RF Excitation. Rotating Frame of Reference. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2012 MRI Lecture 6

Transcription

1 RF Exciaion Bioengineering 8A Principles of Biomedical Imaging Fall Quarer 1 MRI Lecure 6 hp:// RF Exciaion Roaing Frame of Reference Reference everyhing o he magneic field a isocener. hp:// 1

2 Precession dµ d = µ x γb B Analogous o moion of a gyroscope Precesses a an angular frequency of ω = γ Β a) Laboraory frame behavior of M b) Roaing frame behavior of M Images & capion: Nishimura, Fig. 3.3 dµ µ his is known as he Larmor frequency. hp:// hp:// Roaing Frame Bloch Equaion dm ro = M d ro γb eff & B eff = B ro + ω ) ro γ ; ω ( + ro = ( + '( ω * + Noe: we use he RF frequency o define he roaing frame. If his RF frequency is on-resonance, hen he main B 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. Le B ro = B 1 ()i + B k B eff = B ro + ω ro γ % = B 1 ()i + B ω ( ' * k & γ ) If ω = ω = γb hen B eff = B 1 ()i

3 Flip angle τ θ = ω 1 (s)ds where ω 1 () = γb 1 () Nishimura 1996 Nishimura 1996 Le B ro = B 1 ()i + ( B + γg z z)k B eff = B ro + ω ro γ % = B 1 ()i + B + γg z z ω ( ' * k & γ ) If ω = ω B eff = B 1 ()i + ( γg z z)k Nishimura

4 slice Slice Selecion z Δz f rec(f/w) W=γG z Δz/(π) sinc(w) Nishimura 1996 Small ip Angle Approximaion θ θ θ Exciaion k-space For small θ M z M θ M xy M z = M cosθ M M xy = M sinθ M θ τ 1 D τ random τ 3 walk G z () k( τ,) k(τ,) = γ π G τ z ( s)ds 1 seps M θ exp( jπk z (τ 1,)z) 4 seps M θ exp( jπk z (τ 1,)z) M θ 4

5 Exciaion k-space A each ime incremen of widh Δτ, he exciaion B 1 (τ ) produces an incremen in magneizaion of he form ΔM xy jm γb 1 (τ )Δτ 1 seps D random walk (small ip angle approximaion) In he presence of a gradien, his will accumulae phase of he form ϕ=-γ ΔM xy τ zg z ( s)ds, such ha he incremenal magneizaion a ime is ( τ ) Δτ (,z ; τ ) = jm γb 1 (τ )exp jγ zg z ( s)ds N random seps of lengh d Inegraing over all ime incremens, we obain M xy ( τ ) dτ (,z) = jm γb 1 (τ )exp jγ zg z ( s)ds = jm γb 1 (τ )exp( jπk(τ,)z)dτ where k(τ,) = γ π G τ z ( s)ds 4 seps Exciaion k-space M xy (,z) = jm γb 1 (τ )exp( jπk(τ,)z)dτ 1 seps his has he D form random of walk inverse Fourier ransform, where we are inegraing he conribuions of he field B 1 ( τ) a he k - space poin k( τ,). RF N random seps of lengh d 4 seps 1 3 Slice selec gradien G z () k(τ,) = γ π G τ z ( s)ds 3 1 τ k z RF N random seps of lengh d Refocusing M xy (,z) = jm γb 1 (τ )exp( jπk(τ,)z)dτ 1 seps his has he D form random of walk inverse Fourier ransform, where we are inegraing he conribuions of he field B 1 ( τ) a he k - space poin k( τ,). G z () k( τ,) Slice selec gradien Slice refocusing gradien k(τ,) = γ π G τ z ( s)ds τ 3 4 seps 4 1 k z RF G z () G x () G y () Slice Selecion Slice selec gradien Slice refocusing gradien 5

6 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= f rec(fτ) Δf = 1 τ = γg zδz π Δz sinc(/τ) Cardiac agging Nishimura

7 Muli-dimensional Exciaion kspace D random walk ( M xy (,r) = jm ω1 (τ ) exp jγ Exciaion k-space 1 seps 1 seps D random walk G(s) rds)dτ τ = jm ω1 (τ ) exp( jπk(τ ) r ) dτ 4 seps γ where τ ) = d N random seps ofk( lengh π τ G( &)d& 4 seps N random seps of lengh d Pauly e al 1989 Exciaion k-space D random walk Pauly e al seps Example M xy (x) = M cos(4π x) θ M (δ (kx ) + δ (kx + )) gmax = 4 G / cm τ1 F ( M xy (x)) = Gx() γ gmax = 4 cm 1; = 35 µ sec π 4 seps 1 "π % 1 π Compare wih sin $ ' = θ = =.536 #6& 6 π Quesion : Should we use θ = insead? 4 N random seps of lengh d wih small ip angle approximaion --> θ = Panych MRM 1999 k (τ, ) θ D random τ walk - 7

