1Thomas Liu, BE280A, UCSD, Fall 2005Bioengineering 280APrinciples of Biomedical ImagingFall Quarter 2005MRI Lecture 6Thomas Liu, BE280A, UCSD, Fall 2005 Excitation k-spaceN random steps of length d2D random walk100 steps400 stepsPauly et al 19892Thomas Liu, BE280A, UCSD, Fall 2005Moving 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.Thomas Liu, BE280A, UCSD, Fall 2005Phase of Moving SpinΔBz(x)ΔBz(x)xxtime3Thomas Liu, BE280A, UCSD, Fall 2005Phase 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∫Thomas Liu, BE280A, UCSD, Fall 2005Phase 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-axis4Thomas Liu, BE280A, UCSD, Fall 2005Phase 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 momentThomas Liu, BE280A, UCSD, Fall 2005Flow Moment ExampleG0-G0T T€ M0= Gx(τ)dτ0t∫= 0M1= Gx(τ)τdτ0t∫= − G0τdτ0T∫+ G0τdτT2T∫= G0−τ220T+τ22T2T = G0−T22+4T22−T22 = G0T25Thomas Liu, BE280A, UCSD, Fall 2005Phase Contrast Angiography (PCA)G0-G0T TG0-G0T T€ ϕ1= −γvxM1=γvxG0T2€ ϕ2= −γvxM1= −γvxG0T2€ Δϕ=ϕ1−ϕ2= 2γvxG0T2€ vx=Δϕ2G0T2Thomas Liu, BE280A, UCSD, Fall 2005PCA example-G0http://www.medical.philips.com/main/products/mri/assets/images/case_of_week/cotw_51_s5.jpg6Thomas Liu, BE280A, UCSD, Fall 2005Aliasing 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.Thomas Liu, BE280A, UCSD, Fall 2005Aliasing 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 7Thomas Liu, BE280A, UCSD, Fall 2005Velocity 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 obtainThomas Liu, BE280A, UCSD, Fall 2005Velocity 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.8Thomas Liu, BE280A, UCSD, Fall 2005Flow 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.Thomas Liu, BE280A, UCSD, Fall 2005Flow 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.9Thomas Liu, BE280A, UCSD, Fall 2005Flow 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.Thomas Liu, BE280A, UCSD, Fall 2005Inflow EffecttimePrior to imagingRelaxed spins flowing inSaturated spins10Thomas Liu, BE280A, UCSD, Fall 2005Time of Flight AngiographyThomas Liu, BE280A, UCSD, Fall 2005Cerebral 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/ml11Thomas Liu, BE280A, UCSD, Fall 2005Buxton 2002 Thomas Liu, BE280A, UCSD, Fall 2005TimeHigh CBFLow CBF12Thomas Liu, BE280A, UCSD, Fall 2005Arterial 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 imageThomas Liu, BE280A, UCSD, Fall 2005Arterial Spin Labeling (ASL)Arterial Spin Labeling (ASL)Tag by Magnetic InversionWaitAcquire imageControlWaitAcquire image1:2:Control - Tag ∝ CBFCredit: Wen-Ming Luh13Thomas Liu, BE280A, UCSD, Fall 2005Arterial Spin Labeling (ASL)Arterial Spin Labeling (ASL)• water protons as freely diffusible tracersimaging slicealternativeinversionMz(blood)ΔMcontroltagtCourtesy of Wen-Ming LuhThomas Liu, BE280A, UCSD, Fall 2005Multislice CASL and PICORECASLPICOREQUIPSS IICredit: E. Wong14Thomas Liu, BE280A, UCSD, Fall 2005 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 FrankThomas Liu, BE280A, UCSD, Fall 2005 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
View Full Document
Unlocking...