' ' ' t. Moving Spins. Phase of Moving Spin. Phase of a Moving Spin. Bioengineering 280A Principles of Biomedical Imaging

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1 Moving Spins Bioengineering 8A Principles of Biomedical Imaging Fall Quarer 1 MRI Lecure 6 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaaion) and conras has been based upon 1 and proon densiy. We were able o achieve differen conrass by adjusing he appropriae pulse sequence parameers. Biological samples are filled wih moving spins and we can also use MRI o image he movemen. Eamples: blood flow diffusion of waer in he whie maer racs. In addiion we can also someimes induce moion ino he objec o image is mechanical properies e.g. imaging of sress and srain wih MR elasography. Phase of Moving Spin ΔB z () ΔB z () ime "() = # Phase of a Moving Spin $%()d = # ($B()d = # ( G! () ) r! ()d = #( G ()() + G y ()y() + G z ()z() [ ]d 1

2 Phase of Moving Spin Consider moion along he -ais () = + v + 1 a Phase of Moving Spin % "() = #$ M + vm 1 + a M ( ) * "() = #$ G (%)(%)d% = #$ G (%) + v% + 1 a% * ( ) + d% = #$ G (%)d% + v G (%)%d% + a ( ) = #$ M + vm 1 + a M * ( ) + * G (%)% d% + M = M 1 = G (+)d+ G (+)+d+ M = G (+)+ d+ Zeroh order momen Firs order momen Second order momen Flow Momen Eample Phase Conras Angiography (PCA) G -G M = # G (")d" = M 1 = # G (")"d" = $ # G "d" + # G "d" % = G $ " + " ( * )* % = G $ + 4 $ ( * = G ) G -G G -G " 1 = #$v M 1 = $v G " = #$v M 1 = #$v G "# = # 1 $# = %v G v = "# G

3 PCA eample Aliasing in PCA -G Define VENC as he velociy a a which he phase is 18 degrees. # VENC " $G Because of phase wrapping he velociy of spins flowing faser han VENC is ambiguous. +π a VENC -π a -VENC hp:// Aliasing Soluions velociy no aliased Use daa from regions wih slower flow velociy aliased G -G Readou Gradien Flow Arifacs During readou moving spins wihin he objec will accumulae phase ha is in addiion o he phase used for imaging. his leads o Use muliple VENC values so ha he phase differences are smaller han π radians. v " 1 = # VENC 1 v " = # VENC % 1 1 ( " 1 $" = #v $ * VENC 1 VENC ) 3 1) Ne phase a echo ime E =. ) An apparen shif in posiion of he objec. 3) Blurring of he objec due o a quadraic phase erm. 3

4 Plug Flow Laminar Flow Flow Arifacs All moving spins in he voel eperience he same phase shif a echo ime. Flow Compensaion Readou Gradien Echo ime E G Spins have differen phase shifs a echo ime. he dephasing causes he cancelaion and signal dropou. -G 3 A E boh he firs and second order momens are zero so boh saionary and moving spins have zero ne phase. Inflow Effec ime of Fligh Angiography Prior o imaging ime Relaed spins flowing in Sauraed spins 4

5 Cerebral Blood Flow (CBF) CBF = Perfusion = Rae of delivery of arerial blood o a capillary bed in issue. Unis: (ml of Blood) (1 grams of issue)(minue) High CBF Low CBF ypical value is 6 mł(1g-min) or 6 mł(1 ml-min) =.1 s -1 assuming average densiy of brain equals 1 gm/ml ime Arerial spin labeling (ASL) 1: ag by Magneic Inversion Acquire image : Bereczki e al 199 Conrol Acquire image Conrol - ag = ΔM CBF 5

6 Mz(blood) conrol ag I ASL Signal Equaion ΔM - = ΔM PASL / VSASL R ASL Pulse Sequences ag Acquire Conrol Acquire M= CBF A eff A eff is he effecive area of he arerial bolus. I depends on boh physiology and pulse sequence parameers. I = Inversion ime CASL ag Acquire Conrol Labeling ime Pos Labeling Delay Acquire Mulislice CASL and PICORE ASL ime Series ag Conrol ag Conrol CASL! Wai ag by Magneic Inversion ag by Magneic Inversion Image 1 Image Image 3 Image 4 PICORE! QUIPSS II! Perfusion Images Credi: E. Wong 6

7 Diffusion Diffusing Spins D random walk 1 seps ΔB z () 4 seps ΔB z () ime N random seps of lengh d <Δ >= Nd = D D = diffusiviy In brain: D.1 mm /s For =1 msec Δ 15 µ Δ Credi: Larry Frank G -G δ Diffusion Weighing Diffusion Weighed Images weighed Diffusion Weighed Angiogram Signal S "e #$ G % D = e #bd where b = $ G % ( #% /3) Diffusiviy Afer a sroke normal waer movemen is resriced in he region of damage. Diffusiviy decreases so he signal inensiy increases. hp://lehighmri.com/cases/dwi/paien-b.hml 7

8 Resriced Diffusion Diffusion Imaging Eample D depends on direcion z y Diffusion ensor: 3 values of D 3 angles Credi: Larry Frank Q-ball imaging Fiber rac mapping of neural conneciviy uch e al Neuron 3 Couresy of L. Frank 8