1!Bioengineering 280A"Principles of Biomedical Imaging""Fall Quarter 2010"MRI Lecture 6"!Moving Spins!So far we have assumed that the spins are not moving (aside from thermal motion giving rise to relaxation), and contrast has been based upon T1, T2, and proton density. We were able to achieve different contrasts by adjusting the appropriate pulse sequence parameters. !Biological samples are filled with moving spins, and we can also use MRI to image the movement. Examples: blood flow, diffusion of water in the white matter tracts. In addition, we can also sometimes induce motion into the object to image its mechanical properties, e.g. imaging of stress and strain with MR elastography. !Phase of Moving Spin!ΔBz(x)!ΔBz(x)!x!x!time!Phase of a Moving Spin! ! "(t) = # $%(&)d&0t'= #($B(&)d&0t'= #(! G (&) )! r (&)d&0t'= #(Gx(&)x(&) + Gy(&)y(&) + Gz(&)z(&)[ ]d&0t'2!Phase of Moving Spin!! "(t) = #$Gx(%)x(%)d%0t&= #$Gx(%) x0+ v%+12a%2' ( ) * + , d%0t&= #$x0Gx(%)d%+ v Gx(%)%d%+a2Gx(%)%2d%0t&0t&0t&' ( ) * + , = #$x0M0+ vM1+a2M2' ( ) * + , ! x(t) = x0+ vt +12at2Consider motion along the x-axis!Phase of Moving Spin!! "(t) = #$x0M0+ vM1+a2M2% & ' ( ) * M0= Gx(+)d+0t,M1= Gx(+)+d+0t,M2= Gx(+)+2d+0t,Zeroth order moment!First order moment!Second order moment!Flow Moment Example!G0!-G0!T! T!! M0= Gx(")d"0t#= 0M1= Gx(")"d"0t#= $ G0"d"0T#+ G0"d"T2T#= G0$"220T+"22T2T% & ' ' ( ) * * = G0$T22+4T22$T22% & ' ( ) * = G0T2Phase Contrast Angiography (PCA)!G0!-G0!T! T!G0!-G0!T! T!! "1= #$vxM1=$vxG0T2! "2= #$vxM1= #$vxG0T2! "#=#1$#2= 2%vxG0T2! vx="#2G0T23!PCA example!-G0!http://www.medical.philips.com/main/products/mri/assets/images/case_of_week/cotw_51_s5.jpg!Aliasing in PCA!! VENC "#$G0T2Define VENC as the velocity at at which the phase is 180 degrees. !+π at VENC!-π at -VENC!Because of phase wrapping the velocity of spins flowing faster than VENC is ambiguous. !Aliasing Solutions!Use data from regions with slower flow!velocity not aliased!velocity aliased!Use multiple VENC values so that the phase differences are smaller than π radians. !! "1=#vxVENC1"2=#vxVENC2"1$"2=#vx1VENC1$1VENC2% & ' ( ) * Flow Artifacts!G0!-G0!T! 2T! 3T!During readout moving spins within the object will accumulate phase that is in addition to the phase used for imaging. This leads to!Readout Gradient!1) Net phase at echo time TE = 2T.!2) An apparent shift in position of the object. !3) Blurring of the object due to a quadratic phase term. !4!Flow Artifacts!Laminar Flow!Plug Flow!All moving spins in the voxel experience the same phase shift at echo time. !Spins have different phase shifts at echo time. The dephasing causes the cancelation and signal dropout. !Flow Compensation!G0!-2G0!T! 2T! 3T!Readout Gradient!Echo Time TE !At TE both the first and second order moments are zero, so both stationary and moving spins have zero net phase. !Inflow Effect!time!Prior to imaging!Relaxed spins flowing in!Saturated spins!Time of Flight Angiography!5!Cerebral 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 mł(100g-min) or !60 mł(100 ml-min) = 0.01 s-1, assuming average density of brain equals 1 gm/ml!! !Time!!High CBF!Low CBF!Bereczki et al 1992!Arterial spin labeling (ASL)!Acquire image!Acquire image!Tag by Magnetic Inversion!1:!Control!2:!Control - Tag = ΔM ∝ CBF!6!ASL Signal Equation !Aeff is the effective area of the arterial bolus. It depends on both physiology and pulse sequence parameters. !!!∆M= CBF · Aeff!Mz(blood) ΔM control tag t t TI -!=!ΔM ASL Pulse Sequences!Control! Acquire!Acquire!Post Labeling Delay!Tag!Labeling Time! CASL!Tag!Acquire!Acquire!TI = Inversion Time!Control!TR!PASL / VSASL!Multislice CASL and PICORE!CASL!PICORE!QUIPSS II!Credit: E. Wong!Wait Tag by Magnetic Inversion!Tag Image 1 Control Image 2 Tag by Magnetic Inversion!Tag Image 3 Control Image 4 Perfusion Images!-0.5! 1!-0.5!+0.5! +0.5!-1!ASL Time Series!7! Diffusion!N random steps of length d!2D random walk!Δx!<Δx2>= Nd2 = 2DT!D = diffusivity!In brain:!D ≅ 0.001 mm2/s!For T=100 msec,!Δx ≅ 15 µ!100 steps!400 steps!Credit: Larry Frank!Diffusing Spins!ΔBz(x)!ΔBz(x)!x!x!time! Diffusion Weighting!G0!-G0! δ!T!! SignalS " e#$2G02%2DT= e#bD where b =$2G02%2(T #%/3) Diffusivity! Diffusion Weighted Images!http://lehighmri.com/cases/dwi/patient-b.html! T2 weighted! ! Diffusion Weighted ! Angiogram!After a stroke, normal water movement is restricted in the region of damage. Diffusivity decreases, so the signal intensity increases. !8!Restricted Diffusion!x!y!z!D depends on direction!Diffusion tensor:!!3 values of D!!3 angles!Credit: Larry Frank!Diffusion Imaging Example!Q-ball imaging!Tuch et al, Neuron 2003!"!Courtesy of L. Frank Fiber tract mapping of neural
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