5% for the other two approahes ft to all four hromophores and assumpton of no water and lpd ontent. The mages of the ontralateral normal breast exhbt no strkng ontrast features. The hemoglobn values for the nvasve dutal arnoma may be effeted by the presene of the stanless steel ste marker and/or the host nflammatory response to the needle bopsy proedure ourrng two weeks pror. The metal lp was studed n phantom experments and found to have a mnmal effet when maged nsde a 84 mm tssue- 73

188 smulatng objet. The ontrbuton of the host nflammatory response to the NIR fndngs s unlear. Future studes wll be performed pre-bopsy and post-bopsy to assess the nfluene of these potental onfoundng rumstanes upon the resultng hemoglobn mages. Whle a larger number of optal wavelengths may be the key to good separaton of breast hormophores, NIR dode lasers at addtonal optal wavelengths n the lmted regon of PMT senstvty requre addtonal aquston tme, are often dffult to loate, and add to system expense. Usng satterng power nformaton to nfer water and lpd ontent may be suffent for ahevng aurate hemoglobn mages. It s possble some hybrd of frequenydoman and ontnuous-wave CW magng ould mprove spetral range, as noted by Bevlaqua et al. 08 It s not lear that the assumpton of a lnear relaton between lpd, water and satterng power wll hold over the entre female populaton or when appled to spatally resolved mages. The method appears to provde a reasonable estmate of the lpd and water ontent. It s lkely that tumor water and lpd ontent wll be dfferent than surroundng tssue and thus spatally-resolvng these onsttuents wll be neessary for ahevng hghly aurate hemoglobn measurements. The error ntrodued from bulk approxmatons appears ntally to have about 5% nfluene on the Hb-T and SO 2 estmates. If SO 2 s useful n dagnoss, however, these errors may prove mportant. In our urrent mplementaton, we wll ontnue to use the assumpton of 30% water and 60% lpd ontent untl approprate phantom studes are performed. 74

189 Chapter : Conludng remarks.a. Conluson In ths thess, the desgn, onstruton, and testng of a frequeny-doman parallel- deteton NIR data aquston system was presented. Data aquston from the system requres under 30 seonds for a sngle tomograph sle at one optal wavelength wth a measurement repeatablty for a sngle phantom on average of 0.5% n AC Intensty and 0.4 degrees n phase. In addton, methods for mproved reonstruton n the areas of magng addtonal tssue hromophores and the separaton of absorpton and satterng heterogenety were desrbed. Ths researh has led to an mproved novel magng system whh may be potentally useful n the dagnoss and deteton of breast aner. Mult-spetral optal tomography appears apable of n vvo magng of hemoglobn parameters n the breast. Prelmnary results show hgh ontrast n hemoglobn mages of breast lesons. Beause ontrast between lesons and surroundng tssue appears to exst n hemoglobn onentraton, oxygen saturaton, and satterng, t seems that leson haraterzaton based on quanttatve assessments of these parameters may be possble. At the onluson of ths thess, t appears that only one wavelength s needed to mage hemoglobn onentraton, but many wavelengths are needed for oxygen saturaton magng. Water and lpds play a lesser role, and urrent treatment of settng a fxed level of 30% and 60% ontent respetvely does not seem to be adversely effetng the results. Nevertheless, further phantom studes are needed n the areas of oxygen saturaton, water, and lpd ontent n order to better assess the optmal number of wavelengths and potental need for water and lpd magng. The Dartmouth group s now ontnung wth a more thorough and systemat lnal tral. The am of ths tral s to provde an ntal assessment of the dagnost utlty 75

