1Thomas Liu, BE280A, UCSD, Fall 2006Bioengineering 280APrinciples of Biomedical ImagingFall Quarter 2006MRI Lecture 5Thomas Liu, BE280A, UCSD, Fall 2006! Small Tip Angle ApproximationMr(t,z) = jM0exp(" j#(z)t) exp(0t$j#(z)s)#1(s)dsFor symmetric pulse of length %Mr(%,z) = jM0exp(" j#(z)%/2) exp("%/ 2%/ 2$j2&f (z)s)#1(s +%/2)ds = jM0exp(" j#(z)%/2)F#1(t +%/2){ }f =" f (z )="'2&Gzz2Thomas Liu, BE280A, UCSD, Fall 2006Cardiac TaggingThomas Liu, BE280A, UCSD, Fall 2006 Excitation k-spaceN random steps of length d2D random walk100 steps400 stepsPauly et al 19893Thomas Liu, BE280A, UCSD, Fall 2006 Excitation k-spaceN random steps of length d2D random walk100 steps400 stepsPanych MRM 1999Thomas Liu, BE280A, UCSD, Fall 2006Static InhomogeneitiesIn the ideal situation, the static magnetic field is totally uniformand the reconstructed object is determined solely by the appliedgradient fields. In reality, the magnet is not perfect and will notbe totally uniform. Part of this can be addressed by additionalcoils called “shim” coils, and the process of making the fieldmore uniform is called “shimming”. In the old days this wasdone manually, but modern magnets can do this automatically.In addition to magnet imperfections, most biological samplesare inhomogeneous and this will lead to inhomogeneity in thefield. This is because, each tissue has different magneticproperties and will distort the field.4Thomas Liu, BE280A, UCSD, Fall 2006Static Inhomogeneities ! sr(t) = M(r r ,t)V"dV= M(x, y,z,0)e#t /T2(r r )e# j$0te# j$Er r ( )texp # j%r G (&) 'r r d&ot"( )z"y"x"dxdydzThe spatial nonuniformity in the field can be modeled by addingan additional term to our signal equation.The effect of this nonuniformity is to cause the spins to dephasewith time and thus for the signal to decrease more rapidly. To firstorder this can be modeled as an additional decay term of the form ! sr(t) = M(x, y,z,0)e"t /T2(r r )e"t /# T 2(r r )e" j$0texp " j%r G (&) 'r r d&ot(( )z(y(x(dxdydzThomas Liu, BE280A, UCSD, Fall 2006T2* decay ! exp "t /T2*v r ( )( )The overall decay has the form.! 1T2*=1T2+1" T 2whereDue to random motions of spins.Not reversible. Due to staticinhomogeneities. Reversiblewith a spin-echo sequence.5Thomas Liu, BE280A, UCSD, Fall 2006T2* decayGradient echo sequences exhibit T2* decay. Gx(t)Gy(t)RFGz(t)Slice select gradientSlice refocusing gradientADCTE = echo timeGradient echo hasexp(-TE/T2*)weightingThomas Liu, BE280A, UCSD, Fall 2006Spin EchoDiscovered by Erwin Hahn in 1950. There is nothing that nuclear spins will not do for you, aslong as you treat them as human beings. Erwin HahnImage: Larry Frankτ τ180ºThe spin-echo can refocus the dephasing of spins dueto static inhomogeneities. However, there will still beT2 dephasing due to random motion of spins.6Thomas Liu, BE280A, UCSD, Fall 2006Spin EchoImage: Larry FrankPhase at time τ τ τ180ºPhase after 180 pulse ! "(#) = $%E(r r )dt =0#&$%E(r r )# ! "(#+) =$E(r r )#Phase at time 2τ ! "(2#) = $%E(r r )#+%E(r r )#= 0Thomas Liu, BE280A, UCSD, Fall 2006Spin Echo Pulse SequenceGx(t)Gy(t)RFGz(t)ADCτ τ 90 180TE = echo time! exp("t /T2)! exp(" t " TE /# T 2)7Thomas Liu, BE280A, UCSD, Fall 2006Spin-echo ImageGradient-Echo Imagehttp://chickscope.beckman.uiuc.edu/roosts/carłartifacts.htmlThomas Liu, BE280A, UCSD, Fall 2006Image ContrastDifferent tissues exhibit different relaxation rates, T1, T2,and T2*. In addition different tissues can have differentdensities of protons. By adjusting the pulse sequence, wecan create contrast between the tissues. The most basic wayof creating contrast is adjusting the two sequenceparameters: TE (echo time) and TR (repetition time).8Thomas Liu, BE280A, UCSD, Fall 2006Saturation Recovery Sequence90 90 90TR TRTE TE! I(x, y) ="(x, y) 1# e#TR /T1(x,y )[ ]e#TE /T2*(x,y )! I(x, y) ="(x, y) 1# e#TR /T1(x,y )[ ]e#TE /T2(x,y )Gradient EchoSpin Echo90 90 90TE180 180TRThomas Liu, BE280A, UCSD, Fall 2006T1-Weighted Scans! I(x, y) "#(x, y) 1$ e$TR /T1(x,y )[ ]Make TE very short compared to either T2 or T2*. The resultantimage has both proton and T1 weighting.9Thomas Liu, BE280A, UCSD, Fall 2006T2-Weighted Scans! I(x, y) "#(x, y)e$TE /T2Make TR very long compared to T1 and use a spin-echo pulsesequence. The resultant image has both proton and T2 weighting.Thomas Liu, BE280A, UCSD, Fall 2006Proton Density Weighted Scans! I(x, y) "#(x, y)Make TR very long compared to T1 and use a very short TE. Theresultant image is proton density weighted.10Thomas Liu, BE280A, UCSD, Fall 2006ExampleT1-weighted T2-weightedDensity-weightedThomas Liu, BE280A, UCSD, Fall 2006FLASH sequenceθTR TRTE TE! I ( x, y) ="(x, y)1# e#TR /T1( x ,y )[ ]sin$1# e#TR /T1( x ,y )cos$[ ]exp(#TE /T2%)Gradient Echoθ θ! "E= cos#1exp(#TR /T1)( )Signal intensity is maximized at the Ernst AngleFLASH equation assumes no coherence from shot to shot. Inpractice this is achieved with RF spoiling.11Thomas Liu, BE280A, UCSD, Fall 2006FLASH sequence! "E= cos#1exp(#TR /T1)( )Thomas Liu, BE280A, UCSD, Fall 2006Inversion Recovery90180TITR! I(x, y) ="(x, y) 1# 2e#TI /T1(x,y )+ e#TR /T1(x,y )[ ]e#TE /T2(x,y )18090180 180TEIntensity is zero when inversion time is! TI = "T1ln1+ exp("TR /T1)2# $ % & ' (12Thomas Liu, BE280A, UCSD, Fall 2006Inversion RecoveryGE Medical Systems 2003Thomas Liu, BE280A, UCSD, Fall 2006Fast Spin EchoGE Medical Systems 200313Thomas Liu, BE280A, UCSD, Fall 2006Echoplanar ImagingGE Medical Systems
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