8 Moving Spins 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,, 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 Phase of Moving Spin ϕ() = Δω(τ)dτ = γδb(τ)dτ = γg (τ) r (τ)dτ = γ G x (τ)x(τ) + G y (τ)y(τ) + G z (τ)z(τ) [ ]dτ Consider moion along he x-axis x() = x + v + 1 a ϕ() = γ G x (τ)x(τ)dτ ' = γ G x (τ) x + vτ + 1 aτ * ( ) +, dτ ' = γ x G x (τ)dτ + v G x (τ)τdτ + a ( ) ' = γ x M + vm 1 + a M * ( ) +, * G x (τ)τ dτ +, 8

9 Phase of Moving Spin % ϕ() = γ x M + vm 1 + a M ( & ' ) * M = M 1 = M = G x (τ)dτ G x (τ)τdτ G x (τ)τ dτ Zeroh order momen Firs order momen Second order momen G -G Flow Momen Example M = G x (τ)dτ = M 1 = G x (τ)τdτ = G τdτ + G τdτ % = G ' τ &' + τ ( * )* % = G + 4 ( ' * = G & ) Phase Conras Angiography (PCA) PCA example G ϕ 1 = γv x M 1 = γv x G -G -G G ϕ = γv x M 1 = γv x G -G Δϕ = ϕ 1 ϕ = γv x G v x = Δϕ G hp:// 9

10 Aliasing in PCA Define VENC as he velociy a a which he phase is 18 degrees. π VENC γg Aliasing Soluions velociy no aliased Use daa from regions wih slower flow velociy aliased Because of phase wrapping he velociy of spins flowing faser han VENC is ambiguous. +π a VENC -π a -VENC Use muliple VENC values so ha he phase differences are smaller han π radians. v ϕ 1 = π x VENC 1 v x ϕ = π VENC % 1 1 ( ϕ 1 ϕ = πv x ' * & VENC 1 VENC ) 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 Plug Flow Laminar Flow Flow Arifacs All moving spins in he voxel experience he same phase shif a echo ime. 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. Spins have differen phase shifs a echo ime. he dephasing causes he cancelaion and signal dropou. 1

11 Readou Gradien Flow Compensaion Echo ime E Inflow Effec Prior o imaging G -G 3 ime A E boh he firs and second order momens are zero, so boh saionary and moving spins have zero ne phase. Relaxed spins flowing in Sauraed spins ime of Fligh Angiography 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) 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 11

12 High CBF Low CBF ime Bereczki e al 199 1: Arerial spin labeling (ASL) ag by Magneic Inversion Acquire image Mz(blood) conrol ag I ASL Signal Equaion ΔM - = ΔM : Conrol Acquire image Conrol - ag = ΔM CBF M= CBF A eff A eff is he effecive area of he arerial bolus. I depends on boh physiology and pulse sequence parameers. 1

13 PASL / VSASL R ASL Pulse Sequences ag Acquire Conrol Acquire Mulislice CASL and PICORE I = Inversion ime CASL! CASL ag Acquire Conrol Acquire PICORE! QUIPSS II! Labeling ime Pos Labeling Delay Credi: E. Wong ASL ime Series Diffusion ag Conrol ag Conrol D random walk 1 seps Wai ag by Magneic Inversion ag by Magneic Inversion 4 seps Image 1 Image Image 3 Image N random seps of lengh d Δx Perfusion Images <Δx >= Nd = D D = diffusiviy In brain: D.1 mm /s For =1 msec, Δx 15 µ Credi: Larry Frank 13

14 ΔB z (x) Diffusing Spins x G -G δ Diffusion Weighing ΔB z (x) ime Signal S e γ G δ D = e bd where b = γ G δ ( δ /3) x Diffusiviy Diffusion Weighed Images weighed Diffusion Weighed Angiogram Resriced Diffusion D depends on direcion z Afer a sroke, normal waer movemen is resriced in he region of damage. Diffusiviy decreases, so he signal inensiy increases. x y Diffusion ensor: 3 values of D 3 angles hp://lehighmri.com/cases/dwi/paien-b.hml Credi: Larry Frank 14

15 Diffusion Imaging Example Q-ball imaging Fiber rac mapping of neural conneciviy uch e al, Neuron 3 Diffusion MRI racography Couresy of L. Frank from he Human Connecome Projec 15