1、interaction of x-rays with matter and imaging gocha khelashviliassistant research professor of physicsillinois institute of technologyresearch medical physicistexelar medical corporationthe planx-ray interactions with matter used at imaging energies photoelectric effect coherent scattering incoheren

2、t scattering pair and triplet production refraction small- and ultra-small angle scattering radiography how does it work? imaging parameters and sources of x-ray contrast drawbacks of radiographydiffraction enhanced imaging (dei) how does it work? imaging parameters and sources of x-ray contrast dra

3、wbacks of deimultiple image radiography (mir-planar mode) how does it work? sources of x-ray contrast mir parameters and imagesmir model based on discrete scatterers multiple scattering series approach and mir transport equation solution of mir transport equation imaging parameterssummaryphotoelectr

4、ic effectklmllkkmmkkphotoelectric absorptionfluorescent x-ray emission2e (cm /atom) 4 at 0.1 mev, gradually rising to 4.6 at 3 mev.for 3 at 0.1 mev, gradually decreasing to 1 at 5 mev for 0.1 mev, photoelectric efnmzahnhmhvh4322-1e33ect most important (cm /atom) (cmg ) zzaahhthompson (classical) sca

5、ttering2221500211 cos where 2.817 10m classical electron radius2 no energy loss by photon - no recoil by electron.edkerrdm cthompson (classical) scattering222302000181 cos2 sin 66.525 1023drrmdrayleigh scattering (coherent scattering)1 . photons are scattered by bound electrons2. atoms are neither e

6、xcited or ionized3. scattering from different parts of electron cloud - coherent scatteringrayleigh scattering (coherent scattering)22203211q1 cos( ,)2 sin where sin= 222( ,)( ,)( )exp - atomic form factor where ( )( , , ) - total electron densitysin ( ,)4( ) - for sphericdrf x zxdf x zf q zriq r d

7、rrx y zqrf q zrr drqr 00010al symmetry ( ,)( ,)|exp| (atomic scattering factor, atomic structure factor) - ground state wf calculated from hartree-fock theory znnf x zf q ziq r 222 (cm /)rzatomhcompton scattering (incoherent scattering)1. energy is transfered to electron2. electron recoils from coll

8、ision3. electron considered at rest before collision (no bounding effects)4. electron deposits dose in the mediumcompton scattering (incoherent scattering)220220222221sin - klein-nishina cross section211 cos21 cos111(1 cos )11 cos1 cos (in mev)0.511 knknedhhhrdhhhdrfdfhhm c effects of binding energy

9、 in compton (incoherent) scattering 1. electrons are in constant motion in atoms (binding effect)2. electrons recoil after collision3. energy is transfered to electrons4. x-ray photon looses part of its energy inckndddd20120011,( ,)( ,) and ( ,)exp0 ( ,)( ,) - incoherent scattering function,|exp() |

10、( ,)zjjzzmnmns x zs q zf q zs q ziq rs x zs q zs q ziq rrf q z effects of binding energy in compton (incoherent) scattering2011 cos( ,) 2 sin2incknfs x zd pair production222energy conservation - 2; momentum conservation: 2 cos2 cos 2cos2cos2cos , where 1 and cos1 2 (contradiction)pair production can

11、nothhmcpchvphpcmvcmccchmc conserve both energy and momentum unless some other object is involved in the process to carry away part of initial photon momentumpair production in nuclear coulomb force fieldpair production in nuclear coulomb force field 2222012 ( , ,) bethe - heitler cross section - egs

12、4, egsnr424ln4,ln4333c, geant4cdk z eder zeezfz ke ezfk -1/3012,1 = - fine structure constant, - classical radius of electron, =z137 , - coulomb correction, a nd functions acounting for scccz kkmre efz k 22reening effects threshold photon energy is: 22 average energy of and 2eehm chvm ceeepair produ

13、ction in the electric field (triplet production)022min1, - doppler effect11 4emmhm cradiography setup10 kev are absorbed by primary collimators average eneregy of beam increases - hard x-rays penetrate deeperhradiography setup and imaging principles0( , , )1( , , )lnaix y zx y zzi ( , )0( , , )x y z

14、aix y zi edouble crystal monochromator si(333)objectradiology setuparea detector incident x-ray beamattenuation lawimagezxy( , ),aaix yx yiimage contrastdrawbacks of radiographyyxrascatiiiobject pixelyxdetector pixelattenuated beam(by absorption)incoherently scattered beam01( , )lnascatiix yzi ascat

15、ascatiiii image contrastdei setup and imaging principleszxyarea detectorobjectanalyzer crystal si(333)dei setupincident x-ray beamdouble crystal monochromator si(333) formation of de imagesyxobject pixelyxdetector pixelenhanced attenuated beam incoherently scattered beam is blocked by crystalb1050-1

16、0-5low anglesidehigh angleside0.400.200.000.600.801.00analyzer angle ( radians)physics of deipisano, johnston(unc); sayers(ncsu); zhong (bnl); thomlinson (esrf); chapman(iit)relative intensity i/iodata from nsls x27calculation of dei imageslrlzrllzdrii rirdhrhzrhhzdrii rird,(),(), - absorption()()()

17、(),(),(), - refraction,(),()drdrlhhlddrdrdrlhhlddhllhzdrdrlhhlddix yix yix yrrix y rix y rx yix yix y1050-10-5low anglesidehigh angleside0.400.200.000.600.801.00analyzer angle ( rad)relative intensity i/io2dlb2dhbd6 1 0 - 0 5 4mapconventionaldeicomparison - conventional and deiacr - phantomacr phant

