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2 2005 IEEE Nuclear Sciece Sympsium Cferece Recrd M03-06 Fast Mte Carl Estimati f Patiet ad Detectr Scatter ad Crsstalk Ctamiati i SPECT Imagig Jisg Ouyag, Stephe C. Mre, Mi-Ae Park, ad Gerges El Fakhri Brigham ad Wme s Hspital ad Harvard Medical Schl, Bst, Massachusetts 025 Abstract--Mte Carl methds ffer the ptetial t prvide a accurate crrecti fr scatter ad detectr effects, especially whe imagig istpes that emit multiple phts, r dualistpes. Recetly, a grup at Utrecht Uiversity has develped sme prmisig accelerati techiques by cmbiig scatter maps with cvluti-based frced detecti. We exted their wrk i fur ways: usig the Delta Scatterig techique t rapidly determie pht iteracti pits, simulatig scatter maps fr may eergy bis t imprve accuracy, decuplig the simulati f the bject ad the detectr usig pit spread fuctis which iclude all detectr effects, ad icludig cheret scatterig i additi t phtelectric effect ad Cmpt scatterig whe simulatig pht iteractis. We stre pit spread fuctis as multi-dimesial arrays t imprve speed ad accuracy. A sftware package was develped ad validated i a trs phatm experimet. Three spheres filled with I were placed i the -uifrmly atteuatig phatm. CT ad SPECT scas were acquired ad spatially registered. A gd agreemet betwee experimetal ad simulated prfiles was fud fr fur eergy widws (50-95, 8-04, 47-95, kev). Fr the tw lw eergy widws, primary phts ctributi ca be mdeled crrectly ly if the PSF icludes all detectr effects. A triple-eergy widw methd verestimated scatter prfiles cmpared t the Mte Carl simulated scatter.. We use the ubiased Delta Scatterig (DELTA) methd t determie pht iteracti pits, which is faster tha takig may small steps alg each pht s path [4,5]. 2. T imprve accuracy, we simulate scatter maps fr may eergy bis thrughut the useful regi f the spectrum. 3. The simulatis f the bject ad the detectr are cmpletely decupled usig pre-stred pit-spread fuctis (PSFs) which iclude all the effects f peetrati ad scatter i the cllimatr, the NaI(Tl) crystal, ad the materials behid the crystal. We stre simulated PSF as multi-dimesial arrays, elimiatig the eed t cmpute aalytic fuctis Cheret Scatterig Cllimatr E 2 E 3 P 3 E P 3 P 2 E E P 2 P θ E 0 E P P 0 E 0 Cmpt Scatterig Origial Emissi M I. INTRODUCTION ONTE Carl (MC) simulati permits accurate mdelig f pht trasprt i the bject ad detectr based the radiuclide distributi ad its CT map. I priciple, this culd be used t implemet a accurate crrecti fr scatter ad ther surces f ctamiati, especially whe imagig radiuclides that emit multiple phts r dual-radiuclide pairs, fr which crss-talk ctamiati amg differet phtpeak widws ca limit the accuracy f recstructed images. II. METHODS MC simulati requires sigificat cmputatial pwer, which remais the limitig factr fr its rutie implemetati i cliical settigs. I recet years, a grup at the Utrecht Uiversity Medical Ceter has develped sme prmisig accelerati techiques by cmbiig simulated scatter maps with cvluti frced detecti (CFD) [,2,3]. We have exteded their research i fur ways: Crystal Figure : A illustrati f a simulated pht evet. durig CFD, thereby imprvig speed ad accuracy. 4. I bth the bject ad the detectr, we iclude cheret scatterig i additi t phtelectric effect ad Cmpt scatterig whe simulatig pht iteractis. We have develped a sftware package writte i bjectrieted C++, ad validated it experimetally usig a Data Spectrum athrpmrphic trs phatm. We acquired CT ad list-mde SPECT scas f the water-filled phatm, which ctaied three spheres (a 2-cc sphere attached t the liver, a 2-cc sphere i the left lug, ad a 4.2-cc sphere i the right lug). T allw registrati f SPECT ad CT scas, the three spheres were filled with I ad 8 F-FDG, ad the phatm was first scaed a GE PET/CT scaer, which prvided perfectly registered PET ad CT image vlumes. Oce detectable 8 F-FDG was left i the phatm, it was the scaed a Siemes e.cam SPECT scaer ad the SPECT sca was registered t the PET sca by matchig the ceters f the three spheres i bth vlumes, thereby yieldig registered SPECT ad CT scas f the phatm /05/$ IEEE 560

