11: Echo formation and spatial encoding
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1 11: Echo formation and spatial ncoding 1. What maks th magntic rsonanc signal spatiall dpndnt? 2. How is th position of an R signal idntifid? Slic slction 3. What is cho formation and how is it achivd? Echo formation Gradint cho squnc 4. How is a two-dimnsional R imag ncodd? Aftr this cours ou 1. Undrstand th principl of slic slction 2. Ar familiar with dphasing and rphasing of transvrs magntiation and how it lads to cho formation 3. Undrstand th principl of spatial ncoding in RI 4. Can dscrib th basic imaging squnc and th thr ncssar lmnts 5. Undrstand th principl of imag formation in RI and how it impacts spatial rsolution What do w know about magntic rsonanc so far? Adding a 3 rd magntic fild So far 1) Ecit spins using RF fild at L 2) Rcord tim signal (Known as FID) 3) dcas, grows (T 2 and T 1 rlaation) RF coils masur signal from ntir bod (no spatial information) Prcssional Frqunc How to ncod spatial position? B( ) B G L =f() 0 L =B 0 agntic fild B along varis spatiall with,, and/or : G db dr Static agntic Fild B 0 : Static agntic Fild Crats quilibrium magntiation 0.1 T to 12 T» Earth s fild is T B 1 : Radiofrqunc Fild (RF) 0.05mT, on rsonanc Dtction of R signal (RF coils) B ( r ) B 0 G r.g. G=(G,0,0) 11-2
2 How is th gradint fild cratd? On coil for ach spatial dimnsion: G, G, G db G: Gradint Fild G mt/m in ~100μs dr Usd to dtrmin spatial position of signal (frqunc) Cratd b a st of 3 additional coils (gradint coil) Eampl: -gradint coil principl (Hlmholt pair) B 0 G B( r ) 0 dl r I 4 r 3 NB. Wh ar RI scans so loud? Lornt-forc of B (3T) on rapidl switchd currnt in gradint coil (wir) (~100A in ~100μs) 11-3 How is slic-slction achivd? Onl magntiation on-rsonanc is citd On-rsonanc: Frqunc RF of RF fild B 1 matchs th prcssion frqunc of magntiation oving Frqunc RF altrs position of slic : Frqunc RF RF =G Position NB. Not to confus: 0 (,) rfrs to spatial dimnsions or rfrs to transvrs magntiation (in magntiation spac) (coordinat sstms ar diffrnt, but shar ) RF =B 0 +G
3 11-2. What is th basic principl of ncoding spatial information? frqunc ncoding - 1D ampl Spatial-varing rsonanc frqunc B() during dtction B () = B 0 +G B () Dtctd signal = sum of all prcssing magntiation: objct (,0) ig t What dos this rsmbl? objct (,0) it d d Rotating fram: B() = G (, ( ) ( ( ) B t i B t i G t i 0 ) G t i = Invrs Fourir Transformation! FT of (or k)) Rconstruction as in CT (in principl) S ( k) (,0) ik d objct For 2D objct: ( ) (, ) d =Radon Transform Whn is th signal maimal in th prsnc of G? Echo formation: Dphasing and rphasing objct (,0) ig t agntiation in-phas maimal signal (cho formation) d <0) dphasing Echo formation: qual ara Gradint G ( agntiation in-phas initiall Phas of magntiation (=G t =/2: Dphasing ) (,0) objct objct (, ) ig ig t d d t Rphasing objct (,0) i G i G t d =maimal (constant G ) whn t=: cho formation ig t 11-7
