DUAL ENERGY MAMMOGRAPHY: EVALUATION OF SCINTILLATORS FOR X-RAY DETECTORS USING A SIGNAL TO NOISE RATIO MODEL

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1 DUAL ENERGY MAMMOGRAPHY: EVALUATION OF SCINTILLATORS FOR X-RAY DETECTORS USING A SIGNAL TO NOISE RATIO MODEL Adrinos Toutountzis,b, Nikolos Stthonikos, Giorgos Fountos, Giorgos Nikiforidis b, Ionnis Kndrkis Deprtment Medicl Instruments Tenology, Tenologicl Eductionl Institution of Athens, Ag. Spyridonos, Aigleo, 0 Athens, Greece b Deprtment of of Medicl Physics, Medicl Sool, University of Ptrs, 00 Ptrs, Greece Corresponding uthor: kndrkis@teith.gr Keywords: dul energy, mmmogrphy, noise,, GdOS, LSO. Abstrct. The purpose of this study ws to perform n nlysis on microclcifiction visuliztion in dul energy subtrction mmmogrphy. A theoreticl model ws pplied in order to evlute the signl to noise rtio on subtrcted mmmogrphic imges. The detector performnce is investigted nd compred for two different scintilltors; the commercilly used GdOS:Tb, nd LSO:Ce. In ddition, the estimtion of signl nd noise levels is performed for different tissue compositions nd vrious x ry spectr. The imge prmeters were selected for the optimiztion of dul energy subtrction tenique for the improved detection nd visuliztion of microclcifictions. The results re presented nd the dependence on imge prmeters is discussed.. Introduction During the pst decde digitl X ry imging hs led to vriety of new medicl imging pplictions su s dul energy x-ry mmmogrphy. The ltter seems to be n innovtive tenique in specific tissue imging, like microclcifiction or soft tissue visuliztion. In ddition, conventionl mmmogrphy does not provide dequte informtion for tissue rcteriztion su s differentition between benign nd mlignnt tumors. With dul energy tenique, high nd low energy imges re seprtely cquired nd subtrcted from e other in weighted mnner to cncel out the uttered tissue structure so s to decrese the obscurity from overlpping tissue structures. The informtion derived from dul energy mmmogrphy cn be evluted by estimting the noise levels in the finl subtrcted imge. Thus signl to noise () nlysis is necessry to provide dt for imging performnce nd the optimiztion of the dul exposure prmeters used. Previous studies on this subect hve been reported [,] for systems bsed minly on the commercilly vile Thllium ctivted Cesium Iodide (CsI:Tl) nd Terbium ctivted Gdolinium Oxysylfide (Gd O S:Tb) scintilltors. In the present pper dul energy signl to noise nlysis ws performed for Cerium ctivted Lutetium Oxyorthosilicte (Lu SO :Ce) scintilltor whi is widely used in PET

2 detectors, nd hs been recently studied for x-ry mmmogrphy pplictions [,], exhibiting suite imging performnce.. Mterils nd Methods Assuming compressed brest of totl thickness T, composed by three types of tissue: dipose, glndulr nd microclcifiction, with thicknesses t, t b nd t c respectively. The men mesured signls for the high nd low energy will therefore be [] : S de d Φ μ ( E ) t b ( E ) tb c ( E ) tc ( E) e α μ μ A( E) Q( E) () where denotes the high or low energy, Φ ( E ) is the low or high energy spectrum in terms of photon fluence (photons/mm ), μ ( E ) is the energy dependent liner ttenution coefficient for the three types of tissue, b, c, A ( E ) is the detector quntum efficiency of the scintilltor s function of photon energy nd Q ( E ) is the detector gin nd represents the signl generted by e detected X ry photon. The detector quntum efficiency, whi is the frction of incident photons intercting with the scintilltor, ws clculted using the following eqution: μ ( ) ( ) S E t e S A E () μ ( E ) S is the liner ttenution coefficient of the scintilltor used for the conversion of X rys to opticl photons. The energy dependent detector gin is fctor whi describes the signl generted per bsorbed x ry photon, tking into ccount performnce rcteristics of the scintilltor coupled with n opticl detector nd is expressed s: Q ( E ) n c g Λ S E E Opticl () n c is the intrinsic conversion efficiency, expressing the frction of bsorbed x rys converted into light within the scintilltor mteril, E Opticl is the pek vlue of the emitted light spectrum expressed in ev, g Λ is the light ttenution coefficient nd S is the spectrl mting fctor, expressing the spectrl comptibility of the emitted light spectrum with the spectrl sensitivity of the opticl detector. Defining Δ μ b ( E ) μ b ( E ) μ ( E ) nd Δ μ c ( E ) μ c ( E ) μ ( E ), the unsubtrcted imge signl to noise rtio, for high or low energy X rys, is defined by the eqution: S de d de d Φ Φ μα ( E) T b ( E) tb c ( E) tc ( E) e e A( E) Q( E) μα ( E) T b ( E) tb c ( E) tc ( E) e e A( E) Q ( E) () According to the formlism mde by Lemcks et l [], the overll dul energy subtrcted imge for glndulr tissue or microclcifiction cncelltion is:

