1Thomas Liu, BE280A, UCSD, Fall 2007Bioengineering 280APrinciples of Biomedical ImagingFall Quarter 2007MRI Lecture 4Thomas Liu, BE280A, UCSD, Fall 2007Static 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.Thomas Liu, BE280A, UCSD, Fall 2007Field InhomogeneitiesThomas Liu, BE280A, UCSD, Fall 2007Signal DropoutsField inhomogeneities also cause the spins to dephase with timeand thus for the signal to decrease more rapidly. To first order thiscan be modeled as an additional decay term.2Thomas Liu, BE280A, UCSD, Fall 2007Static 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 2007T2* 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.Thomas Liu, BE280A, UCSD, Fall 2007T2* 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 2007Spin 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.3Thomas Liu, BE280A, UCSD, Fall 2007Spin 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#) = $%E(r r )#+%E(r r )#= 0Thomas Liu, BE280A, UCSD, Fall 2007Spin Echo Pulse SequenceGx(t)Gy(t)RFGz(t)ADCτ τ 90 180TE = echo time! exp("t /T2)! exp(" t " TE /# T 2)Thomas Liu, BE280A, UCSD, Fall 2007Spin-echo ImageGradient-Echo Imagehttp://chickscope.beckman.uiuc.edu/roosts/carłartifacts.htmlThomas Liu, BE280A, UCSD, Fall 2007Spin-echo TE = 35 ms Gradient Echo TE = 14ms4Thomas Liu, BE280A, UCSD, Fall 2007Image ContrastDifferent tissues exhibit different relaxation rates, T1, T2,and T2*. In addition different tissues can have differentdensities of protons. By adjusting the pulse sequence, wecan create contrast between the tissues. The most basic wayof creating contrast is adjusting the two sequenceparameters: TE (echo time) and TR (repetition time).Thomas Liu, BE280A, UCSD, Fall 2007Saturation Recovery Sequence90 90 90TR TRTE TE! I(x, y) ="(x, y) 1# e#TR /T1(x,y )[ ]e#TE /T2*(x,y )Gradient Echo! I(x, y) ="(x, y) 1# e#TR /T1(x,y )[ ]e#TE /T2(x,y )Spin Echo90 90 90TE180 180TRThomas Liu, BE280A, UCSD, Fall 2007T1-Weighted Scans! I(x, y) "#(x, y) 1$ e$TR /T1(x,y )[ ]Make TE very short compared to either T2 or T2*. The resultantimage has both proton and T1 weighting.Thomas Liu, BE280A, UCSD, Fall 2007T2-Weighted Scans! I(x, y) "#(x, y)e$TE /T2Make TR very long compared to T1 and use a spin-echo pulsesequence. The resultant image has both proton and T2 weighting.5Thomas Liu, BE280A, UCSD, Fall 2007Proton 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.Thomas Liu, BE280A, UCSD, Fall 2007ExampleT1-weighted T2-weightedDensity-weightedThomas Liu, BE280A, UCSD, Fall 2007FLASH 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.Thomas Liu, BE280A, UCSD, Fall 2007FLASH sequence! "E= cos#1exp(#TR /T1)( )6Thomas Liu, BE280A, UCSD, Fall 2007Inversion 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# $ % & ' ( Thomas Liu, BE280A, UCSD, Fall 2007Inversion RecoveryGE Medical Systems
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