Basic MR image encoding

Transcription

1 Basic MR image encoding HST.583: Funcional Magneic Resonance Imaging: Daa Acquisiion and Analysis Harvard-MIT Division of Healh Sciences and Technology Dr. Larry Wald

2 Physical Foundaions of MRI Wha is NMR? The basic signal we excie and deec. Tricks of NMR The gradien and spin echo How do we encode an image? slice selec, frequency and phase encoding. Wha are some problems (arifacs) relevan o our applicaion.

3 Physical Foundaions of MRI NMR: 60 year old phenomena ha generaes he signal from waer ha we deec. MRI: using NMR o generae an image Three magneic fields (generaed by 3 coils) 1) saic magneic field Bo 2) RF field ha excies he spins B1 3) gradien fields ha encode spaial info Gx, Gy, Gz

4 Wha is NMR? NUCLEAR MAGNETIC RESONANCE A magne, a glass of waer, and a radio wave source and deecor.

5 B proons Earh s Field W N E compass S

6 Nuclei and Magneic Fields No every nucleus lines up wih applied magneic field. Why? Direcion of spins becomes randomized by hermal moion. proons a 1.5 Tesla, a room emperaure ne # aligned wih field is 1 par in 100,000

7 M =

8 Compass needles The vecor sum of all he nuclei can be viewed as a compass needle. Poins Norh. (aligns along he magneic field lines of he exernal field (earh or MR magne) If displaced from Norh, i will wobble abou norh wih a characerisic frequency (called Larmor freq.) υ N W E S

9 Compass needles υ N Earh s Field z Norh Main Field Bo W E y S Freq = γ B MHz/T x

10 EXCITATION : Displacing he spins from Equilibrium (Norh) Problem: I mus be moving for us o deec i. Soluion: knock ou of equilibrium so i oscillaes How? 1) Til he magne or compass suddenly 2) Drive he magneizaion (compass needle) wih a periodic magneic field

11 Exciaion: Resonance Why does only one frequency efficienly ip proons? Resonan driving force. I s like pushing a child on a swing in ime wih he naural oscillaing frequency.

12 z is "longiudinal" direcion x-y is "ransverse" plane z Saic Field y Applied RF Field x The RF pulse roaes Mo he abou applied field

13 "Exciing" Magneizaion Magneizaion processes abou new axis (of oscillaing RF B field) as long as resonan field is applied. Toal amoun vecor processes is called he "ip angle" of he exciaion.

14 "Exciing" Magneizaion ip angle z z y y x x 45 90

15 Deecing he NMR Signal z 90 y x A moving bar magne induces a Volage in a coil of wire. (a generaor ) The RF coil design is he #1 deerminan of he sysem SNR υ o V()

16 Deecing he NMR: he noise z 90 y Noise comes from elecrical losses in he resisance of he coil or elecrical losses in he issue. For a resisor: Pnoise = 4kTRB υ o x V() Noise is whie. >>Power α bandwidh Noise is spaially uniform. R is dominaed by he issue. >> big coil is bad.

17 Signal o Noise Raio in MRI Mos imporan piece of hardware is he RF coil. SNR α voxel volume (# of spins) SNR α SQRT( oal ime of daa collecion) SNR is also dependen on he amoun of signal you hrow away o ge conras.

18 Review: he NMR Signal RF ime Volage (Signal) ime υ o υ B o Mo z y z 90 y z y x υ o x V() x

19 Three Seps in MR: 0) Equilibrium (magneizaion poins along Bo) 1) RF Exciaion (ip magn. away from equil.) 2) Precession induces signal, dephasing (imescale = T2, T2*). 3) Reurn o equilibrium (imescale = T1).

20 Magneizaion vecor durning MR RF Volage (Signal) encode ime Mz ime

21 Three places in process o make a measuremen (image) 0) Equilibrium (magneizaion poins along Bo) 1) RF Exciaion (ip magn. away from equil.) 2) Precession induces signal, allow o dephase for ime TE. 3) Reurn o equilibrium (imescale =T1). proon densiy weighing T2 or T2* weighing T1 Weighing

22 T2*-Weighing Wai ime TE afer exciaion before measuring M. Shorer T2* spins have dephased z z z y y vecor sum y iniially x a = TE x x

23 T2* Dephasing Jus he ips of he vecors

24 1.0 Transverse Magneizaion T2* = 200 T2* = Time (milliseconds)

25 T2 Weighing Phanoms wih four differen T2 decay raes... There is no conras difference immediaely afer exciaion, mus wai (bu no oo long!). Choose TE for max. inen. difference.