3 I emits bth 7.3 kev (90% abudace) ad kev (94% abudace) primary phts. We defied twety 0- kev eergy bis (EBs) which cvered the eergy rage [ kev]. Additially, we defied fur eergy widws (EWs) fr detected phts: [50-95 kev], [8-04 kev], [47-95 kev], ad [ kev]. The upper tw widws are wide widws arud the tw phtpeaks f I-, while the lwest widw is dmiated by lead x-rays, ad the secd kev kev directi at P, the scatted eergy E P is calculated accrdig t the scattered agle, θ. The crrespdig scatter map is selected accrdig t E P. The weight at the vxel where P is lcated fr the selected s-map is icreased by the prduct f the curret pht histry weight ad the prbability per slid agle fr a pht t scatter alg the cllimati directi. Detectr PSF, which are idepedet f the imagig bject, were simulated separately ad represeted by a 4-dimesial array idexed by 4 EW, 20 EB, 32 surce-t-cllimatr distace bis (frm 0.36 cm t 6.55 cm), ad 64 radialdistace bis (frm 0 t cm). All the physics prcesses 8-04 kev kev 8-04 kev kev Figure 3: Simulated prjecti prfiles frm primary ad bject-scattered phts. i all the detectr materials were mdeled kev kev Figure 2: A cmparis f experimetal (blue slid lies) ad simulati (red dashed lies) cut prfiles fr e prjecti agle at fur eergy widws. lwest widw ctais a mixture f lead x-rays ad scattered ctamiati typical f that see i the lwest phtpeak widw f Ga-67. The three spheres with kw activity defied the emissi map (e-map) fr ur iitial tests. Decay phts were first geerated accrdig t this e-map; these were prpagated thrugh the atteuatr t simulate 20 scatter maps (s-maps) fr each 0-keV-wide EB. The s-maps deped the prjecti agle. Fig. illustrates e pht evet, i which a pht emitted frm P 0 uderwet Cmpt scatterig at P, cheret scatterig at P 2, ad ather Cmpt scatterig at P 3, befre escapig frm the imagig vlume. At each iteracti pit, the pht is frced t scatter while the pht histry weight is multiplied by the prbability f phtelectric effect. Each successive iteracti pit is used t update the s-maps. Fr example, if a pht is scattered alg the cllimati Figure 4: TEW crrected (slid blue lies) versus simulated (dashed red lies) cut prfiles fr scattered phts. The weight f each vxel i the e-map ad s-maps was first multiplied by a factr represetig the prbability that a pht emitted frm the vxel i a directi perpedicular t the detectr wuld reach the detectr withut iteracti. The, the e-map ad s-maps were blurred by the PSF, idexed apprpriately fr the surce-plae t cllimatr distace, t prduce the prjectis fr each eergy widw. 56

4 III. RESULTS AND DISCUSSIONS Fig. 2 shws a cmparis betwee experimetal ad simulated results (based 50M geerated pht evets) f prjecti prfiles alg the trasaxial directi by itegratig ver a axial rage which cvers the tw spheres placed i the lugs. The same scalig factr was used fr all fur eergy widws. A very gd agreemet betwee experimetal ad simulated data ca be see. [6] Takashi Ichihara, Kichi Ogawa, Nbutku, Atushi Kub ad Shz Hashimt, Cmpt Scatter Cmpesati Usig the Triple-Eergy Widw Methd fr Sigle- ad Dual-Istpe SPECT, J. Nucl. Med., vl 34,. 2, pp ,993 Fig. 3 shws separate ctributis frm primary ad scattered phts fr the tw lw-eergy widws. As ca be see, the primary pht ctributi is clearly t egligible. This represets the ctributi frm primary phts which reach the detectr withut udergig ay iteracti i the bject but the iteract i the detectr, e.g., by scatterig, r prducig lead X-rays). Fig. 4 cmpares prfiles f scattered phts i the tw I- widws estimated by the MC methd with thse estimated by the triple-eergy-widw (TEW) methd [6]. Fr TEW, we utilized 5-keV widws arud each phtpeak widw. The TEW methd verestimated the scatter, ad the prfiles were isier tha thse btaied by the apprach. IV. CONCLUSIONS I cclusi, we have develped ad validated a prmisig simulati package. Future wrk will iclude the icrprati f ur fast MC simulati it a iterative recstructi algrithm t crrect fr scatter, crss-talk, ad lead X-rays simultaeusly i sigle- ad dual-istpe SPECT imagig. ACKNOWLEDGMENT This wrk was supprted by NIH grats RO-EB00802, RO-EB00989, ad RO-EB ad a Parters Cllabrative Research Grat [] Hug W A M de Jg ad Freek J Beekma, Rapid SPECT simulati f dwscatter i -uifrm media, Phys. Med. Bil., vl. 46,. 3, pp , 200. [2] Hug W.A.M. de Jg, Eddy T.P. Slijpe, ad Freek J. Beekma, Accelerati f MC SPECT Simulati usig Cvluti-Based Frced Detecti, IEEE Tras. Nucl. Sci., vl. 48,., pp , 200. [3] Hug W.A.M. de Jg, We-Tug Wag, Eric C. Frey, Max A. Viergever, ad Freek J. Beekma, Efficiet simulati f SPECT dw-scatter icludig pht iteractis with crystal ad lead, Med. Phys., vl. 29,. 4, pp , [4] E. Wdcck, T. Murphy, P. Hemmigs, ad S. Lgwrth, Techiques used i the GEM cde fr Mte Carl eutrics calculatis i reactrs ad ther systems f cmplex gemetry, Prceedig f the Cferece fr Applicatis f Cmputig Methds t Reactr Prblems, Arge Natial Labratry, pp. 557, 965. [5] S.C. Mre, P.A. Sats, C.H. Hldswrth, ad G. El Fakhri, Accelerati f SPECT MC Simulati Usig DELTA Scatterig, J. Nucl. Med., vl. 43,. 5,

