11/20/200611ENGG 167 - F06MEDICAL IMAGINGWednesday, Nov. 1Spatial Localization and MR ImagesReferences: The Essential Physics of Medical Imaging, Bushberg et al, 2nded., Chapters 14 & 15Principles of Magnetic Resonance Imaging: A Signal Processing Perspective, Liang and Lauterbur, IEEE Press 2000MRI the Basics, Hashemi and Bradley, Williams and Wilkins publ., 1997http://www.cis.rit.edu/htbooks/mri/2Review of Concepts• MRI is sensitive to nuclei with odd mass number or odd charge number•1H is used (high |µ|, high in vivo concentration in H2O)• B0establishes Mz0, individual spins precess at ω = γB0(42.6 MHz / T)• B1(ωrf = γB0) rotates Mz0into transverse plane →Mxy(FID or echo measured)• This excitation is followed by relaxation• Transverse, spin-spin relaxation• T2*, dephasing from intrinsicspin interactions, phase diffusion• T2*, dephasing from stationaryextrinsic B inhomogeneities• Longitudinal, spin-lattice relaxation,return of M to Mz0• T1, transfer of energy to theenvironment (lattice)11/20/200623Excitation, Relaxation and DetectionExcitationRelaxationRotatingFrameLaboratoryFrameDetection4MRI Contrast Summary• T1depends on the efficiencies of tissues to accept energy ∆E=γB0.• T2depends on spin-spin interactions and averaging of the local B fields.• Differences in T1, T2, or PD can be measured using a SE sequence.• TE and TR (and TI) are used to control the weighting.• Gradient echoes can be used for faster imaging experiments.• Forced echoes, can be used for very fast imaging• No T2* refocusing, so data may be T2* weighted.• The flip angle can be used to adjust the contrast.• These concepts form the basis of tissue contrast in MRI.()()()1201Induced ,,,,,,VTT PDBBTE TR TIxyMM t Sk IxSφµ→→ → →→11/20/200635Review: T1 and T2 DependenciesRef: Bushberg6Review: SE Pulse SequencesRef: Bushberg11/20/200647X-Y-Z Magnetic Field GradientsRef: Bushberg0()RF rBGrωγ=+8MRI Whole Body ImagingRef: Bushberg0()RF rBGrωγ=+11/20/200659Z-axis Slice ThicknessRef: Bushberg10Z-axis Slice PulseRef: Bushberg11/20/2006611Z-axis Slice PulseRef: Bushberg12Slice Encoding GradientRef: Bushberg11/20/2006713Frequency Encoding GradientRef: Bushberg14Fourier Transforming signalsRef: Bushberg11/20/2006815Frequency Encoded SignalsFree induction decay (FID) signal,In the presence of a field gradient,after demodulation (phase sensitive detection).Frequency encoding gradient is applied during read out.() ( )000iBtobjectSt re dr Bγρωγ−==∫() ( )()0iBGrtobjectSt re drγρ−+=∫i() ( )()0iGrtiBtobjectSt re dreγγρ−−⎡⎤=⎢⎥⎣⎦∫i() ( )()iGrtobjectSt re drγρ−=∫iRef: Liang and Lauterbur16Phase Encoding GradientRef: Bushberg11/20/2006917Phase Encoding GradientRef: Bushberg18Phase Encoding GradientFree induction decay in the presence of a gradient,after the gradient is turned off,and after demodulation,Phase encoding gradient is applied prior to read out.() ( )()0iGrtiBtobjectSt re dreγγρ−−⎡⎤=⎢⎥⎣⎦∫i() ( )()0peiGrTiBtobjectSt re dreγγρ−−⎡⎤=⎢⎥⎣⎦∫i() ( )()peiGrTobjectSt re drγρ−=∫iRef: Liang and Lauterbur11/20/20061019Spatial Encoding GradientCombining FE and PE gradients yields,Defining,this can be rewritten() ( )()()pe pe feiG rT iG rtobjectSt re e drγγρ−−=∫ii2fefekGtγπ=2pe pe pekGTγπ=fe pekk k=+()()2ikrobjectSk re drπρ−=∫iRef: Liang and Lauterbur()Skis the Fourier Transform of()rρ20Gradient SequencingRef: Bushberg11/20/20061121K-space acquisition for reconstructionRef: Bushberg,2xxfekGtγπ=,2yypepekGTγπ=22K-space acquisition for reconstructionRef: Bushberg11/20/20061223Multi-slice AcquisitionRef: Bushberg()()()12101Induced ,,,,,,VSEGTT PDFEGBBTE TR TI PEGFTxyMMStSkIxφµ−→→ → → →24Spatial Encoding Summary• Spatial encoding is achieved using ∆Bz(x), ∆Bz(y), ∆Bz(z) [∆Bz(r)].• 3 techniques for spatial encoding• Slice encoding (SEG) – narrow-band ωrfand ∆Bzisolate spins where ωLarmor= ωrf .• Frequency encoding (FEG) – A gradient applied during readout encodes spatial information into the frequency components of S(t).• Phase encoding (PEG) – A gradient applied prior to readout encodes spatial information into the phases of the components of S(t).• k-space interpretation• The measured data gives the FT of the spatial object.• k-space can be sampled by applying the FEG with sequential PEG with varying amplitudes.• Inverse FT of k-space gives the image.11/20/20061325Review: CSE 2DFT Pulse SequenceRef: Bushberg,2xxfekGtγπ=,2yypepekGTγπ=26Inversion Recovery AcquisitionRef: Bushberg11/20/20061427Gradient Recalled Echo AcquisitionRef: Bushberg28A few important practical matters...Data acquisition time:Voxel Size Field of ViewReceiver Bandwidthacq pe avgtTRNN=××max1,11xxx obj objrecxx recfGxGFOV BWFOV resolution kkBWtTsNGFOV BWγγγ==∝∝∆==∆=yxzVoxelxyzFOVFOVFOVVNNN=××There is interplay between many of the data acquisition parameters in the determination of image quality.Ref: Hashemi and Bradley* Remember to obey Nyquist...11/20/20061529Signal to NoiseRef: BushbergBW30RF BandwidthRef: Bushberg11/20/20061631Dual Spin Echo ImagingRef: Bushberg32Multi-slice Spin EchoRef: Bushberg11/20/20061733MRI System HardwareRef: Bushberg(RF coils, 3D gradient coils, main field coils)34Main Field Magnet DesignsGE and Fonar magnets. Ref: Corporate websites11/20/20061835MRI System HardwareRef: Bushberg36Main Field Magnet DesignsRef: Bushberg11/20/20061937Fringe FieldsRef: Bushberg38Magnetic Field Gradient GenerationRef: Bushberg11/20/20062039X-Y-Z Magnetic Field GradientsRef: Bushberg40MRI System HardwareRef: Bushberg12RFLCνπ=11/20/20062141MRI Quality ControlRef: Bushberg42MRI safetyRef: Bushberg11/20/20062243The need for