Refocusing t. Small Tip Angle Example. Small Tip Angle Example. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2010 MRI Lecture 5

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1 Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2010 MRI Lecure 5 RF N random seps of lengh d Refocusing ' M xy (,) = jm 0 "B 1 ()exp( jk(,))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 & B 1 () = Asinc( /")rec% ( $ 20" ' Small Tip Angle Example % B 1 (k ) = Asinc k 2" ( % k ' rec 2" ( ' & G $ ) & 20G $ ) Small Tip Angle Example "10 " 10" 20" G - 10 G 10 k = 2 $ dk = 2 d

2 M xy % B 1 (k ) = Asinc k 2" ( % k ' rec 2" ( ' & G $ ) & 20G $ ) ' Small Tip Angle Example (,) = jm 0 "B 1 ()exp( jk(,))d %& & ( = jm 0 "Asinc k + ( k - rec + ' - exp( jk ), ) 20 ) dk %&, "G = jm 0 "A ( ( F %1 sinc k + ( k - rec + + "G - ) ), ) 20 -,, ( = jm 0 "A. rec ) + -/ 20 ( sinc , ), Saic Inhomogeneiies In he ideal siuaion, he saic magneic field is oally uniform and he reconsruced objec is deermined solely by he applied gradien fields. In realiy, he magne is no perfec and will no be oally uniform. Par of his can be addressed by addiional coils called shim coils, and he process of making he field more uniform is called shimming. In he old days his was done manually, bu modern magnes can do his auomaically. In addiion o magne imperfecions, mos biological samples are inhomogeneous and his will lead o inhomogeneiy in he field. This is because, each issue has differen magneic properies and will disor he field. Signal Decay Field Inhomogeneiies Some inhomogeneiy, Some dephasing 0 ime More inhomogeneiy, More dephasing, Decrease in MR signal 2

3 V " " x y Saic Inhomogeneiies The spaial nonuniformiy in he field can be modeled by adding an addiional erm o our signal equaion. s r () = " M( r!,) dv = M(x, y,,0)e /T 2 ( r! ) e j$ 0 e j$! E ( r )! " exp j% " G (&) ' r! d& dxdyd ( o ) The effec of his nonuniformiy is o cause he spins o dephase wih ime and hus for he signal o decrease more rapidly. To firs order his can be modeled as an addiional decay erm of he form ( o ) s r () = M(x, y,,0)e " /T 2 ( r! ) e " / T 2 ( r! ) e " j$ 0! ( exp " j% ( G (&) ' r! d& dxdyd ( ( x y The overall decay has he form. where T 2 decay ( ( ))! exp " /T 2 r 1 T 2 = 1 T " T 2 Due o random moions of spins. No reversible. Due o saic inhomogeneiies. Reversible wih a spin-echo sequence. T 2 decay Gradien echo sequences exhibi T 2 decay. RF Spin Echo Discovered by Erwin Hahn in G () G x () Slice selec gradien Slice refocusing gradien 180º G y () ADC = echo ime Gradien echo has exp(-/t 2 ) weighing The spin-echo can refocus he dephasing of spins due o saic inhomogeneiies. However, here will sill be T 2 dephasing due o random moion of spins. There is nohing ha nuclear spins will no do for you, as long as you rea hem as human beings. Erwin Hahn Image: Larry Frank 3

4 Spin Echo Spin Echo 180º Source: hp://mrsrl.sanford.edu/~brian/mri-movies/ Phase a ime "() = & $% E ( r! )d = $% E ( r! ) Phase afer 180 pulse 0 "( + ) = $ E ( r! ) Phase a ime 2 "(2) = $% E (! r ) + % E (! r ) = 0 Image: Larry Frank Spin Echo Pulse Sequence RF G () G x () G y () exp(" " / T 2 ) ADC exp(" /T 2 ) Spin-echo Image Gradien-Echo Image = echo ime hp://chickscope.beckman.uiuc.edu/rooss/carłarifacs.hml 4

5 Image Conras Differen issues exhibi differen relaxaion raes, T 1, T 2, and T 2. In addiion differen issues can have differen densiies of proons. By adjusing he pulse sequence, we can creae conras beween he issues. The mos basic way of creaing conras is adjusing he wo sequence parameers: (echo ime) and (repeiion ime). Spin-echo = 35 ms Gradien Echo = 14ms Sauraion Recovery Sequence Gradien Echo [ ]e /T 2 (x,y ) I(x, y) = "(x, y) 1 e /T 1 (x,y) T1-Weighed Scans Make very shor compared o eiher T 2 or T 2. The resulan image has boh proon and T 1 weighing. I(x, y) " (x, y) 1$ e $ /T 1 (x,y) [ ] Spin Echo I(x, y) = "(x, y) 1 e /T 1 [ (x,y) ]e /T 2 (x,y ) 5

6 T2-Weighed Scans Make very long compared o T 1 and use a spin-echo pulse sequence. The resulan image has boh proon and T 2 weighing. Proon Densiy Weighed Scans Make very long compared o T 1 and use a very shor. The resulan image is proon densiy weighed. I(x, y) " (x, y)e $ /T 2 I(x, y) " (x, y) Example FLASH sequence θ θ θ T 1 -weighed! Densiy-weighed! T 2 -weighed! Tissue Proon Densiy T1 (ms) T2 (ms) Csf Gray Whie Gradien Echo I(x,y) = "(x,y) 1 e /T1( x,y) [ ]sin$ 1 e /T 1( x,y) cos$ [ ] exp( /T 2 Signal inensiy is maximied a he Erns Angle " E = cos 1 ( exp( /T 1 )) FLASH equaion assumes no coherence from sho o sho. In pracice his is achieved wih RF spoiling. % ) 6

7 FLASH sequence Inversion Recovery TI " E = cos 1 ( exp( /T 1 )) I(x, y) = "(x, y) 1 2e TI /T 1 (x,y ) + e /T 1 [ (x,y) ]e /T 2 (x,y ) Inensiy is ero when inversion ime is TI = "T 1 ln 1+ exp(" /T 1) & $ % 2 ' ( Inversion Recovery GE Medical Sysems