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8 MP/BME 574 Applicati 3 Due Mar 3, Applicati 3 ivlves the Rse Mdel. Dwlad the tw versis f the Rse image (Figs. ad 2), Rseimage ad Rseimage2, frm the website. These are bth matrix, 6 bit Tiff images. I bth images the bject size decreases by a factr f 2 fr each clum frm left t right. I e image the S/N fr each rw decreases by a factr f 2 frm tp t bttm. Fr the ther image the Rse defiiti f ctrast fr each rw decreases by a factr f 2 frm tp t bttm. Aswer the fllwig questis abut the tw images. Figures ad 2: A. Refer t the Rse mdel defiitis f ctrast ad S/N. Which image has cstat S/N fr each rw ad which image has cstat ctrast fr each rw? B. Fr lesis with cstat S/N the ctrast-detail curves shuld defie a lie f is-perceptibility. By selectig the apprpriate lesis make tw ctrast-detail curves, e frm Rseimage ad e frm Rseimage2, that crrespdig t lies f is-perceptibility. At least 5 pits shuld make up each curve. Althugh Matlab is pwerful fr may image-related applicatis, superir measuremet tls are available i the ImageJ sftware package. Specifically, I recmmed usig ImageJ fr peratis requirig regi f iterest (ROI) measuremets. This sftware is free ad ca be dwladed frm the NIH website ( if it is t already available yur system. A lik t this site is available the curse website. TIFF images ca be laded directly it ImageJ.

9 MP/BME 574 Applicati 3 Slutis; 3/3/2006 Please te that I icrrectly referred t bject size decreasig by a factr f 2 frm left t right. I fact the bject diameter is decreasig by a factr f 2. The bject size i terms f area is decreasig by a factr f 4.. A. There are tw appraches t determiig which image has cstat ctrast fr each rw ad which has cstat S/N: Thery ad Experimet. () Thery: Recall that C =. I class it was shw that fr lesis f differet areas but equivalet ctrast, the average sigal per uit area S = /Area will be the same because the differet areas cacel ut f the rati. By visual ispecti Rseimage has cstat ctrast/rw, which meas Rseimage2 has cstat S/N/rw. (2) Methd 2: Direct Measuremet usig ImageJ: Rseimage (Figure): Frm the measuremet iside lesi, = i 2 = 476 cuts. Iside lesi 2, = i 2 = 7 cuts. Outside lesi, = i 2 = 49 cuts. Oside lesi 2, = i 2 = 03 cuts C = = C 2 = = Figure : Rseimage, a) measuremet fr lesi. b) measuremet fr lesi. Bx shws lie f isperceptibility fr ctrast-detail curve. 2 c) ROI measures fr lesi d) ROI measures fr lesi 2.

10 MP/BME 574 Applicati 3 Slutis; 3/3/2006 Rseimage2 (Figure 2): Frm the measuremet iside lesi, Iside lesi 2, = i 2 = 452 cuts. = i 2 = 36 cuts. Outside lesi, = i 2 = 396 cuts. Oside lesi 2, = i 2 = 07 cuts C = = 0. 4, C 2 = = S = C N = =, S = C N 2 = = 2 Figure 2: Rseimage2 a) measuremet fr lesi. b) measuremet fr lesi. Bx shws lie f isperceptibility fr ctrast-detail curve. 2 c) ROI measures fr lesi d) ROI measures fr lesi 2. B. I Rseimage the lies f isperceptibility lie alg the diagals. I chse the mai diagal traspse idicated by the yellw bx i Fig. b. I Rseimage2 the lies f isperceptibility lie alg the rws. Ay rw suffices; I chse the middle rw idicated by the yellw bx i Fig. 2a. Fig. 3 shws the ctrast-detail curves fr these lesis.

11 MP/BME 574 Applicati 3 Slutis; 3/3/2006 Figure 3: Ctrast Detail curves