4 Is it important whn a gradint is applid? gradint applid at diffrnt tim has th sam ffct on magntiation phas Gradint applid squntiall Gradint G ( Gradint applid simultanousl Gradint G ( ( ) (0) (2 ) ( ) ig ig Qustion: Is thr a diffrnc in ffct on cho? ( ) (0) (0) ig ig (2 ) ( ) i G G G r (0) ig ig Application of two orthogonal gradints simultanousl or squntiall gnrats th sam phas for ( ) (2 ) ( ) (0) G / 2 i i G G ig / 2 (0) ig 11-9 What ar th basic lmnts of th Gradint cho squnc? (0)= NB. Wh cho formation? Slic rad (frqunc ncod) gradint RF Slic Slct (G ) Frq. Encod (G ) Gradint switching Finit ris tim Dphasing of magntiation S slic (, ) i G d 0 tim (signal dcas lik FID in prsnc of gradint ) Rphasing (ngativ) gradint lads to cho formation slic (at t=) 0 ig ( dt 0 (, ) d =ma ( dt 0 G Data sampling Sampld First half of cho also masurd (mor signal) 11-10
5 11-4. How is th 2 nd dimnsion ncodd? gradint cho imaging squnc RF Slic Slct (G ) Frq. Encod (G ) G Slic rad gradint phas ncod gradint Phas Encod (G ) Data sampling Sampld Rpatd vr TR sconds With G incrmntd b G 1. Ecitation Slic slction 2. Phas ncoding 3. Frqunc ncoding Echo formation How dos th phas ncoding gradint ncod th 2 nd spatial dimnsion? Phas ncod stp 1 Considr two-dimnsional objct Stp 2 (twic th gradint strngth) vol magntiation Aftr appling phas ncod gradint (G for sconds) imaginar Gradint G ( Phas of vol magntiation i : ral ig ik ig ik Gradint G ( i Gt i k k 11-12
6 How is incrmnting th phas stp-b-stp (phas ncoding) quivalnt to frqunc ncoding? Phas of a singl pil in, plan: Stp 3 Stp 2 Stp 1 t n, G, (, ) d dt of th singl vol: k G t k G of th ntir objct : ik k, k ) (, ) ing ig t i k, k ) (, ) objct k k k dd What dos this rsmbl? Radout (G tim G ( NB. Stp n: G =ng v G ( (, ) objct k, k ) i k k R imag gnration: FT of th signal dk dk How is th spatial information ncodd in RI? scanning k-spac (Fourir or rciprocal spac) squntiall Phas Encod G ( Fourir or rciprocal spac (k, k ) Phas Dirction () Sampld Acq. For k-spac lin vr TR=1s: imag matri > 4 min On lin of k-spac acquird pr TR Subjct movd had during acquisition ~ ms R scans ar long and motion-snsitiv Frqunc Dirction () aimum k (or k ) Rsolution (Nquis Incrmnt k Fild-of-viw Uniform rsolution and snsitivit (Limitd b vol magntiation) Ghosting and ringing artifacts cntr of k-spac (k,k =0) 11-14
7 What ar som ffcts of incomplt sampling? of Fourir spac (k-spac) , k,k Tim of acquisition of cntr of k- spac point (k,k =0) dtrmins contrast of imag: 0,0) objct (, ) dd k 0, k 0 Discrt FFT (priodicit + tim shif = Summar: Spatial ncoding with gradints Phas ncoding, cho formation + 2DFT (r,=(b 0 + G ( r) RF (B 1 ) ng G G flip angl tim agntiation at tim points spcifid: 1: (0,0, ) rotatd b RF puls b 0 about : 2: (0, sin, cos)(0,, ) [now onl considr ] Prcsss with B = -G -G 3: (sin[-(ng +G )], cos[-(ng +G )] [sin(- ), cos((- )], with =G (rotation b angl ) invrting gradint, i.. B = +G : aftr anothr, rotats b angl + maimal signal at =2 (G=0) 4: (0,1, )= (0, sin, cos) Echo formation, ( = m(,,dd = m(,,0) (ng) G(+ dd k,k ) m (,) -k -k dd RI masurs th 2D Fourir transformation of th objct (masuring th 2 nd dimnsion rquirs tim!) 11-16
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