1TT Liu, BE280A, UCSD Fall 2004Bioengineering 280APrinciples of Biomedical ImagingFall Quarter 2004MRI Lecture 4TT Liu, BE280A, UCSD Fall 2004Topics• Velocity Imaging• Perfusion Imaging• Diffusion Imaging• Functional MRI2TT Liu, BE280A, UCSD Fall 2004Moving SpinsSo far we have assumed that the spins are not moving (asidefrom thermal motion giving rise to relaxation), and contrasthas been based upon T1, T2, and proton density. We were ableto achieve different contrasts by adjusting the appropriatepulse sequence parameters.Biological samples are filled with moving spins, and we canalso use MRI to image the movement. Examples: blood flow,diffusion of water in the white matter tracts. In addition, wecan also sometimes induce motion into the object to image itsmechanical properties, e.g. imaging of stress and strain withMR elastography.TT Liu, BE280A, UCSD Fall 2004Phase of Moving SpinΔBz(x)ΔBz(x)xxtime3TT Liu, BE280A, UCSD Fall 2004Phase of a Moving Spin € ϕ(t) = − Δω(τ)dτ0t∫= −γΔB(τ)dτ0t∫= −γr G (τ) ⋅r r (τ)dτ0t∫= −γGx(τ)x(τ) + Gy(τ)y(τ) + Gz(τ)z(τ)[ ]dτ0t∫TT Liu, BE280A, UCSD Fall 2004Phase of Moving Spin€ ϕ(t) = −γGx(τ)x(τ)dτ0t∫= −γGx(τ) x0+ vτ+12aτ2 dτ0t∫= −γx0Gx(τ)dτ+ v Gx(τ)τdτ+a2Gx(τ)τ2dτ0t∫0t∫0t∫ = −γx0M0+ vM1+a2M2 € x(t) = x0+ vt +12at2Consider motion along the x-axis4TT Liu, BE280A, UCSD Fall 2004Phase of Moving Spin€ ϕ(t) = −γx0M0+ vM1+a2M2 M0= Gx(τ)dτ0t∫M1= Gx(τ)τdτ0t∫M2= Gx(τ)τ2dτ0t∫Zeroth order momentFirst order momentSecond order momentTT Liu, BE280A, UCSD Fall 2004Flow Moment ExampleG0-G0T T€ M0= Gx(τ)dτ0t∫= 0M1= Gx(τ)τdτ0t∫= − G0τdτ0T∫+ G0τdτT2T∫= G0−τ220T+τ22T2T = G0−T22+4T22−T22 = G0T25TT Liu, BE280A, UCSD Fall 2004Phase Contrast Angiography (PCA)G0-G0T TG0-G0T T€ ϕ1= −γvxM1=γvxG0T2€ ϕ2= −γvxM1= −γvxG0T2€ Δϕ=ϕ1−ϕ2= 2γvxG0T2€ vx=Δϕ2G0T2TT Liu, BE280A, UCSD Fall 2004PCA example-G0http://www.medical.philips.com/main/products/mri/assets/images/case_of_week/cotw_51_s5.jpg6TT Liu, BE280A, UCSD Fall 2004Aliasing in PCA€ VENC ≡πγG0T2Define VENC as the velocity at at which the phase is180 degrees.+π at VENC-π at -VENCBecause of phasewrapping the velocityof spins flowingfaster than VENC isambiguous.TT Liu, BE280A, UCSD Fall 2004Aliasing SolutionsUse data from regionswith slower flowvelocity not aliasedvelocity aliasedUse multiple VENC values so that the phase differencesare smaller than π radians.€ ϕ1=πvxVENC1ϕ2=πvxVENC2ϕ1−ϕ2=πvx1VENC1−1VENC2 7TT Liu, BE280A, UCSD Fall 2004Velocity k-space€ ϕ(vx) = −γvxG0T2A bipolar gradient introduces a phase modulation across velocitiesof the form€ M(kvx) = m(vx)ejϕ(vx)−∞∞∫dvx= m(vx)e− jγvxG0T2−∞∞∫dvx= m(vx)e− j 2πkvxvx−∞∞∫dvx= F m(vx)[ ] with kvx=γ2πG0T2By making measurements with bipolar gradients of varyingamplitudes/durations and taking the inverse transform ofthe measurements, we can obtain the velocity distribution.We can make measurements with different amounts of phasemodulation and then integrate over velocities to obtainTT Liu, BE280A, UCSD Fall 2004Velocity k-space€ M(kx,kvx) = m(x,vx)e− j 2πkxxe− j 