26 Dephasing: local field variaions homogeneous magne. S() T2* FT S(υ) υ υ υ o inhomogeneous magne. S() FT S(υ) υ υ o z υ

27 Aside: Magneic field gradien Bo Gx x Bo + Gx x Uniform magne z x Field from gradien coils G x = B z x Toal field

28 A gradien causes a spread of frequencies y B o MR frequency of he proons in a given locaion is proporional o he local applied field. z v = γb TOT = γ(b o + G z z) B Field B o B o + G z z z υ o υ # of spins resonance frequency

29 A gradien causes dephasing I caused i, I can reverse i Gradien echo υ = γb TOT = γ Βο + G z z υ = γ B TOT = γ G z z θ = υ τ = γ G z z τ RF G x a 1 a 2 Grauious manipulaion (?) Wha happens if he spin moves? S()

30 Less rivial manipulaion he Spin Echo Refocus he dephased signal wihou resoring o direc conrol of he Bo field.

31 Spin Echo Some dephasing can be refocused because is due o saic fields. z 90 y z y z y Echo! z y = 0 x = T x 180 x = T (+) x = 2T Blue/Green arrows precesses faser due o local field inhomogeneiy han red/orange arrow

32 Spin Echo 180 pulse only helps cancel saic inhomogeneiy The runners can have saic speed disribuion. If a runner rips, he will no make i back in phase wih he ohers.

33 T2 weighed image Signal whie gray CSF Time (ms)

34 Par II Image encoding

35 1D projecion image y B o MR frequency of he proons in a given locaion is proporional o he local applied field. z v = γb TOT = γ(b o + G z z) B Field B o B o + G z z z υ o υ # of spins resonance frequency

36 Sep one: excie a slice y B o While he grad. is on, excie only band of frequencies. z B Field (w/ z gradien) B o B o + G z z z RF NMR signal inen. v v G z Why?

37 Slice profile consideraions A(ω) FT F() ω ω

38 Sep wo: encode spaial info. B o along z y in-plane Frequency encoding B Field (w/ x gradien) B o x B TOT = B o + G z x x Signal Freq. wih gradien υ o υ wihou gradien

39 Pulse sequence so far RF slice selec G z freq. encode (read-ou) G x S() Sample poins

40 Phase encoding slice selec RF G z phase encode G y freq. encode (read-ou) G x S()

41 How does blipping on a grad. encode spaial info? y B o τ y 2 z G y y 1 B Field (w/ z gradien) B o y 1 y 2 y all y locs process a same freq. spins in forehead precess faser... all y locs process a same freq. υ(y) = γb TOT = γ B o yg y θ (y) = υ(y) τ = γ B o y(g y τ)

42 How does blipping on a grad. encode y B o spaial info? y 2 z θ (y) = υ(y) τ = γ B o y(g y τ) y 1 afer RF z 90 z Afer he blipped y gradien... z z x y x y x y x y υ o posiion y 1 posiion 0 posiion y 2

43 How does blipping on a grad. encode spaial info? y The magneizaion vecor in he xy plane is wound ino a helix direced along y axis. Phases are locked in once he blip is over.

44 The bigger he gradien blip area, he igher he helix y θ (y) = υ(y) τ = γ B o y(g y τ) small blip medium blip large blip

45 Wha have you measured? Consider 2 samples: uniform waer 1 cm no signal observed signal is as big as if no gradien

46 Measuremen inensiy a a spaial frequency... k y 1/1.2mm = 1/Resoluion 10 mm 1/2.5mm 1/5mm 1/10 mm k x

47 k y Fourier ransform 1 / Res x k x FOV x = marix * Res x 1 / FOV x

48 Frequency encoding revisied RF G z G x S()

49 Spin-warp encoding slice selec G z phase enc freq. enc (read-ou) RF G y G x S() k y a 1 a 2 k x one exciaion, one line of kspace...

50 Spin-warp encoding mahemaics The image is he spin densiy funcion: ρ(x) Phase due o readou: θ() = ωo + γ Gx x RF G z Phase due o P.E. θ() = ωo + γ Gy y τ G y G x S() a 1 a 2 θ() = ωo + γ Gx x + γ Gy y τ

51 Spin-warp encoding mahemaics Signal a ime from locaion (x,y) S() = ρ(x, y)e iγg x x+iγg y yτ The coil inegraes over objec: S() = objec ρ(x,y)e iγg x x+iγg y yτ dxdy Subsiuing kx = -γ Gx and kx = -γ Gx : S(k x,k y ) = ρ(x, y)e ik x x ik y y dxdy objec

52 Spin-warp encoding mahemaics View signal as a marix in kx, ky S(k x,k y ) = ρ(x, y)e ik x x ik y y dxdy objec : Solve for ρ(x,y,) ρ(x,y) = FT 1 [ S(k x,k y )] ρ(x,y) = S(k x,k y )e ik x x+ik y y kspace dk x dk y

53 k y Fourier ransform 1 / Res x k x FOV x = marix * Res x 1 / FOV x

54 Kspace facs Resoluion is deermined by he larges spaial freq sampled. FOV = marix * resoluion If he objec is real, half he informaion in kspace marix is redundan. We only need o record half of i.