3 i t i kil + Sl t k ih Sh, i b, c () In eqution () the numertor represents the signl for the grnulr or the microclcifiction (b or c respectively) nd the denomintor denotes the squre root of the noise vrince; the coefficients k i re combintions of differences between the dipose, glndulr tissue nd microclcifiction liner ttenution coefficients, verged over the detected energy spectrum: k, k () k, k For the clcultion of signl to noise rtio, compressed brest thickness of cm ws ssumed, consisting of 0% dipose nd 0% glndulr tissue nd microclcifiction size rnging from 00 μm to 00 μm. The incident x ry photon fluence used for equtions () nd (), ws clculted using theoreticl model [] tht describes the energy spectrl distribution of x rys produced by molybdenum, rhodium nd tungsten node trget. The x ry ttenution for the formtion of the men mesured signl, s well s for the quntum detection efficiency nd the finl signl to noise rtio, were clculted by considering exponentil X ry bsorption within the tissue nd the scintilltor mteril. The liner ttenution coefficients for the dipose nd glndulr tissue (ICRU-), for the microclcifictions hydroxyptite [C (PO ) (OH)] nd for LSO:Ce nd GdOS:Tb scintillting mterils were obtined from dt tbulted by NISTR []. The following te shows the vlues of vrious prmeters for GdOS:Tb nd LSO:Ce, su s density, intrinsic conversion efficiency [,], pek vlue of the light emission spectrum in nnometers nd spectrl comptibility with morphous silicon flt pnel detector. ρ GOS LSO.. η C λ Te : Scintilltor prmeters Using reltions (), () nd (), the men mesured signls for the high nd the low energy my be clculted s function of x ry photon energy nd depend on the detector intrinsic prmeters. The finl expression for the subtrcted clcifiction signl to noise rtio depends directly on the microclcifiction thickness, the low nd high energy nd vrious combintions of ttenution coefficient differences verged over the spectr.

4 . Results nd Discussions Clcultions were performed for vrious combintions of tissue composition nd high x ry tube voltges, node trgets, filters nd for both GdOS nd LSO scintilltors. In the following tes we cn see the for microclcifiction signl in subtrcted imges for high nd low energy imges using GdOS nd LSO scintilltor. Combintion of HE LE Anode/Filter/Voltge Exposure of HE - LE Microclcifiction size in μm Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 W/L/ Mo/Mo/0 W/L/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Mo/Mo/ Rh/Rh/0 Mo/Mo/ Rh/Rh/0 Mo/Mo/ Rh/Rh/ Mo/Mo/ Rh/Rh/ Mo/Mo/ Rh/Rh/0 Mo/Rh/ Te : results for microclcifiction subtrcted imges using GdOS scintilltor nd ssuming 0% dipose nd 0% glndulr tissue thickness for cm brest. Tking into considertion the exposure of High nd Low energy imges, we re compelled to select the ones tht mintin low exposure levels when dded together. For exmple in te, Mo/Mo/0 High energy imge (where Mo/Mo/0 is node/filter/voltge) nd Rh/Rh/0 Low energy imge yields vlue of. for 00 μm microclcifiction wheres for Rh/Rh/0 HE nd Mo/Rh/ LE yields vlue of.. The ltter vlue is higher but lso its exposure levels when dded re