190 of hemoglobn based mages, as well as study satterng hanges wthn the normal and anerous breast..b. Future studes.b.. 3-d versus 2-d Lght propagaton n a hghly satterng medum s nherently 3-dmensonal 3-d. The amount of lght that travels wthn any sngle 2-dmensonal 2-d plane s muh less than the amount of lght that samples volume outsde of ths plane. Though the 2-d assumpton that we use n our reonstruton program s nherently nvald, by adjustng the boundary ondtons we have been able to suessfully approxmate the 3-d dffuson of lght. To date, we have seen no advantage to usng a 3-d algorthm for our sngle plane magng system, but t s expeted that a full 3-d magng system and reonstruton algorthm must be used for truly quanttatve magng of heterogeneous tssue. The urrent emphass of the Dartmouth group has been to study the lnal potental of NIR tomograph magng, by lookng at tumors whh have been prevously deteted by other means. For ths type of study, the approxmate sze and loaton of the tumor s known, suh that nterpretaton of the results of our 2-d magng setup and algorthm should be aurate. It s mportant n these studes to remember the lmtatons of the 2-d setup whle nterpretng the mages that are aqured. The 2-d setup s an exellent means of testng the lnal utlty and dagnost potental of NIR magng n ths manner. The development of a 3-d magng system and algorthm wll lkely be mportant to future applaton of NIR magng pendng the realzaton of reasonable aquston and omputaton tme for suh a system..b.2. Satterng and absorbng rosstalk 76

191 For the urrent expermental setup and reonstruton program, we see about a 30% rosstalk of satterng nluson ontrast nto the absorpton mage. Ths effet s somewhat more pronouned n expermental studes than smulatons and should be explored further. Whle t s not expeted that the breast wll have satterng varatons of suffently hgh ontrast to appear as absorbers of dagnost onern, further refnements of the algorthm or data olleton ould mnmze ths effet..b.3. Spatal resoluton As a whole, t appears that quanttatve magng of hemoglobn n vvo s ahevable at moderate spatal resoluton e.g. 5-0 mm n a 00 mm phantom for a 2: ontrast absorbng nluson. 35,89 A promsng aspet of the work reported heren s that t appears that expermental results an be obtaned whh math very losely the expeted results from omputer smulatons. Ths ndates that the lmtng fators n spatal resoluton, objet poston and sze effets, and the separaton of absorpton and satterng an all be tested and mproved through omputer smulaton. In other words, wth mproved data aquston t appears we are now lmted agan by the reonstruton algorthm and not any data-model msmath or measurement nose. It s my mpresson that the engneerng sde of developng a hgh qualty data aquston system s pratally ahevable and that lmtatons n optal tomography suh as the spatally dffuse senstvty and the ll-posed nature of the nverse problem must be addressed n smulaton and theoretal mprovements made. Currently, the spatal resoluton lmts of the NIR method are unlear; resoluton s lkely the most fundamental barrer to eventual lnal utlty. For the urrent setup and reonstruton program, resoluton and mage qualty s lmted not by nstrumentaton but n the reonstruton proess. At present, we use a relatvely oarse FEM mesh spang, suh that resoluton mght be mproved slghtly by usng a fner mesh. In addton, t s possble that addtonal soure and detetor pars mght further mprove spatal resoluton. In general, 77

192 however, the ll-posed nature of the problem and the dffuse nature of lght travel wll lmt resoluton usng urrent reonstruton methods. One avenue beng explored s the norporaton of strutural nformaton from hgh resoluton magng modaltes suh as MRI to mprove the resoluton and auray of NIR hemoglobn mages. Not surprsngly, t s n areas suh as measurng hemoglobn ontent, dynam magng, and magng wth ontrast agents whh provde a dfferent type of nformaton than the strutural hanges seen wth onventonal magng.e. mammography and breast sonography, that show the most promse for future lnal applaton..b.4. Objet sze versus quantfaton Related to spatal resoluton, the ablty to aurately quantfy the hemoglobn levels of an nluson s redued as the sze s redued. It s possble to determne the effet on property estmaton for known sze objets and spef regularzaton shemes. In the same manner, for known sze and loaton objets, regularzaton an be tuned for the spef sze and geometry..b.5. Lmted lght penetraton A seond major lmtaton of optal tomography s the lmted dstane through whh NIR lght an be deteted. Currently, our expermental system an not pass lght through more than about m of breast tssue. Ths lmt an be nreased slghtly through mprovements n ouplng and detetor effeny, but t s probable that some large breasted women wll not be able to be maged and a number of women may not be maged near the hest wall..b.6. Multple modulaton frequenes The magng of the breast brngs up some hallengng albraton ssues. In partular, we are hghly senstve to ntensty hanges at the surfae of the breast. It s mportant n our urrent setup that we have onsstent ouplng of the fber opts wth the 78