55 kspace Image space (magniude) kspace (magniude)

56 kspace arifacs: spike One whie pixel in kspace from a elecric spark

57 Kspace arifacs: Symmeric N/2 ghos Even numbered lines go exp(iφ) Odd numbered lines go exp(-iφ) φ = 12 degrees

58 kspace arifacs: subjec moion k y Yellow = posiion1 Orange = moved 2 pixels k x Movemen in real space = linear phase shif across kspace. => Orange poins have linear phase θ = a ky

59 Fas Imaging Dos hou love life? Then do no squander ime, for ha s he suff life is made of. - Benjamin Franklin

60 Requiremens for brain mapping Consideraions: Signal increase = 0 o 5% (small) Moion arifac on convenional image is 0.5% - 3% Need o see changes on imescale of hemodynamic changes (seconds) Requiremen: Fas, single sho imaging, image in 80ms, se of slices every 1-3 seconds.

61 Wha s he difference? convenional MRI echoplanar imaging RF slice selec G z RF G z G y G y freq. enc (read-ou) G x S() G x S() T2* k y ec... k y k x k x

62 RF G z Echo-planar encoding k y G y G x S() (no grads) T2* T2* ec... k x one exciaion, many lines of kspace...

63 Echo-planar encoding Observaions: Adjacen poins along kx are aken wih shor (= 5 us). (high bandwidh) k y Adjacen poins along ky are aken wih long (= 500us). (low bandwidh) A given line is read quickly, bu he oal encode ime is longer han convenional Imaging. k x Adjacen lines are raversed in opposie direcions.

64 Enemy #1 of EPI: local suscepibiliy gradiens Bo field maps in he head

65 EPI: Local suscepibiliy gradiens Local suscepibiliy gradiens have 2 effecs: 1) Local dephasing of he signal (signal loss) mainly from hru plane gradiens 2) Local geomeric disorions, mainly from local in-plane gradiens.

66 Suscepibiliy: hru plane dephasing Signal from whole slice comes from adding ogeher he MR vecors. When in phase, add consrucively, SNR increases like slice hickness. Magneic Field Uniform =

67 Suscepibiliy Arifac and Slice Thickness Signal from whole slice comes from adding ogeher he MR vecors, which ge ou of phase when he magneic field is no uniform Magneic Field NONUniform =

68 Local suscepibiliy gradiens: hru-plane dephasing Bad for hick slice above fronal sinus

69 Local gradiens: geomeric disorion Local gradien alers he helix of phase we have so carefully wound. Phase error accumulaes over enire kspace. (convenional imaging phase is rese every line) >> faser encoding is beer. Readou poins are aken close ogeher (~5us) Phase encode poins are aken farher apar (~500us) >> disorion occurs in P.E. direcion.

70 Local gradiens: geomeric disorion Two ses of EPI: 1) encode in 32ms 2) encode in 23ms

71 Characerizaion of grad. performance lengh of readou rain for given resoluion (requires fas slew and high grad ampliude) RF G z G y G x echo spacing (esp)= 512 us for 1.5T, readou lengh = 32 ms = 366us for 3T, readou lengh = 23 ms S() (no grads)

72 EPI problems: N/2 ghos Asymmery in alernae lines gives N/2 image ghos. Asymmery from: Eddy currens receiver filer receiver iming head coil uning. objec N/2 ghos

73 EPI problems: frequency offse If one objec has a differen NMR frequency (e.g. fa and waer) i ges shifed in PE direcion. (why?) fa waer fa waer True locaion Echoplanar image

74 EPI and Spirals k y k y k x k x G x G x G y G y

75 EPI Spirals Eddy currens: ghoss blurring Suscepibiliy: disorion, blurring dephasing dephasing k = 0 is sampled: 1/2 hrough 1s Corners of kspace: yes no Gradien demands: very high prey high

76 EPI and Spirals EPI a 3T Spirals a 3T (from G. Glover)