[ ]e TE /T 2(x,y ) Saturation Recovery Sequence. T1-Weighted Scans. T1-Weighted Scans. I(x, y) ρ(x, y) 1 e TR /T 1

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1 Sauraion Recovery Sequence 90 TE 90 TE 90 Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2015 MRI Lecure 5 TR Gradien Echo TR [ ]e TE /T 2 * (x,y ) I(x, y) = ρ(x, y) 1 e TR /T 1 (x,y) Spin Echo TE I(x, y) = ρ(x, y) 1 e TR /T 1 (x,y) [ ]e TE /T 2(x,y ) TR T1-Weighed Scans T1-Weighed Scans Make TE very shor compared o eiher T 2 or T 2 *. The resulan image has boh proon and T 1 weighing. I(x, y) ρ(x, y) 1 e TR /T 1 [ (x,y) ] 1

2 T2-Weighed Scans T2-Weighed Scans Make TR very long compared o T 1 and use a spin-echo pulse sequence. The resulan image has boh proon and T 2 weighing. I(x, y) ρ(x, y)e TE /T 2 Proon Densiy Weighed Scans Example Make TR very long compared o T 1 and use a very shor TE. The resulan image is proon densiy weighed. I(x, y) ρ(x, y) T 1 -weighed! Densiy-weighed! T 2 -weighed! Tissue Proon Densiy T1 (ms) T2 (ms) Csf Gray Whie

3 PollEv.com/be280a a) Which has he longes T1? b) Which has he shores T1? c) Which has he longes T2? d) Which has he shores T2? e) Which migh be pure waer? f) Which has he mos firm jello? Hanson 2009 PollEv.com/be280a a) Which is he mos T1 weighed? b) Which is he mos T2 weighed? c) Which is he mos PD weighed? Hanson 2009 FLASH sequence FLASH sequence TE TE TR TR Gradien Echo I(x,y) = ρ(x,y) 1 e TR /T1( x,y) [ ]sin 1 e TR/T 1( x,y) cos [ ] exp( TE /T 2 Signal inensiy is maximized a he Erns Angle E = cos 1 ( exp( TR /T 1 )) ) FLASH equaion assumes no coherence from sho o sho. In pracice his is achieved wih RF spoiling. E = cos 1 ( exp( TR /T 1 )) 3

4 Inversion Recovery TI 180 Inversion Recovery TE TR I(x, y) = ρ(x, y)[1 2e TI /T1 (x,y ) + e TR /T1 (x,y ) ]e TE /T2 (x,y ) Inensiy is zero when inversion ime is #1+ exp( TR /T1 ) & TI = T1 ln% (' $ 2 Biglands e al. Journal of Cardiovascular Magneic Resonance :66 doi: / x Inversion Recovery Simplified Drawing of Basic Insrumenaion. Body lies on able encompassed by coils for saic field Bo, gradien fields (wo of hree shown), and radiofrequency field B1. Image, capion: copyrigh Nishimura, Fig

5 RF Exciaion RF Exciaion From Levi, Spin Dynamics, 2001 hp:// RF Exciaion A equilibrium, ne magneizaion is parallel o he main magneic field. How do we ip he magneizaion 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 magneizaion vecor as i ips away from he z-axis. - lab frame of reference hps:// hp:// 5

6 RF Exciaion Roaing Frame of Reference Reference everyhing o he magneic field a isocener. hp:// a) Laboraory frame behavior of M b) Roaing frame behavior of M Images & capion: Nishimura, Fig. 3.3 B 1 () = 2B 1 ()cos( ω)i = B 1 () cos( ω)i sin( ω)j ( ) + B 1 ()( cos( ω)i + sin( ω)j) hp:// Nishimura

7 hp:// hp:// 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:// 7

8 Le B ro = B 1 ()i + B 0 k B eff = B ro + ω ro γ % = B 1 ()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 = B 1 ()i Nishimura 1996 Example = 400 µ sec; =π /2 B 1 = γ = π /2 2π (4257Hz / G)(400e 6) = G Nishimura

9 Le B ro = B 1 ()i + ( B 0 + γg z z)k B eff = B ro + ω ro γ % = B 1 ()i + B 0 + γg z z ω ( ' * k & γ ) If ω = ω 0 B eff = B 1 ()i + ( γg z z)k Nishimura 1996 hps:// Nishimura