193 tssue. One possble method to overome ths ssue to reonstrut on the dfferene between two modulaton frequenes. In ths manner, any systemat ouplng error or postonng error wll be the same at both frequenes and not enter nto the reonstruted mage. A prelmnary study of ths dea yelded that for the three nluson phantom desrbed n Chapter 7 and for modulaton frequenes of 50 MHz and 300 MHz, a dfferene n relatve ntensty of about 5% maxmum between the data for a homogeneous objet and the objet wth the 2: nlusons would be measured. These values do not beome muh larger untl frequenes n the GHz range. Conversely, for a sngle modulaton frequeny of 00 MHz, we see a maxmum dfferene n measured ntensty of over 50% for the same objets. Ths 0: dfferene n avalable measurement ontrast may be a lmtng fator n the mplementaton of ths sort of dfferenng sheme. Another use of multple modulaton frequenes?,? 2,...,? n s to nrease avalable data to the reonstruton algorthm. For the dffuson equaton equaton 2.4, absorpton and satterng oeffents an be onsdered onstant for a gven objet wth respet to modulaton frequeny. The measured data at dfferent modulaton frequenes wll provde dfferent and addtonal nformaton whh may mprove spatal resoluton or ad n the separaton of absorpton and satterng heterogenety. Ths addtonal nformaton an be used to reate multple Jaoban matres J, but wll not nrease the sze of the J T J matrx see Chapter 2 for defntons for a gven number of fnte element nodes. The Φ Φ o array and Jaoban matrx wll grow as a multple the number of modulaton frequenes n: o Φ Φ Φ Φ = Φ o ω Φ ω o ω Φ ω 2 o ω Φ ω n M 2 n and J ω J ω2 J = M,. J ω n but the J T J matrx wll reman the same sze wth nreased nformaton 79

194 T T T T J J = J J ω + J J ω + K + J J.2 2 ω n The addtonal nformaton should requre proper normalzaton as desrbed n Chapter 2, though the weghtng of dervatves of phase shft and ampltude wll hange for dfferent modulaton frequenes. Prelmnary smulaton studes mplementng ths method showed no mprovement n reonstruton qualty, however, lttle effort was made to optmze the mplementaton. 80

195 Appendx A: Itemzed Components Lst Itemzed Component Cost Quantty Total ILX Lghtwave LDX-3207B Current Soure $2,800 $2,800 Maron/IFR Systems 2023 RF Frequeny Generator $5,500 2 $,000 Poseond Pulse Lab 5545 Bas Tee $330 $330 PMTs Housng HC20-08, PMT R6537 SMA onnetors PE4589 Pasternak Enterprse $060 $0 6 6 $6,960 $60 Dretonal Coupler P: 99: ZFDC-20-3, Mnruts RF Mxer ZFM-50, Mnruts Low Pass Flter f =.9 MHz BLP-.9, Mnruts $45 $70 $35 2 $90 $70 $35 sxteen RF mxers ZEM-2B, Mnruts $50 6 $800 sx-way RF swth A, DowKey $600 $600 Fber launh module KT-2, Thorlabs Couplng Lenses C220TM-B and C230TM-B $000 6 $6000 x6 Fber opt ombner Custom-bult, Fbergude $000 $000 x6 RF spltter ZFSC-6-2-S, Mnruts $230 $230 DC spltter box bult n house by Sean Stauth $0 5 V supply E360A, Hewlett Pakard, $30 $30 SMA Rgd RF Cables PE382-2 Pasternak Enterprse SMA-BNC RF Cables PE $30 $ $480 $400 Rotary stage 36: B4836-TS, Velmex In Stepper motor LS500 Controller VP900 $3400 $3400 ollmatng lens F220SMA-B, Thorlabs $20 7 $2040 mm 0.39 NA optal fber FT-.0-EMT, Thorlabs SMA onnetors 040A-SMA, Thorlabs -m 6-mm glass fber bundles Custom, Cuba Produts $20 $0 $ $400 $60 $280 entre postonng setup was ustom-bult to our spefatons by Velmex, In. n Bloomfeld, NY $22,000 $22,000 8

