RF Excitation. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging

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1 Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2010 MRI Lecure 4 Simplified Drawing of Basic Insrumenaion. Body lies on able encompassed by coils for saic field B o, gradien fields (wo of hree shown), and radiofrequency field B 1. Image, capion: copyrigh Nishimura, Fig RF Exciaion RF Exciaion A equilibrium, ne magneiaion is parallel o he main magneic field. How do we ip he magneiaion away from equilibrium? Image & capion: Nishimura, Fig. 3.2 B 1 radiofrequency field uned o Larmor frequency and applied in ransverse (xy) plane induces nuaion (a Larmor frequency) of magneiaion vecor as i ips away from he -axis. - lab frame of reference From Levi, Spin Dynamics,

2 RF Exciaion a) Laboraory frame behavior of M b) Roaing frame behavior of M Images & capion: Nishimura, Fig. 3.3 hp:// hp:// B 1 () = 2B 1 ()cos( )i () cos ()i sin ()j ( ) + B 1 ()( cos ()i + sin ()j) hp:// 2

3 hp:// Images from Roaing Frame Bloch Equaion dm ro = M d ro B eff & B eff = B ro + 0 ) ro ; ( + ro = ( 0 + ( % * + Noe: we use he RF frequency o define he roaing frame. If his RF frequency is on-resonance, hen he main B0 field doesn cause any precession in he roaing frame. However, if he RF frequency is off-resonance, hen here will be a ne precession in he roaing frame ha is give by he difference beween he RF frequency and he local Larmor frequency. Le B ro ()i + B 0 k B eff = B ro + ro % ()i + B 0 ( * k & ) If = 0 = B 0 Then B eff ()i 3

4 Flip angle = % 1 (s)ds 0 where 1 () = &B 1 () slice Slice Selecion Δ f rec(f/w) W=γG Δ/(2π) sinc(w) 4

5 Le B ro ()i + ( B 0 + G )k B eff = B ro + ro % ()i + B 0 + G ( * k & ) If = 0 B eff ()i + (G )k Small Tip Angle Approximaion For small M M 0 M xy M = M 0 cos M 0 M xy = M 0 sin M 0 Exciaion k-space A each ime incremen of widh, he exciaion B 1 () produces an incremen in magneiaion of he form M xy jm 0 %B 1 () 100 seps 2D random walk (small ip angle approximaion) In he presence of a gradien, his will accumulae phase of he form & = -% G ( s)ds, such ha he incremenal magneiaion a ime is 400 seps M xy (, ; ) %B 1 ()exp ( j% G ( s)ds ( ) N random seps of lengh d Inegraing over all ime incremens, we obain M xy ( ) d (,) %B 1 ()exp ( j% G ( s)ds () %B 1 ()exp( j2*k(,))d () where k(,) = ( % 2* G ( s)ds Pauly e al

6 Exciaion k-space M xy (,) B 1 ()exp( j2k(,))d 100 seps This has he 2D form random of walk inverse Fourier ransform, where we are inegraing he conribuions of he field B 1 () a he k - space poin k (,). RF N random seps of lengh d 400 seps Slice selec gradien G () k(,) = & 2% G ( s)ds k M xy For a consan gradien: ( ) = k2d, random walk 2 G % Exciaion k-space ( ) = 2 k G seps d = 2 dk G (,) B 1 ()exp( j2k(,))d 400 seps ( 2 + B 1 * k G + - exp( j2k ) 2 dk ), G N random seps of lengh d ( (G exp (% jg ) B 1 (k )exp j2k * ) * -- dk ),, [ ( )] G exp (% j.())f %1 B 1 k 2 B 1 () rec% & ( Small Tip Angle Example M r ( /2,) exp() j*() /2)F )1 * 1 rec k && % % ( exp() j*() /2)* 1 sinc % +G 2, & ( ( +G 2, M r (,) = exp( j() /2)M r (,) exp( j() /2)exp( j() /2)F 1 %B 1 k F 1 [%B 1 ( k )] %G 2& Refocusing [ ( )] %G 2& 6

7 RF N random seps of lengh d Refocusing M xy (,) B 1 ()exp( j2k(,))d 100 seps This has he 2D form random of walk inverse Fourier ransform, where we are inegraing he conribuions of he field B 1 () a he k - space poin k (,). G () k (,) Slice selec gradien Slice refocusing gradien k(,) = 2% & G ( s)ds seps k RF G () G x () G y () Slice Selecion Slice selec gradien Slice refocusing gradien Gradien Echo Small Tip Angle Example RF G () G x () Slice selec gradien Slice refocusing gradien B 1 () = Asinc( /) cos 2 & & )) % % (( = Asinc( /)w() F *1 (B 1 (k )) +G = A rec +G & ),W +G & ) 2 % 2 ( % 2 ( k G y () ADC Spins all in phase a k x=0 Firs ero in k space is a G 2. Therefore, widh of he rec funcion is % = 2 G 7

8 slice Slice Selecion Δ f rec(fτ) f = 1 = G 2% sinc(/τ) Example = 5 mm; = 400 µsec; = %/2 G = 2% & = 1 =1.175 G /cm (4257H /G)(0.5cm)(400e 6) T ) ( & B 1 sinc s T /2, / +. ds ( &B 0 * area of sinc ( ) = &B 1 B 1 = & = %/2 2%(4257H /G)(400e 6) = G & sinc( /)rec% ( ) rec(f ) *2N sinc(2nf ) 2N Duraion = 2N Bandwidh = 1 Transiion Widh. 1 2N ) + = 2, -G 2, ) + / = -G 2N Time 0 Bandwidh Produc (TBW) = 2N 1 = 2N Bandwidh also, TBW= Transiion Widh Time-Bandwidh Produc (TBW) For a fixed duraion pulse, we can increase TBW by increasing he Bandwidh. (Noe : his will also lead o an increase in N). N = number of eros in Sinc This will require a higher B1 ampliude and a higher gradien o keep he slice widh consan - - noe ha wih higher TBW he physical ransiion widh hen decreases. 8

9 Cardiac Tagging Muli-dimensional Exciaion k-space 2D random walk ( M xy (,r) & % 1 ( ) exp j 100 seps & G(s)( rds)d & % 1 ( ) exp( j2)k( )( r ) d 400 seps! where ) = d N random seps ofk( lengh 2% G( &)d&! Pauly e al 1989 Exciaion k-space 2D random walk Exciaion k-space 100 seps 2D random walk 400 seps N random seps of lengh d 100 seps 400 seps N random seps of lengh d Pauly e al 1989 Panych MRM