MRI. Chapter 1. Larmor equation. Net magnetization. Rotating frame of reference 1/31/2017. ω0 (rad/s) = γ (rad/s/tesla) x B0 (Tesla)

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1 37 RI Chape FYS-KJ 474 loch equaions an main pinciples FYS-KJ 474 he loch equaion Lamo equaion ωl ωl ωl ω as = γ asesla esla ωl γhogen =.68 *8 asesla π Figue Eo! No e of specifie sle in ocumen.-. he magneic momen oaes aoun Joseph Lamo he magneic momen oaes aoun he saic -fiel a he Lamo fequenc fl H = γ Hesla esla γhogen = 4.58 Hesla FYS-KJ Roaing fame of efeence ω FYS-KJ 474 Aleøneu 4 Ne magneiaion ` o ` Laboao fame FYS-KJ 474 ` Roaing fame Hanson: Inoucion o agneic Resonance Imaging echniques 5 FYS-KJ 474 6

2 37 Flipping awa he agneiaion fom is equilibium In RI, sho RF pulses aiowaves ae use o o change he iecion of he magneiaion RF eciaion o ge o oae aoun o ais, A lineal polaie magneic fiel is use uing sho ime pulse o ge o oae aoun ais ` ` hp: FYS-KJE FYS-KJ he RF-coil geneaes a magneic fiel along he -ais FYS-KJE Roaion he magneic fiel ue o he RF pulse,, is geneae b wo ciculal polaie fiels wih opposing iecion of oaion wih angula fequenc +- loch equaion cos cos cos sin sin cos - he oaing fame,, -cooinaes ime - + eff FYS-KJ 474 eff= + + γ

3 37 RF-eksiason me Lamo fekvens oaing fame = γ eff Using ai fomalism : α ω eff = Asin cos Using he bouna coniions = an = a =, we ge cos sin R sin cos FYS-KJE FYS-KJ RF pulse RF pulse uaion is popoional o he wane flip angle, a. ω Roason = a α Oppgave.: eegn -feles ske ve en.5ms, 45 RF puls. FYS-KJ Relaaion Relaaion * 7 FYS-KJE 474 Fééic Couivau PhD 8 3

4 37 4 R eff R Relaaion FYS-KJ ep ep ep Coniion: elaaion uing RF eciaion is neglece FYS-KJ 474 R R eff Summa wih eciaion an elaaion FYS-KJ 474 -weighe poon -weighe -weighe Chap. Slice-Selecive RF eciaion Image fomaion FYS-KJ Slice Selecive RF pulse 4

5 37 aiens coing in space Z sample volume agneic Fiel aiens voel δ, = δ, = Y δ, = X Use of fiel gaien pulses in he 3 iecions 5 FYS-KJ agnefel gaien Pinciples of Slice Selecion aien-ske mm Signingsi ms aien ske Slew ae mmms = Signingsi 7 RF pulse geneaion Effec of agneic Fiel aien Eample: use of fiel gaien FAVOURALE SIUAION ω g Z q m Spaial infomaion inclue in he pecession fequenc pecession fequenc : ω applie fo a ceain uaion ms Applie fiel gaien g pulse fequenc pofile HZ 9 3 5

6 37 6 eff If we se: =γ +, hen he effecive fiel a = becomes: eff Wha woul happen if + γ >>?? Slice-selecive = Slice selecive RF eciaion 3 =ω L ; eff = All effecs ogehe: eciaion, pecession an elaaion FYS-KJ Pecession aoun -ais Eciaion aoun -ais ansvese elaaion Longiuinal elaaion All effecs ogehe: eciaion, pecession an elaaion FYS-KJ ansvese magneiaion,, Relaaion an pecession = + ep ep = eive! Longiuinal magneiaion, ep ep eive! As we have seen befoe FYS-KJ ansvese agneiaion,, Eciaion an Pecession = + = Coniion: How can his be achieve? A ep eneal Soluion: FYS-KJ ansvesal magneiseing,, eksiason og peseson Desom vi sie a RF puls sae ve og vae i sek: = ep, - FYS-KJ

7 37 Fo a consan gaien along he -ais: = Fo a consan gaien along he -ais: =, ep ep -, ep ep Slice pofile = Fouie ansfom of he phase iecion of in he -- plane is a funcion of Phase ispeion Fouie ansfom of he envelope geen shape FYS-KJ FYS-KJ Eliminaion of he phase ispesion in - plane use of an ea gaien of opposie polai an half he lengh: - - his gives k, k k ep k k ep k=γ an k =γ. FYS-KJ We wish o have a block eciaion: = sinα beween og an = elsewhee sin ep Fin he pofile fom he Fouie inegal: Develop a home! FYS-KJ RF pulse geneaion Slice selecive RF eciaion - pulse fequenc pofile HZ applie fo a ceain uaion ms FYS-KJ FYS-KJ

8 37 in pacice an uncaion - uaion can no be oo long he shape is uncae as a compomise beween uaion an achieve RF pulse a he cos of he slice pofile aien can no be pefecl ecangula Hawae limiaions Slew ae = aien sengh ime o each he sengh Slew ae mmms Summa selecing lobe ephasing lobe Slice pofile & coss-alk selece slice selecing lobe ephasing lobe ime Eecise hp: We wan a slice eciaion wih a given slice hickness of 3mm an a gaien sengh of mm. We Assume he use of a sinc pulse shape fo. Fin he half-wih uaion of he envelope shape Now, having his envelope, fin he inensi of m o ge a 9 egee RF pulse. FYS-KJ FYS-KJ