2πkvxvx−∞∞∫dxdvx−∞∞∫In addition, we can apply imaging gradients so that we caneventually obtain the velocity distribution at each point inspace. A full k-space acqusition would then yield 6dimensions -- 3 spatial dimensions and 3 velocitydimensions.8TT Liu, BE280A, UCSD Fall 2004Flow ArtifactsG0-G0T 2T 3TDuring readout moving spinswithin the object willaccumulate phase that is inaddition to the phase used forimaging. This leads toReadout Gradient1) Net phase at echo time TE= 2T.2) An apparent shift inposition of the object.3) Blurring of the object dueto a quadratic phase term.TT Liu, BE280A, UCSD Fall 2004Flow ArtifactsLaminar FlowPlug FlowAll moving spins in thevoxel experience thesame phase shift atecho time.Spins have differentphase shifts at echotime. The dephasingcauses the cancelationand signal dropout.9TT Liu, BE280A, UCSD Fall 2004Flow CompensationG0-2G0T 2T 3TReadout GradientEcho Time TE At TE both the first and secondorder moments are zero, so bothstationary and moving spins havezero net phase.TT Liu, BE280A, UCSD Fall 2004Inflow EffecttimePrior to imagingRelaxed spins flowing inSaturated spins10TT Liu, BE280A, UCSD Fall 2004Time of Flight AngiographyTT Liu, BE280A, UCSD Fall 2004Cerebral Blood Flow (CBF)CBF = Perfusion = Rate of delivery of arterial blood to a capillary bed in tissue.Units: (ml of Blood) (100 grams of tissue)(minute)Typical value is 60 ml/(100g-min) or60 ml/(100 ml-min) = 0.01 s-1, assumingaverage density of brain equals 1 gm/ml11TT Liu, BE280A, UCSD Fall 2004Buxton 2002 TT Liu, BE280A, UCSD Fall 2004TimeHigh CBFLow CBF12TT Liu, BE280A, UCSD Fall 2004Arterial Spin Labeling•Magnetically tag inflowing arterial blood•Wait for tagged blood to flow into imaging slice•Acquire image of tissue+tagged blood•Apply control pulse that doesn’t tag blood•Acquire control image of tissue•Control image-tag image = blood imageTT Liu, BE280A, UCSD Fall 2004Arterial Spin Labeling (ASL)Arterial Spin Labeling (ASL)Tag by Magnetic InversionWaitAcquire imageControlWaitAcquire image1:2:Control - Tag ∝ CBFCredit: Wen-Ming Luh13TT Liu, BE280A, UCSD Fall 2004Arterial Spin Labeling (ASL)Arterial Spin Labeling (ASL)• water protons as freely diffusible tracersimaging slicealternativeinversionMz(blood)ΔMcontroltagtCourtesy of Wen-Ming LuhTT Liu, BE280A, UCSD Fall 2004Multislice CASL and PICORECASLPICOREQUIPSS IICredit: E. Wong14TT Liu, BE280A, UCSD Fall 2004 DiffusionN random steps of length d2D random walkΔx<Δx2>= Nd2 = 2DTD = diffusivityIn brain:D ≅ 0.001 mm2/sFor T=100 msec,Δx ≅ 15 µ100 steps400 stepsCredit: Larry FrankTT Liu, BE280A, UCSD Fall 2004 Diffusion WeightingG0-G0δT€ Assume δ<< Tϕ(t1) ≈ −γG0x t1( )δϕ(t2) ≈ +γG0x t2( )δ€ Net Phaseϕ≈ϕ(t1) +ϕ(t2) =γG0x t2( )− x t1( )[ ]δ=γG0ΔxδAverage Squared Phaseϕ2=γ2G02δ2Δx( )2=γ2G02δ22DTSignalS ∝ e-ϕ2/ 2= e−γ2G02δ2DT= e−bD where b = γ2G02δ2TA more careful analysis yields b = γ2G02δ2(T −δ/3)b-factor15TT Liu, BE280A, UCSD Fall 2004 Diffusion Weighted
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