RF Excitation. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2013 MRI Lecture 4

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1 Bioengineering 80A Principles of Biomedical Imaging Fall Quarer 013 MRI Lecure 4 TT. Liu, BE80A, UCSD Fall 01 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 From Levi, Spin Dynamics, 001 hp:// 1

2 RF Exciaion A equilibrium, ne magneizaion is parallel o he main magneic field. How do we ip he magneizaion away from equilibrium? On-Resonance Exciaion Image & capion: Nishimura, Fig. 3. B 1 radiofrequency field uned o Larmor frequency and applied in ransverse (xy) plane induces nuaion (a Larmor frequency) of magneizaion vecor as i ips away from he z-axis. - lab frame of reference hp:// Hanson 009 hp:// RF Exciaion Roaing Frame of Reference Reference everyhing o he magneic field a isocener. hp://

3 a) Laboraory frame behavior of M b) Roaing frame behavior of M Images & capion: Nishimura, Fig. 3.3 B 1 () = B 1 ()cos( ω)i () cos( ω)i sin( ω)j ( ) + B 1 ()( cos( ω)i + sin( ω)j) hp:// Nishimura 1996 hp:// hp:// 3

4 Precession Roaing Frame Bloch Equaion dµ d = µ x γb B dµ µ Analogous o moion of a gyroscope Precesses a an angular frequency of ω = γ Β This is known as he Larmor frequency. dm ro = M d ro γb eff & B eff = B ro + ω 0 ) ro γ ; ω ( + ro = ( 0 + '( ω * + 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. hp:// Le B ro ()i + B 0 k B eff = B ro + ω ro γ % ()i + B 0 ω ( ' * k & γ ) Flip angle = ω 1 (s)ds 0 where ω 1 () = () If ω = ω 0 = γb 0 Then B eff ()i Nishimura

5 Example = 400 µ sec; =π / B 1 = γ = π / (457Hz / G)(400e 6) = G Nishimura 1996 Le B ro ()i + ( B 0 + γg z z)k B eff = B ro + ω ro γ % ()i + B 0 + γg z z ω ( ' * k & γ ) If ω = ω 0 B eff ()i + ( γg z z)k Nishimura

6 slice Slice Selecion z Δz f rec(f/w) W=γG z Δz/() sinc(w) Nishimura 1996 Small Tip Angle Approximaion Exciaion k-space For small M z M 0 M z = M 0 cos M 0 = M 0 sin M 0 1 D random 3 walk G z () k(,) k(,) = γ G z ( s)ds 100 seps M 0 exp( jk z ( 1,)z) 400 seps M 0 exp( jk z (,)z) M 0 6

7 Exciaion k-space A each ime incremen of widh Δ, he exciaion B 1 ( ) produces an incremen in magneizaion of he form Δ jm 0 ( )Δ 100 seps D random walk (small ip angle approximaion) In he presence of a gradien, his will accumulae phase of he form ϕ=-γ Δ zg z ( s)ds, such ha he incremenal magneizaion a ime is ( ) Δ (,z ; ) = jm 0 ( )exp jγ zg z ( s)ds N random seps of lengh d Inegraing over all ime incremens, we obain ( ) d (,z) = jm 0 ( )exp jγ zg z ( s)ds = jm 0 ( )exp( jk(,)z)d where k(,) = γ G z ( s)ds 400 seps Exciaion k-space (,z) = jm 0 ( )exp( jk(,)z)d This has he D form random of a Fourier walk ransform, where we are inegraing he conribuions of he field B seps ( ) a he k-space poin k, RF N random seps of lengh d 400 seps 1 3 Slice selec gradien G z () k(,) = γ G z ( s)ds 3 1 ( ). k z RF N random seps of lengh d Refocusing (,z) = jm 0 ( )exp( jk(,)z)d This has he D form random of a Fourier walk ransform, where we are inegraing he conribuions of he field B 1 G z () k(,) Slice selec gradien Slice refocusing gradien k(,) = γ G z ( s)ds seps ( ) a he k-space poin k, 400 seps 4 ( ). 1 k z RF G z () G x () G y () Slice Selecion Slice selec gradien Slice refocusing gradien 7

8 Gradien Echo slice Slice Selecion z RF G z () G x () G y () ADC Slice selec gradien Slice refocusing gradien Spins all in phase a k x=0 f rec(f) Δf = 1 = γg zδz Δz sinc(/) Example (x) = M 0 cos(4π x) ( ) = M 0 ( ) F (x) δ(k )+δ(k + ) x x g max = 4 G / cm γ g max T = 4 cm 1 ; T = 35 µ sec wih small ip angle approximaion --> = 1 " Compare wih sin π % $ ' = 1 # 6 & = π 6 = Quesion : Should we use = π 4 insead? 1 D random walk G x () T k(,) - Nishimura 1996 Exercise: Skech he quiver diagrams corresponding o he conribuions of he wo RF pulses and show ha hey produce he desired paern. 8

9 Muli-dimensional Exciaion kspace D random walk ( (,r) = jm 0 ω1 ( ) exp jγ 100 seps G(s) rds)d Exciaion k-space 100 seps D random walk = jm 0 ω1 ( ) exp( jk( ) r ) d 400 seps γ where ) = d N random seps ofk( lengh G( &)d& 400 seps N random seps of lengh d Pauly e al 1989 Pauly e al 1989 Exciaion k-space D random walk Cardiac Tagging 100 seps 400 seps N random seps of lengh d Panych MRM