18、om (gammex rmi - model 156) - tumor-like masses, microcalsifications, cylindrical nylon fibrids 40-45 mm thick compressed breast. conventional radiography - synchrotron at 18 kev.dei image of acr phantom - smallest calcificationsdata from nsls x27conventionaldei - absorptiondei - refractioncancer in

19、 breast tissuebnl sept 1997pisano, johnston(unc); sayers(ncsu); zhong (bnl); thomlinson (esrf); chapman(iit)drawbacks of deiyxobject pixelyxdetector pixelexperimental evidence of problems in dei 00( , , )() (, , )()( , , )ix yifx y difx y 0012iirrm. wernick multiple - image radiograp hy phys. med. b

20、iol. 48 (2003) 3875et al1235678sheets of paperlucite substratelucite rodalignment target4 0, , ,agx yifx yr18 kev x-ray beam-9.6 to 8.8 rad (0.8 rad)1256 444 pixels image50 m 50 m each pixelexperimental results-1-0.6-0.20.20.61x 10-5rod, off-centerx 10-1-0.6-0.20.20.61-5thick paper200400600-1-0.6-0.

21、20.20.61x 10-5background200400600 x 10-1-0.6-0.20.20.61-5rod and paper200400600( ; , )fx y( ; , )fx y( ; , )fx y( ; , )fx y200400600m. wernick multiple - image radiography phys. med. biol. 48 (2003) 3875et alrefraction imagesprofilesthick paperthin paperno paper05010015020000.20.40.60.81position (pi

22、xels)mirdeideimir dei m. wernick multiple - image radiography phys. med. biol. 48 (2003) 3875et al00,1( , )lnln, , - attenuation imaget x ya x yfx y dii 0, ,( , ) - refraction image( , )fx yrr x ydt x yi2, ,( , )( , ) - ultra-small angle scattering im age,fx yw x yr x ydt x ym. wernick multiple - im

23、age radiography phys. med. biol. 48 (2003) 3875et algeneralization to ct reconstructionzzzz0zaii e0i0i12()0nzaii e1234n3112400( , , )nnnzzzzzaix y zi eeeei e10( , )ln( , , )nannlip x yzx y z dzi ( , )ln ( , , )( , , )rrllr x ygradn x y zdzgradx y zdz( , )? w x yza physical model of mir- scattering c

24、enters - , , asspnobject voxel - nonscattering medium ( ), zgradn khelashvili, brankov (iit), chapman (u.sask), anastasio, yang (iit), zang (bnl), wernick (iit) phys. med. biol. 51 (2006) 221-236 multiple ultra-small angle scatteringradiation intensity of x-ray beam in at position in the direction (

25、sincos ,sinsin ,cos )rs s s radiation transport theory approach( , )( , , ) - specific intensity (radiance or brightness)i r si r ddds - particles in volumedsds ( , )- phase function - fraction of the radiationscattered from into . p s sdsds mir radiation transfer equation4( , )( ) ( , )( )( , )( )(

26、 , ) + ( , )( , )( , ) ( , )4rnansnextssi r sr i r sri r sri r sb r si r sp s s i r s d ultra-small angle approximation2( , , )( , , )( , , )( , , )( , , ) () ( , , )4tnextnextdi zssi zsi zsb zsi zszdsp ss i zs d s 2,sincossinsin txyrzkxiyjzkijsijxyd sds ds ln ( , )rbn x y 00( , )xynnn x ynxynn xn y

27、xygeneral solution222011( , , )exp() exp()(2 )2 exp ()( , , )( , , )nti zsdd qiis qibqib z ziszf zq k zq 220002( , )( , )exp()( , , )exp()4( )( )exp()znextfqisiis q dd sk zqp qz dzp qp sis q d s phase function2( , )sdp s sa d 36251010111210speannrv 2222222222222022222224, sin, sin;444 ( , ) ( )4444x

28、yxyssextdasssd sds dsd dd ddsdp s sp swa dss aaphase function22222|( )24ln1( )psp s d sp s d s22202| |( )1( )4exp, ( )pppsp s d sp swsp s d s221124ln1ppplane wave solution00( , )( )isis 2020200() exp(/4)( , , )exp()exp()(2 )! , () and ,exp(kpksextnextnextwkqii zsiq sbzd qkwzziq 2222224)exp(/4)exp, (

29、)()pppxysbzkqd qsbzkksbzsbzsbz plane wave solution2000()( , , )exp()exp!kppkwii zssbzk kk 00if 0 () and ) ( , , )exp() ()nsnextnextextaswzzzi zsizsbz imaging parameters 22000 ( , , )exp( )ln - absorption imagetnaztmirnaii zs d siziazzdzi 2220201( , , )( , , )( ); 1( , , )( , , )( );zxxxtzyyytx y zs

30、i zs d sb z dzix y zs i zs d sb z dzi 2220( )( )1( , , )( , , ) ultra-small angle scattering imageznsrpzzw x y zsbzi zs d sdzirefraction - angle imageexperimental conformation lucite container wedge shaped. polymethylmethacrylate (pmma) microspheres in glycerin.experimental conformationlabdei system

31、detectoranalyzerpre-mono & monox-ray sourcemorrison, nesch, torres, khelashvili (iit), hasnah (u. qatar) chapman (u.sask)1cmcartilagebonelab dei system tissue imagesmorrison, nesch, torres, khelashvili, chapman (iit)muehleman (rush medical college)human tissue image using prototype laboratory dei system using mo k (17.5kev) radiation. image is o