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

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1 Moving Spins Bioengineering 28A Principles of Biomedical Imaging Fall Quarer 28 MRI Lecure 7 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaxaion), and conras has been based upon 1, 2, 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. Examples: 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 (x) x ΔB z (x) x ime "() = # ' ' Phase of a Moving Spin $%(&)d& = # ($B(&)d& = # ( G r (&) ) r (&)d& ' ' = #( G x (&)x(&) + G y (&)y(&) + G z (&)z(&) [ ]d& 1

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

3 PCA example Aliasing in PCA -G Define VENC as he velociy a a which he phase is 18 degrees. # VENC " $G 2 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 Readou Gradien G -G 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. " 1 = # VENC 1 v x v x " 2 = # VENC 2 % 1 1 ( " 1 $" 2 = #v x ' $ * & VENC 1 VENC 2 ) 2 3 1) Ne phase a echo ime E = 2. 2) 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 voxel experience he same phase shif a echo ime. Spins have differen phase shifs a echo ime. he dephasing causes he cancelaion and signal dropou. Readou Gradien G -2G Flow Compensaion 2 3 Echo ime E 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 Relaxed 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 2: Bereczki e al 1992 Conrol Acquire image Conrol - ag = ΔM CBF 5

6 Mz(blood) conrol ag I ASL Signal Equaion ΔM - = ΔM PASL / VSASL R ag ASL Pulse Sequences Acquire Conrol Acquire A eff is he effecive area of he arerial bolus. I depends on boh physiology and pulse sequence parameers. M= CBF A eff 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 PICORE QUIPSS II Image 1 Image 2 Image 3 Image Perfusion Images Credi: E. Wong 6

7 Diffusion Diffusing Spins 2D random walk 1 seps ΔB z (x) x 4 seps ΔB z (x) ime N random seps of lengh d <Δx 2 >= Nd 2 = 2D D = diffusiviy In brain: D.1 mm 2 /s For =1 msec, Δx 15 µ Δx x Credi: Larry Frank G -G δ Diffusion Weighing Diffusion Weighed Images 2 weighed Diffusion Weighed Angiogram Signal S "e #$ 2 G 2 % 2 D = e #bd where b = $ 2 G 2 % 2 ( #% /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 Example D depends on direcion z y x Diffusion ensor: 3 values of D 3 angles Credi: Larry Frank Q-ball imaging uch e al, Neuron 23 Fiber rac mapping of neural conneciviy Couresy of L. Frank 8

9 fmri MRI sudies brain anaomy. Funcional MRI Funcional MRI (fmri) sudies brain funcion. hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm fmri Seup fmri Acquisiion High spaial resoluion MP-RAGE Voxel volume: 1 mm3 Imaging ime: 6 min hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm High emporal resoluion EPI Voxel volume: 45 mm3 Imaging ime: 6 msec Buxon 22 9

10 Hisory of Funcional MRI homas Liu, BE28A, UCSD, Fall e 28 Source: Ogawa al., 1992 Finger apping ask Hemoglobin and Field Inhomogeneiies Signal Decay Oxygen binds o he iron aoms o form oxyhemoglobin HbO2 Release of O2 o issue resuls in deoxyhemoglobin dhbo2 Some dhb, Some dephasing Field Maps E ime More dhb, More dephasing, Decrease in MR signal B More dhb Less dhb hp:// 1

11 Blood Flow and Oxygen Meabolism Cerebral Blood Flow (CBF) measures delivery of blood o brain issue (unis of ml/(g-min)) Cerebral Meabolic Rae of (CMRO 2 ) is he rae of oxygen consumpion (unis of µmol/(g-min)) Deoxyhemoglobin [dhb] venous E [O 2 ] arerial / 4 = CMRO 2 / 4CBF O 2 CBF [O 2 ] arerial Oxygen exracion fracion (E) CMRO 2 [dhb] venous CMRO 2 CBF [dhb] venous CMRO 2 = E CBF [O 2 ] arerial fmri: areriole Spaial capillary emporal bed venule Dynamics EPI Scans CBF Neural aciviy CMRO 2 oxyhb deoxyhb Posiive BOLD CBF CMRO 2 CBV dhb Iniial dip CBF CMRO 2 dhb CBV Pos-simulus Response CBF CMRO 2 dhb CBV GE Medical Sysems 23 Phase Encode 11

12 Field Inhomogeneiies EPI Disorions and Signal Dropous Credi: R. Buxon Slower Faser Fig Credi: R. Buxon Precesses slower because of local field inhomogeneiy 12

13 Field Map Correcion Slower rajecory->more displacemen Nyquis Ghoss J. Clarke, UC Berkeley 13

14 J. Clarke, UC B J. Clarke, UC Berkeley Seeley e al, JMR 24 Seeley e al, JMR 24 14

15 Compressed Sensing Compressed Sensing F F Randomly hrow away 83% of samples Minimum - norm convenional linear reconsrucion Slide Credi: hp:// * E.J. Candes, J. Romberg and. ao. Min. oal Variaion (V) A convex non-linear reconsrucion * E.J. Candes, J. Romberg and. ao. Slide Credi: hp:// 15