5 significntly lower; in the first cse the exposure is. R wheres in the second cse it s. R. If we consider tht higher exposure vlues leds to higher men glndulr dose for the ptient then it s impertive to keep exposure low. If we dopt minimum threshold of in order to be e to detect microclcifictions nd mintin mximum limit of ~00 mr exposure then, for GdOS scintilltor (te ) we cn see tht the optimum combintion of node, filter nd voltge for High energy is Rh/Rh/-0 nd for low energy is Mo/Mo-Rh/-0 llowing us to detect microclcifictions the size of 00 μm. If we set the threshold to then the minimum microclcifiction size tht we cn detect is 00 μm. Combintion of HE LE Anode/Filter/Voltge Exposure of HE - LE Microclcifiction size in μm Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Mo/Mo/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 Rh/Rh/ Mo/Mo/0 W/L/ Mo/Mo/0 W/L/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Mo/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Rh/Rh/ Rh/Rh/0 Mo/Mo/ Rh/Rh/0 Mo/Mo/ Rh/Rh/0 Mo/Mo/ Rh/Rh/ Mo/Mo/ Rh/Rh/ Mo/Mo/ Rh/Rh/0 Mo/Rh/ Te : results for microclcifiction subtrcted imges using LSO scintilltor nd ssuming 0% dipose nd 0% glndulr tissue thickness for cm brest. Results from LSO scintilltor seem to produce lower vlues of. More prticulrly, High energy imge Rh/Rh/0 nd Mo/Mo/ yields. for 00 μm microclcifiction size using GdOS wheres the sme setting yield. for LSO scintilltor below the threshold.

6 for Different microclcifiction sizes 0 Rh/Rh/0 - Mo/Mo/ LSO Rh/Rh/0 - Mo/Mo/ GdOS Microclcifiction size in μm Digrm : Chrt showing the difference in for LSO nd GdOS scintiltor for Different Microclcifiction Sizes Rh/Rh/ - Mo/Mo/0 LSO Rh/Rh/ - Mo/Mo/0 GdOS Microclcifiction size in μm

7 for different microclcifictions 0 Rh/Rh/ - Mo/Mo/0 LSO Rh/Rh/ - Mo/Mo/0 GdOS microclcifiction size in μm Digrm : Chrt showing the difference in for LSO nd GdOS scintiltor for different microclcifiction sizes Rh/Rh/0 - Mo/Rh/ LSO Rh/Rh/0 - Mo/Rh/ GdOS microclcifiction size in μm Digrm : Chrt showing the difference in for LSO nd GdOS scintiltor

8 Digrm : Rh/Rh/0 spectrum (in ue) nd Mo/Mo/ spectrum (in green). Rhodium filter thickness is μm nd Molybdenum filter thickness is 0 μm.. Conusions This pper described theoreticl frmework for clculting the signl to noise rtio in dul energy mmmogrphy using tbulted dt, simulting ttenution of x rys in brest tissues nd modeling the detector performnce for two different scintillting mterils; GdOS:Tb nd LSO:Ce. The present study ws contribution to the optimiztion of the exposure prmeters t Rh/Rh/-0 for high energy nd Mo/Mo-Rh/-0 for low energy. The performnce of the LSO:Ce scintilltor bsed detector showed vlues thn GdOS:Tb.

9 . Referrences [] Lemcks R.M., Kppdth S.C., Shw C.C., Liu X., Whitmn G.J., (00), A dul-energy subtrction tenique for microclcifiction imging in digitl mmmogrphy, Medicl Physics, (), - [] Brndn M-E., Rmirez-R V., (00), Evlution of dul energy subtrction of digitl mmmogrphy imges under conditions found in commercil unit, Phys. Med. Biol., 0-0 [] Miil C., Dvid S., Liprinos P., Vlis I., Nikolopoulos D., Klivs N., Toutountzis A., Cvours D., Kndrkis I., Pnyiotkis G, (00), Evlution of the imging performnce of LSO powder scintilltor for use in X ry mmmogrphy, Nu. Instr. Meth. Phys. Res. A, 0, - [] Dvid S., Miil C., Vlis I., Nikolopoulos D., Liprinos P., Klivs N., Kltzis I., Toutountzis A., Efthimiou N., Loudos G., Sinoudis I., Cvours D., Dimitropoulos N., Nomikos C.D., Kndrkis I., Pnyiotkis G.S., (00), Efficiency of LSO powder phosphor s X ry to light converter under mmmogrphic conditions, Nu. Instr. Meth. Phys. Res. A,, - [] Boone M.J., Fewell T.R., Jennings R.J, (), Molybdenum, rhodium nd tungsten node spectrl models using interpolting polynomils with ppliction to mmmogrphy, Medicl Physics, (), - [] Storm, E., Isrel, H., (). Photon cross-sections from 0.00 to 00 MeV for elements through 00. Report LA-, Los Almos Scientific Lbortory, University of Cliforni, CA. [] Kndrkis I., Cvours D., (00). Role of the ctivtor in the performnce of scintilltors used in X ry imging. Applied Rdition nd Isotopes, -

Jim Lambers MAT 169 Fall Semester Lecture 4 Notes

Jim Lambers MAT 169 Fall Semester Lecture 4 Notes Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of