196 Itemzed Component Cost Quantty Total massage table desgner, Kevn Grady, Stratford, VT $950 $950 AT-GPIB ard Natonal Instruments NI $000 $000 PCI-6703 Analog Output Board NI SCB68 Connetor Blok and SH6868 Cable $200 $200 PCI-603E A/D Data Aquston Board NI SCB00 Connetor Blok and Cable $2400 $2400 BNC oupled box FBU-6, Audon Eletrons, England $700 $700 Labvew Software NI $2000 $2000 Computer System Luky Star -- ask Greg Burke $2000 $2000 Dartmouth FORTRAN Reonstruton Program Preless Laser Dodes all are 9 mm wth pnode 9A 849 nm, 00 mw SDL-54-G, SDL 826 nm, 00 mw SDL-54-G, SDL 808 nm, 200mW, MLD As, Polarod through Intelte In. 785 nm, 50 mw HL785G, Htah, through Thorlabs 760 nm, 30 mw FIDL-30s-760x, Frankfurt, through Laser Components 66 nm, 40 mw ML20G8, Mtsubsh, through Laser Components $485 $480 $385 $85 $20 $220 $485 $480 $385 $85 $20 $220 TOTAL $83,000 82

197 Appendx B: Fle namng onventons Ths appendx attempts to haraterze the fle namng onventons wthn the data aquston system and the reonstruton program. Many of the data fles are output for plottng purposes. Other fles are used to pass data between the varous programs. All of the data nterhanges between FORTRAN and LabVew are done through these text fles. Parts of ths appendx were wrtten by Shudong Jang. B.. Major data aquston and reonstruton programs "New System Man Program.v" alls program to determne gan settngs: "Smultaneous Fnd 8 gan new al PS.v" whh has many subroutnes and data aquston program: "Parallel Aquston new albraton.v" whh has many subroutnes and alls FORTRAN programs: "d:\reon\hom8a.for" = Homogeneous fttng algorthm for albraton fle "d:\reon\het8a.for" = Same fttng algorthm but for expermental fle "d:\reon\both8a.for" = Reonstruton program B.2. Data fles used by the FORTRAN and LabVew programs. B.2.. CALIBRATION and GAIN SETTING fles "Smultaneous Fnd 8 gan new al PS.v" These fles are the nputs and outputs of the gan settng program. The xxx stands for the sx wavelengths => 66, 76, 785, 808, 826, and 849. The outputs of the gan settng program are used n the data aquston program "Parallel Aquston new albraton.v" PMT_xxx_newalb.as Gan_setnew_xxx.dat New_xxx_albraton.as INPUT albraton for the 6 detetors. Determned prevously usng fber n enter of phantom and varyng lght level and gan settngs as desrbed n 4.D.2. Calbraton fle format s frst row = gan settngs 2nd row through 7 row = log-log slope/detetor 8th row through 33rd row = log-log onstant 34th row through 49th row = phase fator olumns are for eah gan settng OUTPUT optmal gan settngs for the partular objet as determned n program: "Smultaneous Fnd 8 gan new al PS.v". OUTPUT fnal albraton terms for eah detetor based on the gan settngs n Gan_setnew_xxx.dat. 83