10 slice Slice Selecion z Δz Small Tip Angle Approximaion M z M 0 f M xy rec(f/w) W=γG z Δz/(2π) sinc(w) For small M z = M 0 cos M 0 M xy = M 0 sin M 0 1 G z () k(,) 2 2D random walk 2 k(,) = γ 2π 3 G z Exciaion k-space ( s)ds 100 seps M 0 exp( j2πk z ( 1,)z) 400 seps 2M 0 exp( j2πk z ( 2,)z) G z z z Exciaion k-space A each ime incremen of widh Δ, he exciaion B 1 ( ) produces 100 seps an incremen 2D in random magneizaion walk of he form ΔM xy jm 0 ( ) = jm 0 ( )Δ (small ip angle approximaion) ( ) B seps 2D random walk ( ) = ( )Δ N random seps of lengh d jm 0 ( )Δ Δ k z Consider analogy wih 3D Prining M 0 10

11 Exciaion k-space In he presence of a gradien, his will accumulae phase of he form ϕ=-γ zg z ( s)ds, such ha he incremenal magneizaion 100 a ime seps is 2D random walk ΔM xy (,z ; ) = jm 0 ( )exp( jγ zg z ( s)ds) Δ z G z z 400 seps 100 seps N random seps of lengh d jm 0 ( )Δ ΔM xy (,z ; ) = jm 0 ( )Δ exp( jϕ ) ( ) Δ = jm 0 ( )exp jγ zg z ( s)ds Exciaion k-space Inegraing over all ime incremens d, we obain 100 seps M2D xy (,z random ) = jmwalk 0 ( )exp jγ zg z ( s)ds ( ) d = jm 0 ( )exp( j2πk(,)z)d where k(,) = γ 2π G z ( s)ds This has he form of a Fourier ransform, where we are inegraing he conribuions of he field B seps ( ) a he k-space poin k, ( ). For a hisorical perspecive see hp:// M xy Exciaion k-space (,z) = jm 0 ( )exp( j2πk(,)z)d This has he 2D form random of a Fourier walk ransform, where we are inegraing he conribuions of he field B seps ( ) a he k-space poin k, ( ). M xy Refocusing (,z) = jm 0 ( )exp( j2πk(,)z)d This has he 2D 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 Slice selec gradien G z () k(,) = γ G z ( s)ds 2π seps 2 1 k z RF N random seps of lengh d G z () k(,) Slice selec gradien Slice refocusing gradien k(,) = γ 2π G z ( s)ds seps k z 11

12 Slice Selecion Gradien Echo RF RF G z () G x () Slice selec gradien Slice refocusing gradien G z () G x () Slice selec gradien Slice refocusing gradien G y () G y () ADC Spins all in phase a k x=0 slice Slice Selecion z Δz f rec(f) Δf = 1 = γg zδz 2π sinc(/) Nishimura

13 Example M xy (x) = M 0 cos(4π x) M0 (δ (kx 2) + δ (kx + 2)) 2 gmax = 4 G / cm F ( M xy (x)) = 1 Gx() γ gmaxt = 4 cm 1; T = 235 µ sec 2π wih small ip angle approximaion --> = 2D random 2 walk T "π % 1 π Compare wih sin $ ' = = = #6& 2 6 π Quesion : Should we use = insead? seps 2D random walk k (, ) Exercise: Skech he quiver diagrams corresponding o he conribuions of he wo RF pulses and show ha hey produce he desired paern. (Paerns shown below scaled for display purposes) 400 seps N random seps of lengh d -2 Exercise: Skech he quiver diagrams corresponding o he conribuions of he wo RF pulses and show ha hey produce he desired paern. Muli-dimensional Exciaion kspace 2D random walk ( M xy (,r) = jm 0 ω1 ( ) exp jγ 100 seps G(s) rds)d Exciaion k-space 2D random walk 100 seps = jm 0 ω1 ( ) exp( j2πk( ) r ) d 400 seps γ where ofk( ) = d N random seps lengh 2π G( &)d& 400 seps N random seps of lengh d Pauly e al 1989 Pauly e al

14 Exciaion k-space Cardiac Tagging 2D random walk 100 seps 400 seps N random seps of lengh d Panych MRM