198 Calbraton fle format s 6 rows one for eah detetor frst olumn = log-log slope seond olumn = log-log onstant thrd olumn = phase fator *********************************************************************** B.2.2. OUTPUT FILES from measurement program: "Parallel Aquston new albraton.v" "flename.dat" s nput by user, "flename.as" and "flename.paa" are reated automatally n "New System Man Program.v". Only.as fle s used n the reonstruton program. "flename.dat"? ontans all settngs and the raw measured and referene data flename.as? measured albrated magnary & real data nterleaved. Data s ordered as below: Soure : Detetor Imagnary Soure : Detetor Real Soure : Detetor 2 Imagnary Soure : Detetor 6 Imagnary Soure : Detetor 6 Real Soure 2: Detetor 2 Imagnary Soure 2: Detetor 2 Real Soure 2: Detetor 3 Imagnary Soure 2: Detetor 3 Real Soure 2: Detetor 6 Real Soure 2: Detetor Imagnary Soure 2: Detetor Real Soure 3: Detetor 3 Imagnary Ths order orresponds to our old sngle detetor system s way of aqurng data. Ths.as fle s the one used by the RECONSTUCTION program! flename.paa? measured albrated ampltude & phase data Data s tab-delmted and s ordered n detetor order followed by soure order. Note: Ths s dfferent than the.as fle and orresponds to the parallel system s way of aqurng data. 84

199 Soure Detetor Ampltude Phase Soure Detetor 2 Ampltude Phase Soure Detetor 6 Ampltude Phase Soure 2 Detetor Ampltude Phase Soure 2 Detetor 2 Ampltude Phase Soure 2 Detetor 6 Ampltude Phase Soure 3 Detetor Ampltude Phase Soure 6 Detetor 5 Ampltude Phase Soure 6 Detetor 6 Ampltude Phase *********************************************************************** B.2.3. OUTPUT RECONSTRUCTED IMAGE FILES for FORTRAN programs flename a.dat: Reonstruted absorpton mage. Absorpton oeffent s reported for eah node n the FEM mesh flename D.dat: Reonstruted satterng mage. Redued satterng oeffent s reported for eah node n the FEM mesh. For hstoral reasons, a "D" s appended to the flename, however, redued satterng oeffent s reported, NOT dffuson oeffent. *********************************************************************** B.2.4. COMMON DATA FILES for FORTRAN programs flenames do not hange for eah reonstruton. They are overwrtten eah tme the reonstruton program s run. Dretory = C:\watom\magng\felement Tssure6.dat? Optal propertes of homogeneous ft Output by the homogenous fttng program. Ths fle s used by the reonstruton program Hom_off.dat? Intensty of I and Phase offset between homogeneous alulated & measured data Output by the homogeneous fttng program. Ths fle s used by the reonstruton program hom_b.dat? Value of a for boundary ondtons eq. 2.5 and seton 6.D..4. Ths fle s used by the reonstruton program and the heterogeneous ft. Hetero6.dat? same as "tssue6.dat", but for heterogeneous ft. Reon 85

200 Het_off.dat? same as "hom_off.dat", but for heterogeneous ft. Reon Heter.out? albrated data & orgnal ft for all 256 =6*6 Ths s output near the begnnng of the reonstruton program and are used only for plottng purposes Heter2.out? Calbrated data & fnal ft after reonstruton for all 256 Ths s output at the end of the reonstruton program and are used only for plottng purposes. Note: Calbrated data =? alb? alb =? hetero? homo? homoft Dretory = C:\labvew\automag Hom_ft.out alulated data for homogeneous ft averaged over all soures 6 ponts Hom_org.out measured data for homogenous objet average over all soures 6 ponts Output by the homogeneous fttng program and are used only for plottng purposes. Het_ft.out same as above for heterogeneous Het_org.out same as above for heterogeneous Output by the heterogeneous fttng programs and are used only for plottng purposes. 86

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